The New Theory of Time General Introduction By Quentin Smith

In Aspects of Time George Schlesinger writes about the importance of the issue of temporal becoming. “We shall consider what fairly may be called the profoundest issue in the philosophy of time: the status of temporal becoming. Some philosophers have even regarded it as the profoundest issue in all of philosophy.”[1] Although this statement may be an exaggeration, it cannot be denied that the issue of temporal becoming is central to meta physics, the philosophy of science, the philosophy of mind, the philosophy of religion, the philosophy of logic, and the philosophy of language, as well as other fields of philosophy. The issue of temporal becoming is often formulated differently by different philosophers, but one of the most familiar formulations represents the issue as one about the ontological status of events that occupy different temporal locations. According to this formulation, the issue of temporal becoming is whether events are first future, then become present, and finally become past, or whether events do not “come into being” in this sense but merely exist “without becoming” at their respective temporal locations. If there is temporal becoming, then future events do not yet exist, present events exist, and past events no longer exist; but if there is no temporal becoming, then all events exist equally, regardless of whether they are located in 5,000 B.C., the twentieth century, or the twenty-fourth century.

Philosophers who claim that all successively ordered events have the same ontological status may be called “detensers,” or proponents of the tenseless theory of time. They hold that the nature of time can be captured completely by tenseless sentences, such as “The birth of Plato is earlier than the birth of Russell.” Philosophers who hold that there is temporal becoming are called “tensers” and are proponents of the tensed theory of time. They believe that tensed sentences, such as “Plato was born a long time ago,” are necessary if the complete nature of temporal reality is to be described.

An important issue discussed by tensers and detensers concerns whether temporal properties of a certain sort are exemplified. Some philosophers characterize the debate between tensers and detensers in terms of whether events have monadic temporal properties of presentness, pastness, or futurity (A-properties) or whether the only temporal properties of events are the polyadic properties (relations) of earlier than, later than, and simultaneity (B-relations). For these philosophers, the issue of temporal becoming is whether events possess A-properties in addition to B-relations. Some de fenders of the tensed theory of time, such as A. N. Prior and his followers, reject the thesis that there are events with properties of futurity, presentness, and pastness and state the issue between tensers and detensers in terms of whether some propositions change their truth-value with time or whether all propositions have permanent truth-values. What is common to the various versions of the tensed theory of time is the rejection of the claims that the temporal system consists of successively ordered events which are equally real and that tenseless sentences are sufficient to describe the temporal system.

This Introduction focuses upon the implications of the debate about the tensed and tenseless theories for a variety of philosophical subjects. Although the focus of this book is the new tenseless theory of time and the response to it by tensers, in this Introduction I shall indicate the broader implications and importance of this debate by explaining some of its consequences for certain issues in the philosophy of science, the philosophy of mind, the philosophy of religion, the philosophy of logic, and the philosophy of language. The new tenseless theory of time and its relation to the old tenseless theory of time will be explained at the beginning of Part I, but this distinction is not crucial to the ideas discussed in what follows here.

Which of these theories of time is true has important consequences for the interpretation of our best-established scientific laws and theories. As an example, I shall mention the relevance of the tensed/tenseless debate to Einstein’s special theory of relativity.

It should be noted at the outset that many thinkers believe the reverse of the above statement; that is, they believe that the result of the philosophical debate about tensed/tenseless theories does not determine how Einstein’s special theory of relativity should be interpreted, but rather, that Einstein’s theory has conclusive implications for the debate. Some philosophers, such as Grünbaum, Smart, Quine, and Putnam, as well as virtually all physicists, believe that Einstein’s special theory of relativity implies the tenseless theory of time, such that empirical confirmation of the theory of relativity is ipso facto confirmation of the tenseless theory of time. Their reasons for thinking this are not convincing, however, and in the course of explaining why, I will show why my earlier statement is true, namely, that the outcome of the philosophical debate about time will determine how the physical theories are to be interpreted.

