Sentence Type Version Tenseless Theory of Time

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There are two traditional tenseless theories of time, the token-reflexive theory (e.g., Mellor 1981; Oaklander 1994) and the date—analysis theory (e.g., Smart 1980; Oaklander 1994). These two theories have been subject to much criticism in the literature (e.g., Craig 1996a, 1996b, 1997, forthcoming; Smith 1987, 1993). But recently, L. A. Paul (1997) has for mulated a third and novel “sentence-type” version of the tenseless theory that she shows escapes the problems with the two traditional versions of the tenseless theory, the token-reflexive version and the date—analysis version. She presents an original account of the tenseless truth conditions of tensed sentences, and argues that her new account escapes the criticisms put forth in Smith (1987, 1993), in Oaklander and Smith (1994) and elsewhere. I agree that her new theory escapes these criticisms, but I also believe there is a new set of criticisms that her theory does not escape.

Relevant to these criticisms is some recent work by William Lane Craig. Craig has made some important and positive contributions to the tensed theory of time in general (e.g., Craig 1996a,b, and has in 1996a criticized the tensed token-reflexive account in Smith (1993). I shall show at the end of this paper that Craig’s criticism is unsound as it stands, but can easily be reformulated in a sound way and, consequently, that the critique of the various versions of the tenseless theory of time needs be modified in a certain respect.

L. A. Paul argues there is a third and successful version of the tenseless theory of time, different than the token-reflexive version (which postulates truth conditions such as “simultaneously with the sentence-token S”) and the date—analysis version (which postulates

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truth conditions such as “occurs at May 1, 1999”). Paul agrees with Smith (1987, 1993) that these two standard versions of the tenseless theory of time, the token-reflexive theory and the date—analysis theory, are false. A brief review of some of the reasons why they are false will help show why Paul cannot appeal to either of these two standard tenseless theories to defend her new “sentence-type” tenseless theory against the criticisms I shall put forth. It will also show why the criticism of these two theories needs to incorporate a modification suggested in Craig (1996a), a point I shall discuss in Section 4.

One of the problems with the token-reflexive theory is that it implies there are non-equivalent truth conditions of the statements made (pro positions expressed) by two synonymous sentence-tokens. Suppose that a token U of “Jane is falling asleep” states a true proposition if and only if U is simultaneous with Jane falling asleep, and a simultaneous token V of this sentence states a true proposition if and only if V is simultaneous with Jane’s falling asleep. What is stated by the two simultaneous and synonymous tokens of “Jane is falling asleep” (the propositions they express) are identical or at least logically equivalent. (Naturally, we are assuming they are uttered in the same context, so that “Jane” refers to the same person in both tokenings.) We have the undesirable result that two simultaneous and synonymous tokens U and V of the sentence-type “Jane is falling asleep” state logically equivalent propositions that have truth conditions which are not logically equivalent; the truth conditions are not logically equivalent since it is possible for U to be uttered and V not to be uttered. The proposition expressed by the token U of “Jane is falling asleep” entails the proposition simultaneously expressed in the same con text by the token ,V of “Jane is falling asleep”, but U is simultaneous with Jane‘s falling asleep does not entail V is simultaneous with Jane‘s falling asleep. There is a possible world in which U is uttered while Jane is falling asleep, but in which V is not uttered. Likewise, it might have been the case that V is uttered and U not uttered.

