Insight Editions · No. 251
Time, Tense, and Causation
Michael Tooley
Tooley defends an open future and a settled past: the world is dynamic because the stock of tenseless facts grows, and causation forces that picture on us.
A study guide to Time, Tense, and Causation by Michael Tooley. Shared free for personal reading; not for sale and not endorsed by the authors or publishers. Please read and buy the original.
The past and present are real; the future is not. Tooley defends this growing block by arguing that causation is possible only in such a world, while denying any irreducible tensed facts: tensed truths supervene on which tenseless facts are actual as of each time.
Analytic metaphysics of time: static vs dynamic worlds, truth at a time and three-valued logic, the analysis of tense, a causal theory of temporal order, replies to McTaggart, Mellor, Smart, Quine, and a modified special relativity with absolute simultaneity.
12 chapters, 6 parts; 4 causal-law postulates (C1)–(C4); 6 actuality postulates; 5 traditional tensed theses rejected; a causal definition of earlier than and simultaneous; 3 arguments that modified relativity beats STR.
Readers of philosophy of time and causation; anyone weighing the A-theory vs B-theory debate, the growing block, or the metaphysics behind relativity and quantum non-locality.
The Book on One Page
Michael Tooley (Oxford, 1997) argues that the oldest intuition about time, an open future and a settled past, is coherent and indeed forced on us by causation. The world is dynamic because the stock of tenseless facts grows; nothing more, and nothing less, is needed for time to pass.
- Two questions, not one. Tenseless theorists say the world is static and tensed facts supervene on tenseless facts; traditional tensed theorists say the world is dynamic and tenseless facts supervene on tensed ones. Tooley separates the questions and answers dynamic to the first and tenseless-first to the second: tensed facts supervene on what tenseless facts are actual as of different times.
- New primitives. A dynamic theory needs actuality as of a time as well as existence simpliciter: two unanalysable notions where the static theory needs one. A mild cost.
- Preventability fails; causation succeeds. The intuition that what can still be prevented is not yet a fact cannot stand alone: it needs a neutral proof against backward causation, and Tooley's segregated-world cases show backward causation without loops is conceivable. The real argument is the argument from causation: causation is a realist, singularist, theoretical relation fixed by postulates (C1)–(C4) on how causal laws transmit probability from cause to effect; those postulates can hold only if causes are actual as of their effects' times but not conversely, i.e. In a growing block (or something very close). Our world, full of otherwise improbable regularities, contains such laws, so it is a growing block. As a bonus, backward causation is impossible.
- Semantics. Truth is relative to times and three-valued (true, false, indeterminate); the connectives are defined by factual-truth-functionality, so "p or not-p" can be true now with neither disjunct true. Truth simpliciter, bivalent, is still needed for logical truths, atemporal entities and unrestricted generalisations.
- Tense analysed. Tensed concepts are not basic and temporal priority is not tensedly analysable. E is present at t iff E is actual as of t and nothing later is; past and future follow by "earlier/later than the present". Ordinary tense is indexical, but the basic tensed sentences ("E is present at t") are not.
- Rivals fall. Intrinsic tensed properties (moving spotlight, Broad), presentism (classical and tensed-facts), McCall's branching tree and all tenseless theories fail, chiefly to the argument from causation.
- Time from causation. A is earlier than B iff a chain of causal and spatial links with at least one causal link runs from A to B; simultaneity is spatial relatedness. Absolute space-time whose points cause one another answers the classic counterexamples. Temporal distance is not causal but a realist relation that makes clocks possible.
- Objections answered. Smart's "unreal future" incoherence, Quine on quantifiers, Broad's meta-time, McTaggart (via tenseless dating) and Mellor's arguments all fail against this view. Special relativity is met by a modified theory with absolute simultaneity, empirically equivalent, more explanatory, free of the untestable one-way light postulate and supported by Bell-type non-locality.
| Ch | Title | One-line payload |
|---|---|---|
| Intro | A dynamic world without tensed facts | The plan: positive arguments (3–4), semantics (5), tense (6–8), causal time (9), objections (10–11) |
| 1 | The Nature of Time: Alternative Accounts and Basic Issues | Static/dynamic is the basic question; indeterminism is neither necessary nor sufficient; five traditional theses rejected |
| 2 | Actuality and Actuality as of a Time | Facts are structured states of affairs; "actual as of t" is primitive, a mild extra cost |
| 3 | Temporally Relative Facts and the Argument from Preventability | Preventability needs an unavailable neutral proof against backward causation and works in static worlds |
| 4 | Facts, Causation, and Time | Causal laws obeying (C1)–(C4) exist only where past and present are real and the future is not |
| 5 | Truth and Truth at a Time | Three-valued truth at a time, factual-truth-functional connectives, and bivalent truth simpliciter |
| 6 | Tensed Accounts of the Nature of Time | Priority and the quantifier resist tensed analysis; tensed truths supervene on tenseless facts as of times |
| 7 | Past, Present, and Future | E is present at t iff actual as of t with nothing later actual; nested tenses by quantifying over times |
| 8 | Past, Present, and Future: Alternative Accounts | Indexicality, intrinsic tensed properties, presentism and McCall's tree all fail |
| 9 | Causation and Temporal Relations | Earlier-than = causal/spatial chain with a causal link; space-time points cause one another |
| 10 | Philosophical Objections | Actual simpliciter vs actual-as-of answers Smart; tenseless dating answers McTaggart; Mellor fails |
| 11 | The Special Theory of Relativity and the Unreality of the Future | A modified, empirically equivalent STR with absolute simultaneity is preferable |
| 12 | Summary and Conclusions | A third way: dynamic world, no irreducible tensed facts, causation at the heart of time |
- 4 causal-law postulates (C1)–(C4) carry the whole argument from causation.
- 6 actuality postulates (reducible to 5) link causation to what is actual as of a time.
- 5 traditional tensed theses are rejected: tensed analysis of priority, basic tensed concepts, non-indexical ordinary tense, tensed quantifiers, and abandonment of truth simpliciter.
- 3 truth-values at a time (true, false, indeterminate); 2 for truth simpliciter.
- 3 reasons the modified relativity beats STR: explanation of space-time regions, no untestable one-way-light postulate, Bell-type non-locality.
Perhaps the truth about time lies somewhere between traditional tensed and tenseless approaches.Michael Tooley
A Dynamic World without Tensed Facts
Tooley sets out to defend the most natural picture of time, that the past and the present are real but the future is not, against the philosophical and scientific objections that have driven most philosophers to a static, tenseless view. His distinctive move is an intermediate position: the world is dynamic, yet tensed facts are logically supervenient on which tenseless facts are actual as of different times. Causation is the engine of the whole account, both for the reality of becoming and for the direction of time.
The book has two kinds of argument for its view. Positive arguments (chapters 3 and 4) try to show that the world must be dynamic, with tensed facts supervenient on tenseless ones. Negative arguments (chapters 6, 7 and 8) try to show that every rival, tenseless or traditionally tensed, faces decisive objections. Chapters 10 and 11 then answer the objections that have made tensed views unpopular, the a priori ones (McTaggart, Williams, Quine, Smart, Mellor) and the scientific one from special relativity.
Two dividing lines, three positions
The Introduction already states the key structural claim of chapter 1. Tenseless and traditional tensed accounts differ on two independent questions, and Tooley answers them in a combination nobody else has chosen.
| Position | Static or dynamic world? | Which facts are basic? |
|---|---|---|
| Tenseless (B-theory) | Static: what facts there are does not depend on the time | Tensed facts supervene on tenseless facts |
| Traditional tensed (A-theory) | Dynamic | Tenseless facts supervene on tensed facts |
| Tooley | Dynamic | Tensed facts supervene on what tenseless facts are actual as of different times |
The plan of the argument
The six parts of the book
- Part I: Causation, time and ontology (chapters 1–4). Static versus dynamic worlds; the concept of actuality as of a time; the argument from preventability (rejected as an independent argument); the argument from causation, which needs a specific theory of causation: realist, singularist, and tying causal laws to probabilities.
- Part II: Semantical issues (chapter 5). The notion of truth at a time, defended through a correspondence theory, and the continued need for truth simpliciter.
- Part III: Tensed facts (chapters 6–8). Temporal priority is not analytically basic and has no tensed analysis; past, future and finally the present are analysable; the tenseless existential quantifier is basic; every alternative account of past, present and future fails.
- Part IV: Temporal relations (chapter 9). Temporal priority is analysed through causation; quantitative temporal relations are not causally analysable; the account combines a causal theory of temporal priority with absolute space and time.
- Part V: Objections (chapters 10–11). A priori objections, including the second half of McTaggart's argument; the challenge of special relativity, met by a modified theory with absolute simultaneity.
- Part VI: Summary (chapter 12). The central role of causation and the account's position between tenseless and traditional tensed views.
Why preventability fails and causation succeeds
The first positive argument, the argument from preventability, turns on the idea that something cannot be a fact as of a time if someone at that time could have the power to ensure it does not obtain. It seems to yield that what facts there are depends on the time and that only past and present are real. Two problems sink it as an independent argument:
- It needs the premise that backward causation is logically impossible, which is not a trivial analytic truth like "bachelors are unmarried". Standard attempts to prove it are really arguments against causal loops, and one could have backward causation without loops.
- The counterfactuals at its heart can be true even in a static world.
The two failures point to two better arguments in chapter 4, one from the truth conditions of counterfactuals and the more fundamental one from the nature of causation: causation presupposes a dynamic world in which the past and present are real and the future is not.
Many philosophers have linked time and causation. Tooley's bolder claim links tense and causation: only a dynamic world can contain causally related events, and it must be a world where the future is unreal.
Truth simpliciter survives
Most tensed theorists think truth simpliciter belongs only to static views. Tooley gives three reasons to keep it alongside truth at a time: statements about possible non-temporal entities (numbers, propositions, uninstantiated universals); logical truths; and certain universally quantified contingent temporal statements that may be true simpliciter without being true at any time.
The relativity cloud
The view requires absolute simultaneity, which seems to put it on a collision course with the Special Theory of Relativity. Rather than modify the metaphysics, as many sympathisers have done, Tooley argues that STR can be modified into an empirically equivalent theory with absolute simultaneity, and that the modified theory is preferable on grounds of explanatory power.
The strategy of chapter 11, to prefer a physics with a hidden privileged frame because a metaphysics requires one, is the most contested move of the book. Many philosophers of physics regard any undetectable absolute simultaneity as surplus structure; others (neo-Lorentzians, some quantum-gravity theorists) find a preferred foliation respectable. The verdict depends on how much weight one gives metaphysical argument against empirical parsimony.
The Nature of Time: Alternative Accounts and Basic Issues
Tooley maps the main theories of time and raises three issues: static versus dynamic worlds, the direction of supervenience between tensed and tenseless facts, and the relation of indeterminism to an open future. The most fundamental question in the philosophy of time is whether the world is static or dynamic, and that question is independent of whether tensed concepts are basic. His own view keeps a dynamic world while siding with tenseless theorists on concepts, and puts causation at the heart of time.
1.1 Alternative views of the nature of time
Ordinary belief holds two things: there is a deep asymmetry between past and future (the past fixed and settled, the future open), and this asymmetry belongs to time itself, not merely to the pattern of events in time; and time has an intrinsic direction, it flows, carrying enduring things forward while events recede into the past. Philosophers split sharply. Probably the majority accept a tenseless or static view: there may be asymmetries in the pattern of events, but none intrinsic to time, and a fortiori time does not flow. A large minority holds that time flows, has an intrinsic direction, and that past, present and future differ ontologically.
Tensed theorists disagree about what the ontological difference is.
The tensed family and its rival
- Presentism. Only the present is real; past and future are not.
- Past and present real, future not. The moderate view (the "growing block", Tooley's own).
- All real, with tensed properties (one property). Events lack presentness, acquire it for a moment, then lose it forever (the "moving spotlight").
- All real, with three tensed properties. Events have futurity, lose it as they gain presentness, then immediately gain pastness, which they keep forever.
- Tenseless (static) view. No difference in reality and no special tensed properties. Tensed concepts are explained by tenseless temporal concepts plus indexicals: "now" and "then" work like "here" and "there". A statement is true or false because of a temporal relation between the event and something picked out indexically.
1.2 Dynamic versus static conceptions of the world
Tooley explains the difference through two concepts of change.
- Static change. For an object to change is simply for it to have different properties at different times: the glass is warm at one time, cool at an earlier one. The world changes when it has different properties at different times.
- Dynamic change. An object changes if and only if the totality of monadic states of affairs involving it changes over time. The world changes only if the totality of temporal facts is different at different times. The restriction to monadic states of affairs excludes "Cambridge" change, where an object's relation to another alters only because the other object changes.
Critics of the static concept (McTaggart among them) ask why differing properties of earlier and later stages should count as change when differing properties of different spatial parts do not. Tooley thinks that dissatisfaction carries little weight until an alternative is in focus, and the dynamic concept supplies one. Its price is a new basic notion: facts must be temporally relative, so that the fundamental notion is not a state of affairs being actual simpliciter but being actual as of a particular time. Given that, nothing is puzzling in the totality of facts actual as of one time differing from the totality actual as of another. Whether actuality as of a time is coherent is taken up in chapter 2, and McTaggart's attack on it only in chapter 10.
Static world: what states of affairs exist does not depend on what time it is; change is just possession of different intrinsic properties at different times. Dynamic world: what states of affairs exist does depend on what time it is; change is a difference in the totality of states of affairs actual as of different times.
A rejected argument for the dynamic view
One argument (from Michael Dummett's defence of McTaggart) says the world can only be described consistently from some temporal perspective. If E occurs at t, then as of t it is a fact that E is present and not past, while later it is a fact that E is past and no longer present; a perspective-free description would have to contain both "E is present" and "E is past", a contradiction. Tooley rejects this: on his view the totality of facts that exist as of different times never includes incompatible states of affairs, so there can be a complete, consistent, perspective-free description of the world. He must therefore argue for the dynamic view in another way (chapters 3 and 4).
1.3 Tensed facts versus tenseless facts, and supervenience
The usual way to divide the camps uses two families of concepts.
| Concept family | What it does | Examples |
|---|---|---|
| Tensed | Says how an event is related to the present | past, present, future; further in the past; five years ago; three minutes in the future |
| Tenseless | States temporal relations between events, with no reference to the present | simultaneity, temporal priority, betweenness; five years earlier; three minutes later |
Tenseless theorists hold that the truth conditions of tensed sentences can be given in tenseless terms, so once all tenseless facts are fixed, all tensed facts are settled: tensed facts are logically supervenient on tenseless facts. An utterance of "E took place five minutes ago" is true iff it is five minutes later than E, and nothing else is relevant. Traditional tensed theorists reverse this: tenseless sentences can only be understood through tensed ones. "There are (tenselessly) dinosaurs" means "Either there were dinosaurs, or there are now dinosaurs, or there will be dinosaurs", so tenseless facts supervene on tensed facts.
Are the two dividing lines the same line?
Most philosophers would say yes, holding both (a) that tensed concepts can be basic only if the world is dynamic and (b) that tenseless concepts can be basic only if the world is static. Tooley accepts (a) and rejects (b).
Argument for (a): basic tensed concepts require a dynamic world
- Let E be an instantaneous event happening now, and consider two utterances of "E lies in the present", one now and one five minutes from now. The first must be true, the second false.
- If tensed utterances have tenseless truth conditions, a static world handles this: the first utterance is simultaneous with E, the second is not.
- If instead tensed utterances express irreducible tensed propositions, both utterances express the same proposition.
- In a static world the totality of facts never changes, so that one proposition would be true both times or false both times.
- That is unacceptable. So if tensed concepts are semantically basic, the world cannot be static.
Against (b): for a world to be dynamic, all that is needed is that the facts actual as of one time differ from those actual as of another. The difference need not be in irreducible tensed facts; it can be a matter of which tenseless states of affairs have become actual.
Purple sheep. Suppose the past and present are real and the future is not. The states of affairs actual as of 1990 include none involving purple sheep; given advances in genetic engineering, those actual as of 2000 might. That difference is fully describable without tensed terms: there is a spatiotemporal region where non-temporal properties such as being purple are instantiated, and it is actual as of 2000 but not as of 1990. A dynamic world needs no tensed facts at all.
So the asymmetry is this: a static world entails there are no irreducible tensed facts, but a dynamic world does not entail that tenseless concepts are non-basic. Indeed a dynamic world is compatible with tensed concepts being analysable in terms of tenseless concepts plus the general concept of a dynamic world. It then needs no irreducible properties of presentness, pastness or futurity.
Two lessons follow. First, it is a mistake to define tensed theories by the analysability of tenseless concepts in tensed terms, by the basicness of tensed concepts, or by irreducible tensed properties: what is essential to a tensed approach is simply that the world is dynamic rather than static. Second, there is a third alternative, dynamic but without the traditional tensed theses, and if chapters 4, 6, 8 and 10 are right it is the only acceptable one.
1.4 Indeterminism and the openness of the future
A less fundamental issue: is indeterminism necessary, sufficient, both or neither for a dynamic world? The question arises naturally if one says the future differs from the past in being open, and then reads openness as the existence, at every time, of many possibilities about what will happen. Two accounts make indeterminism central.
1.4.1 Reichenbach
Hans Reichenbach (1953) held that past and present are real and consist of determinate events, while the future consists only of possibilities with associated probabilities. The present is where possibilities become actual: "becoming" means "becoming determined". He apparently held two theses: (i) the strong notion of becoming can be explicated only through physical indeterminism, and (ii) quantum indeterminism entails a dynamic view, since undetermined future events cannot be determinate, and the present is where they become so.
Tooley rejects both directions.
- Not sufficient. A static world can contain indeterministic laws. On a reductionist view of laws (laws supervene on the total history of the world), indeterministic laws are just statistical relations between event types at different stages, which gives no reason to think events are indeterminate before they occur. On Tooley's realist view (laws as relations among universals), the related properties are perfectly determinate, so again nothing future need be indeterminate. Adolf Grünbaum and Storrs McCall made similar criticisms.
- Not the source of becoming. Ask why, at t, earlier events are determined and later ones are not. The natural answer is that earlier events are already actual as of t and later ones are not. Without such an answer, there is no rationale for the asymmetry. But with that answer, "becoming determined" is idle: in a deterministic world there is only one possibility for the state at t, yet a change still occurs at t, a possibility becomes actual.
The concept of becoming determined explains nothing about a dynamic world unless one can already invoke an event coming into existence. Once one has that notion, determinism or indeterminism is irrelevant.
1.4.2 Storrs McCall's branching model
In "Objective Time Flow" (1976) and A Model of the Universe (1994), McCall gives the world at any time a tree structure: the trunk is the history up to the present; branches are all future possibilities. Comparing the tree at s with the tree at a later t, the trunk at s is a proper part of the trunk at t, while the branches at t are a proper part of the branches at s. The passage of time is the dropping-off of unrealised branches; the surviving branch becomes the newest part of the trunk.
The difference from Reichenbach is ontological. For Reichenbach future possibilities do not exist as past and present facts do; McCall, like David Lewis with possible worlds, is a realist about future possibilities: they are made of the same stuff as past and present actualities. Nothing marks off the branch that will be realised.
On McCall's model indeterminism is essential: a deterministic world would be a single unbranching structure, and since future and past are ontologically on a par, there would be no difference between the world at one time and at another. A deterministic world would be static.
Tooley's reply is a parity argument. If McCall's model (the universe changes by deletion of branches) makes sense, then so must C. D. Broad's (1923) model, where the universe changes by addition of new states of affairs. And on Broad's model, indeterminism is irrelevant: a deterministic world has one possibility for time t, but until t no actual state of affairs corresponds to it.
| Broad (addition) | McCall (deletion) | |
|---|---|---|
| How the world changes | New states of affairs come into existence | Unrealised branches drop off |
| Status of future | Nothing exists | All possibilities exist, as real as the past |
| Deterministic world | Can be dynamic | Must be static |
| Ontology as of a time | Past and present states only | Uncountably many branchings per future instant, and again at every point of every branch |
| Verdict | Simpler and more widely applicable | Considered further in §8.7 |
Tooley gives two reasons to prefer Broad: wider applicability (it captures the intuition that even a deterministic world can be one where states of affairs come into existence) and much greater ontological economy. McCall claims his model solves many hard philosophical problems; that claim is examined in chapter 8.
Conclusion of 1.4: indeterminism is neither necessary nor sufficient
- Not necessary. In a dynamic, indeterministic world two things happen at each present moment: possibilities are reduced to one, and that one is actualised, by addition (Broad) or deletion (McCall). Only deletion requires indeterminism, and there are reasons to prefer addition. Since actualisation alone makes a world dynamic, indeterminism is not required.
- Not sufficient. Whether laws are reductionist or realist, a static world can contain indeterministic laws.
1.5 Divergences from other tensed views
The view that the present is the point where states of affairs become actual is old. Aristotle's sea fight (De Interpretatione 9): it is true, indeed necessary, that either there will be a sea battle tomorrow or not, yet neither disjunct is now true or false. Later holders of an unreal future include Thomas Aquinas and Peter de Rivo in the Middle Ages, C. S. Peirce in the nineteenth century, and C. D. Broad in the twentieth. Tooley stays in this tradition but departs from all traditional tensed views in two ways, often coming closer to tenseless views.
1.5.1 Tenseless concepts and facts as more basic than tensed ones
Tooley agrees with traditional tensed theorists that the world is dynamic, and so that being actual as of a time and being true at a time are intelligible and fundamental. But on tensed concepts and facts he sides with tenseless theorists: tenseless concepts and facts are more basic. He therefore rejects five theses almost always bundled with tensed views.
Five traditional tensed theses Tooley rejects, and what he puts in their place
| Traditional thesis | Tooley's counter-thesis |
|---|---|
| 1. Tenseless temporal concepts are analysed in tensed terms (so simultaneity and priority cannot be basic, nor causally analysed) | Tenseless concepts cannot be analysed in tensed terms |
| 2. Past, present and future are semantically basic (at least the present) | Tensed concepts are analysable, the present included |
| 3. Familiar tensed statements are not indexical; a tensed sentence always expresses the same proposition | Some tensed statements are non-indexical, but ordinary tensed statements do involve indexicals |
| 4. No basic tenseless existential quantifier; existence is "existed, exists now, or will exist" | There is a basic tenseless quantifier over all existents, temporal or not |
| 5. Truth simpliciter must give way to truth at a time | Truth at a time is legitimate and so is truth simpliciter |
None of the five is essential to a tensed view; each faces strong objections on its own; and including any of them exposes the whole position to objections it cannot answer. Chapter 10 will argue, for example, that a tensed view accepting thesis 1 may have no good reply to McTaggart. Thesis 5 is forced only by dynamic models in which no consistent state of affairs can contain all the states of affairs existing at different times. On Tooley's model all facts that exist at some time or other are consistent with one another, so both kinds of truth are legitimate.
1.5.2 Time and the role of causation
Traditional tensed views give causation no role; for Tooley causation lies at the heart of time. Two logically independent claims of very different strength express this.
- The moderate claim (time and causation). Having refused to analyse tenseless concepts in tensed terms, Tooley needs some account of them, and adopts an idea familiar from tenseless theories: the direction of time is defined by the direction of causation.
- The radical claim (tense and causation). On a satisfactory account of causation it is a necessary truth that causes bring their effects into existence, so events can be causally related only in a dynamic world.
The resulting theory conjoins a dynamic world with (i) the thesis that tensed truths are logically supervenient on what tenseless facts are actual as of different times, and (ii) the view that causation is basic both to temporal order and to the passage of time. The difficulties of the growing-block view come, Tooley claims, not from dynamism itself but from unsound subsidiary theses traditionally bolted onto it.