The reason why physicists think that Einstein’s theory implies the tenseless theory of time is that they adopt Minkowski’s 1908 formulation of Einstein’s theory and Minkowski presupposes the tenseless theory of time in his interpretation of Einstein’s theory. Minkowski writes:

A point of space at a point of time, that is, a system of values, x, y, x, t, I will call a world-point. The multiplicity of all thinkable x, y, x, t systems of values we will christen the world. . . . Not to leave a yawning void anywhere, we will imagine that everywhere and everywhen there is some thing perceptible... . We fix our attention on the substantial point which is at the world-point x, y, x, t and imagine that we are able to recognize this substantial point which is at the world-point x, y, x, t and imagine that we are able to recognize this substantial point at any other time. Let the variation dx, dy., dz of the space co-ordinates of this substantial point correspond to a time element dt. Then we obtain, as an image, so to speak, of the everlasting career of the substantial point, a curve in the world, a world-line, the points of which can be referred unequivocally to the parameter t from -00 to + 00. The whole universe is seen to resolve itself into similar world-lines.[2]

This presupposition of the tenseless theory of time, however, is no more implied by Einstein’s theory than is the thesis that the tensed theory of time is true. Storrs McCall, D. Dieks, Howard Stein, William Lane Craig, I, and others have shown how Einstein’s theory may be interpreted in terms of the tensed theory of time.[3] For example, the Lorentz transformations do not imply that “everywhen there is (tenselessly) something perceptible,” since it is consistent to suppose that solutions to these equations correspond to physical events only when these events belong to the origin or past light cone of the relevant reference frames. It may be the case that future light cones do not consist of determinate events but involve what is not yet real. No scientific observation or test can decide between these two interpretations of Einstein’s theory; in terms of scientific observations, they are equivalent. (It is arguable, however, that human temporal experience in general confirms one of the two theories. See Part III.) Defenders of the Minkowski interpretation of special relativity sometimes say that Newton’s assumption of absolute space is a metaphysical assumption that cannot be verified by scientific observation; but the same could be said of Minkowski’s assumption that the tenseless theory of time is true. The tensed/tenseless issue is a matter not of physics but philosophy, and it can only be resolved by the sorts of considerations presented in this book.

However, some thinkers have presented an argument that Einstein’s theory implies the tenseless theory of time. It is worth seeing why their arguments are unsound. The first argument was put forward by Pumam and Rietdijk and was later restated by Maxwell.[4] It may be stated as a reduction to absurdity of the premise that some events are future, that is, not yet real.

Suppose there is an observer 01 at the space—time position p. Some event E is in 01’s future, so is not yet real to 01 (this is the premise to be reduced to absurdity). Now there is another observer 02 rapidly in motion relatively to 01. 02 passes 01 at the space-time position p. While 02 is at the space— time position p, 02 is real to 01. However (we may coherently suppose), event E is present to 02 while 02 is at p; that is, according to 02’s reference frame, E occurs simultaneously with 02’s occupation of the space—time position p. Thus, E is real to 02 at p. Now this shows the tensed theory of time is false, the argument goes, since if 02’s being at p is real to 01, and E is real to 02 at p, then E is real to 01 at p. This contradicts the original assumption that E is not yet real to 01 at p.

A similar sort of argument can be constructed for any event E that is said to be future and not yet real for some observer. Thus it follows that all events are equally real; there are no events that are not yet real. Thus, the tensed theory of time, which implies that some events are not yet real, is false.

However, this attempt to show the special theory of relativity implies the tenseless theory of time fails, since it depends on accepting the dubitable metaphysical assumption that the relation of being real to is a transitive relation. This assumption is not part of Einstein’s special theory of relativity, and there is no good reason to accept it; indeed, there are good reasons for rejecting it, since the special theory of relativity implies that analogous relations are intransitive. For example, is simultaneous with is intransitive. Now the defender of the tensed theory of time can coherently adopt the assumption that being real to is intransitive. The tenser believes that reality is dependent on an event’s position in the A-series, whether it is present, not yet present, or no longer present, and therefore that being real is no less relative than being present. Thus, it is natural to think that is real to is similar to being present to in being relative and intransitive. Accordingly, the tenser can coherently maintain that E is present and real to 02 at p. that 02 at p is present and real to 01 at p, but that E is future and not yet real to 01 at p. Given that this interpretation of the special theory of relativity is possible, it follows that relativity theory does not entail the tenseless theory of time.