Paul, like Tooley (1997), Craig (1995a,b), Mellor (1998) and others, are to be credited with insightfully reasoning that this critique of the token reflexive theory, or rather the longer version of it presented in Chapter 3 of Smith (1993) and in Smith (1987), suffices to refute the token-reflexive tenseless theory of time. Writing about Mellor’s token-reflexive theory in Mellor (1981), Tooley says: “Thus Quentin Smith, for example, argues that the truth conditions Mellor and others have offered generate the wrong truth-values in certain cases (Smith 1993, 72—7). Smith is certainly right that there is a problem that needs to be addressed . . .“ For similar reasons,

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Mellor (1998) rejected the token-reflexive theory presented in his Real Time (1981). Mellor writes: “In Real Time I defended the token-reflexive view that an A-proposition like ‘e is present’ is true at a B-time t if and only if a token of it — e.g., a statement of it, or someone’s belief in it — at t would be true. But Quentin Smith (1993, Chapter 3) and others have shown that this cannot cope with propositions like ‘there are no tokens now’, which can be true even though they can have no true tokens” (Mellor 1998, xi—xii).

However, while Mellor and Tooley can be credited with insightfully reasoning about the token-reflexive tenseless theory, some questions may be raised about the extent of their appreciation of the criticisms of the data-analysis tenseless theory of time. For example, after conceding the untenability of the token-reflexive theory, a concession based on arguments in Chapter 3 of Smith (1993), Mellor adopted a date-analysis theory in his Real Time II (1998). But he adopted the date-analysis theory without at tempting to respond to the criticisms of the date-analysis theory presented in Chapter 2 of Smith (1993) or in (Smith 1987). What does it mean that a philosopher abandons a theory due to criticisms presented in Chapter 3 of a certain book, but then proceeds to adopt a theory criticized in Chapter 2 of the same book, and to adopt this theory without attempting to address the criticisms directed against that theory in chapter 2? Did Mellor lack the space in his revision of his book to address the problems with the date- analysis theory? Or is Mellor suggesting the several arguments in Chapter 2 of Smith (1993) and in Smith (1987) again the date-analysis theory are self-evidently unsound and thereby do not need to be defended against? There is no apparent answer to such questions. Thus, I remain somewhat mystified as to why Mellor thinks the much-criticized date-analysis theory can be simply assumed (as he assumes it in Real Time II without any attempt at an argumentative defence of this theory.[1]

Tooley also responded in Mellor’s somewhat curious way to Smith (1993) in Tooley’s nonstandard version of the tensed theory of time (Tooley 1997, 246). After arguing that the considerations in Chapter 3 of Smith (1993) demonstrated the falsity of the token-reflexive theory of truth conditions, he proceeds to say it is a “straightforward matter” (Tooley 1997, 246), requiring no further argumentation, to substitute date analysis truth conditions for token-reflexive truth conditions and thereby have an adequate theory. Did he, perhaps, not have the opportunity to read Chapter 2 of Smith (1993), with time-constraints confining his reading to Chapter 3 and later chapters? Or did Tooley conclude the arguments in Chapter 2 of Smith (1993) are self-evidently unsound, not needing to be addressed?[2] It has seemed otherwise to B-theorists such as Oaklander

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(1994, forthcoming), Le Poidevin (1995, forthcoming), Smart (1993), Paul (1997) and Heather Dyke (forthcoming); they argue that the date-analysis theory is rendered at least prima facie untenable by the arguments in Smith (1993, Chapter 2) and that the B-theorist can no longer assume the date-analysis theory as if it is somehow “straightforward and self- evident’. These tenseless theorists wisely adopted the course of either abandoning the date-analysis theory or pursuing the project of developing a considerably modified, new and original version of the date-analysis theory.

It seems to me that the most plausible response to the problems with the date-analysis theory discussed in Smith (1993, Chapter 2; Smith, 1987) are given by L. A. Paul (1997) and William Lane Craig (1996a,b), since they recognize the date-analysis version of the tenseless theory of time is equally as unsalvageable as the token-reflexive version. In the following, I will briefly present a small number of the plethora of arguments that can be presented against the date-analysis theory.

The date-analysis version of the tenseless theory of time cannot give adequate accounts of the truth conditions of the statements made by tensed sentence-tokens. This is the case regardless of whether we adopt a reductionist (relational) theory of time or a substantivalist (absolute) theory of time.