Two points of contention. Critics argue that once tensed properties are abandoned, Tooley's "dynamic" view risks collapsing into a B-theory plus an extra growth fact that does no explanatory work, a charge pressed against growing-block theories generally. And his rejection of Reichenbach rests on a realist theory of laws that most Humeans reject. (Tooley's text spells Peirce as "Pierce"; the philosopher meant is Charles Sanders Peirce.)
Philosophical opinion is still divided much as Tooley described it. The 2020 PhilPapers Survey found roughly 38% leaning B-theory and 27% leaning A-theory, with the rest undecided or holding other views. The growing block now has full-length defences, notably Fabrice Correia and Sven Rosenkranz, Nothing to Come (2018), which builds its version on tense logic, the opposite of Tooley's tenseless foundations.
Actuality and Actuality as of a Time
Before arguing for a dynamic world, Tooley fixes two preliminaries: what facts are (structured states of affairs serving as truth-makers) and what it is for a world to be dynamic. The concept of being actual as of a time cannot be analysed, but neither can actuality simpliciter, so a dynamic theory is only mildly costlier than a static one: it needs two primitives where the static theory needs one.
The view to be defended has three parts: the world is dynamic, not static; the present is the point at which states of affairs come into existence; and once a state of affairs is actual it remains part of reality from then on. So past and present are real, and the future is not.
2.1 Facts, states of affairs and truth-makers
2.1.1 Facts as states of affairs
"Fact" has two uses: a true proposition (mental or a "third world" denizen), or whatever in the world makes a true proposition true. Tooley uses the second, and adds an account of the structure of truth-makers.
Tooley's ontology of facts (five theses)
- Facts are states of affairs: entities of various sorts having or not having properties, standing or not standing in relations.
- Properties and relations are universals, features of reality that account for objective sameness, not concepts or meanings. Two green things of different shades are not identical in respect of greenness, so there is a concept of greenness but no property of greenness. Consequences: no one-to-one match between concepts and properties; no negative properties; and no guaranteed disjunctive properties. (The view follows David Armstrong's realism about universals.)
- No disjunctive states of affairs. "a has P" and "a has Q" may be states of affairs, but "a has P or Q" is not. So there is no one-to-one correspondence between facts and true propositions, which makes it harder to dismiss facts as hypostatised sentences.
- The mereological sum of any two states of affairs is a state of affairs. Hence states of affairs can be complex, and there is (tenselessly) a state of affairs that is the sum total of existence.
- Three types of basic states of affairs: (a) first-order particulars having properties or standing in relations; (b) properties or relations of any order having higher-order properties or standing in higher-order relations; (c) states of affairs having properties or standing in relations.
Type (a) needs no defence once universals are accepted. Type (b) is needed for laws of nature, which Tooley identifies with relations among universals, not Humean regularities. Type (c) is needed because in a dynamic world states of affairs themselves come into existence at a time, and because causal relations hold between states of affairs. The second reason is controversial: many hold that causal relations supervene on laws plus non-causal facts about particulars. Chapter 4 argues that this reductionism fails, so relations between states of affairs must be basic.
2.1.2 Truth conditions and states of affairs
What matters for the rest of the book is not the detail but two general ideas: true propositions must have truth-makers, and truth-makers have structure. It follows that any explanation of a sentence's meaning must imply what types of individuals, properties and relations would have to exist if it were true. Tenseless theories meet this constraint easily, as do many tensed theories. But some tensed accounts talk freely about tensed grammar and about which metaphysical pictures are wrong, yet never say what states of affairs make a tensed sentence true.
The truth-maker constraint. No contingent sentence can be true, or true at a time, without a truth-maker that exists tenselessly or at an appropriate time, and no truth-maker is structureless. Any acceptable account of tensed sentences must describe the states of affairs that make them true. This constraint will later be used against tensed-facts presentism and Priorean accounts.
2.2 The idea of a dynamic world
In a dynamic world the real/unreal distinction is not enough: since what exists may differ at different times, one needs the concept of existing, or being actual, as of a given time. Tenseless theorists such as J. J. C. Smart ("The Reality of the Future", 1981) argue that this concept cannot be explained and is probably unintelligible. The best reply would be an analysis, but Tooley doubts one is possible. Instead he argues that taking it as primitive is unobjectionable.
2.2.1 Reality, existence, actuality
Robert Adams distinguishes two families of accounts of actuality.
| Account | Ontology | What "actual" means |
|---|---|---|
| Possibilist | All logically possible worlds exist; ours is one | Must explain what marks ours out as the actual one |
| Hard actualist | Nothing outside the actual world | Possible-worlds talk is a heuristic |
| Soft actualist | Possible worlds are logical constructions from actual items (sentences, propositions, sets of individuals and properties, thoughts in a divine mind) | e.g. The true-story theory |
Adams's argument against possibilist actuality
- Possible worlds are completely determinate, so for any worlds w and w′, "w is actual" is either true or false in w′.
- Either some world w is actual according to every world, or not.
- If so, it is a necessary truth that w is actual, and other worlds are not really possible.
- If not, the only sensible option is that each world is actual according to itself.
- Then actuality is not an absolute property of any world, only a property a world has relative to itself.
Possibilists must therefore take the second horn, as David Lewis does: "actual" is an indexical picking out the world one inhabits. That relativity is unappealing and Lewis's version faces specific objections; in any case few tenseless theorists are modal realists, so they will not use a possibilist account.
Actualists may adopt the true-story theory: "In the actual world, p" means "The proposition that p is true". Adams says it is natural to treat truth as prior to actuality, but his defence only attacks analysing truth as truth in a possible world. The decisive objection comes from within actualism: for contingent propositions, truth is not intrinsic but a relation to something outside the proposition, and that something can only be characterised as what is actual. The true-story theory is implicitly circular. The remaining actualist option, and the better one, is to take existence or actuality as primitive, since being actual, unlike being true, does not seem to be a relation to anything else.
2.2.2 Actuality as of a time
So the static theorist also needs an unanalysed notion of actuality. Does that neutralise Smart's objection? Not quite, because the dynamic theorist needs two notions: actuality as of a time and existence simpliciter. There are two reasons.
- Non-temporal entities. States of affairs are actual as of a time because of events at that or some appropriate time. But we must be able to make sense of hypotheses about numbers, propositions, uninstantiated universals or a world of Platonic forms, which need a notion of existence with no relation to time.
- The total dynamic world. We must make sense of what was and will be actual, and of the totality of what is actual at some time or other: a whole dynamic world, rather than its history up to now.
Can existence simpliciter be defined from actuality-as-of? Two candidate definitions
- Mereological: X is an actual temporal entity or state of affairs iff X is part of the mereological whole composed of every state of affairs actual as of some time t or other.
- Set-theoretic: X is an actual temporal state of affairs iff X is a member of the set of all and only states of affairs actual as of some time t or other.
These work only if every time is actual as of every other time, as on some dynamic views. On a view where only past and present are real, the quantifier "some time t" must range over absolutely all times, including those not yet actual, so the definitions presuppose the notion they were meant to define.
The complete chronicle. Imagine trying to write the history of a growing-block world using only "actual as of t", with t restricted to times that are actual now. Your chronicle stops at the present and can never mention the states of affairs that will be added. To speak of the whole dynamic world you need a quantifier over all times and a notion of the totality of existence that no time-relative notion supplies. Even if every event were actual as of every time, you would still need that notion for numbers or Platonic forms, unless their existence is logically impossible.
| Theory | Primitive notions needed |
|---|---|
| Dynamic (growing block) | Actuality as of a time + totality of existence (temporal and non-temporal) |
| Dynamic (all times actual as of all times) | Still needs totality of existence as primitive (for non-temporal entities) + actuality as of a time |
| Static (tenseless) | Existence only: the complete static world is the mereological union (or set) of all existing temporal states of affairs; "temporal" is then given by a causal theory of time (chapter 9) |
The dynamic framework is slightly more complex than the tenseless one, which is a reason, other things equal, to prefer the tenseless view. Tooley concedes this advantage but calls it mild, and promises much weightier considerations for dynamism.
Tooley's ontology of sparse universals, no disjunctive or negative states of affairs, and causal relations between states of affairs as basic, is a heavy commitment that many of his targets (Humeans such as Lewis, Mellor's tenseless theory, nominalists) reject. Several later arguments in the book inherit this dependence: if universals and singularist causation are given up, the argument from causation in chapter 4 loses much of its force. Note too that the "dynamic world needs two primitives" conclusion assumes the existence of non-temporal entities is at least possible.
Temporally Relative Facts and the Argument from Preventability
Tooley tests a natural argument for the growing block: nothing can be a fact as of a time if it is logically possible that someone at that time could prevent it, so future facts do not yet exist. He builds the argument carefully, then sinks it with two objections: it needs a neutral proof that backward causation is impossible, which no one has supplied, and its preventability counterfactuals can be true in a static world. Each failure points to a deeper argument, from counterfactuals and from causation, developed in chapter 4.
3.1 The argument from preventability
3.1.1 Preventability and the concept of time-dependent facts
The nuclear war of 1986. In 1980 it was a fact that Einstein had revolutionised physics years earlier. Was it also a fact, in 1980, that no nuclear war would occur in 1986? In 1987 it was certainly a fact that none had occurred. Many philosophers would say it was therefore already a fact in 1980, adding that "fact at a time" is misleading talk for facts simpliciter. But before the end of 1986 some people had the power to start a nuclear war that year; now nobody does. And what someone has the power to prevent at t cannot yet be a fact at t. So it was not a fact in 1980 that there would be no war in 1986.
Chapter 2 suggested that actuality as of a time may have to be primitive. Preventability offers a possible analysis. Whether p is a fact at t should not hinge on whether there merely happens to be someone able to prevent it: if there could have been such a person, p is not yet a fact. The modality must be logical, not nomological, otherwise a deterministic world could never be dynamic.
Analysis of time-dependent facts (via preventability)
"It is a fact that p at time t" means the same as: p, and it is logically impossible for there to exist anyone who would have been able, at time t, to prevent its being the case that p.
Tooley calls this natural but will show it is not really satisfactory.
3.1.2 The argument and the time-dependence of facts
Argument from preventability: version A (no simultaneous causation)
- The world contains states of affairs S1 at t1 and S2 at t2, with t1 earlier than t2.
- A free and omnipotent person is logically possible.
- Such a person could have existed and, at t1, prevented S2 at t2. So S2 is not a fact at t1.
- It is logically impossible for a cause to be simultaneous with its effect, so not even an omnipotent being could, at t2, prevent S2 at t2. So S2 is a fact at t2.
- Therefore what facts there are differs from time to time, in any world with states of affairs at different times.
Version B replaces premise 4 with "a cause cannot be later than its effect" and runs a dilemma. If simultaneous causation is impossible, proceed as in A. If it is possible, an omnipotent being could prevent S1 at t1 at t1, so S1 is not a fact at t1; but no one at t2 can prevent S1 at t1, so S1 is a fact at t2. Either way facts vary with time. Version C (ignoring two-instant worlds): with t1 < t2 < t3 and S at t2, an omnipotent being at t1 could have ensured S did not exist; at t3 that is logically impossible if causes cannot follow their effects. So S is a fact at t3 but not at t1.
Because S1, S2 and S can be tenseless states of affairs, the conclusion is stronger: what tenseless facts there are differs from time to time.
3.1.3 Preventability and past, present and future facts
- Future. Facts as of t can include no later states of affairs, so there are no future facts. This refutes every view, tensed or tenseless, on which past, present and future are equally real.
- Past. Could one accept "no simultaneous causation" but allow backward causation, and so hold that only states at t are facts as of t (presentism)? Not plausibly. If backward causation is possible, a chain E1 causes later E2, which causes earlier E3 is possible, and then why not with E1 and E3 simultaneous? So backward causation brings at least indirect simultaneous causation with it. If causes cannot succeed their effects, the past is real, which would refute presentism.
- Present. Showing that present facts are real needs the impossibility of simultaneous causation, most naturally obtained by adapting an argument against backward causation.
So everything rests on one premise: it is logically impossible for an effect to precede its cause (the simultaneity premise being plausible only if this one is).
3.2 The question of backward causation
Tooley surveys six arguments for that premise. Two presuppose or quickly need a tensed view; four are neutral between static and dynamic views.
3.2.1 Causes as bringing effects into existence
Suppose (i) causation is one event bringing another into existence; (ii) that means that as of the time of the cause, the effect does not exist, while as of the time of the effect, the cause does; and (iii) whatever is earlier than or simultaneous with an event exists as of its time. Then a cause cannot be later than or simultaneous with its effect. But (a) if this were right, the argument from preventability would be unnecessary, and (b) without a separate defence, the claim that causation involves "tensed succession" simply begs the question against tenseless views.
3.2.2 Causation and potential control
The argument (from Antony Flew 1954 and Max Black 1955–6) starts from an analytic link between causation and control: causes could in principle be used as effective means of producing their effects. Suppose C at s2, t2 is sufficient for an earlier E at s1, t1. After t1 one can know whether E occurred. If E did not occur, producing C cannot make it have occurred; if E did occur, producing C is unnecessary. Either way C is no effective means, so backward causation is impossible.
Tooley replies that both horns ignore counterfactuals. If E did not occur, C is nomologically impossible at t2, but it may still be true that if C were to occur, E would have occurred. If E did occur, it may be true that if C had not occurred, E would not have occurred. Those counterfactuals would make C an effective means.
The defender may ban backtracking (hold fixed everything before C when evaluating "if C"). Tooley's answer: the right rule is causal, not temporal. What must be held fixed is what is not causally downstream of C: exclude causal backtracking, not temporal backtracking. Without backward causation they coincide, but with time travel they come apart.
Dr Who's red scarf. Dr Who steps into the Tardis in AD 2050 wearing a red scarf and emerges in AD 2020. Surely: had he not been wearing the scarf on entering in 2050, he would not have been wearing it on emerging in 2020. Evaluating that counterfactual requires changing an event temporally earlier than the antecedent. Only a defender who says we must hold fixed whatever is objectively fixed as of 2050, including the 2020 emergence, can call the counterfactual false. But that assumes a tensed view on which the past is fixed and the future open, so the argument is no longer neutral and cannot serve the argument from preventability.
3.2.3 Four neutral arguments against backward causation
3.2.3.1 Bringing about contradictions
Tim and Grandfather (David Lewis, 1976). Tim hates his grandfather, whose munitions fortune paid for Tim's time machine. Grandfather died in bed in 1957. Tim travels to 1920, buys a rifle, practises, and in winter 1921 lies in wait on Grandfather's route. Surely Tim can kill him. Yet history leading to Tim contains no killing of Grandfather in 1921. If Tim succeeds, Grandfather is both killed and not killed in 1921. So, the argument runs, if backward causation were possible, contradictions could be true; hence backward causation is impossible.
3.2.3.2 Bilking: undercutting causal chains
Flew, Black and others: faced with the hypothesis that later L-events are causally necessary for earlier E-events, an experimenter should wait for an E and then try to prevent the L. If she sometimes succeeds, the hypothesis is falsified. If she never succeeds, the best explanation is that L's causes are not independent of E: E is causally sufficient for L by ordinary forward causation. So belief in backward causation could never be justified. (Michael Scriven criticised this in 1956–7.)
3.2.3.3 Causation and increase in probability (Mellor)
Hugh Mellor's Real Time (1981), extending Dummett's "Bringing about the Past" (1964), is the most careful version. It has two steps.
- Backward causation entails causal loops, or at least their physical possibility. Mellor holds that every event has spatiotemporally contiguous effects. If L causes earlier E, E's effects propagate forward until they reach L's time; a forward chain could then intersect the backward chain.
- Causal loops are impossible, because "causes have inter alia to make their effects more likely than in the circumstances they would otherwise have been".
Mellor's match-and-fire test. Suppose striking matches at t2 can cause fires to ignite at earlier t0. By t1 we can see which fires ignited (about equal numbers each way). We tell half of each group's "igniters" to strike matches at t2 and half to refrain. Three outcomes are possible:
- Correlation because some igniters disobeyed. Rerun with "more glorious rewards" and "more exciting punishments". If correlation persists anyway, the right conclusion is that fires at t0 make igniters more likely to strike at t2: forward causation constrains their acts statistically.
- Correlation although all obeyed. Then the early perceptions of which fires lit must have been wrong; enough accurate observers and recorders drive such errors to near zero.
- Accurate perceptions, obedient igniters. Then ignition shows no correlation with later striking, and since causes must raise the probability of their effects, striking cannot cause earlier ignition.
3.2.3.4 A formal approach: transmission of probabilities
The last route seeks postulates that are plausible conceptual truths about causation and that entail the impossibility of loops in a deep, unobvious way. Simply stipulating that causation is irreflexive and transitive would beg the question. Tooley's postulates concern causal laws. This is compatible with singularism: causation can be characterised as the relation such that, if it enters into laws, those laws are causal laws as defined below. And there are reasons to go this way: causation is not observable, no reductionist account works, and no theory that does not mention causal laws can uniquely characterise the relation.
Two radioactive elements. Elements P and Q have half-lives of 5 minutes and 10 minutes everywhere except in environments with property R, where a P-atom decays when and only when a Q-atom does. Three hypotheses fit: (1) P's decay is, given R, necessary and sufficient for Q's; (2) Q's for P's; (3) some property S causes both. Now add: under R, both half-lives are 5 minutes. Then P's decay causes Q's, since P keeps its usual probability while Q has acquired P's. If both were 10 minutes, Q's decay would cause P's. The direction of causation coincides with the direction in which probabilities are transmitted.
Notation: P ⇒ Q says it is a causal law that having P is causally sufficient for having Q. Prob(Px, E) = k says the logical probability that x has P given only evidence E is k. C is information that is either tautological or only about which causal laws exist.
Postulates for causal laws (simplified, deterministic version)
- (C1) Prob(Px, P ⇒ Q & C) = Prob(Px, C)
- (C2) Prob(Qx, P ⇒ Q & C) = Prob(Px, C) + Prob(∼Px, C) × Prob(Qx, ∼Px & P ⇒ Q & C)
- (C3) Prob(Qx, ∼Px & P ⇒ Q & C) = Prob(Qx, ∼Px & C)
- (C4) Prob(Qx, P ⇒ Q & C) = Prob(Px, C) + Prob(∼Px, C) × Prob(Qx, ∼Px & C)
(C1): learning that P causes Q does not change the probability of the cause; a cause's posterior probability is not a function of the priors of its effects. (C2): it does change the probability of the effect, making it a function of the prior of the cause. (C3): given that x lacks P, the law tells us nothing more about Q. (C2) + (C3) entail (C4), which states the effect's posterior using priors alone. The core content is (C1) and (C4): posterior and prior probabilities relate differently for causes than for effects.
Applied to the radioactive case, (C1) says P's posterior decay probability equals its prior, and (C4) says Q's equals P's prior: the right values. Besides this intuition, three further grounds support the postulates: they avoid the decisive objections to reductionist accounts of causal direction; strengthened versions generate the formal properties of causal relations; and they explain how causal beliefs can be justified.
What the postulates entail about loops. Loops in which each event is causally sufficient for the next are logically impossible; so are loops in which each is causally necessary for the next; and, defining "causally prior" as "sufficient or necessary for", so are loops where each event is causally prior to the next. The derivations are long, so the postulates do not beg the question. A loop-believer must find a weaker set with the same merits that allows loops.
3.2.4 The basic difficulty: backward causation without causal loops
All four neutral arguments first prove that loops are impossible. To reach the impossibility of backward causation they need the bridge "backward causation entails the possibility of loops". If the direction of time were independent of causation, a world with only backward causation would be possible and the bridge would fail at once. Mellor sees this and relies on a causal theory of time's direction; many others overlook it. Tooley also holds that causation fixes the direction of time, so a purely backward world is impossible. He therefore argues that a world with both directions of causation but no possible loops is possible.
The segregated world and the backward golf course. Two regions are separated by a wall that has always existed, is indestructible, cannot be bypassed, and is one-way: from the other side only light comes through; from your side nothing goes back. On your side life is normal. Across the wall is a golf course: a ball on a green starts to roll unprompted, hops into an indentation that then vanishes, flies toward a golfer swinging in reverse, while a loose piece of turf leaps up and fits exactly into a divot; the ball halts on the backward-moving clubface. Everything over there runs as if causation were reversed, and we suppose it is. You can predict the golfer's swing from the ball, but you can never test the connection experimentally; experimenters on the other side test it easily and find they control the ball. The chain swing → ball → your perception → memory, then swing → your later perception → combined memory, looks loop-like but is harmless: going round it, one link is "is caused by", not "causes".
A second, stronger world removes even that interaction in two steps. First, the two sides have different fundamental particles that cannot interact directly, so light from the far side must be absorbed by the wall and re-emitted as a different kind of light: the wall is necessary for any interaction. Second, remove the wall. The sub-worlds are then causally isolated but spatially related, and may even overlap completely. One can then have structures like: C1 causes E1; E1 is co-located with C2; C2 causes E2; E2 is co-located with C1, with no causal loop.
Oppositely directed causal processes are possible in worlds where causal loops are impossible, either because the opposed processes cannot be causally connected or because the world's structure blocks the connections that would close a loop. So arguments against loops, however good, do not establish the impossibility of backward causation.
Possible reply: analyse spatiotemporal relations causally, which might show such worlds impossible. Tooley thinks the prospects poor. The best such analysis, Alfred Robb's axiomatisation of STR space-time (A Theory of Time and Space, 1914), must use causal connectibility, not actual causal relations, since actual causal relations need not fix the whole structure of space-time. Connectibility is counterfactual, and the only plausible truth-maker for "A and B could have been causally connected" appeals to laws, intrinsic properties and the spatiotemporal relation between A and B, which is circular if spatiotemporal relations are themselves analysed causally. Until something better appears, backward causation need not entail the possibility of loops.
| Argument against backward causation | Neutral? | Verdict |
|---|---|---|
| Causes bring effects into existence | No: assumes tensed succession | Begs the question; makes preventability redundant |
| Causation and control (Flew, Black) | Only if "objectively fixed" past assumed | Ignores counterfactuals; rescue presupposes tensed view |
| Contradictions (Lewis's Tim) | Yes | Targets loops only |
| Bilking (Flew, Black) | Yes | Targets loops only |
| Probability raising (Mellor, Dummett) | Yes | Targets loops; bridge needs causal theory of time |
| Transmission postulates (C1–C4) | Yes | Rules out loops deeply, but not backward causation |
3.3 A second objection to the argument from preventability
The final step, from "p is preventable at t1 but not at t2" to "the world is dynamic", slips by easily, since a dynamic world just is one where facts differ at different times. But preventability has been defined through subjunctive conditionals, and a static theorist can accept that p is preventable at t1 and not at t2 while denying dynamism. Standard accounts of counterfactual truth conditions give satisfactory truth conditions for the preventability conditionals, and they are formulated entirely in static terms (or in many static worlds, given Lewis's modal realism).
What the preventability theorist would have to show
- Possible-worlds accounts (Stalnaker 1968, Lewis 1973), explicitly static, are inadequate: perhaps sustainable, given their known problems.
- Causal accounts such as Frank Jackson's (1977), which face no really serious objections, implicitly presuppose dynamic worlds. The only way to show this is that causal connections themselves presuppose a dynamic world.
But if the defence of preventability rests on "events can be causally related only in a dynamic world", that thesis does all the work and the rest of the argument is unnecessary.