A second familiar argument is Grunbaum’s general argument that physics makes no mention of physical events possessing the property of presentness, and that if physical events did possess presentness, this would be mentioned in physical theories.[5] Grunbaum regards this as a reason for thinking that physics is committed to the tenseless theory of time. However, his reasoning is arguably based on a confusion, namely, a belief that a subject matter which uniquely pertains to observational physics should be represented in theoretical physics if it is recognized in physics. Which event or year is present must be decided by observation, just as the location of the earth in the Milky Way galaxy must be decided by observation. Certainly, the presentness of some events does not appear in the Lorentz transformations of the special theory of relativity or in the ten field equations of the general theory of relativity; but that no more shows that no event is present than the fact that the location of the earth is not mentioned in these equations shows that the

In fact, the tenser may well argue that which time is present is mentioned in observational physics and cosmology. For example, one of the most important concepts in observational cosmology is what the physicist R. Dickie calls “the present value of T,” T being the Hubble age (how long the universe has been expanding). The present value of T is 15 billion years.[6] Numerous other tensed temporal locutions appear in observational cosmology.[7] Of course, this does not prove that observational cosmology implies that events possess A-properties, for the use of tensed locutions does not by itself show that the theory is committed to A-properties. It is a philosophical question whether tensed expressions ascribe A-properties or merely refer to B-positions. But it does show that the truth of the tensed or tenseless theory of time cannot be read off from our current physics. It is rather the case that the correct interpretation of physical theories remains an open question until the metaphysical issue regarding the tensed versus the tenseless theory is resolved by philosophers. This supports my earlier contention that the philosophical debate about the tensed and tenseless theories has consequences for how our scientific theories should be interpreted.

It should be added that philosophers of time need not be confined to the assumption that temporal determinations are relative, as described in the special theory of relativity. One may argue on metaphysical grounds that temporal properties and relations are possessed absolutely.[8] If simultaneity or presentness is absolute, this is consistent with the observable behavior of light rays, clocks, rigid bodies, and so forth, being relativistic in nature. If time is absolute, then the word “time” and the variable “t” in the special and general theories of relativity should be interpreted as signifying the observable states or changes in the relevant physical bodies, rather than time itself Such an interpretation of physics is observationally equivalent to the interpretation that regards the physicists’ t as referring to time. The assumption that time is not absolute but instead consists of the observably relative behavior of physical bodies because the variable t in physical equations refers to this behavior is not a scientific thesis but a philosophical one that may be proved correct or incorrect on the basis of philosophical considerations.[9]

A number of philosophers believe that the debate in the philosophy of mind between defenders of the substantival and temporal parts theory of personal identity hinges upon whether the tensed or the tenseless theory of time is true. Philosophers such as Delmas Lewis, Robin Le Poidevin, L. Nathan Oaklander, and Ronald Hoy, among others, believe one or both of the following two theses about time and personal identity: (1) that the substantival theory of personal identity is true only if the tensed theory of time is true, and (2) that the temporal parts theory of personal identity is true only if the tenseless theory of time is true.[10]

The substantival theory of personal identity holds that a person is a substance or particular that endures through time and successively acquires or loses various properties that are normally ascribed to a person (waking, sleeping, being angry, being sad, and so on). The temporal parts theory of personal identity implies that there is no continuing particular but rather a succession of particulars, each being a different temporal part that helps to make up the whole person. On the substantival theory, a person Alice exists through various times and acquires or loses various properties; whereas on the temporal parts theory, “Alice” refers to the whole that is made up of the temporal parts, Alice at t₁ Alice at t₂ Alice at t₃ and so on.

Some philosophers argue that the identity through time implied by the substantival theory requires the tensed theory of time. For example, Delmas Lewis and Roderick Chishoim point out that the same person cannot have (tenselessly) incompatible properties, but that this is possible on a tensed view. Chishoim writes:

There aren’t two you’s, a present one having one set of properties, and a past one having another. It is rather that you are now such that you have these properties and lack those, whereas formerly, you were such that you had those properties and lacked these. The “former you” has the same properties that the “present you” now has, and the “present you” had the same properties that the “former you” then had.[11]