According to the reductionist theory of time, an instantaneous time is a set containing an instantaneous event E and all other instantaneous events that are simultaneous with E. A time that is an extended interval contains an extended event or process E and all events or processes (or parts of events or processes) that are simultaneous with E. According to the date- analysis theory, if “Beth is waking up” is uttered some time from 12:00 p.m. to 12:01 p.m. on April 1, 1998, this utterance U states a truth if and only if the event of Beth’s waking up occurs at the time mentioned, some time between noon and 12:01 on April 1, 1998. If the reductionist theory of time is true, this time is the set of all events that are simultaneous with Beth’s waking up (it includes Beth’s waking up as well, since simultaneity is a reflexive relation). Call this set t. In the actual world, set t includes Beth’s waking up, the utterance U and the event of a certain ultraviolet ray x hitting the top of the Empire State Building, as well as numerous other simultaneous events. Since sets have their members essentially, set t does not exist in some possible world in which the utterance of “Beth is waking up” is simultaneous with the event of Beth waking up and all the other events in t except for the event of the relevant ultraviolet ray hitting the top of the Empire State Building. Since the sentence-token U of “Beth is waking up” is uttered simultaneously with Beth waking up in this possible

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world, the utterance U states something true in this world, even though the set t does not exist in this world. This shows that it is false that an utterance of “Beth is waking up” at time t states a truth if and only if Beth’s waking up occurs at t.

Similar problems arise on the substantivalist theory of time, where a time t is a particular that is logically independent of any events that occupy that time. There is some merely possible world w in which the substantival time t, which is actually occupied by the event of Beth’s waking up, is not occupied by this event and in which some other time, time t’, is occupied by this event and by the utterance of “Beth is waking up”. This is sufficient for the utterance to state something true in this possible world. Since the utterance states a truth in this world even though the event of Beth waking up is located at t’ rather than t, it is false that an utterance of “Beth is waking up” at time t states a truth if and only if Beth’s waking up occurs at t. Thus, the alleged truth conditions proposed by the date-analysis theory are not truth conditions.

It is also not the case (contra some arguments suggested in Oaklander 1994) that truth conditions are given by saying “The utterance U at t in the world w states a truth in w if and only if Beth’s falling asleep occurs at t in w”. Once the truth conditions are world-indexed, they have no bearing or an accidental bearing on the meaning of the sentence-utterance. To see this, note the peculiarity of world-indexed sentences. If the actual world. w includes the event of there being rain in Paris on June 1, 1914, it is necessarily true that w includes this event (but it is contingently true that w rather than some other possible world w’ is actual). If w includes this event and Beth’s waking up, then the utterance of “Beth is waking up” at t in w states a truth in the world w if and only if it rains in Paris on June 1, 1914 in w. Since the clause after the biconditional has no bearing on the meaning of the utterance of “Beth is waking tip” at t in w, despite the logical equivalence stated in the biconditional, world-indexing the truth conditions prevents sentences stating truth conditions from explaining or having a relevant bearing on the statement whose truth conditions are given. These are not ‘truth conditions’ in the intended and proper semantic sense of ‘truth conditions’.

L. A. Paul seeks to rescue the tenseless theory of time from these problems by offering a new theory of tenseless truth conditions. She argues that we should reject the underlying premise of both the token-reflexive and date-analysis versions of the tenseless theory of time, namely, the premise that truth condition analyses should give truth conditions for tokens of tensed sentence-types (or for the statements made by these tokens). She argues that we should instead give truth conditions for tensed sentence-types

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and that these truth conditions should mention a context for evaluating the sentence-type. Thus for any context c, the sentence-type ‘Beth is waking up’ is true with respect to c if and only if Beth is (tenselessly) waking up in c. This new version of the tenseless theory of time avoids the problems with the two standard versions of the tenseless theory, the token-reflexive theory and the date-analysis theory. The reason is that Paul avoids sentence-tokens and thus does not run into the above-discussed problems about the relations of sentence-tokens to times, events or other sentence-tokens.