3.4 Alternative lines of argument
Two facts generate the belief that the past is fixed and the future open: what happens later causally depends on what happens now, while the past does not; and as a result the future would be different if the present were, whereas the past would not. The argument from preventability tries to get from this counterfactual asymmetry to a dynamic world and hits two obstacles. Each points to a better argument.
| Obstacle | What it suggests |
|---|---|
| No ontologically neutral proof that effects cannot precede causes | Prove the impossibility of oppositely directed causation from the premise that the world is dynamic, which is legitimate if only a dynamic world can contain causal relations: the argument from causation |
| Preventability conditionals can be true in a static world on standard accounts | Since they seem to express an asymmetry of dynamic worlds, ask whether standard accounts of counterfactuals are unsatisfactory or covertly dynamic: the argument from counterfactuals |
Tooley's two-world construction is widely cited, but critics note that it makes causal direction independent of any physical asymmetry within each region, which Humean and agency theorists (Huw Price later argued causal direction is perspectival) reject outright. The literature since 1997 has also become more hospitable to backward causation: retrocausal interpretations of quantum mechanics (Price, Wharton, Sutherland, Leifer and Pusey) treat limited backward influence as a live physical hypothesis, which cuts against any premise that backward causation is logically impossible.
Facts, Causation, and Time
Tooley replaces preventability with two deeper arguments. The argument from counterfactuals says that only a dynamic world can justify the temporal bias in our truth conditions for counterfactuals. The argument from causation, built on a realist, singularist theory in which causal laws satisfy probability postulates (C1)–(C4), says causal laws can exist only in a world where the past and present are real and the future is not, or something very close to it. As a bonus, the same postulates make backward causation logically impossible, loops or no loops.
The argument from causation rests on three claims: realism (causal relations do not supervene on non-causal facts, even with laws added); singularism (causal relations do not presuppose laws, deterministic or probabilistic); and the characterisation of causal laws by postulates (C1)–(C4) from chapter 3. If sound, it rules out every familiar rival, tensed and tenseless.
4.1 Counterfactuals and the direction of counterfactual dependence
Accounts of "if A were the case, B would be the case" fall into two groups: those that give an essential role to temporal priority or causal priority, and those that use only comparative similarity of possible worlds. Any adequate account must deliver the direction of counterfactual dependence: later events depend on earlier ones, not vice versa. A dry, oxygenated, unstruck match: "had it been struck, it would have lit" is true; "had it been struck, it would not have been dry" is false.
Temporal-priority accounts. "If A at t, then B at later t′" is true iff B holds at t′ in all worlds where A holds at t that differ as little as possible from the actual world up to and including t and share its laws from t onward. This gets the match right, because the dry-match counterfactual needs bigger changes at or before t. But it fails if backward causation is possible: had Tim not loaded nuclear weapons into his time machine, he would have had none in 1921. The fix is a causal-priority account: hold fixed what is causally prior to the antecedent event and keep the laws for what is causally posterior.
Similarity accounts. "If A, B" is true iff some A-and-B world is closer to actuality than any A-and-not-B world. The classic worry is Nixon's button: a world where Nixon presses the button but a wire breaks and no war follows seems closer to ours than a world with a nuclear holocaust.
David Lewis's similarity weighting (1979), most to least important
- Avoid big, widespread violations of the other world's laws.
- Maximise the region of exact match of particular fact.
- Avoid small, localised violations of law.
- Secure approximate (partial) similarity of particular fact.
How the recipe handles Nixon. The broken-wire world needs a small miracle but still achieves only a partial match with our future, since the button-press starts many inconspicuous causal chains: factor 3 is paid for a factor-4 gain, a bad trade. A world where the pressing leaves no trace at all (no heat, light rays miraculously rerouted) gets an exact future match but only through many violations: factor 1 is lost. So had Nixon pressed the button, there would have been a nuclear war. And not every earlier event would have been different, because an exact match of the past costs only a small miracle.
Why is matching the past cheap and matching the future dear? Because in our world events have many diverging effects but rarely many converging causes: causal forks open toward the future (outgoing spherical light waves are common, incoming ones are not). That is a contingent fact.
Worlds with the forks reversed or absent. In a world where events typically had many causes and never many effects, Lewis's recipe would make earlier events counterfactually depend on later ones. In a world with causation but neither multiple causes nor multiple effects, it would make neither depend on the other, since an exact match of particular fact outweighs a small miracle. Both verdicts are unacceptable.
Lewis replies that both worlds are logically impossible: the direction of causation is defined by the orientation of open forks, and the direction of time by the majority of causal processes; a world without forks has no causation and so no dependence asymmetry. That reply presupposes reductionism about causal direction, which §4.2 attacks. If it falls, pure similarity accounts cannot capture the asymmetry.
Priority-based accounts get the right values even in the fork-reversed and fork-free worlds. But generating the right values is not enough: we need to know why they are right.
Adding a law to a simple world (Tooley's Figures 4.1–4.3). World W has only three event types, P, Q, R, no two co-located. Its only laws: P causes a later Q and Q causes a later P, so there are endless alternating chains. Events of every type sometimes occur uncaused. There are exactly two R events, neither causing anything: one is followed, at distance d, by a P that starts a P–Q chain; the other is followed at distance d by a Q that starts a Q–P chain. Now ask: how would things be if it were also a law that R causes P at distance d? In W1 the second R remains and causes a P, so the infinite Q–P chain is replaced by an infinite P–Q chain (divergence at t4). In W2 the second R simply does not exist (divergence at t3). On any sensible similarity measure W2 is far closer to W: one event deleted versus infinitely many replaced. Priority accounts, matching the past until forced to diverge, pick W1. W1 is surely right.
What justifies that temporal bias, and the choice of the far less similar world? Tooley runs the question twice.
- In a static world all events are equally real. Choosing W1 means deleting infinitely many actual events and adding infinitely many non-actual ones rather than deleting one. With no ontological difference between earlier and later, no justification is possible.
- In a dynamic world where past and present are real and the future is not, imagine W with the new law growing state by state, changing nothing unless the laws force it. Nothing changes until the R at location (4), time 3. That R is actual and nothing later is; the law then requires a P at time 4, the nomological incompatibility of P and Q removes the Q, and the other two laws replace P with Q and Q with P step by step. The divergence is explained.
The argument from counterfactuals. Similarity accounts have a natural, static-friendly rationale but give wrong truth values. Priority accounts give right values but with a built-in bias that cannot be justified in a static world. So the only satisfactory account of counterfactuals presupposes a dynamic world; if counterfactuals as we use them are ever true, the world is dynamic.
4.2 The nature of causation, I: realism
Realism is needed twice: to make the postulates the best account of causal direction (reductionist accounts offer simpler rivals), and to redeem the promissory note against Lewis.
Two forms of reductionism about causal relations
- Strong reductionism. Any two worlds that agree on all non-causal properties of and relations between particular events agree on all causal relations. Causal relations logically supervene on non-causal facts.
- Weak reductionism. Any two worlds that agree on all non-causal properties and relations and on all causal laws agree on all causal relations.
- Realism = rejection of both.
4.2.1 Direction-of-causation objections
Reductionists ground causal direction in features of our complex world: (1) entropy increase in the same direction in almost all isolated systems (Reichenbach, Grünbaum); (2) propagation of order, such as outgoing ripples and spherical light fronts (Popper 1956); (3) open forks, a fork being open if it lacks either a common cause or a common effect, which in our world almost all open toward the future (Reichenbach, Salmon).
4.2.1.1 Causation and simple worlds
Two simple worlds. (a) A world containing one particle and no force fields: still causal, since the particle's identity over time depends on causal relations between its temporal parts. (b) A Newtonian world with only contact forces: two objects joined by a rod, rotating about each other forever, each accelerating at constant magnitude because of the rod's force. Both are causal, yet both have no entropy change, no propagation of order and no open forks. And both are time-symmetric, so no pattern of events marks cause-to-effect from effect-to-cause.
So a reductionist must reduce causal direction to the direction of time, and must then be a realist about time's direction. What then grounds it? Not causation (circular for the reductionist). Treating the asymmetry of "earlier than" as an intrinsic, unexplained necessity is doubtful (Tooley prefers that all non-a posteriori necessary truths be analytic), and in any case asymmetry alone does not say which way time points. A dynamic account of time's direction (criticised in §6.1) would only give a shortcut to Tooley's own conclusion that causation requires a dynamic world.
4.2.1.2 Inverted worlds
The Laplacean deity's inverted twin. In 4004 BC a Laplacean god plans a Newtonian world, chooses AD 2000 for Armageddon, and computes its state just before. He creates two spatially unrelated worlds: the first from the Garden-of-Eden state; the second starting from the pre-Armageddon state with every velocity reversed. Since Newtonian laws are time-reversal invariant, the second runs through B, then A (reversed copies of the first world's later B and earlier A), ending in a reversed Eden. In the first world causal direction matches entropy increase, order propagation and open forks. In the second, causation runs from the created initial state forward, yet entropy decreases, order converges and forks open toward the past along it. Any reductionist criterion gets the second world wrong.
Again the reductionist can retreat to the direction of time only by being a realist about it, since no account based on event patterns gets inverted twins both right.
4.2.2 Underdetermination objections
These show that worlds can agree on all non-causal facts, all causal laws and the direction of causation yet differ in which events cause which. Tooley has four such arguments; one suffices.
4.2.2.1 The argument from indeterministic laws
Indeterministic laws need not be probabilistic: a law may say P produces either Q or R with no probability attached. Given quantum physics, such laws are surely possible. Take a world with just two laws:
- L1. For any x, having P for an interval Δt causes x to acquire either Q or R, but not both.
- L2. For any x, having S for an interval Δt causes x to acquire either Q or R, but not both.
| From t to t + Δt | At t + Δt | Possibility 1 | Possibility 2 |
|---|---|---|---|
| Pa and Sa | Qa and Ra | Pa causes Qa, Sa causes Ra | Pa causes Ra, Sa causes Qa |
If a had only P and then got Q, P caused Q; P and S with only Q would be harmless overdetermination. But with P and S yielding both Q and R, the laws plus all non-causal facts plus causal direction do not settle which possibility holds. Reductionism can give no answer.
| Reductionist reply | Tooley's rejoinder |
|---|---|
| No causal relations at all in the P+S case | Then the laws (which say P always causes Q or R) are impossible; that needs independent argument, and the case recurs with probabilistic laws |
| P causes "Q-or-R", nothing more determinate | Confuses states of affairs with disjunctive descriptions of them; there are no disjunctive states of affairs (ch. 2), so P must have caused Q or caused R |
4.2.3 Realism or reductionism?
Reductionism has dominated for three reasons: past realists rested on the observability of causation, which is implausible; realist accounts of theoretical terms arrived only recently; and, unlike other fields that switched to realism swiftly once theoretical realism was available, causation lacked a complete theory with the right postulates. Tooley thinks the arguments above make a strong prima facie case against reductionism and that the needed postulates are now available, so realism should be preferred.
4.3 The nature of causation, II: a singularist approach
Singularism: two events can be causally related without instantiating any law, basic or derived; this suggests causation is possible even in a world with no laws. Traditional realists were singularists because they thought causation observable in a single case, and a single observation cannot reveal a law. Tooley rejects that ground: causation is a theoretical relation.
4.3.1 Causation and immediate observation
Two senses of "immediately observable": strong, the relation itself can be given in experience; weak, it is analytically connected with something so given (as colours are, if they are powers to produce experiences).
The empiricist argument that causation is not given in experience
- A property or relation is given in experience E only if it would be part of any experience phenomenologically indistinguishable from E.
- For any experience E, perceptual or introspective (willing, reasoning), direct brain stimulation could produce an indistinguishable E with no causally related elements*: thoughts seeming to follow deductively, all actually caused from outside.
- So causal relations cannot be given in experience.
God suppresses a collision. God calculates the forces two colliding objects would exert, suppresses them, and moves the objects to their subsequent positions by direct action. Nothing in anyone's experience would differ. If causation had a reliable observable indicator, as colour and spatial arrangement do, experience would differ. So causation is not observable even in the weak sense.
4.3.2 An argument for singularism
| View | (1) Causal relations presuppose laws | (2) Causal relations supervene on laws + non-causal facts |
|---|---|---|
| Supervenience view | Yes | Yes |
| Intermediate view | Yes | No |
| Singularist view | No | No |
The underdetermination argument refutes thesis (2) and so the supervenience view, but not thesis (1), since every causal relation in that case falls under a law. Against the intermediate view Tooley offers a "somewhat modest" two-part argument.
- Richer ontology. Combine singularism with laws as relations among universals (Dretske, Armstrong, Tooley 1977): two kinds of basic facts, relations between particular states of affairs and relations between universals; causal laws are just laws in which one universal is the causation relation. The intermediate view needs the same two kinds plus a separate account of causal laws; otherwise nothing would explain why causation cannot occur outside laws.
- Unexplained necessity. Both the supervenience and the intermediate views say causally related events entail a law. The supervenience view explains this by reduction; the intermediate view cannot explain it at all. Singularism denies the entailment and owes no explanation.
4.3.3 A singularist conception of causation
Is the concept of causation basic? Not if traditional empiricism is right that a concept is analytically basic only if it picks out something we are directly acquainted with; and even on a looser view, basic concepts would have to pick out the weakly observable, which causation is not. Reductive analyses fail (§4.2). So causation must be a theoretical relation fixed by a theory.
A theory mentioning only the relation, not laws, is hard to find. "Causes precede effects" is disputed; "causes are spatiotemporally contiguous with immediate effects" is disputed, since gaps involve no contradiction; and even together they cannot tell causing from merely preceding and adjoining. Hume fell back on regularities. Powers would usually bring laws back in (an object has a power in virtue of categorical properties plus laws); ultimate powers are on a par with laws that apply to an individual as such, a last resort.
Tooley's indirect characterisation. Assume events can be causally related outside laws; assume causal and non-causal laws are both possible, so "law" is analysable without causal notions; then causal laws are those involving causation, and further necessary truths may distinguish them. Hence: causation is that unique relation between events or states of affairs such that, if there are laws involving it, those laws must satisfy postulates (C1)–(C4). This mentions laws without requiring that causal relations instantiate them, and avoids the disputed postulates of temporal priority and contiguity.
4.4 The nature of causation, III: causal laws and probability
4.4.1 Laws linking simple and very complex events
Two electrons and a solar system. Simple event type: two electrons exactly a mile apart. Complex type: a solar system exactly duplicating ours at midnight, 1 January 2000. A priori the first is far more probable: fewer particles, and moving electrons often hit a one-mile separation, whereas the second needs an incredible coincidence. Learn that each is nomologically necessary and sufficient for the other: probabilities must be equalised, but there is no reason to adjust one rather than the other; it seems best to move both toward each other. Learn instead that the electrons are causally necessary and sufficient for the solar system: now there is a clear answer, and the solar system's posterior probability becomes the electrons' prior. If the causation ran the other way, the electrons would become as improbable as the solar system was.
The general rule: when one event type is causally sufficient and necessary for another, set the posterior of the effect equal to the prior of the cause. For causes that are sufficient but not necessary, postulates (C1)–(C4) give the more complex relation. If they are correct and complete:
Tooley's analysis of causation
Causation is that unique relation between events or states of affairs such that, if there are laws involving it, those laws must satisfy:
- (C1) Prob(Px, P ⇒ Q & C) = Prob(Px, C)
- (C2) Prob(Qx, P ⇒ Q & C) = Prob(Px, C) + Prob(∼Px, C) × Prob(Qx, ∼Px & P ⇒ Q & C)
- (C3) Prob(Qx, ∼Px & P ⇒ Q & C) = Prob(Qx, ∼Px & C)
- (C4) Prob(Qx, P ⇒ Q & C) = Prob(Px, C) + Prob(∼Px, C) × Prob(Qx, ∼Px & C)
4.5 The argument from causation
4.5.1 The structure of the argument
Compactly: our world contains causal laws; causal laws require a dynamic world; so our world is dynamic.
The argument from causation, expanded
- Our world contains many types of events that are, prima facie, absent a certain kind of explanation, extremely improbable.
- They have causal explanations, and that fact makes them not, all things considered, extremely improbable iff causal laws satisfy (C1)–(C4).
- So it is reasonable to believe our world contains causal laws satisfying (C1)–(C4).
- It can be explained how causal laws satisfy (C1)–(C4) iff the world is dynamic rather than static.
- So it is reasonable to believe our world is dynamic: what facts there are depends on what time it is.
4.5.2 The reality of causation
Rain. Scattered water drops near the earth are not improbable in arrangement, but their motion is: almost all move toward the ground. Impact points look random, yet the drops then converge into puddles whose bottoms fit the ground and whose tops are almost perfectly flat: improbable again. Hit a puddle with a drop and molecules form concentric rings above and below the surface, an increasingly improbable arrangement as the rings multiply. Is the world just a stream of unlikely accidents? Not if gravitational forces and accelerations are causal laws obeying (C1)–(C4): then the posterior probability of these states is no lower than that of their causally sufficient initial states.
Could some other theory of causation do the same job? The only candidate is "causes raise the probability of their effects", and it fails twice. There are counterexamples: a weak cause can pre-empt stronger ones and lower the effect's probability. More importantly, probability-raising is symmetric: if P(E|C) > P(E) then P(C|E) > P(C), so effects raise the probability of causes just as much. It cannot ground the direction or even the asymmetry of causation. Hence it is reasonable to believe in laws satisfying (C1)–(C4).
4.5.3 Causation and a dynamic world
The decisive asymmetry is between (C4), the effect's posterior depends on the cause's prior, and (C1), the cause's posterior does not depend on the effect's prior.
| In a static world | Argument for (C4) | Mirror argument for (C4*) |
|---|---|---|
| Starting point | Prob(Px, C) = chance of a P in a time slice | Prob(Qx, C) = chance of a Q in a time slice |
| Law P ⇒ Q implies | Every P is followed by a Q in the next slice | Every absence of Q is preceded by an absence of P |
| So | Posterior of Q ≥ prior of P | Posterior of ∼P ≥ prior of ∼Q |
| Hidden assumption | Posterior of P = its prior | Posterior of ∼Q = its prior |
| Result | (C4) | (C4*): Prob(∼Px, P ⇒ Q & C) = Prob(∼Qx, C) + Prob(Qx, C) × Prob(∼Px, Qx & C), which contradicts (C1) |
In a static world neither hidden assumption can be justified, and the two arguments are equally good. So a static world cannot explain how (C1) and (C4) hold together.
Nor can most dynamic worlds. If past, present and future are all real and only tensed facts change, the situation is as in a static world. If only the present is real, cause and effect are equally unreal from any moment. What is needed is an ontological asymmetry: past and present real, future not.
Why the growing block explains (C1)–(C4). Suppose a P now and a law that P brings about a slightly later Q. If in fact there is no such law and no later Q, that cannot support "had the law held, the P would have been absent", because as of the time of the P, the absence of the later Q is not actual: the future is unreal. The world is fixed by the laws plus what is actual as of a time, so the P would produce a Q, and posterior(Q) ≥ prior(P). The reverse argument fails: the earlier P is actual as of the later time, so the law would add a Q rather than remove the P. Causal laws are not patterns in history; they control history, by determining, with what is actual as of a time, which states of affairs are added to reality.
4.6 Causation and what is actual
The argument shows causation is possible in a growing-block world, impossible in static worlds and most dynamic ones. What is the minimum a world needs? Tooley collects postulates linking causation and actuality that hold in growing-block worlds and checks whether they suffice for (C1)–(C4) without entailing the full growing block.
4.6.1 Causality, simultaneity and actuality postulates
The six actuality postulates
- I. Occurrence and actuality. An event or state of affairs is actual as of the time of its occurrence.
- II. Causal posteriority. A cause is always actual as of the time of any of its effects (the reality of the past).
- III. Causal priority. An effect is never actual as of the time of any of its causes (the unreality of the future).
- IV. Simultaneity. If two states of affairs are simultaneous, there is no time as of which one is actual and the other not.
- V. Backward transmission of non-actuality. If A is not actual as of the time of B, neither is it actual as of the time of any cause of B.
- VI. Forward transmission of actuality. If A is actual as of the time of B, it is also actual as of the time of any effect of B.
Given I, the special case of VI with A = B yields II, so only I, III, IV, V and VI are needed.
Why each is needed comes from simple worlds (Tooley's Figures 4.4 and 4.5). To show (C1)–(C4) can hold, one must show, for instance, that if a law said P prevents a later Q at the same place, the P would remain and the Q would vanish; that needs the Q to be not actual as of the P's time. Postulates I–III cannot deliver this: III only shows that an effect (S, caused by R) is not actual as of its cause's time. IV carries non-actuality to anything simultaneous with S. In a richer world IV still is not enough, so V carries non-actuality back along causal chains, and VI carries the P's actuality forward to the later time.
4.6.2 The ontological status of past, present and future
Define: P and Q are directly linked iff P causes Q or P is simultaneous with Q; indirectly linked iff joined by a chain of direct links; times r and s are causally linked iff some state at r is directly or indirectly linked to some state at s.
- The past is real. Suppose E occurs at r, earlier than s, but is not actual as of s. If r and s are causally linked, postulates I and VI make every state at r actual as of s. Contradiction.
- The future is unreal. Suppose E occurs at s, later than r, but is actual as of r. If r and s are causally linked, postulates I and V make no state at s actual as of r. Contradiction.
So a world satisfying the postulates can depart from the growing block only if some times are not causally linked. Could they fail to be? Causal processes might have been rare or absent; there might be empty absolute space-time. Tooley's answer anticipates chapter 9: the direction of time is given by the direction of causation, so "no causation, no time"; and empty space-time is still possible because space-time points can stand in causal relations to one another. If so, any two times one of which is earlier are causally linked, and only a world where past and present are real and the future is not can contain causation. If not, a world satisfying I–VI is still a very close approximation to one.
4.7 Backward causation revisited
Chapter 3 left backward causation without loops apparently possible, which is unwelcome for most dynamic views, including Tooley's (presentism may be an exception, if it allows causation at all). Now it can be excluded.
Proof that backward causation is impossible (given causally linked times)
- Postulates I and V: if r is earlier than and causally linked with s, no state of affairs at s is actual as of r.
- Suppose A at s causes B at earlier r.
- Postulates I and II: a cause is actual as of the time of its effect, so A is actual as of r.
- Contradiction. So backward causation is logically impossible, even without causal loops.
If times need not be causally linked, the proof fails, which is another strong reason for dynamic theorists to adopt a causal theory of the direction of time: if temporal order depends ultimately on causal order, there cannot be causally unlinked times.
4.8 Summing up
- Ch. 3 Preventability fails: no neutral proof against backward causation; preventability counterfactuals hold in static worlds.
- §4.1 Similarity accounts give wrong values; priority accounts can be justified only in a dynamic world.
- §§4.2–4.4 Causation is realist, singularist, and fixed by (C1)–(C4).
- §4.5 (C1)–(C4) can hold only where past and present are real and the future is not.
- §4.6 Postulates I–VI: the growing block, or a very close approximation, is required.
- §4.7 Backward causation is impossible given causally linked times.
The two arguments are connected: counterfactual truth conditions need a dynamic world because they must refer to causation, and causation itself presupposes a world where the past and present are real but the future is not.
The argument from causation is the book's engine and its most disputed part. Critics question whether logical probabilities of the kind (C1)–(C4) use are well defined, and whether the postulates express conceptual truths rather than a theory-laden choice. Humeans deny that laws "control" history at all, so the explanatory demand that drives step 4 has no grip on them. Others argue that a block universe with a primitive causal or nomic direction (for example Tim Maudlin's primitive directed time, 2007) can explain the asymmetry without growth. And the inverted-worlds argument assumes that creation by a deity fixes causal direction independently of every physical asymmetry, which a Price-style perspectivalist rejects.
Truth and Truth at a Time
Tooley defends a temporally relative notion of truth against two objections: that it confuses propositions with propositional functions, and that it commits one to a suspect three-valued logic. His answer to the second is the chapter's most original idea: the defining property of the logical connectives is not truth-functionality but factual-truth-functionality, which holds in both two-valued and three-valued settings. He then argues, against most tensed theorists, that truth simpliciter is still needed and definable.