By contrast, other philosophers, such as Ronald Hoy and Oaklander, believe that the temporal parts theory of personal identity implies the tense-less theory of time.[12] If the temporal parts theory were conjoined with the tensed theory, then a certain paradox would arise that was first articulated by J. J. C. Smart, who writes that the

notion of pure becoming is connected with that of events receding into the past and of events in the future coming back from the future to meet us. This notion seems to me unintelligible. What is the “us” or “me”? It is not the whole person from birth to death, the total space—time entity. Nor is it any particular temporal stage of the person. A temporal stage for which an event E is future is a different temporal stage from one for which event E is present or past.[13]

If the substantival theory of personal identity is true, then the “me” that future events come to meet is a continuing particular that passes from one present moment to the next. But if the temporal parts theory is true, then there is no candidate for this moving “me” according to Smart, Oaklander, and others. Accordingly, if the temporal parts theory of personal identity is true, the tenseless theory of time is true.

If these arguments are correct, then one of the central issues in the philosophy of mind—whether the self is a substance or a series of temporal parts—cannot be resolved until we know which of the theories of time is true. For example, if considerations based on McTaggart’s paradox (see Part II) show that the tensed theory of time is false, then we will know that the substantival theory of personal identity is false. On the other hand, if arguments from the semantic properties of tensed language (see Part I) and from the psychological properties of the experience of temporal passage (see Part III) show that the tensed theory of time is true, then we will know that the temporal parts theory of personal identity is false.

Of course, the claim that the substantival/temporal parts theories in the philosophy of mind are logically dependent on the tensed/tenseless theories in the philosophy of mind can be challenged. And indeed, I myself have challenged this connection, although Oaklander has countered that my argument against the temporal parts—tenseless time connection is unsound.[14] But, at the very least, it is safe to say that the tense/tenseless issue in the philosophy of time has an intimate and controversial bearing on the substantival/temporal parts issue in the philosophy of mind. Philosophers who work in the field of philosophy of mind can ignore the tense/tenseless debate in the philosophy of time only at their own peril.

The distinction between the tensed and the tenseless theories of time has relevance for a number of issues in the philosophy of religion, such as whether God should be conceived as existing timelessly or at all times, the nature of divine foreknowledge, and the question of whether God’s foreknowledge is compatible with human freedom. The literature on divine foreknowledge has burgeoned since the mid-1960s, and this topic is cur rently among the most widely discussed issues in the philosophy of religion. Some of the implications of the tensedltenseless distinction for the issue of the nature of divine foreknowledge may be mentioned.

If the tenseless theory of time is true, then the thesis that God foreknows future events, including future contingents, has a relatively clear formulation. Since all times are equally real and the nature of the universe at each time is fully determinate—note that being determinate is not to be confused with being causally determined—then there is no special difficulty in God knowing what occurs at every time, those later than 1992 as well those earlier than 1992. For example, it is true at every time (or timelessly) that Jane decides to commit suicide in the year 3002. This proposition corresponds to reality eternally; that is, it corresponds eternally to the 3002 event of Jane committing suicide, and thus is known by God eternally. “Future events,” on this theory, is understood in terms of the tenseless locution “events later than some specified time t.”

If, on the other hand, the tensed theory of time is true, the theory of divine foreknowledge is considerably more complicated. One reason for this is that there are many versions of the tensed theory of time, ranging from the full future theory to the empty future theory. The full future theory is analogous to the tenseless theory of time in holding that all times later than 1992 are fully determinate; but it differs in implying that the events occupying these later times have the monadic property of futurity and are in the process of becoming present. A half-empty future theory may hold that future times are partly determinate, consisting (say) of events that are effects of deterministic causal chains that extend from the present time but that these future times do not consist of future contingents, which are events that are not effects of deterministic causal chains. For example, it may be said the future time, tomorrow noon, includes the causally determined future event of the sun shining on the earth but that it is indeterminate in respect of John’s free decision to read a book during lunch or his free decision not to read a book during lunch (tomorrow noon contains neither a future event of John reading nor a future event of John not reading). The empty future theory holds that (assuming 1992 is present) that there are no determinate events (be they future contingents or causally determined events) later than 1992 and that there is literally nothing to possess a monadic property of futurity. But even these distinctions are not straightforward, and various complications arise in attempting to state them clearly and explain their relevance to divine foreknowledge.