To better appreciate this point, let us see why Paul is not correct when she says her theory is relevantly analogous to Richard Montague’s theory. In fact, Paul’s theory is more successful than Montague’s. Montague’s theory succumbs to one of the very criticisms that Paul’s theory escapes.

In the following paragraph, quoted from Montague (1974, 230), the symbols have these meanings:

A model for L = a pair á b, ái, jñ ñ, such that b is a Fregean interpretation for L and ái, jñ is a point of reference of b. Here i is the actual world and j is the actual context of use specified by the model (Montague 1974, 229).

Here we regard p as a possible point of reference. ... If áj, pñ and áY, pñ are tokens in L, then áj, pñ K-entails áY, pñ in L if and only if j, Y Î DS_L and, for every Fregean interpretation b for L, if áb, pñ is in K and j is a true sentence of L with respect to áb, pñ, then áb, qñ is in K and j is a true sentence of L with respect to áb, qñ. If j, Y Î DS_L, then the sentence-type j K-entails the sentence-type Y in L if and only if áj, pñ K-entails áY, pñ for every ordered pair p. (Montague 1974, 230)

This may seem similar at first glance to Paul’s theory, but this similarity quickly disappears once we inquire about Montague’s “possible point of reference p”. The “possible point of reference p” might seem to have the same role in Montague’s theory as the “the context c” in Paul’s theory.

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But there is at least one crucial difference. Montague calls possible con texts of use “points of reference” (Montague 1974, 98) and says “if the only indexical feature of [ language] L were the occurrence of tense operators, the points of reference might naturally be chosen as moments of time, regarded as possible moments of utterance” (Montague 1974, 98, my italics). Accordingly, Montague’s theory, unlike Paul’s, succumbs to one of the criticisms of the token-reflexive tenseless theory of time. Consider the sentence-type, “The time t = 0 at the big bang singularity is not a possible moment of utterance”. This sentence-type is true with respect to a context that includes such a singularity. But on Montague’s theory, this sentence- type comes out as an implicit logical contradiction; it is a contradiction that the possible moment of utterance t = 0 at the big bang singularity is not a possible moment of utterance. Since this sentence-type is true with respect to the time t = 0 of the big bang singularity, it follows that Montague’s theory (which implies this sentence-type is false of logical necessity) is false. By contrast, Paul’s theory escapes this criticism, since she does not characterize her contexts in terms of possible utterances or sentence-tokens.

Nonetheless, all is not well with Paul’s theory. For example, what does she mean by the expression “true with respect to a context c”? Paul states it does not mean that a true token of the type exists in the context c. Nor does it mean that the sentence-type is true simpliciter, since the sentence- type is false with respect to some contexts and true with respect to others. It seems that Paul is not giving truth conditions for the sentence-type, but truth-with-respect-to-a-context conditions.

Paul argues that ordinary tensed sentence-types do not have truth values simpliciter but merely truth values with respect to contexts. Paul writes that a sentence-type “must be evaluated with respect to its context (I will call this the ‘context of evaluation’) in order to determine its truth value. By ‘context of evaluation’ I mean an index that includes a possible world, a time, a place, and an agent (and anything else that is necessary to give the sentence a truth value)” (Paul 1997, 62, my emphasis). Paul’s theory is immediately falsified by sentence-types such as “there are no agents”, since this sentence-type is true with respect to worlds containing only inanimate matter. Paul’s contexts are partly defined as indexes that include agents, and this has the unpalatable consequence that possibly true sentence-types such as “there are no agents” are turned into logically necessary false hoods. But I will let this pass (Paul can easily eliminate “agents” from her definition of a context) and concentrate on the temporal issues. Similar considerations about possibly true sentence-types such as “only timeless

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abstract objects exist” may require the elimination of times and places from her definition of contexts.