Tensed theorists almost always adopt a temporally relativised truth, on which a proposition can have different truth-values at different times; tenseless theorists call it problematic or incoherent. Most objections wait until chapter 10; two are met here.
5.1 Truth at a time: an initial objection
5.1.1 Propositions versus propositional functions
C. J. Ducasse (1941) says qualifying "true" by place-date adverbs is as absurd as saying the cube of 8 is married or single: the truth of a proposition is not an event and has no date. It may seem that when rain starts, "it rains here now" becomes true, but that is "to mistake a propositional function for a proposition". Utterances of "It is now raining here" at five and at six o'clock express different propositions, so no proposition changes value.
Tensed writers have fed the suspicion. Arthur Prior (1953) notes that ancient and medieval logicians, Aristotle included, called "Socrates is sitting down" a proposition true at some times and false at others; Pavel Tichý (1980) holds that "Mrs Brown is at home" always affirms the same state of affairs, which is intermittent, so the proposition is sometimes true and sometimes false.
Tooley's reply: his notion of truth at a time does not rest on any such confusion. Take a tenseless, dated, indexical-free sentence: "There are (tenselessly) unicorns on earth in AD 2000." It expresses the same proposition whenever uttered, yet on the growing-block view it may be true in 2001 while it is certainly not true in 1996. (Colin Allen noted that if "unicorn" is a Kripkean natural-kind term one should switch to purple sheep.) On a tensed view where past, present and future are all real, tenseless statements cannot change value, but such theorists still say "E is present" expresses one proposition with changing values.
Read charitably, Ducasse's real target is the claim that ordinary tensed sentences ("World War II is now taking place") express one proposition on every utterance. On that, Tooley agrees with the tenseless theorist: ordinary tensed statements involve indexicals (§8.3). But truth at a time does not depend on that controversial claim; it follows from a dynamic world in which which tenseless facts exist changes over time.
5.1.2 Dynamic worlds, correspondence and truth at a time
So tensed theorists should not argue from the rejection of indexical accounts to relativised truth. The right route is short: given a correspondence theory, if which tenseless temporal facts exist depends on the time, define truth at a time as correspondence between a proposition and the states of affairs actual as of that time. If a dynamic world is coherent, so is temporally relative truth, at least for tenseless propositions about temporal states of affairs.
The details of the correspondence theory do not matter. Tooley's own preferences: truth-bearers are basically propositions, understood as constituents of mental states rather than third-world denizens; correspondence for simple propositions is explained by causal theories of reference and meaning, and for complex ones recursively.
5.2 Tensed views of time and three-valued logic
5.2.1 Reasons for adopting a three-valued logic
A tensed view with all times equally real plus tensed properties neither needs nor wants three values. But if there is an ontological gulf between the future and the past and present, a statement can fail to be true at a time in two very different ways.
| Statement | Status in 1980 | Why it is not true in 1980 |
|---|---|---|
| S: There are (tenselessly) no dinosaurs | False | A positive truth-maker for a denial of S ("there are dinosaurs") is actual as of 1980 |
| T: There are (tenselessly) unicorns in AD 2000 | Indeterminate | Nothing actual as of 1980 makes T true, and nothing makes its denial true |
A second reason. On a two-valued view, "not-T" would be true in 1996 and perhaps not true in 2001, so statements could go false to true and true to false; why not oscillate? In fact a proposition can change value only once, and explaining why already uses three values: true or false means a relevant truth-maker exists (for the statement or its denial), which never goes away; indeterminate means no relevant truth-maker exists yet. Three-valued logic makes the metaphysics perspicuous.
5.2.2 The third truth-value
Treat indeterminateness as metaphysically inferior: truth and falsity are the "real" values, and i is a truth-value gap. Three advantages follow.
- One-way change. A proposition lacking a genuine value can acquire one; one that has a genuine value can never lose it.
- A rationale for the tables. Where no i occurs, the three-valued table must match the two-valued one (otherwise it is not the same connective). Where i occurs, consider every way of filling the gaps with t or f: if all give the same value, enter it; if some give t and some f, enter i (otherwise a tenseless statement could have different genuine values at different times). So t ∨ i = t, but f ∨ i = i.
- Logical truth. In three-valued tables "p or not p" gets i when p is i. But Bas van Fraassen's supervaluations (1966), which fill the gaps, capture exactly the classical tautologies: logical truths are true under every assignment of genuine values, so, on a natural reading of "possible world", true in all possible worlds.
Three-valued disjunction built by gap-filling (Tooley's Fig. 5.1 completed)
| p ∨ q | q = t | q = i | q = f |
|---|---|---|---|
| p = t | t | t | t |
| p = i | t | i | i |
| p = f | t | i | f |
The corner entries are fixed by two-valued logic; the bold entries come from filling gaps (for unrelated p and q).
5.2.3 Three-valued logic as a stumbling-block
Non-classical logics breed suspicion: intuitionism denies that p or not-p always holds; dialetheic logics (Graham Priest, 1987) allow p and not-p. When a logic declares ordinary tautologies non-logical, it is natural to suspect its "negation" is not negation, and that the logic cannot express the standard connectives at all.
Jan Łukasiewicz's 1920 system, Prior's "classical" three-valued logic, grew out of reflection on Aristotle's sea fight.
Łukasiewicz's three-valued tables (Tooley's Figs 5.2–5.5)
| p | ¬p |
|---|---|
| t | f |
| i | i |
| f | t |
| p, q | p ∧ q | p ∨ q | p → q |
|---|---|---|---|
| t, t | t | t | t |
| t, i | i | t | i |
| t, f | f | t | f |
| i, t | i | t | t |
| i, i | i | i | t |
| i, f | f | i | i |
| f, t | f | t | t |
| f, i | f | i | t |
| f, f | f | f | t |
Negation, conjunction and disjunction interrelate normally (p ∨ q = ¬(¬p ∧ ¬q); p ∧ q = ¬(¬p ∨ ¬q)). But: (a) the conditional breaks the usual link: with p and q both i, ¬p ∨ q is i while p → q is t; and (b) excluded middle and non-contradiction fail, since with p = i both p ∨ ¬p and ¬(p ∧ ¬p) are i. Fixing (a) by making i → i = i makes "if p then p" non-tautologous.
The truth-functionality objection
- If p is i, then ¬p is i.
- If p and q are unrelated and both i, p ∨ q is i.
- p ∨ ¬p is a necessary truth, so it is t whatever p's value.
- So when both disjuncts are i, "or" sometimes yields i and sometimes t: "or" is not truth-functional.
- Truth-functionality is the essence of the ordinary connectives. So three-valued logic cannot contain them, and since the growing block needs three values, the growing block is in trouble.
5.3 Truth-functionality and the logical connectives
Tooley accepts premise 4 and rejects premise 5. His reply has three stages: distinguish factual truth from logical truth; show that the connectives are functions of factual-truth-values as well as of truth-values; argue that factual-truth-functionality is the more basic property. He notes that neither philosophers nor logicians had asked which of the two properties is fundamental.
5.3.1 Factual truth and logical truth
Definitions
- Factually true simpliciter: there is an external truth-maker, a fact outside the proposition sufficient to ensure it is true.
- Factually true at t: some external truth-maker for it is actual as of t.
- Logically true: true in virtue of logical form alone; no external truth-maker required.
- (In the three-valued case all "truth-values" are understood as indexed to a time.)
The concepts overlap, because the truth-maker need only be sufficient, not necessary. In two-valued logic every logical truth is also a factual truth: "unicorns exist or do not" has a truth-maker, namely whatever makes the true disjunct true. In three-valued logic a logical truth need not be factually true at a time: nothing actual as of a time may make either disjunct true.
5.3.2 Connectives as functions of factual truth
Two-valued case. Two claims hold: (1) p is true simpliciter iff p is factually true simpliciter; (2) p is false simpliciter iff p is factually false simpliciter. The "if" halves are trivial. For "only if": the atomic propositions relevant to a true p are each true or false, and their values make p true by the tables; atomic propositions cannot be true by form, so each is factually true or false, and the facts making them so, with the tables, make p factually true. Likewise for falsity. So replacing "true/false" with "factually true/false" in the classical tables yields sound factual-truth-tables.
Three-valued case. That route is closed, since the connectives are not truth-functional here. Instead Tooley proves directly that every three-valued connective built by gap-filling from a non-constant two-valued truth-function is factual-truth-functional at a time.
The proof in outline
- Exclude constant functions. A connective built from a constant two-valued function stays constant, so it maps the all-i tuple to t or f. Read factually, that would let the absence of truth-makers entail the existence of a truth-maker for something else: impossible. Constant functions are not real logical connectives anyway.
- Mapping to factual truth. For a non-constant connective, a tuple mapped to t cannot be all i. Its non-i members alone fix the output (every gap-filling gives t). Those members correspond to propositions factually true or false at t, so the world as of t contains states of affairs sufficient for the compound's truth: it is factually true at t.
- Mapping to factual falsity. Exactly parallel.
- Mapping to factual indeterminateness. i is assigned only when some fillings give t and others f, so the existing truth-makers cannot suffice for truth or falsity: the compound is factually indeterminate at t.
So the familiar tables, read as truth-tables, are unsound in the three-valued case; read as factual-truth-tables, they are sound in both cases.
5.3.3 Which property is basic?
Suppose a growing-block theorist says: "Either there are unicorns in 2000 or there are not" is true now, though neither disjunct is true now. If truth-functionality defines "or", she is either contradicting herself in an immediate and obvious way, or using "or" eccentrically, so that switching between dynamic and static metaphysics would change the meanings of the connectives. Neither is plausible.
If factual-truth-functionality defines the connectives, the utterance is coherent, and the meanings do not change with one's metaphysics, because factual-truth-functionality entails truth-functionality in a two-valued setting (by claims 1 and 2). So the view also explains why the connectives are truth-functional in two-valued logic but not in three-valued logic, and the failure of truth-functionality is no objection to three-valued logic.
5.4 Truth simpliciter
Most tensed theorists, Quentin Smith (Language and Time, 1993) for example, reject truth simpliciter. Tooley disagrees.
5.4.1 Truth simpliciter as two-valued
Truth at a time is three-valued; truth simpliciter is necessarily two-valued. This is often why dynamic theorists drop it: at every moment some propositions are neither true nor false at that moment. Tooley proves bivalence from Tarski's material adequacy condition (Convention T, 1944): an adequate definition of truth must entail every instance of (T) X is true iff p.
Tarskian proof that truth simpliciter is bivalent
- 'p' is true iff p. (instance of T)
- 'not p' is true iff not p. (instance of T)
- p or not p. (logical truth)
- So either 'p' is true or 'not p' is true. (1, 2, 3)
- 'p' is false iff 'not p' is true. (definition)
- So either 'p' is true or 'p' is false. (4, 5)
5.4.2 The need for truth simpliciter
5.4.2.1 Logical truths and correspondence
"Either there are (tenselessly) dinosaurs or there are not" is true in 1980, since something actual as of 1980 makes it true; but "either there are unicorns or there are not", of the same form, is not. So if logical truths are to be called true, the relevant concept is truth simpliciter. Reply: define truth at a time by supervaluation and distinguish it from factual truth at a time; then logical truths are true at every time. Rejoinder: that abandons a correspondence theory for logical truths, since nothing actual as of 1980 makes either unicorn disjunct true. With truth simpliciter, the totality of what is actual makes one disjunct true, and correspondence is preserved.
5.4.2.2 Atemporal entities
Propositions about entities without temporal location, if there are any, cannot be true at a time. Candidates fall into two classes.
| Class | Examples | Why atemporal | Tensed theorist's options |
|---|---|---|---|
| Necessary existents | numbers, propositions, logical possibilities, Platonic universals | Some numbers characterise no instantaneous set; some propositions are never thought or uttered; some possibilities are never actualised; some universals are never instantiated | Call them fictions; logical constructions from temporal items; or give them temporal location (Quentin Smith tries this for numbers and propositions) |
| Contingent existents | laws as second-order states of affairs (relations between universals); uninstantiated universals | No basis for locating them in time | Harder to dismiss, since true nomological statements require such states of affairs |
David Armstrong locates a law in its instances. Tooley objects: it makes uninstantiated basic laws impossible, which is counterintuitive; and with an unreal future, a law would not exist before its first instance, leaving no ground for counterfactuals about earlier times.
Laws for feelings that never arose. Suppose basic laws link complex neurological states with raw feel qualities. Had the world been slightly different, those neurological states might never have occurred: the laws would be uninstantiated and some phenomenal properties never instantiated. If laws are relations between universals, those universals would still exist in that world, with no temporal location. Since laws are contingent, this argument is harder to brush off than the one from numbers, where necessary truths may be analytic and carry no ontological commitment.
5.4.2.3 Universally quantified propositions
Three neutrinos. "There will never be three neutrinos forming an equilateral triangle with sides of exactly one metre." This could be false at a time but never true at a time, because a later state of affairs could always falsify it. The same holds for any temporally unrestricted universal proposition. Yet such propositions are consistent and can be true: the truth in question must be truth simpliciter.
5.4.3 The definability of truth simpliciter
Every dynamic theory needs the totality of existence (chapter 2), if only for statements quantifying over all times ("there never were, are not, and never will be purple sheep"). Given it, truth simpliciter is defined, at least for tenseless propositions, as recursive correspondence with the sum total of what exists.
The difference between dynamic theories lies in whether every proposition is bivalent simpliciter.
| Tooley's growing block | Traditional tensed views |
|---|---|
| The world changes only by adding tenseless facts | Change also deletes facts: "WWII is now taking place" is false in 1936, true in 1942, false after 1945 |
| There is a consistent mereological whole of all states of affairs actual as of some time | No consistent whole; only the set of such states of affairs |
| Every temporal proposition is true or false simpliciter | Truth simpliciter cannot be defined for all temporal statements: "WWII is now taking place" would be both true and false simpliciter |
Both truth at a time and truth simpliciter are coherent, and no dynamic theory is satisfactory without both. If ordinary tensed sentences are indexical (§8.3), or if the world changes only by accretion, then every proposition is either true or false simpliciter.
Two pressure points. Supervaluationism, which Tooley borrows for logical truth, has known costs: a disjunction can be true with no true disjunct, and an existential true with no true instance, which some regard as abandoning the meaning of "or" and "some" in a different way. And the factual-truth-functionality thesis has attracted little uptake; some later growing-block theorists prefer to keep classical bivalent logic, treating claims about an unreal future as simply false (there is nothing to come) rather than indeterminate, which avoids the three-valued machinery altogether.
Worked example: values in 1980 and in 2001 (growing block)
| Proposition | In 1980 | In 2001 | Simpliciter |
|---|---|---|---|
| There are (tenselessly) dinosaurs | t | t | t |
| There are unicorns in AD 2000 | i | t or f, fixed forever | t or f |
| Unicorns in AD 2000 or not | t (supervaluation; no factual truth-maker yet) | t, factually | t |
| Unicorns in 2000, or dinosaurs never existed | i | t or f | t or f |
| There will never be three neutrinos in a one-metre triangle | i or f | i or f | t or f |
| World War II is now taking place (uttered 1942) | indexical: evaluates "WWII is present at 1942", t from 1942 on | t | t |
Aristotle's sea fight, Tooley-style. On the eve of the battle, "there will be a sea battle tomorrow" is indeterminate: nothing actual makes it or its negation true. "Either there will be a sea battle tomorrow or not" is true now, though no disjunct is, because its truth is secured by logical form, not by any present truth-maker; its factual truth arrives tomorrow. "There will be a sea battle or an air battle", with both disjuncts equally indeterminate, is not true now. So the value of a disjunction is not a function of its disjuncts' values at a time: Aristotle was right, and the connective "or" means the same as ever, because it is defined by its factual-truth table. And at all times it is true or false simpliciter whether the battle happens.
Tensed Accounts of the Nature of Time
Tooley clears the ground for his own semantics by attacking three theses almost every tensed theorist holds: that temporal priority can be analysed in tensed terms, that the tenseless quantifier can be analysed as "was, is or will be", and that tensed concepts are unanalysable. All three fail. A supervenience argument then shows that in a growing-block world all tensed truths are fixed by which tenseless facts are actual as of each time, so tensed language must be analysable in tenseless terms plus "actual as of a time".
6.1 A tensed analysis of temporal priority?
Is "earlier than" analytically basic? One might argue that we have non-inferential knowledge of priority because we see motion. But psychological immediacy is not absence of inference: perceiving motion may be inferential knowledge built from an immediately perceived momentary state plus memories of slightly earlier states (as representative theorists of perception argue). On the other side, earlier-than has apparently necessary properties, irreflexivity, transitivity, asymmetry, and the best explanation of a necessity is to derive it from logical truths by substituting definitional equivalents, Quinean doubts about analyticity notwithstanding. Treating priority as basic forfeits that explanation of why no event is earlier than itself.
So priority is analysable. Three routes: in terms of past, present and future; in terms of more basic concepts some tensed theories accept; or causally (chapter 9).
6.1.1 Priority via past, present and future: events and properties
The entailment from "A is past and B is present" to "A is earlier than B" invites a disjunctive analysis: X is earlier than Y iff (X past and Y present) or (X past and Y future) or (X present and Y future). It misses cases where both are past or both future.
Tensed analyses of "X is earlier than Y" and why each fails
| Author | Analysans | Circularity 1: relational tensed concept | Circularity 2: uses "future" |
|---|---|---|---|
| Wilfrid Sellars (1962) | X present and Y future; or X was present and Y future at the time of X; or X will be present and Y future at the time of X | "Y is future at the time of X" is analysed via "Y is later than X" (Richard Gale's objection) | Yes |
| George Schlesinger (1980) | Some t: (X past at t, Y present at t, t present) or (same, t past) or (same, t future) | "X is past at t" = X is earlier than t (plus perhaps "there are past events") | Yes |
| Richard Gale (1968) | X past and Y present, or past/future, or present/future, or X more past than Y, or X more future than Y | "P is more future than Q" has no analysis except "Q is earlier than P, and Q is future" | Yes |
| Arthur Prior (tense logic, 1968) | P(Y ∧ P X) ∨ (Y ∧ P X) ∨ F(Y ∧ P X) with operators P "in the past", F "in the future" | Nested operators need "present at t" and "past at t" | Yes: uses F |
| C. D. Broad (1923) | t is later than t′ iff the sum total of existence at t includes that at t′ plus something more | None, but the claim is a substantive truth, not a definition | No |
Gale's objection to Sellars is slightly flawed, Tooley thinks: "Y is future at the time of X" may say more than "Y is later than X" (on Tooley's own analysis it does). But the circularity stands so long as the former is analysed using the latter plus something like "there are future events". Gale defended his "more past than" by denying that it must be analysed as "P is earlier than Q and Q is now past"; Tooley shifts to "more future than", which cannot be basic if "future" cannot, and has no analysis except via priority.
6.1.2 The tense-logic account
Prior treats tense words not as predicates of events but as operators on sentences: "Julius Caesar was killed by Brutus" becomes "In the past, Julius Caesar is killed by Brutus". Operators stack ("in the past, in the future, in the past, ..."), but there is no present-tense operator, because the core sentences are present-tensed; if they were tenseless, tenseless language could not be analysed tensedly.
Why tense logicians like operators. "The world's strongest chess player was either female or a computer" becomes "In the past, the world's strongest chess player is either female or a computer". "It will be the case that the strongest player was either female or a computer" just adds an operator: "In the future, in the past, ...". The event-predicate approach must introduce a new event at each embedding: "The event that is the lying-in-the-past of the event that is the strongest player's being female or a computer lies in the future."
Convenient for logic, but not metaphysically perspicuous. A perspicuous syntax should show what things figure in the truth-makers and whether truth is a matter of properties or relations. Saying "In the past, Caesar is killed" is true iff "Caesar is killed" was true never gets back to the state of affairs that makes it true. So no defensible tensed view can treat tense-logical form as fundamental (compare Quentin Smith).
Waiving that, the tense-logic analysis still fails. It uses F, so it inherits circularity 2. It looks free of relational tensed concepts, but is not, given premise (*), defended in §8.3: the proposition expressed by a token of an ordinary tensed sentence, and so its truth-value, depends on the time of the token.
Argument that nested tense operators need relational tensed concepts
- Operators select a time; the core sentence, evaluated at that time, fixes the value. Three options for the core: tenseless ("dinosaurs roam the earth at t"); relational tensed ("dinosaurs' roaming lies in the present at t"); ordinary present tense ("dinosaurs are now roaming").
- Given (*), the present-tense option fails: truth conditions must mention tokens at the selected time, and hypothetical tokens can give the wrong value.
- Tensed theorists reject tenseless cores, so they need at least "present at t".
- The priority analysis puts a conjunction of a present- and a past-tense sentence inside an operator, P(Y ∧ P X), whose core must be "Y's occurring is present at t and X's occurring is past at t". So "past at t" is needed too, and with it temporal priority.
Before minds existed. "Once upon a time there were neither languages nor psychological states." Tense logic regiments it as "In the past, there are now neither languages nor psychological states." At the relevant past time there were no tokens of the core sentence, and had there been any, they would have been false, since a token requires a language and a mind. Yet the original sentence is true. Hypothetical tokens cannot rescue a present-tense core.
Every tensed analysis of priority is doubly circular: it uses relational tensed concepts (past quo ad an event, more past than, past at t) that are neither basic nor analysable except via priority; and it uses past and future, which (§6.3) are not basic and are analysed via priority.
6.1.3 Broad's account of the later-than relation
Broad: "A moment t is later than a moment t′ if the sum total of existence at t includes the sum total of existence at t′ together with something more." This uses no past/present/future yet is plainly tensed, since what exists differs at different times. Tooley thinks it is true, even analytically true, if (1) causation requires a growing-block world (chapter 4) and (2) the direction of time is defined by the direction of causation. But it cannot be the definition of later-than.
The inverted growing block. Imagine a world in which present and future are real but the past is not: the present is where things drop out of existence. Unlike McCall's tree it has no realism about unactualised possibilities (only the actual future exists), and it is more radical, since no past survives. One might motivate it by saying we cannot interact with the past and what we cannot interact with is unreal. In such a world, t is later than t′ iff the sum at t′ includes the sum at t plus more, so Broad's definition gets direction backwards.
Tooley thinks the inverted world is logically impossible, yet the objection stands: if Broad's definition were right, the impossibility would be immediately obvious, like that of unmarried wives, and it is not. Likewise a static world with an earlier-than relation would be trivially impossible, and clear-headed tenseless theorists could not have missed it. If tenseless views are impossible, it must be through subtle conceptual connections. Since the only remaining analysis of later-than is causal (chapter 9), and that is not tensed, tenseless relations cannot be analysed in tensed terms. Recent tensed theorists (Smith 1993) seem to have abandoned the project anyway.
6.2 Are tenseless quantifiers analysable in tensed terms?
Quantifiers can be read so that "there are dinosaurs" is true though none exist now, and "there are no unicorns" is not just "there are none now". Tenseless theorists (Quine 1953, D. C. Williams 1951) hold that the same quantifier occurs in "there are dinosaurs" and "there is a prime between six and ten": existence is univocal. Tensed theorists, Sellars for instance, analyse "there are (tenselessly) dinosaurs" as "there were, or are now, or will be dinosaurs".
Two objections to the tensed analysis of the quantifier
- Univocity. No equivocation occurs in saying there are physical objects, minds, uninstantiated universals, sets and numbers (Quine, "On What There Is"). The disjunctive "was, is or will be" sense does not apply to numbers and sets, so it cannot be what "exists" means.
- The future needs analysis (decisive). "Will exist" is not basic (§6.3). It cannot be analysed through past and present alone, since those never entail anything about the future. The only available analysis uses the present, temporal priority and tenseless existential quantification. So the tenseless quantifier cannot itself be analysed through the future-tense quantifier on pain of circularity.
Tenseless quantification is analytically more basic than tensed quantification.