Some of these difficulties can be illustrated in terms of William Lane Craig’s recent attempt to combine the tensed theory of time with divine foreknowledge. Craig endeavors to conjoin certain features of the full future theory with certain features of the empty future theory. He adopts both the thesis that God knows propositions about the future free decisions of humans and the thesis that future events do not exist in any sense. He writes of future events that what is “future does not merely not yet exist; it does not exist at all.”[15] Yet Craig holds that future-tense propositions are true, where truth is defined in terms of a correspondence theory. Future-tense propositions are propositions expressible by such sentences as “The race will begin.” But if future events do not exist in any sense, then to what do future-tense propositions about future free decisions correspond? It would seem natural to suppose that future-tense propositions lack truth-values if future events do not in any sense exist. But Craig rejects this position. He writes that “a denial of Bivalence for any future-tense propositions based on truth as correspondence is a non sequitur, for that view only requires that reality will correspond to the description given in a future-tense proposition, not that it does now correspond.”[16]

But Craig’s formulation does not seem entirely happy, since it arguably entails a contradiction. When the described event takes place, it is present and then corresponds to a present-tense proposition (a proposition stating the event is present), not a future-tense one. When the race is beginning, the future-tense proposition that the race will begin does not correspond to the race’s beginning; what corresponds is the present-tense proposition that the race is beginning. Indeed, the assumption that future-tense propositions are now true but do not now correspond to anything is an explicitly logical contradiction if truth is correspondence. Consider this statement of Craig’s: it is false that “future-tense propositions lack [current] truth-value due to lack of current correspondence.”[17] If truth is correspondence, then (omitting “value”) this sentence is synonymous with: it is false that future-tense propositions lack current truth due to lack of current truth.

One solution to this problem would be to allow that all future events exist in some sense and that future-tense propositions are now true by virtue of corresponding to these existents. This would amount to a full future theory. In fact, this solution is entailed by another position Craig adopts, that “tenseless propositions concerning future contingents would seem to be always true or false.”[18] If the tenseless proposition that the race begins on June 15 is always true, it is true on June 14; given that truth is correspondence to the item described, it follows that it is true on June 14 that there is something to which this proposition corresponds, namely, the race’s be ginning on June 15. Thus it seems that if divine foreknowledge consists of a knowledge of all future contingents, including all future free decisions of humans, then the full future version of the tensed theory of time is true (if any version of the tensed theory is true).

These reflections show that one must settle one’s position on the tensed! tenseless theories of time before one can adopt a position on the nature of divine foreknowledge. Moreover, this latter position must be settled before one can begin discussing whether divine foreknowledge is compatible with human freedom. For these reasons and others, philosophers of religion are dependent on the tensed/tenseless debate no less than are philosophers of science and philosophers of mind.

It is not possible to decide which logic is adequate until it is first determined whether the tenseless or tensed theory of time is true. The issue of which theory of time is true will determine whether the temporal structure of reality and the semantic content of natural language can be represented by a tenseless logical symbolism—for example, the extensional symbolism of first-order sentential logic—or whether they require a tensed symbolism— for example, Prior’s intensional logic with tense operators (“It will be the case that” and “It was the case that”). Moreover, if the tensed theory of time is true, then the particular version of it that is true will have consequences for the symbolism and valid formulae of tense logic.

This tensedltenseless issue was not addressed at great length by Frege, Russell, Peano, and the other founders of modern predicate and sentential logic. Rather, they tended to build their logics on the basis of the unargued for philosophical assumption that the tenseless theory of time is true, much as post-Minkowski physicists introduced this philosophical assumption into the interpretation of their equations. This issue in the philosophy of logic did not become widely discussed until Prior and Quine addressed it in the 1950s and 1960s.

Quine aimed to preserve the tenseless extensional symbolism of first-order predicate and propositional logic, which he believed to be adequate to represent the temporal structure of reality and natural language. He defended his belief about the temporal structure of reality by appealing to the fact that physicists, following Minkowski, accepted the tenseless theory of time; but he did not seem to be aware that their acceptance of this theory was a metaphysical assumption.[19] Regarding natural language, Quine believed that it could be paraphrased by a tenseless language that substitutes singular phrases denoting dates for tenses; thus “John was running” as uttered at noon, 1 November 1992, becomes “John runs (tenseless) before noon, 1 November 1992,” which is a tenseless locution that can be represented in an extensional logic.[20] However, Quine’s belief about the de-tensing of natural language has been challenged frequently, and it runs into many of the difficulties discussed in Part I. Thus, Quine’s belief in the adequacy of extensional logic seems to rest on both a faulty understanding of physics and controversial assumptions in the philosophy of language.

Prior adopts a different approach. He believes that the temporal structure of reality and natural language can be represented only in a tense logic. He begins with the first-order sentence calculus but regards the sentences as being in the present tense rather than tenseless. He introduces the tense operators F and P, “It will be the case that” and “It was the case that,” so that if p is “John is running,” Pp is “It was the case that John is running.” Further elements of his tense logic are added to these basics.

Prior is aware that the issue of the advantages of tense logic vis-à-vis tenseless logic turns on controversial philosophical issues about the nature of time and natural language and cannot simply be assumed without argument. He himself advanced some arguments in favor of the tensed theory of time, such as the argument from the experience of passage,[21] but his arguments have been met by counter-arguments—for example, by some of the arguments that are presented in Part III. It seems more difficult to establish the tensed theory of time than Prior’s brief arguments for it might lead one to suppose. Moreover, Prior himself advanced only some of the possible versions of the tensed theory of time, and many tensers have rejected his versions. For example, Prior rejected the view that there are events with properties of futurity, presentness, and pastness and never adequately clarified the positive ontological import of his tense operators. For example, if “it was the case that” does not involve the ascription of a property of pastness, then what are its semantic content and ontological import? Mellor interprets Prior as meaning that this operator ascribes the property of pastness to a tensed fact,[22] but Prior himself nowhere says this. Contemporary followers of Prior also adopt his reticent line. For example, Ferrel Christensen says that the information conveyed by tenses or tense operators cannot be rep resented in “an ontology of individuals and their properties and relations,” but he never specifies to which ontological category the relata of tenses or tense operators belong.[23] Christensen and other tensers who follow Prior seem to think that the assumption that events have properties of pastness, presentness, and futurity leads to McTaggart’s paradox, but it can be argued that this is not the case (see Part II). If it turns out that events have such properties, then we will want a tense logic that reflects this, and Prior’s tense operators may be inadequate for this purpose. If these tense operators are interpreted as ascribing temporal properties, it would seem natural to interpret them as ascribing properties to the truth-values of sentences, propositions, or facts, rather than to events. Pp would ascribe pastness to p’s being true, and we would need a different symbolism to represent the ascription of pastness to the event described by p.

These considerations reflect the fact that the question of which logic is adequate to represent the temporal form of reality and the semantic content of natural language is a question of metaphysics and the philosophy of language rather than logic, and requires the sort of complex, detailed metaphysical and linguistic investigations that are undertaken in the book.

The most important development in the philosophy of language in the past twenty or thirty years is the New Theory of Reference of Marcus, Kripke, Kaplan, Putnam, N. Salmon, H. Wettstein, J. Perry, and numerous others. But whether this theory is true depends on whether the tenseless theory of time is true or, if the tensed theory of time is true, on which version of the tensed theory is true.

The New Theory of Reference holds that many expressions, including indexicals such as “now,” “here,” and “I,” refer directly and rigidly to particulars and do not ascribe properties. For example, David Kaplan argues that a use of “now” at noon refers directly to noon and does not ascribe any property. However, if the tensed theory of time is true and uses of “now” ascribe the property of presentness, then the New Theory of Reference is false. Temporal indexicals such as “now” will not be “purely referential,” to borrow a phrase from Marcus,[24] but will express a characterizing sense, the property of presentness.

In the introduction to Part I, the relation of the New Theory of Reference to the tensedltenseless issue will be discussed further, and I will show how the New Theory of Reference was partly instrumental in motivating the new tenseless theory of time. The conflict between the New Theory of Reference and the tensed theory of time will be discussed at length in chapters 11 and 12, by David Kaplan and myself, where the issue of whether the indexical “now” is purely referring will be examined in light of the relevant linguistic data.