6.3 Are tensed concepts unanalysable?
Two kinds of analysis must be distinguished. A translational analysis turns every statement using a concept into one using more basic concepts. A truth-conditional analysis states, in simpler terms, when such statements are true. Every translational analysis yields truth conditions, but not conversely.
"Sandra is here." An utterance is true iff Sandra is in the vicinity of the speaker of that utterance. But "Sandra is in the vicinity of the speaker of this utterance" refers to its own token, while no utterance of "Sandra is here" does, so it is not a translation. Indexicals refer directly; specifying their truth conditions requires naming or describing the referent, which adds material not in the original. Translation is sometimes possible: a speaker who learned "at this location" first and then used "here" as its abbreviation could have "Sandra is here" translated. The lesson: truth conditions without indexicals are never translations, and analysis should be understood broadly, as any specification of truth conditions in simpler terms.
The tenseless programme treats "It rained yesterday" like "There is a mountain over there": "yesterday" is indexical, so no translation into tenseless terms exists; but its truth depends only on the tenseless relation between token and event, so tenseless truth conditions exist. Tensed theorists usually say tensed concepts are not analysable at all. Broad was a partial exception: past and present statements reduce to the sum total of existence at times, but "we cannot analyse will away"; future judgements involve two unanalysable assertions, that further events will become and that a characteristic will characterise some of them.
The future is analysable
Two arguments that "future" is not basic
- Acquaintance. A descriptive concept is basic for someone only if it picks out something that is or was an object of direct non-causal awareness or immediate perception, which implies non-inferential knowledge of instances. Whatever is logically possible, humans have no non-inferential knowledge of the future.
- Necessity as analyticity. (1) Any event causally dependent on a present event lies in the future; (2) any event later than a present event lies in the future. Most philosophers take (1), and nearly all take (2), as necessary. To explain their necessity as analytic while keeping "future" basic, one would need causation to involve priority (rejected: Tooley's account of causation uses no temporal concepts) and later-than to be analysable tensedly (rejected in §6.1). So "future" must be analysable.
The analysis (completed in chapter 7): ordinary future-tense sentences involve indexicals, so only a truth-conditional analysis is possible; but their truth conditions use a more basic, non-indexical relational tensed concept:
E is future at time t means the same as E is later than time t, and time t lies in the present at time t.
E is past at time t means the same as E is earlier than time t, and time t lies in the present at time t.
Tensed theorists will object on three counts: (a) ordinary tensed sentences are not indexical; (b) "future at t" is not even a tensed concept, since it says only "later than t"; (c) the analysis is circular, because later-than is tensedly analysable. Replies: (a) the sound intuition is that indexicality cannot be intrinsic to tensed sentences, but ordinary ones may be indexical while more basic ones are not; (b) "E lies in the future at t" entails that E is later than t and more, a tensed proposition implying that the future is not real (chapter 7); (c) relies on §6.1's failed thesis.
The past is analysable too
The acquaintance argument is less straightforward, since some claim non-inferential memory knowledge of the past. Tooley thinks memory is non-inferential knowledge of present beliefs plus inference to the best explanation. But he can bypass this: one cannot be directly aware of a state of affairs without being directly aware of all its constituents, so direct awareness of an event's pastness would require direct awareness of the event's other properties. Phenomenologically, remembering greenness lacks the raw feel of experiencing greenness. So we are not acquainted with pastness. The necessity argument runs exactly in parallel with (1) "any event causally prior to a present event lies in the past" and (2) "any event earlier than a present event lies in the past".
So the basic tensed concepts are the relational ones: present at t, past at t, future at t. As stated, the analyses of past-at-t and future-at-t are compatible with a tenseless view, which can read "t is present at t" as "t is simultaneous with itself". The difference will come from Tooley's analysis of present at t through actuality as of a time and truth at a time, which takes becoming seriously.
6.4 An argument for the analysability of tensed concepts
Three options on tensed versus tenseless language
- Tensed is basic; all tenseless statements analysable tensedly.
- Tenseless is basic; all tensed statements analysable in tenseless terms, alone or plus the general idea of a dynamic world.
- Both basic; neither analysable in terms of the other.
Tenseless twins. Try to imagine two worlds that (a) are both growing blocks (what is actual as of t is everything simultaneous with or earlier than t), (b) agree on all tenseless states of affairs actual as of every time, yet (c) differ in some tensed truths. They could differ only if some special fact of presentness sat at different places relative to the tenseless facts, which would require presentness somewhere other than the cutting edge of reality. That is impossible: presentness must lie where facts are coming into existence. And with presentness fixed, pastness and futurity are fixed too, since earlier-than is a tenseless fact and differences in them would mean differences in temporal order.
Conclusion: what tensed truths there are is logically supervenient on what tenseless facts are actual as of different times. Hence at least a truth-conditional analysis of tensed sentences in terms of the supervenience base is possible, and that base is fully describable by tenseless sentences plus the concept of being actual as of a time. (More complex mixed positions are set aside as unexplored.)
6.5 Summing up
| Traditional tensed thesis | Tooley's verdict |
|---|---|
| (1) Temporal priority is analysable in tensed terms | False: every attempt is doubly circular; Broad's equivalence is true but not a definition |
| (2) Tenseless quantifiers over temporal things are analysable by tensed quantifiers | False: existence is univocal, and "will exist" itself needs the tenseless quantifier |
| (3) Tensed concepts are unanalysable | False for past and future now; for the present in chapter 7; and in general by the supervenience argument |
Tooley's verdict on Prior's tense logic was a minority view in 1997 and remains contested. Tense logic is now standard, and presentists (Prior's heirs, e.g. Craig Bourne, Thomas Crisp, Jonathan Tallant) reply to the "where are the truth-makers?" challenge with tensed truth-makers, ersatz times, or by rejecting truth-maker maximalism. Tooley's argument that nested operators need relational concepts also depends on premise (*), deferred to chapter 8, which many A-theorists simply deny. Finally, his supervenience argument assumes presentness must coincide with the growing edge; moving-spotlight and "growing block with a separate present" theorists deny precisely this, and that separation is what powers the epistemic objection discussed in chapter 8.
Past, Present, and Future
Tooley gives his positive semantics for tense in three layers: ordinary indexical tensed statements get truth conditions from non-indexical tensed statements ("E lies in the present at time t"), and these are analysed in tenseless terms plus actuality as of a time or truth at a time. The present at t is simply the latest edge of what is actual as of t: E is present at t iff E is actual as of t and nothing later than E is. Nested tenses are handled by quantifying over times, avoiding the token problems that sink Prior's and Mellor's recipes.
The account rests on three theses: some tensed statements are indexical and some are not, and the non-indexical ones are more basic; indexical truth conditions are given by non-indexical tensed statements; and the latter are analysed by tenseless statements plus actuality-as-of (or truth-at). Unlike tenseless theories, tenseless statements alone cannot do it; and indexicality is not intrinsic to tense.
7.1 Simple, non-indexical tensed statements
7.1.1 Are all tensed statements indexical?
Because the present moves, any statement about the present must specify a time, either by content (an explicit time reference, same proposition whenever uttered) or by context (the time of utterance fixes it, so different utterances express different propositions). English tensed verbs ("It is raining in London") and tenseless verbs plus "at present", "in the past" use the second method.
That makes the tenseless theory look strong. If every tensed sentence fixes its time by context, it must contain an indexical; and then the natural model is "here" and "there", whose truth is fixed by ordinary spatial facts plus the speaker's location, with no facts of "hereness". Why not say tensed sentences describe ordinary tenseless facts from the speaker's temporal perspective? A further argument: if there were special tensed facts, there should be non-indexical sentences true just in virtue of them; if there are none, there are no tensed facts.
Tooley denies the premise. There are non-indexical tensed sentences:
"Event E lies (tenselessly) in the present at time t." It expresses the same proposition whenever uttered, so all its tokens agree in value at a given time. Writers such as Mellor, Gale and Schlesinger define tensed sentences as those whose tokens can differ in truth-value with the time of utterance; that definition is simply mistaken, because a tensed sentence must specify a time but need not do so indexically.
7.1.2 Non-indexical statements about the present
Tenseless theorists (and some tensed ones, such as Gale) analyse "E lies in the present at t" as "E exists (tenselessly) at t" or "E is simultaneous with t". These are entailed by it but do not entail it, since the tensed statement also implies the world is dynamic. If dynamism were incoherent or false, those proposals would be recommended revisions to remove a false presupposition, not analyses.
The analysis of the present
Version 1 (ontological). Event E lies (tenselessly) in the present at time t means the same as: E is an instantaneous state of affairs, E is actual as of t, and no state of affairs later than E is actual as of t.
Version 2 (semantic). Event E lies in the present at t means the same as: E is an instantaneous state of affairs such that it is true at t that E exists (tenselessly), and indeterminate at t that there is (tenselessly) any state of affairs later than E.
Either version implies E is simultaneous with t. What is actual as of t includes only states at t and earlier, so E is not later than t; and if E were earlier, the existence of the instant t itself would be something later than E that is actual as of t. Both versions use later-than, so they presuppose chapter 6's result that priority has no tensed analysis.
7.1.3 Non-indexical statements about past and future
Two equivalent analyses of past and future at a time
First (past = earlier than the present): - E lies in the past at t iff E is earlier than t, and t lies in the present at t (that is, t is instantaneous, actual as of t, and nothing later than t is actual as of t). - E lies in the future at t iff E is later than t, and t lies in the present at t.
Second (past = was present; suggested by Colin Allen): - E lies in the past at t iff there exists (tenselessly) a time t* earlier than t such that E is present at t* (E instantaneous, actual as of t*, nothing later than E actual as of t*). - E lies in the future at t iff there exists a time t* later than t such that E is present at t*.
They are provably equivalent given the actuality postulates of chapter 4 and the causal theory of priority of chapter 9. From the first to the second: if E is earlier than t, the postulates ensure nothing later than E's time is actual as of it, so E is present at its own time. From the second to the first: the causal analysis gives E earlier than t, and with the postulates, t is present at t.
7.1.4 Consequences of the analyses
Five constraints the account satisfies
Neutral constraints (any theory should meet them): 1. Right relations to priority. If E is past and F present at t (or E present and F future, or E past and F future), E is earlier than F. 2. Mutual incompatibility. If E were both past and present at t, E would be earlier than itself.
Tensed constraints (accepted by those who deny the future is real): 3. In a static world nothing is past, present or future, because every tensed statement implies some time at which later states of affairs are indeterminate, and in a static world nothing is indeterminate. 4. Non-analytic statements about what is future at t are indeterminate at t. 5. Every momentary event is first future, then momentarily present, then forever past (assuming every momentary state of affairs is present at some time and every moment has a later one).
Consequence 5 must be read carefully. It does not mean that it is first true that E is future, since nothing about E is true before E occurs. It means it is true simpliciter that there is exactly one time t0 at which E is present, and that E is future at every earlier time tp (since tp is present at tp and E is later) and past at every later time tf.
7.2 Indexical tensed statements
7.2.1 Statements about specific events
"Now" is indexical, so the account is truth-conditional, not translational, and it delivers three values.
Truth conditions for indexical tensed utterances
- Any utterance or inscription at t* of "Event E is now occurring" is true (false, indeterminate) at t iff it is true (false, indeterminate) at t that E lies in the present at t*.
- "Event E has occurred" at t*: iff at t, E lies in the past at t*.
- "Event E will occur" at t*: iff at t, E lies in the future at t*.
Beliefs, doubts and desires about what is now happening can occur without any token, even a conscious thought, so "utterance or inscription" must be generalised. That problem is common to all indexicals and needs no special treatment here.
7.2.2 Statements without event-referring terms
Sentences like "It is now snowing heavily" or "The grass was very green in England" are handled by existential quantification over events:
- "It is now snowing heavily" means there is (tenselessly) an event E of the snowing-heavily variety, and E lies in the present.
- "The grass was very green in England" means there is (tenselessly) an event E of the grass-being-very-green-in-England variety, and E lies in the past.
7.3 More complex tensed statements
"By the year 2000, the first unicorn will have been created" says it will be the case that something was the case: nested operators.
7.3.1 The tense-logic recipe and its failure
Mellor (Real Time, 1981) states the standard tense-logic recipe clearly: put the sentence into standard form, a sequence of A-series positions prefixed to a present-tense core; shift the present by the first position, then the next, and so on; ask whether the core would be true if the present had the resulting date. His tenseless version shifts dates instead and asks whether a token of the core sentence would have been true on the date reached.
Two sentences that break the recipe. (1) "There was a time when the universe was less than 10⁻¹⁰⁰ seconds old." It is true iff a token of "The universe is less than 10⁻¹⁰⁰ seconds old" would have been true then; but the early universe may have nomologically excluded any tokens, so the counterfactual has no clear sense. (2) "There was a time when there were no sentence tokens at all." It is true iff a token of "There are no sentence tokens at all" would have been true then; but no such token could ever be true, because its existence falsifies it. Yet sentence (2) is plainly true.
The fault is not tenselessness: tense logicians face the same problem (§6.1.2). The fault is the assumption that all tensed sentences are indexical, which makes embedded sentences depend on tokens at other times. Holding that no tensed sentences are indexical would solve it, and many tensed theorists hold that, but chapter 8 argues it is untenable. So: some tensed sentences are indexical and some are not, and anything inside a tense operator must be non-indexical.
7.3.2 Tooley's analysis of nested operators
Structure: an indexical outer operator with non-indexical inner operators. Then the only token whose existence is required is the utterance itself. Use operator sentences with an explicit time:
Operator rules
- At t, it was the case that E is present iff there exists a time t* earlier than t, and at t*, E is present.
- At t, it will be the case that E is present iff there exists a time t* later than t, and at t*, E is present.
Each operator does three things: adds an existential quantifier over a new time; adds a clause that the new time is earlier (or later) than the current one; and moves the evaluation time to the new time.
Worked example: "At t, it will be the case that it was the case that E" becomes first "there is a time t1 later than t such that, at t1, it was the case that E is present", then "there is a time t2 and a time t1 such that t2 is earlier than t1, t1 is later than t, and at t2, E is present." Operators are stripped one by one until only "E is present at t2" remains.
Indexical nested sentences. If "At t*, Np" is a non-indexical sentence with operator string N, then any utterance at t* of the indexical "Np" is true (false, indeterminate) at t iff "At t*, Np" is true (false, indeterminate) at t. Nothing beyond the simple case is needed except existential quantification over times, which (§6.2) is tenseless and basic.
7.4 A retrospective view
| Issue | Tenseless theories | Traditional tensed theories | Tooley |
|---|---|---|---|
| Is priority analysable in tensed terms? | No | Yes | No |
| Are tensed concepts basic? | No | Yes (at least the present) | No: all analysable, the present included |
| Which language is more basic? | Tenseless | Tensed | Tenseless |
| Are ordinary tensed sentences indexical? | Yes, all | No, none | Yes, but more basic non-indexical tensed sentences exist |
| Are there tensed facts? | No | Yes, irreducible | Tensed truths, supervenient on what is actual as of times |
What makes a statement tensed is simply the presence of tensed concepts. Any statement applying such a concept to an event must specify a time, either indexically or by explicit reference, so there are two kinds of tensed sentence. Most writers say a sentence with an explicit tenseless time reference is not really tensed, because it translates without loss into a tenseless one: "In 1900, the birth of Bertrand Russell lies in the past" supposedly means "Russell's birth is earlier than 1900". Tooley denies it: the first immediately entails that the world is dynamic and nothing later than 1900 is actual as of 1900; the second does not.
Misdrawing the class of tensed sentences has two costs: writers mistake a feature of the indexical subclass (tokens at different times can differ in value) for a defining feature of tense; and they are pushed to treat indexicality as essential, which makes tensed facts look impossible. Recognising non-indexical tensed sentences is essential to any defence of a dynamic view of time.
Critics observe that on Tooley's account "E is present at t" and "E is simultaneous with t" differ only by a dynamism clause ("nothing later is actual as of t") that a tenseless theorist can mimic: in a block universe one can define "actual as of t" as "located at or before t", making every analysis come out true. Tooley's reply is that "actual as of" is a primitive, not that definition, but this makes the dynamic content rest wholly on a primitive the B-theorist finds unintelligible (Smart's objection from chapter 2). The epistemic objection (chapter 8 update) also targets exactly this construal of "present" as the edge of the block.
Past, Present, and Future: Alternative Accounts
Tooley now turns his guns on every rival. The argument from causation eliminates all tenseless views and every tensed view except "past and present real, future not". A battery of narrower arguments then disposes of the rest: ordinary tensed sentences must be indexical; intrinsic tensed properties are impossible for instantaneous events; presentism in both forms has no truth-makers for the past; and McCall's branching tree buys nothing Broad's growing block lacks. The surviving view is the growing block stripped of irreducible tensed properties, and only metaphysical argument, not conceptual analysis, can establish it.
8.1 The argument from causation (recap)
Part one. Reductionist accounts of causal direction fail; a realist account works if causal laws satisfy (C1)–(C4); those postulates cannot hold in a static world or most dynamic ones; they require that a cause be actual as of the time of its effect but not vice versa, which means past and present real, future not, or a close approximation. Part two. Our world is full of prima facie improbable events; causal explanation removes the improbability iff causal laws satisfy the postulates; so it is reasonable to believe they do. Result: all tenseless approaches and almost all tensed ones are ruled out.
8.2 The alternative tensed views
All traditional tensed views share: irreducible tensed facts, tenseless facts reducible to tensed ones, and the semantic corollary that ordinary tensed sentences are not indexical.
8.3 Tensed sentences and indexicality
Tenseless theorists say all tensed sentences are indexical; traditional tensed theorists say none are; Tooley says some are, including all ordinary ones.
8.3.1 Ordinary tensed sentences are indexical
8.3.1.1 Time and the applicability of tensed concepts
David Hume's birth. In 1711 "lies in the present" applied to Hume's birth and "lies in the past" did not; at every later time the reverse. Since a tensed concept applies to an event at some times and not others, no definite proposition is expressed unless a time is specified. "The birth of David Hume lies in the past in the year 1992" specifies one by meaning. "The birth of David Hume lies in the past" does not, so the time must be fixed by the time of utterance, which requires an indexical.
8.3.1.2 Ordinary tensed sentences and propositions
The quick refutation ("It is now winter in Canada" is true in January, false in June, so the utterances express different propositions) fails once truth at a time is available: the non-indexicalist can say the January token is true in January and the June token false in June, while all tokens share a value at any given time. A better argument considers truth-makers.
Why "E lies in the present" cannot express one proposition on every utterance
Case A: the truth-maker is a state of affairs actual as of t. Let instantaneous E at t1 and F at t2 (t1 < t2) have truth-makers PE (actual as of t1) and PF (actual as of t2). E's being present is earlier than F's being present; since priority has no tensed analysis, the truth-maker for that is a complex state: an external relation between PE and PF. 1. If it is actual as of some time t, t differs from t1 or from t2; then PE (or PF) is actual as of a second time, making "E is now taking place" true at two times, impossible for an instantaneous event. 2. If it is actual simpliciter, it is hard to see how a concrete state neither actual as of a time nor a sum of such states could be; and it would make "E is present" and "F is present" true simpliciter, so E and F would be simultaneous.
Case B: the truth-maker includes an absence. Modify Tooley's own analysis by removing "at t": - "E is instantaneous and no later state of affairs is actual simpliciter": never true (except at the last moment of time). - "... And for every time t, no later state is actual as of t": never true. - "... And there is a time t as of which no later state is actual": if ever true, true forever after. - "... And no later state is actual as of this specific time": needs a time reference, so "now" is indexical.
So ordinary tensed sentences must contain an indexical.
8.3.2 Is indexicality a threat to tensed views in general?
Why do tensed theorists resist? Replace each indexical in a sentence by a name and the kind of fact expressed is unchanged; so if "A is present" expresses a tensed fact and is indexical, then "A is present at t" must also express a tensed fact. But most tensed theorists say "present/past/future at t" is not tensed: Schlesinger, "being in the future at t1 is exactly the same as being later than t1"; Gale, "is past at" and "is future at" are synonyms of "earlier than" and "later than". Then indexical tensed sentences would express no tensed facts and, since they would be the only tensed sentences, nothing would. Hence the insistence on non-indexicality.
The hidden premise, that "A is present at t" is not tensed, is false (chapter 7: it entails the world is dynamic). Drop it, and ordinary tensed sentences can be indexical while still expressing tensed facts, via the non-indexical sentences that give their truth conditions. The failure to find a non-indexical reading of ordinary tense refutes traditional tensed views, not dynamism as such.
8.4 Instantaneous events and intrinsic tensed properties
Some views keep all times real and add presentness alone, or pastness, presentness and futurity; growing-block traditionalists (Broad) add pastness and presentness. Quantitative properties (five minutes past) or tensed relations (more past than) may also be needed; that matters only in §8.5.2.
8.4.1 The basic argument: two or more tensed properties
Broad's argument from "Ostensible Temporality" (1938), as developed by Tooley
- Something true of an entity can differ between times in only two ways: it depends on other parts of the world, which change; or the entity has temporal parts with different properties.
- For an intrinsic property the first way is excluded; for an instantaneous event the second is.
- So an instantaneous event cannot have different intrinsic properties at different times.
- If past and present are real and pastness and presentness are intrinsic, every event, instantaneous ones included, has presentness at one time and pastness at another.
- Contradiction.
8.4.2 Extension to a single tensed property
Reply: an instantaneous event can have presentness at the one time it exists and simply not exist at other times. But any tensed view must make the world dynamic. If all times are real and presentness is just a property every event has at the moment it exists, never gained or lost, the world is static. So presentness must be had at some times and lacked at others, and if intrinsic, the same contradiction follows.
8.4.3 Intrinsic versus relational tensed properties
Tooley escapes: with an unreal future, tensed properties are relational. It can be true at one time but not another that there are events later than a given event, so even an instantaneous event can be present at one time and past at another.
8.5 Views with two or more intrinsic tensed properties
8.5.1 Necessary relations
8.5.1.1 Between tensed properties. Pastness and presentness are incompatible. If pastness is analysed (E is past at t iff E is present at some t* earlier than t), and an instantaneous event is present at only one instant, then past-and-present requires a time earlier than itself, analytically impossible. If both are unanalysable, the incompatibility is a non-analytic necessary truth. It cannot be Kripkean a posteriori necessity, since that involves identities and this truth looks a priori. Tooley finds accounts of synonymy more promising than accounts of the synthetic a priori, so other things equal he prefers theories that make a priori necessities analytic.
8.5.1.2 Between tensed properties and tenseless relations. If E is past and F present, E is earlier than F is necessary and a priori. It is analytic if pastness is relational (presentness plus earlier-than, or presentness plus causation with a causal analysis of priority), or if priority were tensedly analysable (it is not). With intrinsic tensed properties it is inexplicable.
8.5.2 Fixed relations between changing tensed properties
An event is past by a definite amount, and grows more past. Analysing "ten years past" as "past and ten years earlier than the present" makes quantitative tenseless relations basic, and then it is odd not to analyse qualitative pastness similarly. So there is pressure to make quantitative tensed properties basic.
A and B in lockstep. Event A lies exactly 5 minutes 24 seconds in the past when B occurs. From then on both recede, their quantitative tensed properties changing constantly, yet perfectly in step: at the instant B becomes 1 minute past, A becomes exactly 6 minutes 24 seconds past. Why? Not a cosmic accident. If tensed properties are analysable, the invariance is analytic; if they are basic, nothing explains it.
8.6 Presentism
Two theses: ontological, only states of affairs existing at t are actual as of t; semantic, a statement is true at t iff something existing at t makes it true. (Quentin Smith's "presentism" allows past states of affairs, an unfortunate usage.)