In this general introduction to the book, I have hoped to bring out the centrality of the debate between tensers and detensers to a number of issues in various fields of philosophy. I have argued that the outcome of the tensed/tenseless debate is crucial to important theories in the philosophy of science, the philosophy of mind, the philosophy of religion, the philosophy of logic, and the philosophy of language. This debate has crucial import for other philosophical issues as well, for example, the metaphysical question about the nature of existence (for example, on some versions of the tensed theory of time, existence may be identified with presentness), but the few sample topics I have discussed suffice to suggest the wide-ranging ramifications of the debate. We shall now turn to the debate itself, beginning (in Part I) with the linguistic, or semantic, dimension of the argument between the detensers and the tensers.

[1] George Schlesinger, Aspects of Time (Indianapolis, 1980), p. 23.

[2] H. Minkowski, “Space and Time,” in Albert Einstein et al., The Principle of Relativity (New York), 1952), p. 76.

[3] Storrs McCall, “Objective Time Flow,” Philosophy of Science 43 (1976): 337-362; D. Dieks, “Special Relativity and the Flow of Time,” Philosophy of Science 55 (1988): 456-460; Howard Stein, “On Einstein-Minkowski Space-Time,” Journal of Philosophy 65 (1968): 5-23; idem, “On Relativity Theory and Open ness of the Future,” Philosophy of Science 58 (1991): 147-167; Quentin Smith, Language and Time (New York, 1993); William Craig, “God and Real Time,” Religious Studies 26, no. 3 (1990): 335-347.

[4] H. Putnam, ‘1I’ime and Physical Geometry,” Journal of Philosophy 64 (1967): 240-247; C. W. Rietdijk, “A Rigorous Proof of Determinism Derived from the Special Theory of Relativity,” Philosophy of Science 33 (1966): 341-344; N. Maxwell, “Arc Probabilism and Special Relativity Compatible?” Philosophy of Science 52 (1985): 23-43.

[5] Adolf Grunbaum, Modern Science and Zeno’s Paradoxes (Middletown, Conn.; 1967).

[6] R. Dickie, “Dirac’s Cosmology and Mach’s Principle,” Nature 192 (1961): 440.

[7] See Quentin Smith, “The Mind-Independence of Temporal Becoming,” Philosophical Studies 47 (1985): 109-119.

[8] This is argued in Quentin Smith, Language and Time.

[9] Ibid.

[10] Delmas Lewis, “Persons, Morality, and Tenselessness,” Philosophy and Phenomenological Research 47 (1986): 305-309; Robin Le Poidevin, Change, Cause, and Contradiction: A Defense of the Tenseless Theory of Time (New York, 1991); L. Nathan Oaklander, “ Persons and Responsibth . A Critique of Delmas Lewis,” Philosophy Research Archives 13 (1987-88): 181-187; Ronald Hoy, “Becoming and Persons,” Philosophical Studies 34 (1978): 269-280.

[11] R. Chishoim, Person and Object (La Salle, III., 1976), p. 92.

[12] Hoy, “Becoming and Persons”; Oaklander, “Persons and Responsibility.”

[13] J. J. C. Smart, “Time and Becoming,” in P. van Inwagen, ed., Time and Cause (Boston, 1981), p. 6.

[14] Quentin Smith, “Personal Identity and Time,” Philosophia 22 (1993): 155-167; L. Nathan Oaklander, ‘ Passage and Temporal Parts,” Noüs 26 (1992): 79-84.

[15] William Lane Craig, Divine Foreknowledge and Human Freedom (Leiden, Brill, 1991), p. 226.

[16] Ibid., p. 58.

[17] Ibid., p. 59.

[18] Ibid., p. 61.

[19] W. V. O. Quine, Word and Object (Cambridge, Mass., 1960), p. 172.

[20] Ibid., sec. 36.

[21] A. N. Prior, “Thank Goodness That’s Over,” Philosophy 34 (1959): 12-17.

[22] D. H. Mellor, Real Time (Cambridge, 1981), p. 95.

[23] Ferrel Christensen, “McTaggart’s Paradox and the Nature of Time,” Philosophical Quarterly 24 (1974): 299.

[24] Ruth Barcan Marcus, “Modalities and Intensional Languages,” Synthese 130 (1961): 303-322.