8.6.1 Classical, or austere, presentism
Only present-tense states of affairs exist at any time. Then how can it be true that there were dinosaurs but not that there were unicorns?
| Presentist move | Tooley's reply |
|---|---|
| It is not now true that there were dinosaurs, which only means nothing now makes it true; the past is captured by "'There are now dinosaurs' was true" | "Was true" means true at a past time. A past time now having pastness must be actual now: not allowed. An internal earlier-than relation needs an intrinsic pastness: same problem. An external relation between two times exists at no instant and does not supervene on instantaneous states: so it is actual as of no time |
| Allow actuality simpliciter: "there were dinosaurs" is true simpliciter though not true now (Colin Allen's suggestion) | The totality of what is actual as of some time contains only instantaneous states, unordered: dinosaur-slices with no temporal relations to each other or to now, so still no truth-maker |
| Analyse past-tense statements as present-tense ones (truth-maker: present fossils) | Immensely implausible in itself; needs a verifiability theory of meaning, indeed verifiability now; and makes the past unfixed |
Łukasiewicz and the forgiving past. Jan Łukasiewicz and Arthur Prior could be presentists because they reduced the past to present evidence. Łukasiewicz embraced the consequence: facts whose effects have entirely vanished belong only to possibility, so moments of suffering and guilt may be effaced from actuality. "Time calms our cares and brings us forgiveness." In an indeterministic world, evidence for an event can exist at one time and be gone later, so the past itself changes.
8.6.2 Tensed-facts presentism
The present contains past-tense (and perhaps future-tense) states of affairs as truth-makers, without reducing the past to present evidence.
Objections to tensed-facts presentism
- Constituents. Caesar's having crossed the Rubicon now exists, so its constituent Caesar now exists. But an enduring thing exists at a time only if wholly present or with a temporal part there; Caesar is neither. Reply (pointed out by George Bealer): reject "existentialism", the view that particulars are parts of states of affairs they figure in. Rejoinder: a state of affairs just is an individual's having a property or individuals standing in a relation; it can no more exist without its constituents than a thing can have a property when it does not exist. Do not confuse states of affairs with propositions, whose constituents are not parts.
- Basic tensed concepts. No basic temporally extended states exist, so earlier-than must supervene on tensed states; past cannot be "earlier than the present", so "future" must be basic, which §6.3 rejected.
- Brute incompatibility of tensed properties.
- Unexplained systematic change. Now: E occurring, F 5 minutes past; two minutes later: E 2 minutes past, F 7 minutes past; F always exactly five minutes further back than E, and so for every pair. This exceptionless regularity demands an explanation that basic tensed facts cannot give.
Presentism became the most actively defended A-theory after 1997. The truth-maker objection Tooley presses here is now central to the debate: presentists answer with tensed properties of the present world (Bigelow's "Lucretian" properties), ersatz past times (Bourne, Crisp), or by rejecting truth-maker maximalism (Tallant, Ingram's "thisness presentism"). The constituents objection, that past-tensed facts cannot exist without their constituents, remains a standard line against tensed-facts presentism.
8.7 Only the past and the present are real
Two questions divide this family: what the unreality of the future amounts to, and whether there are irreducible tensed properties.
8.7.1 Modal realism and the indeterminateness of the future
McCall's tree has future states of affairs, but all possible futures with nothing marking the actual one, so statements about the future are not now true or false. Chapter 1 gave two reasons to prefer Broad: it allows deterministic dynamic worlds, and it is simpler. McCall's counter is an inference to the best explanation: the branched model explains "temporal direction and temporal flow; the ontological basis of laws of nature; the interpretation of quantum mechanics including quantum non-locality, state vector reduction, and measurement; the definition of probability; semantics for counterfactuals and other conditionals; transworld identity of individuals; essential properties; and finally deliberation, decision, and free will."
Tooley's audit of McCall's ten benefits
- Alternatives exist, some static-friendly. Transworld identity without counterpart theory does not need ontologically real futures; other explanations of quantum non-locality compatible with relativity are available.
- No edge over Broad. Broad's unreal future explains direction and flow and leaves as much room for deliberation, decision and free will.
- Parasitic. McCall's essential properties ("possessed at all times on all branches from its origin") beat "possessed at origin and nomologically impossible to lose" only if nomological possibility needs branching; his counterfactual semantics beats rivals only if his accounts of probability and laws do.
- So the crux is probability and laws, and both fail.
Probability as proportion of branches. Infinite branching makes proportions undefined; finite branching cannot give irrational values. McCall's fix: branching continues infinitely often within an interval, like an infinite decimal.
Tooley's three objections: the ever-accelerating infinite branching is an ad hoc hypothesis; it gives no precise or irrational probability for events at an instant, or over short intervals; and if space is infinitely divisible, an electron can hit a screen at infinitely many points, so branching at an instant is infinite and probabilities are undefined. (Tooley calls the solution "ingenuous", evidently meaning ingenious.)
Laws from possibilities. McCall reverses the usual order: possibilities fix laws. Objections: a law becomes an enormously, perhaps infinitely, complex state of affairs, whereas on the universals view it is a single atomic fact; and since the possibilities at any single instant typically fix all the laws, the infinitely many instants yield infinitely many exact correspondences that, if possibilities are basic, are a cosmic coincidence worse than anything facing regularity theories.
8.7.2 Future states of affairs are not real
Broad and others combined the growing block with four extra theses: basic tensed properties, non-indexical ordinary tense, tensed analysis of tenseless concepts, and tenseless facts supervening on tensed ones. All are mistaken, and the tensed properties bring the problems of §§8.4–8.5. The moral: if a dynamic view is accepted, embrace the reality of past and present only, but reject basic and irreducible tensed properties.
The growing block's best-known problem was formulated after this book. Craig Bourne (2002) and David Braddon-Mitchell (2004, "How do we know it is now now?") argued that past people in the block are thinking, just as we are, that they are present, and are wrong; so we have no reason to believe we are at the edge. Peter Forrest (2004) replied with the "dead past": only the present edge hosts consciousness. Tooley's version is relevant here because it defines "present at t" as the edge of what is actual as of t, and every past time was the edge as of itself: critics debate whether this relativised presentness defuses the objection or merely relocates it. Book-length defences now include Correia and Rosenkranz, Nothing to Come (2018).
Tooley's scorecard of the rival views:
| View | Argument from causation | Indexicality (8.3) | Intrinsic tensed properties (8.4) | Necessary relations, lockstep (8.5) | Truth-makers for past (8.6) |
|---|---|---|---|---|---|
| Tenseless (B-theory) | Fails | Unaffected | Unaffected | Unaffected | Unaffected |
| All real + presentness | Fails | Fails | Fails | Unaffected | Unaffected |
| All real + past/present/future | Fails | Fails | Fails | Fails | Unaffected |
| Classical presentism | Fails | Fails | Unaffected | Unaffected | Fails |
| Tensed-facts presentism | Fails | Fails | Fails | Fails | Fails (constituents) |
| McCall branching | Approximation at best | Unaffected | Unaffected | Unaffected | Unaffected; fails on probability and laws |
| Broad growing block | Survives | Fails | Fails | Fails | Unaffected |
| Tooley growing block | Survives | Survives | Survives | Survives | Survives |
8.8 Tenseless accounts of past, present and future
Tooley thinks the argument from causation is the only decisive refutation of tenseless theories; the standard objections fail.
| Objection to tenseless views | Tooley's verdict |
|---|---|
| Token-reflexive truth conditions are wrong: the propositions could be true with no tokens | Confuses truth-conditional with translational analysis. Quentin Smith says the "new token-reflexive theory" (credited by him to Smart 1980, actually in Smart's 1967 encyclopedia article) collapses into the old; Tooley thinks his support unsound. Better: ordinary tensed sentences are indexical but not token-reflexive: the indexical refers to a time, not a token |
| Nested tenses get wrong values (Smith against Mellor) | True of Mellor's recipe, but fixable: take Tooley's §7.3 analysis and replace "E is present at t" by "E is simultaneous with t" |
| "Thank goodness that's over" (Prior 1959): the relief is not about a token's being later than a pain | "That's over" picks out a time by its simultaneity with the utterance; one is glad that time contains no continuation of the pain. No token is involved |
| Asymmetric attitudes (Schlesinger 1980): relief at past pain, dread of future pain, because the one recedes and the other approaches | Since causes precede effects, concern about the future pays: it helps avoid the bad and secure the good; concern about the past would not (compare Smart 1981) |
8.8.2 The need for metaphysical argument
Even if those objections succeeded, they would not show the world dynamic. Showing that common attitudes are rational only if there are tensed facts leaves open whether they are rational. Showing that tensed sentences resist tenseless analysis shows only that speakers believe the world dynamic. Conceptual analysis reveals our conceptual framework, not whether the world conforms to it. Tensed theorists (Quentin Smith, 1993) have leaned on analysis because it was unclear what a metaphysical argument could look like; the argument from causation is Tooley's answer.
The intrinsic-properties argument (§8.4) assumes that change in an instantaneous thing requires either relational change or temporal parts. A-theorists reply that tensed change is sui generis: an event's being present simpliciter and past simpliciter at different "times" is exactly what the A-theory posits, and to demand that it be modelled on ordinary property change begs the question. Similarly, the lockstep argument assumes that basic facts cannot exhibit necessary patterns; moving-spotlight defenders (Cameron's 2015 The Moving Spotlight, Deasy, Skow) build quantitative tensed facts from a single changing present plus tenseless distances, which escapes it. The table above is Tooley's scorecard, not a consensus.
Causation and Temporal Relations
Tooley completes his theory by analysing temporal priority and simultaneity causally: A is earlier than B iff a chain of links, each either a causal link or a spatial relation, runs from A to B and contains at least one causal link; A and B are simultaneous iff they are spatially related. Unusually, he joins this causal theory to absolute (substantival) space-time whose regions cause one another, which disarms the standard counterexamples. Quantitative temporal relations, by contrast, are not causal: they are realist theoretical relations that explain why clocks are possible.
9.1 Different conceptions of a causal theory of time
Causal theories reduce temporal relations to causal relations, or to causal plus other non-temporal (e.g. Spatial) relations. They differ along three axes.
| Axis | Options | Tooley's choice |
|---|---|---|
| Logical status | Contingent identification (Philip Von Bretzel 1977: "not a claim about the meanings of terms but a theory about the nature of time") or analysis, hence necessary identity | Analysis |
| Scope 1 | All temporal relations, or only some (always including direction and order) | Order and direction only; quantitative relations resist |
| Scope 2 | Time, or space-time (the post-Einstein fashion) | Non-relativistic time (chapter 11 defends the cost) |
| Reduction base | Causal relations alone, or causal plus spatial | Causal plus spatial, and actual, not possible, connections |
9.2 Four preliminary considerations for a causal analysis
Why analyse time through causation
- Structural similarity. Temporal and causal priority are both irreflexive, asymmetric and transitive, and each has a privileged direction. (Grünbaum's case for circular time rests on the identity of indiscernibles, which is open to sound objections; and loops are excluded by chapter 4 and by Mellor's arguments.) A merely contingent reduction cannot explain the similarity as necessary; an analytic link can. Since Tooley's account of causation uses no temporal concepts (unlike Hume's), the link must run from causation to time.
- Explaining formal properties. An analysis derives time's formal properties from causation's, and the argument from causation explains causation's.
- Mixed necessary truths. "A cause is always earlier than its effect" is necessary; the natural explanation is analyticity.
- The direction of time. Reductionist accounts (entropy, propagation of order, cosmic expansion) give at most a contingent identification, failing in simple and inverted worlds. A realist account (direction as brute fact) fails epistemically: it gives no reason why the usual evidence, such as order propagation, is evidence. What remains is direction of time = direction of causation, with realism about causation, which preserves justified belief.
9.3 An absolute or a relational account?
Substantivalism: the totality of space-time points is a substance, capable of independent existence, either over and above objects and events or such that objects are portions of space-time with properties. Relationism: space and time are nothing over and above objects, events and their relations. Causal theories have almost always been relational, because combining substantivalism with a causal theory requires space-time regions to stand in causal relations, or empty space-time would have no temporal order. General relativity lets curvature and matter interact, but the Newtonian and ordinary pictures have regions that interact with nothing, so the combination looks unavailable, and if our ordinary concept of time allows empty space and time, a causal analysis would seem doomed.
Regions can be causes. First, Hume was right that anything can cause anything: the concept of causation restricts what contingent, non-simultaneous states can be related, not at all, and a region's existence is contingent. Second, do not equate causal relations with causal interactions. The persistence of an electron consists in its later temporal parts depending causally on earlier ones with no interaction. On substantivalism space is an enduring thing, and its later temporal parts can depend on earlier ones just as an electron's do.
Three reasons to prefer a substantival causal theory
- Substantivalism is probably true. Newton's globes: two globes joined by a cord and rotating about their centre of mass put the cord under tension, though they do not move relative to each other, and would do so even if nothing else existed; so there is absolute rotation. Newton inferred absolute velocity and location too; John Earman (1970) showed models with absolute acceleration but no absolute velocity, but a relational view is still unsatisfactory. Also, empirical possibilities of an object's being at an empty location need a categorical basis; field-based or remote-property groundings are "extremely speculative", so the basis is plausibly properties of locations themselves.
- It solves the actual-versus-possible connections dilemma. Actual causal connections may not fix temporal relations; possible connections need truth-makers, which would cite spatiotemporal relations, circularly. If every complete temporal slice of space is causally connected with every other, actual causal relations between slices plus spatial relations within slices locate every event.
- It defuses standard objections (Smart 1971): empty space-time points, times when nothing exists, uncaused and effectless events, and totally empty GR worlds. Fatal to relational causal theories, harmless here (§9.8).
9.4 A causal theory of time, or of space-time?
The causal theory goes back to Leibniz and Kant; twentieth-century versions (spurred by relativity) became theories of space-time. A growing block in which the future is unreal seems to require absolute simultaneity, so Tooley analyses non-relativistic temporal relations, promising in chapter 11 a modified relativity with absolute simultaneity and greater predictive and explanatory power. A philosophical theory on a collision course with confirmed science tends to have a life that is, "though not necessarily nasty or brutish", short.
9.5 Modal versus non-modal analyses
A purely causal theory, or a theory of all spatiotemporal relations, must use causal connectibility, since some earlier/later pairs are not causally connected. The connectibility idea: causally related events are temporally ordered; unrelated events that could have been related are also ordered; events that could not be related are simultaneous. But what categorical fact makes two events connectible? Tooley holds that empirical possibilities are cashed out by subjunctive conditionals whose truth-makers are categorical facts plus laws. The obvious truth-maker is geometrical: in relativity, F inside E's forward light cone is connectible with E. Using it makes a reduction of spatiotemporal or temporal relations to causation alone circular, and there is no other candidate. A theory reducing time to causation plus space could use connectibility without circularity, but then it is clearer to use actual causal connections plus spatial relations directly.
9.6 Qualitative temporal relations
9.6.1 The analysis of simultaneity and temporal priority
Our ordinary, non-relativistic concept: simultaneity is reflexive, symmetric, transitive; priority is transitive, asymmetric, irreflexive; they are mutually exclusive and, with the inverse of priority, exhaustive. So events form a total linear order. (All events below are instantaneous.)
From weak assumptions to a causal analysis
- (P) If A is earlier than B and B is simultaneous with C, then A is earlier than C. (Exhaustiveness: C earlier than A would make C earlier than B, contradicting B–C simultaneity; A–C simultaneous would make A–B simultaneous.)
- (Q) If A is simultaneous with B and B is earlier than C, then A is earlier than C.
- (R) If A causes B, then A is earlier than B. Accepted by nearly all causal theories (except holistic ones that define direction by the dominant direction of causal processes to allow backward causation; chapter 4 rules that out).
- (S) R + P: if A causes B and B is simultaneous with C, A is earlier than C.
- (T) R + Q: if A is simultaneous with B and B causes C, A is earlier than C.
- (U) S + T + transitivity: if in a chain A1 ... An each link is "causes" or "is simultaneous with", and at least one link is causal, then A1 is earlier than An.
- (V) If A and B are spatially related instantaneous events, they are simultaneous. (Spatial relations across times, "five miles apart" at different times, smuggle in sameness of place over time, which Tooley analyses causally; V concerns pure spatial relations.)
- (W) U + V: if in a chain A1 ... An each link is "causes" or "is spatially related to", and at least one is causal, then A1 is earlier than An. A sufficient condition in non-temporal terms.
- (W*) The converse: if A1 is earlier than An, such a chain exists. If W* is not necessary, an actual-connection analysis is hard to see; the causal analysis stands or falls with W*.
The definitions (assuming W and W* necessary)
A is earlier than B means: for some n, there are instantaneous events A1 ... An with A = A1, B = An; for every i < n, either Ai causes Ai+1 or Ai is spatially related to Ai+1; and for some i < n, Ai causes Ai+1.
A is simultaneous with B means: A is spatially related to B.
9.6.2 Consequences
- Simultaneity is symmetric (the inverse of a spatial relation is spatial) and transitive (spatially related to spatially related is spatially related).
- Priority is transitive (concatenate chains). Asymmetry needs more than the impossibility of loops: it needs the impossibility of oppositely directed causal processes, which chapter 4's argument supplies.
- "A cause is earlier than its effect" follows immediately. "An effect never precedes its cause" follows given the impossibility of opposite processes: C causes E with E earlier than C would mean opposite processes.
9.7 Quantitative temporal relations
Order and direction are fixed; but events are also five years apart or ten minutes later. Directed relations reduce to undirected temporal distance plus simultaneity and priority. Options for distance:
- Discrete time (distance = number of intervening moments): drastic, since an analysis would make dense time logically impossible.
- Patterns of intervening events: suits relationism, but a substantivalist needs distances even in an empty world.
Measurement theory reduces quantities to comparative relations: given "at least as long as" plus a unit (a metre), any length, even π metres, is defined. So one needs only a comparative relation of temporal distance, either "at least as great as" or "equal to" plus simultaneity, priority and part/whole: define the interval AB (all points simultaneous with A or B, or later than A and earlier than B); then AB ≥ CD iff some proper or improper part of AB equals CD.
Constraints on temporal-distance relations (a theoretical relation)
Formal: equality of temporal separation is directionless (AB = BA), symmetric and transitive.
Links to simultaneity and priority (assuming any two intervals are comparable): 1. If A sim C and B sim D, AB = CD. 2. If A earlier than B and B sim C, AB = AC (zero-width intervals add nothing). 3. If A sim B and B earlier than C, AC = BC. 4. If A sim B and B sim C, AB = AC. 5. If A sim B and C sim D, AB = CD (all zero intervals equal). 6. If A earlier than B and B earlier than C, AC > AB and AC > BC (non-zero intervals add). 7. If A earlier than B and C sim D, AB > CD.
Causal-law role: the relation's involvement in causal laws is what makes laws more than laws of pure succession, entailing potential correlations among causal processes.
These constraints still leave quantitative relations undefined; the missing element is the third.
A world without clocks. Pendulums behave as ours do, swinging with slowly decaying amplitude to rest. But two identical pendulums released together, though passing through the same states in the same order, do not keep step: when one's amplitude has fallen 10%, the other's has fallen only 7%; later the lead reverses, and so on. If all causal systems, of the same and different kinds, were uncorrelated like this, no reliable clocks could exist, and the laws would be laws of pure succession: fixing order and direction but not temporal distance. So a world can be temporally ordered yet lack quantitative temporal relations.
The analysis is realist, not reductionist: quantitative relations are real relations among events, characterised by their role in laws, and they explain correlations among causal processes rather than being identical with them.
Reductionist rival. One could instead posit complex laws of pure succession: two simultaneous A1s give rise to two simultaneous A2s; A1-with-B1 gives A2-with-B2; etc. That is coherent, but simplicity favours realism.
- 5 basic laws with a realist temporal-distance relation versus at least 5 + 15 = 20 laws of pure succession: 5 for same-type correlations and 10 for the pairs of different types.
- Even one realist law may require infinitely many reductionist laws: correlations must also hold between out-of-phase sequences (A1 simultaneous with A3), and a continuous process has unlimited state types; continuous variation of arrangements yields unlimited distinct causal sequences.
9.8 Objections to causal theories of time
9.8.1 The equivalences are not analyses
| Objection | Source | Tooley's reply |
|---|---|---|
| 9.8.1.1 Causal priority presupposes temporal priority: without earlier/later, how tell cause from effect, given time-symmetric laws? | Smart 1971 | Retreating to a symmetric relation (Grünbaum, Mehlberg: causal connectedness) fails, since symmetric relations are analysed via asymmetric causation, not vice versa. Direct reply: chapter 4's account of causal direction uses no temporal relations |
| 9.8.1.2 Modal concepts need categorical bases that involve spatiotemporal relations; laws themselves may presuppose space-time structure | Smart | Fatal to connectibility theories; no force against an analysis in terms of actual connections, including connections between regions |
| 9.8.1.3 Intensional contexts make causal analyses obscurer than what they analyse | Smart | Agreed that modal notions cannot be basic. But causal statements are fully extensional in a language with terms for properties and relations; non-extensionality arises only in nominalistic languages |
9.8.2 Possible counterexamples
Six counterexamples and the replies:
- Empty space-time points; times when nothing exists. The latter is possible if temporally gappy laws (action at a temporal distance) are, since their gaps could all coincide (compare Sydney Shoemaker, "Time without Change", 1969). Fatal to relational theories; harmless when space-time points are causally related.
- Events neither causes nor effects (Smart). Relational theories cannot supply truth-makers for possible connections of isolated events; points of space-time handle it.
- Totally empty space-time, as in some GR vacuum solutions (Smart; Mehlberg 1966). Tooley grants its possibility; it rules out relational theories only.
- Quantum mechanics lacks continuous genidentical chains (Smart). To bite, it would need a discrete space-time; but QM uses continuous mathematics, and discrete geometry faces incommensurable ratios and Zeno's stadium.
- Eternal recurrence. In a world of indistinguishable repeating segments, S causes T and its exact duplicate S* (later than T) does not. Without time to tell them apart, what grounds the difference? Grünbaum denies such worlds via the identity of indiscernibles; Tooley rejects that principle and instead denies Humean supervenience: "whether E causes F is fixed by non-causal properties and relations of E and F plus the laws". Given that principle, S and S* would have to cause alike; but it is false (chapter 4's indeterministic-laws argument).
- Global causal loops consistent with GR's field equations (Sklar 1974; Susan Weir 1988 against Mellor). If one admitted them one would also give up time's asymmetry; anyway, since oppositely directed processes are impossible, such a world, however GR-consistent, is not logically possible.
Eternal recurrence. Imagine a universe of one particle circling a platform without friction forever, or any world of endlessly repeated, qualitatively indistinguishable epochs. Event S causes T; S*, the "same" event one cycle later, comes after T and does not cause it. S and S* share every intrinsic and relational non-causal property, and one world has one set of laws. Only singular causal facts distinguish them. Tooley's singularism is what lets a causal theory of time survive recurrence.
9.8.3 Objections to a realist view of space and time
9.8.3.1 Leibnizian arguments. Lawrence Sklar finds three in the Leibniz–Clarke correspondence: verificationist, identity of indiscernibles, and sufficient reason (dismissed as implausible). The verificationist one (no observation could fix the world's absolute position or velocity, so such claims are meaningless) falls with verificationism, which would make realism about theoretical entities unintelligible. The indiscernibility argument uses Sklar's P.3: worlds identical in every qualitative feature are the same world; then the actual world and the actual world shifted five feet north are one world, so substantival space does not exist.
The vanishing billiard balls. A world has always contained an infinite line of motionless, equally spaced, indistinguishable billiard balls. Call one of them X. At one moment every other ball vanishes. That can happen in two ways: X vanishes (world A) or X survives (world B). A and B are plainly distinct (one contains X throughout, the other only at first) yet qualitatively identical. So P.3 is false.
9.8.3.2 Causation, absolute space and Humean supervenience. In an empty world with points P earlier than Q and R simultaneous with P, suppose P's existence causes Q's but R's does not. Points have no intrinsic differences; in an empty world no relational ones; P and R are simultaneous; so only a different spatial relation across times could distinguish them, and absolute location across time is widely thought unintelligible. Tooley accepts the conditional: if Humean supervenience holds, regions cannot be causally related. He can even make sense of absolute location, but causally: two space-time points are at the same place iff they are causally connected, which is not a non-causal difference. So the argument stands as a conditional, and he rejects its antecedent: Humean supervenience is false.
9.9 The pervasiveness of the direction of time
Non-causal accounts (Popper; Reichenbach, Grünbaum) make time's direction depend on initial or boundary conditions: Grünbaum seeks it in "de facto conditions" plus statistical mechanics. Henryk Mehlberg objected that the excess of expanding over contracting light waves depends on factual cross-sections, not laws, since Maxwell's equations allow any ratio. Feeling that a real direction must be pervasive, and finding the laws time-reversal invariant, Mehlberg concluded time is isotropic.
On the causal theory, time can have a direction even if all laws are time-reversal invariant, and that direction does not depend on initial or boundary conditions; changing particle positions or velocities in a cross-section would not alter it, and it is not statistical. It is the direction of every causal process, including the persistence of particles and of space-time itself. The direction of time is about as pervasive a fact as there could be, part of the very fabric of space-time.
9.10 Summing up
Four merits of the causal analysis
- It yields the right formal properties: simultaneity reflexive, symmetric, transitive; priority transitive, irreflexive, asymmetric.
- It explains the structural similarities between temporal and causal priority.
- It makes mixed necessary truths ("a cause is never later than its effect") analytic.
- It makes the direction of time pervasive, independent of initial conditions.
Physics has since produced a programme strikingly close to Tooley's split between order and quantity. Causal set theory (Bombelli, Lee, Meyer and Sorkin, 1987; developed by Rafael Sorkin, Fay Dowker and others) takes space-time to be a discrete partial order of causal relations, with the slogan "Order + Number = Geometry": the causal order fixes the conformal structure, and counting elements supplies volume. Unlike Tooley's continuum, it secures quantitative relations through discreteness, the option Tooley called "drastic". The classical sequential growth dynamics of Rideout and Sorkin (1999) even models the universe as growing element by element, a physical analogue of a growing block (see chapter 11).
Three pressure points. W* (every earlier/later pair is linked by such a chain) is supported only by the assumption that every complete slice of space causally connects with every other, a strong, untestable posit. Making space-time regions causes is controversial even among realists about causation; critics see it as a device to rescue the theory from Smart's counterexamples. And defining simultaneity as spatial relatedness builds absolute simultaneity into the definitions, which is precisely what relativity denies, so the whole analysis is hostage to chapter 11.
Philosophical Objections
Tooley defends his account against the a priori objections that have made tensed theories unpopular: semantic charges from Ducasse, Williams, Smart, Quine and Chapman; worries about meaningful and rational talk of the future; Broad's meta-time regresses; McTaggart's paradox in its Mellor and Dummett readings; and Mellor's arguments against tensed facts. The same two tools answer almost everything: the distinction between being actual (or true) simpliciter and being actual (or true) as of a time, and the thesis that tensed properties are relational facts about what is actual as of a time.
10.1 Semantic objections
10.1.1 Propositions, propositional functions and truth at a time
Donald Williams ("The Sea Fight Tomorrow", 1951) echoes Ducasse: the common man "regards with healthy abhorrence the sophist" who says what is true at one time may not be at another; propositional functions are true of a time, propositions at none. Tooley grants the charge sticks to tensed views on which past, present and future are all real: there only indexical tensed sentences ("The four-colour problem has not yet been solved") can change value, and they express propositional functions. It fails against a growing block, where indexical-free tenseless propositions change value.
10.1.2 The incoherence objection
Smart's soldier. J. J. C. Smart (1981) imagines a soldier in the twenty-first century, "cold, miserable and suffering from dysentery", told that twentieth-century philosophers thought the future unreal. He would hardly be mollified to hear his sufferings were real then but not real now. "Reality is not a property which anything can acquire. To be real is to be part of the universe", and "an F is real" just means (∃x)(Fx) with a tenseless quantifier. The twenty-first century is part of the universe, hence real; but it is future; so denying the reality of the future is contradictory.
Reply: the future is part of the totality of reality and so actual simpliciter; it is not actual as of the present moment, and that is all "the future is unreal" should mean.
A tensed version: (1) "It will be true that there are (tenselessly) unicorns" entails (2) "There will be unicorns", which entails (3) "It is true that there will be unicorns", which makes the future real. But (3) is ambiguous between (3a) it is (tenselessly) true and (3b) it is now true. Given truth at a time, (3a) does not entail (3b), and only (3b) conflicts with the unreality of the future.
10.1.3 The primacy of tenseless quantification
Quine (1953): "the only tenable attitude toward quantifiers ... Is to construe them always, in all contexts, as timeless". Tooley agrees, against most tensed theorists. Smart says tenseless quantification "presupposes the reality of the future". It presupposes the future is actual simpliciter, not that it is actual as of now.
10.1.4 Inescapable truths about the future?
Williams: unreal-future theorists concede some future truths. (i) "Either there is a sea fight tomorrow or there is not" is true, so Aristotle "allow[s] some reality to the future". (ii) Broad must admit "'It will rain tomorrow' will become true or false" is true now; "having confessed to this much truth about the future ... They might better confess to it all." Reply: (i) is analytic and entails no state of affairs later than the present. (ii) read as "tomorrow will exist and then the proposition will be true or false" is not now true (no truth-maker for tomorrow's existence); read as "if tomorrow exists, it will then be true or false" it is analytic. The only statements about the future that are now true are analytic ones, which entail no future states of affairs.
10.1.5 Bivalence and truth-functionality
Four objections look independent but all rest on truth-functionality.
- Bivalence objection. Truth simpliciter is bivalent; truth at a time is not, and insisting every acceptable truth concept be bivalent begs the question: a proposition needs some truth-value, not one of two.
- "Neither p nor not-p true" is "as nearly incredible as any proposition could be" (Williams). With three values, negation is defined as true iff the original is false, not iff it fails to be true.
- "p or not-p" true with neither disjunct true is "a sheer contradiction" (Williams).
- A disjunction cannot be true unless a disjunct is (Quine: "the desperate extremity of entertaining Aristotle's fantasy").
Tooley's reconstruction of what the objectors need
Assumptions: (1) disjunction is truth-functional; (2) truth is stable: what is true at t is true at every later t (guaranteed by correspondence plus the reality of the past); (3) three-valued tables agree with two-valued tables wherever the third value is absent.
Stage 1: if neither p nor q is true at t, and both could be false together later, then p ∨ q cannot be true at t: when both are false later, by (3) p ∨ q is false then, so by (2) it was not true at t. Example (in 1980): "unicorns on earth in 2000, or dinosaurs never existed". Stage 2: for any r ∨ s with no true disjunct at t, pick p, q with the same values at t that could be jointly false later; by (1) r ∨ s has the same value as p ∨ q, so it is not true either.
Then: (a) "true at t that p or q" suffices for "true at t that p, or true at t that q" (from 1–3); (b) "p or not-p" cannot be true at t without a true disjunct; with (4) "p or not-p" always true at t: (c) for every p, p or not-p is true at t; with (5) "p is false at t iff not-p is true at t": (d) bivalence at t.
Tooley accepts (2)–(5), so everything turns on (1). A sea-battle disjunction with its negation is true now, while "sea battle tomorrow or air battle tomorrow", with equally indeterminate disjuncts, is not: so disjunction is not truth-functional here. Prior (1953) thought Aristotle "quite excusably muddled" on this point. Chapter 5's factual-truth-functionality shows Aristotle was not muddled: truth-functionality is a secondary property of the connectives, holding only in two-valued logic.
10.1.6 Logical truths
Tobias Chapman (1972) objects that in Łukasiewicz's logic, if P and not-P are indeterminate, so is P and not-P, so a contradiction "might be true"; the only escape is to deny truth-functionality. Tooley: right on both counts, and the escape is not absurd but well motivated.
10.2 Statements, assertions and beliefs about the future
10.2.1 Meaningfulness
Williams: a significant statement that is neither true nor false "is intolerable". Question-begging: significance requires a truth-value, and there is a third; besides, truth simpliciter is bivalent. The real problem besets most tensed views: if "future" is unanalysable (Broad), it must name something we are acquainted with, and we are not; if analysable, then not via past and present, so via tenseless statements, which most tensed views analyse tensedly, hence circularity. The only way out is Tooley's: tenseless statements are not analysed tensedly.
10.2.2 Rational belief and knowledge about the future
On a foundationalist epistemology, no one has non-inferential beliefs about the future, and the unreality of the future does not alter non-inferential beliefs about past and present, nor logical relations among beliefs. So which beliefs are justified, and how much, is unaffected by whether the future is real. Knowledge requires truth: impossible for views that drop truth simpliciter, but on Tooley's view a future proposition, not true now, may be true simpliciter and so known.
10.3 Meta-time objections
10.3.1 The speed of time's passing
Broad (Examination of McTaggart's Philosophy, 1938) against the moving present: anything that moves has a velocity; "How great a time-lapse will presentness have traversed in unit time-lapse?" seems meaningless, so a meta-time is needed, then a meta-meta-time: a regress. Williams turns it on Broad's own growing block: "Instead of a bull's-eye which moves along the existence-fence in meta-time, he gives us a fence which lengthens itself in meta-time."
How far does something move in travelling a mile? The question is not meaningless and needs no meta-space: the answer is a mile, analytically. Likewise "how fast does the present advance?" needs no meta-time; the answer, "sixty minutes an hour", is analytic and "not overly exciting".
The rate-of-passage objection was revived by Eric Olson (2009) and Huw Price, who argue that "one second per second" is not a rate at all (the units cancel). Defenders such as Tim Maudlin (The Metaphysics Within Physics, 2007) and Bradford Skow reply as Tooley does, that it is a perfectly good, trivially fixed rate, comparable to an exchange rate of one dollar per dollar. The exchange remains a standard test case for A-theories.
10.3.2 Meta-time and the changing of events
Broad's second objection: if an instantaneous event loses presentness and gains pastness, it changes and so must exist at different times; to avoid contradiction one needs a second time dimension in which an event of zero duration has "an indefinitely long duration and a history". Repeat for the meta-time: regress. Schlesinger (1980) replies that Broad shows neither that the regress is vicious nor that it is a regress rather than a circle (each series could serve the other). Tooley grants both points but finds the core untouched.
Russell's birth in 1873. "In 1873 the birth of Bertrand Russell lay in the past." If this attributes an intrinsic pastness to the birth in 1873, the birth would need a temporal part in 1873, which it lacks: contradiction. Saying "1873" names a stretch of meta-time abandons the logical grammar of the original statement and replaces it with a different one. Postulating meta-time is an admission that tensed statements as they stand cannot be made coherent. The objection defeats every view with intrinsic tensed properties, and every view with relational ones plus a real future. Only an unreal future plus relational pastness escapes: in 2005 an event of 2000 has the property "there are events at least four years later", which, with an unreal future, it lacks in 2002.
10.4 McTaggart's argument
J. M. E. McTaggart (1908; The Nature of Existence, vol. 2, 1927) argued that time is unreal, in two parts.
McTaggart, part one: time requires the A-series
- "There could be no time if nothing changed."
- Russellian change (different properties at different times; Russell 1903) is not real change: events must change.
- Events cannot come into or go out of existence, so they change only in properties.
- They cannot change in tenseless properties.
- So they change only in tensed properties: no time without A-characteristics (past, present, future).
McTaggart, part two: the A-series is contradictory
- "Past, present, and future are incompatible determinations."
- Every event has all three.
- Reply: not at once, but successively: M is present, will be past, has been future.
- But that means M is present at a moment of present time, past at a moment of future time, future at a moment of past time, and every moment is past, present and future, so the contradiction recurs at the level of moments.
- Each further "successively" restarts it: an infinite, vicious regress.
On part one Tooley is non-committal: McTaggart's question why a poker hot at one time and cold at another counts as change while one hot end and one cold end does not is a real challenge to tenseless views, but not obviously unanswerable (Mellor 1981 offers an answer). Part two is read two ways.
| Reading | The argument | Tooley's reply |
|---|---|---|
| Mellor: times must be specified in tensed terms | Tensed specifications are indexical, so different tokens express different propositions, and no consistent assignment results | Why must the time be specified tensedly? Specify it tenselessly (by date) and no contradiction arises. This reply is closed only to views that analyse priority tensedly, which Tooley rejects |
| Dummett (1960): reality must have a complete, observer-independent description | A tenseless description omits what is happening now; tensed expressions are token-reflexive; so a temporal world has no complete description, and since there must be one, time is unreal | Read tenseless-ly, indexical sentences add nothing: a complete tenseless description fixes every token's value. Read dynamically, a static description omits that the totality of tenseless facts grows, but this can be stated with non-indexical tensed sentences. The static description plus all true non-indexical tensed sentences is complete and observer-independent, and fixes the value of every actual or possible indexical token |
Dummett's completeness premise became the centre of a newer debate. Kit Fine ("Tense and Reality", 2005) reconstructs McTaggart as forcing a choice among realism about tense, neutrality (no privileged standpoint), absolutism and coherence, and develops "fragmentalism", which accepts tensed reality but gives up the requirement that reality be a single coherent whole. Tooley's response is the opposite trade: keep one coherent, observer-independent totality and locate dynamism in growth, not in incompatible tensed facts.
10.5 Mellor's arguments
Hugh Mellor's Real Time (1981) argues that McTaggart proves the unreality of tense (not of time), and adds two arguments plus a critique of Richard Jeffrey's "the world grows by accretion of facts" (1979).
10.5.1 McTaggart and token-reflexive truth conditions
Mellor's dilemma for tensed facts
- Non-token-reflexive tensed truth conditions would give all tokens of a tensed sentence the same value; but a 1942 token of "World War II is over" is false and a 1947 one true.
- Token-reflexive tensed truth conditions ("'Hume's birth is past' is true iff Hume's birth is past when the token is present") let "past" and "present" do no work: only the tenseless consequence, Hume's birth is earlier than the token, matters.
Tooley's reply. Against the first horn: granted that ordinary tensed sentences are indexical, there is a more basic class, "E lies in the present at t", that is not. Mellor would say these are just "E is simultaneous with t"; but on Tooley's coherent analysis they say more: no state of affairs later than E is actual as of t. Against the second horn: the tensed condition entails, and the tenseless one does not, that the world is dynamic: what is actual as of later times need not be actual as of earlier ones.
10.5.2 Mellor's second argument
"The sole function of tensed facts is to make tensed sentences and judgments true or false. But that job is already done by the tenseless facts ... Provided a token of 'e is past' is later than e, it is true ... So in reality there are no such facts."
A tenseless temporal world. Suppose a world with priority and simultaneity but no tensed properties and no ontological gulf between past, present and future. A token of "e is past" later than e is true on the tenseless account but false on Tooley's, since in that world it is never indeterminate at t whether anything is later than t. So something besides the token's date does matter: whether a tenseless statement is indeterminate at a time. Either such worlds are impossible (if chapter 4 is right, they lack causation, and with a causal theory of time, lack time), and tenseless accounts fail; or they are possible, and they show exactly what tenseless truth conditions leave out.
10.5.3 Mellor and "coming true"
Mellor ("McTaggart, Fixity, and Coming True", 1981) also attacks John Mackie (events becoming fixed) and Jeffrey (propositions coming to pass). Simple relational accounts exist: "E happened at t" iff E is simultaneous with t. Jeffrey must reject them, and so needs "real non-relational properties" that events acquire on occurring; but sentences attributing them ("E has happened") are indexical and fixed by dates, leaving no role for such properties. Reply: non-relational properties are not needed. With a world growing by accretion, "E happened at t" is explained by a relational property that E lacks when it occurs and immediately acquires: there being something later than it.
| Objection | Objector | Tooley's key move |
|---|---|---|
| Truth at a time confuses propositions and functions | Ducasse, Williams | Tenseless indexical-free propositions change value in a growing block |
| Unreal future is contradictory | Smart | Actual simpliciter vs actual as of now |
| Tenseless quantifier presupposes real future | Quine, Smart | Presupposes actual simpliciter only |
| Some future truths are inescapable | Williams | Only analytic ones, entailing no future states |
| Bivalence, excluded middle, disjunction, contradictions | Williams, Quine, Chapman | Connectives are factual-truth-functional, not truth-functional |
| Future statements meaningless; future knowledge impossible | Williams | Third value; truth simpliciter |
| Rate of passage needs meta-time | Broad, Williams | "Sixty minutes an hour", analytic |
| Changing events need meta-time | Broad | Relational tensed properties + unreal future |
| McTaggart's paradox | McTaggart, Mellor, Dummett | Tenseless dating; complete description via non-indexical tensed truths |
| Tensed facts idle | Mellor | They fix indeterminacy; tenseless worlds show the difference |
Tooley's replies largely work by relocating the dynamism into the primitive "actual as of a time". Smart's soldier objection then returns in a new key: as of 2100, the soldier's suffering is actual, and as of now it is not; B-theorists ask what this "as of" adds beyond "the suffering is later than now", and A-theorists of other schools ask whether a single growing totality, coherently describable from nowhere, has really kept anything tensed at all. Tooley's answer, that the difference shows up in the indeterminacy of propositions, depends on accepting his three-valued semantics and factual-truth-functionality, which few logicians have adopted.
The Special Theory of Relativity and the Unreality of the Future
Tooley faces the strongest objection to his view: a world-wide line between the real past-and-present and the unreal future requires absolute simultaneity, which special relativity (STR) does not contain. Rather than relativise becoming to light cones (Stein), he argues that absolute simultaneity is definable within STR once space-time points are causally related, that STR can be modified into an empirically equivalent theory that entails it, and that the modified theory is better: more explanatory, free of the untestable one-way-light postulate, and demanded by quantum non-locality.
11.1 The challenge
Two arguments from STR against "past and present real, future not".
Argument 1: the Rietdijk–Putnam argument (Rietdijk 1966; Putnam 1967; Weingard 1972)
- STR, plus an auxiliary premise: if two events are simultaneous relative to some frame, then if one is real so is the other (reality is transmitted by frame-relative simultaneity).
- For any events E and F, either they are simultaneous in some frame, or F is in E's future light cone, in which case some event S is simultaneous with E in one frame and with F in another.
- So E is real iff F is real: all events, past, present and future, are equally real.
Argument 2: Putnam's parsimony argument
- A universe-wide divide between the real and the not-yet-real would define absolute simultaneity: events are simultaneous iff at some location both lie in the present.
- STR contains only frame-relative simultaneity (Malament 1977), and it is very well confirmed.
- No better theory results from adding absolute simultaneity, for which there is no empirical evidence.
- Simpler theories are preferable, so reject the ontological gulf; STR gives a complete account of spatiotemporal relations.
11.2 Possible responses
Howard Stein (1968) shows the first argument cannot work: one can make reality relative to space-time locations and count as real, at a point, the point plus its past light cone. That also escapes the second argument while keeping a dynamic world. Tooley declines it for two reasons:
- Arbitrariness. Why exclude events outside both light cones? One could equally count everything real except the future light cone; no way to decide.
- The present would not be where things come into existence. Moving along a world-line, ever more remote past events enter the past cone, so most things that become real for an observer are past, not present; past-tense statements could become true at a point with no corresponding present-tense statement ever true on that world-line.
The first argument can be blocked more cheaply by rejecting its auxiliary premise. The second cannot: it requires directly arguing that STR is incomplete.
11.3 The basic strategy
Three theses
- Definability. Absolute simultaneity is definable within any version of STR that (a) does not reduce space-time to relations among events and (b) includes causal relations.
- A modified theory. Starting from Einstein's 1905 version: (i) move to an ε-Lorentz formulation, replacing the constancy of the one-way speed of light by the constancy of the average round-trip speed; (ii) add postulates implying sameness of place over time, absolute simultaneity, and a fixed speed of light relative to absolute space; (iii) the round-trip postulate is then derivable and can be dropped.
- Superiority, on three counts: explanatory and predictive power (it explains the existence of space-time regions); it avoids the untestable one-way-light assumption; and Bell-type quantum results require absolute simultaneity.
11.4 Absolute simultaneity and STR
11.4.1 Definability
Relative simultaneity is defined by synchronising clocks, by infinitely slow clock transport or by light signals (or by Robb's optical parallelograms). Standard signal synchrony: a signal leaves clock C at t1, reaches D at D-time t*, returns to C at t2; set t* = (t1 + t2)/2. E1 and E2 are simultaneous in frame F iff co-located clocks at rest in F, so synchronised, would read the same. The halfway rule is justified only if light's speed is the same both ways, which no experiment has shown.
Absolute simultaneity = simultaneity relative to frames at rest in absolute space. What is "at rest in absolute space"? Space-time points are contingent (their existence grounds empirical possibilities), so their existence wants explaining; otherwise it is a brute and "extraordinarily improbable" fact that there is a point at each of the non-denumerably many possible locations in every future light cone. The natural explanation: each point is caused by an earlier point. If those causal chains are non-branching, sameness of place is definable.
Definitions
Distinct space-time points S and T are in the same location means: either S's existence causes T's or T's causes S's, and the following principle holds.
The Principle of the Parallel, Non-Branching Conservation of Space 1. Every space-time point's existence causes that of at least one other point. 2. Every space-time point's existence is caused by that of at least one other point. 3. If P and Q are causally connected and S lies on the line through P and Q, S is causally connected with both (no causal gaps). 4. If P causes Q and R causes S, the line PQ is parallel to the line RS (betweenness and congruence preserved; no branching: strict conservation of space).
Clauses 1–2: space endures. Clause 3: no gappiness. Clause 4: no branching.
E and F are absolutely simultaneous means: E and F are simultaneous relative to some frame at rest with respect to absolute space, i.e. No part of which is ever at different locations at different times.
11.4.2 A modified theory
Adding the conservation principle to STR gives absolute simultaneity as a relation present in the world, provided light's speed is the same in all directions in the rest frame, so that signal synchrony there captures the intended relation. Tooley argues that it is: space itself is the medium of light in vacuo. The ether was posited because space was thought to be nothing but empirical possibilities; but possibilities need categorical bases, and if space does not depend on objects, the bases are non-dispositional properties of space-time points. Then space can carry light, with constant speed relative to absolute space.
The consistency problem. STR + conservation of space + constant light speed relative to absolute space is inconsistent: in a frame moving through absolute space, light must go faster one way than the other, contradicting STR's one-way light postulate. So one must also subtract that postulate. The question becomes whether STR's claim that the one-way speed of light is the same in all directions in all inertial frames is justified.
Einstein (1905) treated equal travel times both ways as true "by definition"; only the round-trip speed is empirical. Reichenbach (1924, 1928), Grünbaum (1960, 1973), Winnie (1970) and Salmon (1969, 1977) defended this conventionality; physicists keep proposing one-way measurements (e.g. Nissim-Sabat 1984, Stolakis 1986), and every proposal so far presupposes the one-way constancy it was meant to test (criticised by Norton, Øhrstrøm, Petkov, Morris). John Winnie came close to proving that versions with different one-way assumptions are kinematically equivalent. What matters for Tooley: there is no experimental evidence for one-way constancy.
Dropping it replaces the Lorentz transformations by Reichenbach's ε-Lorentz transformations, where ε = c / 2c₊ (c₊ the one-way speed in the positive direction, c the round-trip speed); ε = ½ gives the standard Lorentz transformations.
Winnie's synchrony-free STR and Tooley's modification
| Principle | Winnie | Tooley's modified theory |
|---|---|---|
| One-Way Light Principle (one-way c constant in all frames) | Dropped | Dropped |
| Reciprocity of relative velocities / lengths | Dropped (hold only with one-way constancy) | Dropped |
| 1. Round-Trip Light Principle: average round-trip speed in vacuo = c in all inertial frames | Kept | Dropped as a postulate; derived |
| 2. Equal Passage-Times: a rod of rest length s passing a point takes the same time Δt = Δt′ in either frame | Kept | Kept |
| 3. Proportional Time-Passage: passage-time ∝ rest length (implies Linearity) | Kept | Kept |
| Conservation of Space (parallel, non-branching) | Absent | Added |
| Constancy of c relative to absolute space | Absent | Added |
Consistency: adding conservation of space cannot create inconsistency (Winnie's theory says nothing about causal relations among points); adding constant c relative to absolute space could do so only by contradicting the round-trip principle, which it does not. So the modified theory is inconsistent only if STR is. Strength: constant c relative to absolute space gives a constant round-trip speed there, hence ε-Lorentz transformations with ε = ½ for motion relative to absolute space, hence:
- Absolute Fitzgerald–Lorentz contraction: a rod moving at v through absolute space along its length has length L* = L√(1 − v²/c²), L being its length at absolute rest.
- Absolute time dilation: a process involving objects moving at v through absolute space lasts T* = T / √(1 − v²/c²).
- These plus constant c relative to absolute space entail the Round-Trip Light Principle as measured within every inertial frame. So the modified theory entails everything Winnie's version of STR entails.
- In a frame moving at v through absolute space, light's speed relative to the frame is c − v one way and c + v the other; corrected for contraction and dilation the measured one-way speeds still differ, though the measured round trip is c.
This is not the most fundamental formulation: following Hartry Field (Science Without Numbers, 1980), a fundamental theory should describe causal processes intrinsically, without numbers, and state basic causal laws; Tooley thinks such a version straightforward to build.
11.4.3 The superiority of the modified theory
- Explanatory and predictive power. By its conservation law the modified theory explains each temporally bounded region of space-time as caused by an earlier region and predicts later regions. Unexciting, like other conservation-law explanations, but genuine, repeatedly confirmed and never falsified; STR offers neither.
- No untestable assumption. STR assumes the one-way constancy of light "more than ninety years after Einstein" with absolutely no experimental support, and possibly untestable in principle: "a gratuitous metaphysical assumption". (This counts against standard STR, not against ε-Lorentz versions.)
- Quantum non-locality (below).
When does the distant electron get its spin? Create two electrons with fixed total spin along an axis, separate them, and measure one at t. Either (a) both had determinate spins from creation, and measurement merely reveals them: the Einstein–Podolsky–Rosen view (1935), which makes QM incomplete; or (b) both acquire determinate spins only through measurement. On (b), the second electron cannot acquire its spin earlier. If later, with a temporal gap, a measurement on it during the gap could give a value that, with the first, violates conservation of spin. If at the same time, "same time" cannot mean frame-relative simultaneity, since some other frame would then show a gap with the same risk. If throughout an open interval immediately after, the boundary instant must still be simultaneous with the first measurement, again absolutely. So: either QM is incomplete, or STR is incomplete.
John Bell (1964) showed QM's predictions exclude pre-existing spin values of the EPR kind, so the dilemma becomes: either STR is incomplete or QM is false. Aspect, Grangier and Roger (1981, 1982) confirmed QM. Hence the distant electron acquires its spin at a time absolutely simultaneous with the measurement, or has one at every moment after such a time: experimental grounds for absolute simultaneity. More generally, wave-packet collapse seems to require it.
The experimental side has only strengthened: loophole-free Bell tests (Delft, Vienna and NIST, 2015) closed the locality and detection loopholes together, and Aspect, Clauser and Zeilinger received the 2022 Nobel Prize in Physics for this line of work. The one-way speed of light remains unmeasured; conventionality of simultaneity is still the standard view. But Tooley's inference from non-locality to absolute simultaneity is contested: relativistic collapse models (e.g. Tumulka's relativistic GRW "flash" theory, 2006) reproduce QM's predictions without a preferred foliation, while Bohmian mechanics does need one. Preferred-foliation approaches also appear in quantum gravity (Hořava–Lifshitz gravity, shape dynamics), and some growing-block theorists now prefer causal set growth, whose order of birth is not a global simultaneity (Sorkin argues relativity does not imply that the future already exists).
11.5 Objections
11.5.1 Absolute rest and simultaneity are physically meaningless
Hartry Field: in Newtonian mechanics there is no "objective" comparison of spatial distances across times without absolute rest, which "makes no objective sense" and which "the positivists have quite rightly objected to". As a meaning criterion this is verificationism, with its familiar defects. As a demarcation criterion it fails too: the conservation of space principle has testable consequences, no logically weaker nomological statement has the same consequences, so it is scientifically admissible, and it entails (with one space-time point) that two points share a location at different times, which is admissible by entailment.
11.5.2 Definable equivalence relations (Malament)
David Malament (1977) proved that, from causal connectibility plus "is a point on this frame", the only non-trivial, non-universal equivalence relation definable (even implicitly) is standard frame-relative simultaneity; so absolute simultaneity is not definable in STR. Reply: (i) Malament's space-time is metaphysically unsound: connectibility is counterfactual and the theory supplies no categorical truth-makers; (ii) add actual causal relations between points, as the conservation principle does, and the world-line of a place is explicitly definable, and with it absolute simultaneity.
11.5.3 The conspiracy-of-silence objection
John Mackie ("Three Steps towards Absolutism", 1983) defended absolute acceleration, absolute duration and, most controversially, absolute rest and motion. His argument from corresponding points on two oppositely directed light rays fails (Jon Dorling): a second source moving relative to the first, emitting at the same point, yields a different corresponding point, through the Doppler shift. Mackie himself raised the deeper worry: "Why, and how, does it come about that although there really is such a thing as absolute rest, we cannot identify it? There must be something odd about the laws of nature that enables them to constitute such a conspiracy of silence."
Elie Zahar: like Lorentz (who conceded after learning by 1909 that Maxwell's equations are fully covariant and the Lorentz transformations form a group), Mackie must accept that "Nature conspires systematically to conceal" the privileged frame; deep asymmetries exactly nullified by compensating factors are improbable, like a series of coincidences with one global effect.
The two conspiracies are one. If the one-way speed of light can be measured, the issue is experimentally decidable: equal one-way speeds everywhere refute the modified theory; speeds varying as it predicts reveal each frame's velocity through absolute space. If it cannot be measured, then STR (standard and ε-Lorentz alike) already entails that nature conceals whether one-way speeds are equal, and the modified theory's concealment of absolute rest is, or derives from, that same conspiracy. Zahar's objection cannot tell against the modified theory without telling equally against special relativity.
11.5.4 Other modified theories
Two rivals combine synchrony-free STR with an expansive conservation of space, using linear causal processes (all events along a geodesic): Principle I, each point causes, via a linear process, every point on the surface of its future light cone; Principle II, every point inside its future light cone. They avoid absolute simultaneity, share the explanatory gain, and drop the one-way-light assumption.
| Feature | Standard STR | ε-Lorentz STR | Expansive I / II + synchrony-free STR | Tooley's modified theory |
|---|---|---|---|---|
| Explains existence of space-time regions | No | No | Yes | Yes |
| One-way light constancy assumed | Yes | No | No | No |
| Absolute simultaneity | No | No | No | Yes |
| Fits Bell / collapse | No | No | No | Yes |
| Causal structure among points | None | None | Uncountably many chains, branching infinitely at every point | Non-branching chains |
| Overdetermination | n/a | n/a | Massive: non-denumerably many sufficient causes per point | None |
| Analogue in physics | n/a | n/a | None | Like conservation of mass-energy, momentum, charge, spin |
| Round-trip light law | Basic or derived | Basic | Basic | Derived |
The last row carries a separate argument. A reflected ray's return speed cannot causally depend on its outgoing speed (all rays going that way share a speed whatever their history), so the round-trip speed is fixed by two causally independent facts and cannot be a basic law; it must follow from laws about one-way speeds. The rivals have none and must take it as basic; the modified theory derives it from contraction, dilation and constant c relative to absolute space.
11.6 Summing up
STR seriously challenges the unreality of the future. Stein's route modifies the metaphysics; Tooley instead holds that STR is exposed to strong objections and that a modified theory avoids them, gains explanatory and predictive power, and does so precisely because it entails absolute simultaneity.
This chapter is where most readers part company with Tooley. The "explanation" of space-time regions by earlier regions is not a prediction any experiment could fail; the modified theory is empirically equivalent to STR by construction, so the choice rests on metaphysical virtues that physicists rarely weigh. The Bell argument assumes collapse is a real physical event; on no-collapse (Everettian) or relativistic collapse views it lapses, and retrocausal views reject its framing. And the argument from general relativity, where no global inertial frames exist and some solutions (Gödel's) admit no global time at all, is not addressed; the book's absolute space is Newtonian-flat. Tooley's strategy is coherent, but it shows the price of a global growing block: a hidden preferred frame.
- 1905 Einstein: one-way equality of light's speed holds "by definition".
- 1914 Robb: causal axiomatisation of Minkowski space-time.
- 1924–28 Reichenbach: ε and the conventionality of simultaneity.
- 1935 Einstein, Podolsky and Rosen: is quantum mechanics complete?
- 1964 Bell's theorem.
- 1966–67 Rietdijk and Putnam: relativity makes the future real.
- 1968 Stein: becoming relative to the past light cone.
- 1970 Winnie: special relativity without one-way velocity assumptions.
- 1977 Malament: only standard simultaneity is definable from causal connectibility.
- 1981–82 Aspect, Grangier and Roger confirm quantum predictions.
- 1983 Mackie, Dorling and Zahar debate absolute rest and the conspiracy of silence.
- 1997 Tooley: modified relativity with absolute simultaneity.
- 2015 Loophole-free Bell tests; 2022 Nobel Prize to Aspect, Clauser and Zeilinger.
Summary and Conclusions
Tooley gathers the account into eight features and eight advantages, and names it a third way between tenseless and traditional tensed theories. The world is dynamic because, and only because, which tenseless states of affairs are actual changes with time; there are no irreducible tensed facts; and causation, not experience, is what makes time pass and gives it its direction.
12.1 Central features of the approach
Tenseless and traditional tensed theories disagree on two issues: whether the world is dynamic, and whether tenseless facts supervene on tensed ones or the reverse. Tooley sides with the traditional view only on the first.
Eight central features
- A dynamic world in which past and present are real and the future is not. Even which tenseless facts are actual depends on the time; and the world is dynamic because, and only because, what tenseless states of affairs are actual changes with the passage of time, not because of irreducible tensed facts.
- Causation at the heart of time. The direction of time is defined by the direction of causation; more importantly, the main argument for the growing block rests on causation being a theoretical relation whose postulates can be satisfied only in such a world.
- Tensed facts supervene on tenseless facts actual as of times. Tenseless concepts cannot be analysed tensedly; past and future need analysis via temporal priority; with priority plus actuality as of a time (or truth at a time), all tensed concepts, the present included, are analysable.
- Indexicality is not essential to tense. Familiar tensed sentences are indexical; the most fundamental tensed sentences are not.
- Both truth at a time and truth simpliciter. Since the world grows by adding tenseless states of affairs and there are no irreducible tensed facts, there is a totality of all states of affairs, so what is actual simpliciter makes sense. Tenseless and traditional tensed theories each reject one of the two truth concepts.
- No dependence on indeterminism. Determined or not, the present is where the hitherto non-actual becomes actual.
- A causal analysis of temporal priority, as in many tenseless theories, but with absolute space-time whose points stand in causal relations.
- Objective time. Grounded in causation, the coming into existence of events is a fully objective feature of the world, independent of human or other consciousness, unlike tensed views centred on the phenomenology of temporal experience.
12.2 Some advantages
Eight advantages
- Robust dynamism. Grounding becoming in causation means it depends on no accidental feature (experiences) and no special tensed property: any world with causally related events is a growing block.
- No problem of intrinsic tensed properties. Pastness and presentness are relational (whether later states of affairs are actual as of a time), so an instantaneous event can be present at one time and past at another.
- A decisive answer to McTaggart. With tenseless concepts not analysed tensedly, the times at which an event has tensed properties are given by dates, and the regress "does not even get started".
- Indexicality handled. Some tensed sentences indexical, others not: no need to say an ordinary tensed sentence always expresses one proposition, and Mellor's anti-tense arguments are avoided.
- Past and future analysed: the past is what is earlier than the present, the future what is later. Traditional views, analysing priority tensedly, must make past and future basic, contrary to traditional empiricism.
- Not a hostage to fortune. Views premised on indeterminism would make the world static if a deterministic theory replaced quantum theory; Tooley's does not care.
- A comprehensive account of time and causation. A non-temporal analysis of causation, plus the impossibility of backward causation even without loops, permits defining time's direction by causation's; realism about causation avoids the objections from simple worlds and inverted worlds (where time runs against entropy increase, cosmic expansion, the propagation of order and apparent control).
- Absolute, causally connected space-time, which (i) gives spatiotemporal location to events causally unrelated to all others; (ii) makes absolute simultaneity reasonable, answering the STR objection; (iii) makes time all-pervasive, part of the fabric of space-time.
12.3 A third way?
Einstein and the Now. In his intellectual autobiography Rudolf Carnap recalls Einstein saying "the problem of the Now worried him seriously": the experience of the Now means something special, essentially different from past and future, yet "this important difference does not and cannot occur within physics", which Einstein accepted with "painful but inevitable resignation". Carnap replied that physics describes the sequence of events and psychology describes and explains our attitudes to past, present and future, so "science in principle can say all that can be said"; he suspected Einstein confused experience and knowledge. Einstein thought something essential about the Now lies outside science altogether.
The exchange marks one of metaphysics' great divides, dating back at least to the pre-Socratics, and no argument so far has settled it. Tooley's contribution is a different line of attack, through the relation between time and causation, and a diagnosis of the stalemate: perhaps the truth lies between the two traditions, combining the tenseless rejection of irreducible tensed facts with the tensed insistence on a dynamic world.
Tooley's Einstein episode cuts both ways. Tooley gives Einstein's "Now" a home in physics, as the edge of a growing causal order, but at the price of a preferred simultaneity Einstein's own theory denies. Later growing-block work has tried to keep the edge while dropping the global frame (causal set growth, light-cone relativised becoming), and later critics press the epistemic objection that nothing in a growing block tells us we are at the edge. The book's lasting contributions are its sharp separation of the two dividing questions, its demand for truth-makers, and its attempt to make the direction of causation do metaphysical work.
Master Takeaways
Tooley's book is a sustained attempt to make becoming respectable by tying it to causation and stripping it of tensed properties. Its lasting lesson is methodological: decide first whether the world is static or dynamic, then demand truth-makers for every tensed claim.
- The static/dynamic question is independent of the tensed/tenseless-supervenience question. A static world rules out irreducible tensed facts, but a dynamic world does not require them.
- A dynamic world can be built from tenseless facts alone: the world changes when which tenseless states of affairs are actual changes; tensed truths supervene on what is actual as of each time.
- Causation requires a growing block. Causal laws must satisfy (C1)–(C4): learning that P causes Q leaves P's probability alone but lifts Q's to P's prior; that asymmetry is explicable only if causes are actual as of their effects' times and effects are not actual as of their causes'.
- Backward causation is impossible, even without causal loops, once the actuality postulates hold and all times are causally linked.
- Temporal priority is causal: A is earlier than B iff a chain of causal and spatial links, at least one causal, runs from A to B; simultaneity is spatial relatedness.
- Absolute simultaneity can be restored by an empirically equivalent modified relativity in which space-time points cause their successors along non-branching lines; its conspiracy of silence is the same as STR's over the one-way speed of light.
- Preventability is suggestive but not probative: it presupposes a neutral proof against backward causation and its counterfactuals hold in static worlds.
- Backward causation without loops is conceivable: the segregated world with a one-way wall, and fully overlapping sub-worlds of non-interacting particles.
- Similarity semantics for counterfactuals fails (wrong verdicts in fork-reversed worlds, and the added-law case), while priority-based semantics is justifiable only if the future is unreal.
- Reductionism about causation fails: simple worlds and inverted worlds defeat pattern-based accounts of causal direction; indeterministic laws underdetermine which cause produced which effect.
- Causation is singularist and theoretical: not observable even in the weak sense (God could suppress a collision unnoticed), defined as the relation whose laws must satisfy (C1)–(C4).
- Truth at a time is three-valued, truth simpliciter two-valued: a statement can be indeterminate for lack of any truth-maker, and changes value at most once.
- Connectives are factual-truth-functional: their defining job is mapping factual truth-values, which explains why they are truth-functional in two-valued logic but not in three-valued logic.
- Truth simpliciter is indispensable for logical truths (to keep correspondence), atemporal entities (uninstantiated laws and universals) and unrestricted generalisations ("never three neutrinos in a one-metre triangle").
- Tensed concepts are analysable: E is present at t iff E is actual as of t and nothing later than E is; past = earlier than the present; future = later.
- Indexicality is not intrinsic to tense: ordinary tense is indexical, but the basic tensed sentences ("E lies in the present at t") are not; that dissolves both the tenseless "no tensed facts" argument and the tensed refusal of indexicality.
- Intrinsic tensed properties are incoherent for instantaneous events, leave necessary relations unexplained, and cannot explain why receding events stay in lockstep; relational tensed properties with an unreal future avoid all three problems.
- Presentism lacks truth-makers for the past: classical presentism leaves dinosaur-slices unordered; tensed-facts presentism makes Caesar a constituent of a present fact.
- McCall's branching tree adds nothing Broad lacks, and its accounts of probability (infinitely accelerating branching) and laws (possibilities fix laws) fail.
- Most a priori objections dissolve with the split between actual simpliciter and actual as of now: Smart's soldier, Quine's tenseless quantifier, Williams's "inescapable" future truths.
- McTaggart's paradox needs a tensed specification of times; date the tensed properties tenselessly and the regress never starts; Dummett's completeness demand is met by adding non-indexical tensed truths.
- Temporal distance is not causal: a world of uncorrelated pendulums would be ordered but clockless; realism about quantitative relations is far simpler than infinitely many laws of pure succession.
- The direction of time is maximally pervasive on a causal theory: it does not depend on initial conditions and holds even if all laws are time-symmetric.
- Conceptual analysis cannot show the world dynamic; only metaphysical argument can, and causation supplies it.
Frameworks & mental models
| Name | What it says | Use it when |
|---|---|---|
| Two dividing questions | Static vs dynamic, and which facts supervene on which, are separate | Classifying any theory of time |
| Growing block without tensed facts | Reality grows by adding tenseless states of affairs; tensed truths supervene | Wanting becoming without McTaggart-style tensed properties |
| Actual as of t vs actual simpliciter | Two primitives: time-relative and total actuality | Answering "the future is unreal" incoherence objections |
| Truth-maker constraint | Every contingent truth needs a structured truth-maker, existing tenselessly or at a time | Testing presentism, tense logic, any semantic proposal |
| Postulates (C1)–(C4) | Causal laws transmit probability from cause to effect, never back | Explaining causal direction without patterns or time |
| Argument from causation | Improbable regularities need (C1)–(C4) laws; those need a growing block | Arguing metaphysically, not conceptually, for dynamism |
| Six actuality postulates | Occurrence-actuality; causal posteriority and priority; simultaneity; backward non-actuality; forward actuality | Deriving the growing block and excluding backward causation |
| Backward causation without loops | Oppositely directed processes can be causally walled off | Testing arguments that only refute loops |
| Three-valued truth at a time | True, false, indeterminate; change at most once | Future contingents, sea-fight problems |
| Factual-truth-functionality | Connectives map factual truth-values; truth-functional only when bivalent | Defending "p or not-p" true with neither disjunct true |
| Translational vs truth-conditional analysis | Indexicals have truth conditions but no translations | Analysing "now", "here", "I" |
| Causal chain definition of priority | Earlier = chain of causal or spatial links with one causal | Building a causal theory of time |
| Conservation of space | Space-time points cause their successors along parallel, non-branching lines | Defining sameness of place and absolute simultaneity |
| Two conspiracies are one | Hiding absolute rest = hiding the one-way speed of light | Rebutting "undetectable preferred frame" objections |
On the whole book. Tooley's system is rigorous and unusually complete, but it is built on contested foundations: realism about universals and laws, logical probabilities, singular causation, and causally active space-time points. A Humean, a nominalist or a perspectivalist about causation (Price) can reject the argument from causation at its first step. His three-valued, factual-truth-functional logic has found few takers; later growing-block defenders mostly keep classical logic. The relativity chapter buys a global present with an undetectable preferred frame and does not engage general relativity. And since 1997 the growing block has faced the epistemic objection (Bourne, Braddon-Mitchell): if past people are as conscious as we are and also believe they are present, what assures us that we are at the edge? Tooley's relativised "present at t" is a natural reply, but the debate continues. The book remains the most thorough attempt to ground the growing block in causation rather than experience.
Who's who
| Person | Role in the argument |
|---|---|
| C. D. Broad | Growing-block pioneer (1923); his later meta-time and intrinsic-property arguments are turned against tensed rivals |
| J. M. E. McTaggart | Argued time requires the A-series and the A-series is contradictory |
| D. H. Mellor | Tenseless theorist: probability-raising argument against backward causation, token-reflexive critiques of tensed facts |
| J. J. C. Smart | Tenseless critic: "reality is not a property which anything can acquire"; objections to causal theories of time |
| W. V. O. Quine, D. C. Williams | Tenseless quantification; attacks on three-valued future contingents |
| Arthur Prior | Tense logic; presentism; target of the truth-maker critique |
| Storrs McCall | Branching-tree model with real future possibilities |
| Hans Reichenbach | Becoming as becoming determined; ε-notation for conventional simultaneity |
| David Lewis | Similarity semantics for counterfactuals; Tim and Grandfather |
| Richard Gale, George Schlesinger, Wilfrid Sellars | Tensed analyses of temporal priority, all judged circular |
| Michael Dummett | Reading of McTaggart via complete description; bringing about the past |
| Hilary Putnam, C. W. Rietdijk, Howard Stein | Relativity against an unreal future; Stein's light-cone becoming |
| John Winnie, David Malament | Synchrony-free relativity; undefinability of absolute simultaneity |
| John Mackie, Elie Zahar, Jon Dorling | Absolute rest; the conspiracy-of-silence objection |
| Antony Flew, Max Black | Bilking argument against backward causation |
| Jan Łukasiewicz | Three-valued logic; presentist who welcomed a forgiving, unfixed past |
Connect it
- Bitemporal data in banking. Core banking and regulatory systems store both valid time and transaction time and answer "as of" queries; that is Tooley's actual as of t versus actual simpliciter, and his insistence that facts are only added, never deleted, mirrors append-only ledgers and event sourcing, where a consistent total history coexists with time-relative views.
- Causal AI and counterfactuals. Tooley's case against similarity-based counterfactuals in favour of ones driven by causal laws and what is fixed at the time of the antecedent parallels the move in causal inference from correlation to structural causal models, where interventions propagate forward through laws and never rewrite upstream facts.
- Model risk and three-valued states. Distinguishing false (a contrary truth-maker exists) from indeterminate (no truth-maker yet) is a useful discipline for forecasts and pending decisions in credit and fraud pipelines: a not-yet-observed outcome is not a negative one, and once settled it should never flip.
About this book
Time, Tense, and Causation by Michael Tooley, 1997. This is a chapter-by-chapter study of the book, with summaries, maps, tables and diagrams; short quotations keep their page references. It is shared free for personal study, is not for sale, and is not endorsed by the author or publisher. Please read and buy the original.
Insight Editions · rajeshrmahapatra.com/insight-editions