It is somewhat misleading for Paul to say that a sentence-type “must be evaluated with respect to its context (I will call this the ‘context of evaluation’) in order to determine its truth value (1997, 62, my emphasis).” For example, there is no such thing as “its context” or “its truth value” for the sentence-type “Jane’s nightmares are presently occurring”. Rather, this sentence-type is true with respect to some of its contexts of evaluation (the contexts where she is having nightmares) and is false with respect to other contexts of evaluation (e.g., the contexts where she doesn’t exist or is not having nightmares). Of course, Paul is well aware of this point, but it is worth clarifying the needed terminology as precisely as possible.

But even with these various conceptual and terminological problems fixed, can Paul’s theory account for the tensed aspect of ordinary sentence- types? Consider the sentence-type, “Jane’s nightmares are presently occur ring”. Suppose it is now 11 p.m., April 3, 1998 and that Jane is now having nightmares. The sentence-type “Jane’s nightmares are presently occurring” is now true with respect to this context; that is, the sentence-type “Jane’s nightmares are presently occurring” is (present tense) true with respect to a context that includes the present time, 11 p.m., April 3, 1998 and an instance (token) of the event-type Jane having nightmares.

But the sentence-type “Jane’s nightmares are presently occurring” can not be true with respect to each context in which is located an event-token of Jane’s having nightmares. (Event-types are universals; event-tokens are nonrepeatable particulars.) For suppose a token of the event-type Jane having nightmares occurred last night at 11 p.m. The sentence-type “Jane’s nightmares are presently occurring” is not now true with respect to last night, since last night is no longer presently occurring, and thus this con text fails to include a condition (presently occurring) specified by the sentence-type.

It is at this juncture that we first glimpse the problem with Paul’s ori ginal version of the new tenseless theory of time. Paul says the context of evaluation includes “a time” and anything else necessary to give the present tense sentence-type a truth value. As we have seen, the present tense sentence-type, “Jane’s nightmares are presently occurring”, is now true with respect to the present time, 11 p.m., April 3, and now false with respect to a past time, e.g., last night, 11 p.m., April 2. What else (besides the times 11 p.m., April 3 and 11 p.m., April 2, and some tokens of the event-type Jane having nightmares) is necessary to give the sentence-type “Jane’s nightmares are presently occurring” the value of being now true

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with respect to 11 p.m., April 3 and the value of being now false with respect to 11 p.m., April 2?

Paul allows that “anything else that is necessary to give the sentence a truth value” should be added to the contexts. But here it seems that it is necessary to add some irreducibly tensed conditions, i.e., the exemplification of some A-properties, such as the condition that 11 p.m., April 3 exemplifies presentness and that 11 p.m., April 2 exemplifies pastness.[3]

The sentence-type, “Jane’s nightmares are presently occurring”, is now true with respect to the context c that includes 11 p.m., April 3 and a token of the event-type Jane having nightmares, since c also includes the exemplification of the A-property of presentness by this time and event- token. Since 11 p.m., April 3 is present, the token of the event-type Jane having nightmares that is located at this time also has presentness. This ex plains why the sentence-type “Jane’s nightmares are presently occurring” is (present tense) true with respect to the context, 11 p.m., April 3.

Since 11 p.m., April 2 is not present, the token of the event-type Jane having nightmares that is located at this time does not have the A-property of presentness, and this is why the sentence-type “Jane’s nightmares are presently occurring” is now false with respect to the context, 11 p.m., April 2. The event-token of Jane having nightmares that is located at 11 p.m., April 2, and this time itself, have the A-property of pastness.

The last few remarks are not making B-statements, such as the state ment that Jane’s nightmares are present at 11 p.m., April 3 (which just means that Jane’s nightmares are simultaneous with 11 p.m., April 3) or the trivial B-statement that 11 p.m. is present at 11 p.m.[4] Rather, it is a statement of an A-proposition, specifically, a proposition that ascribes the A-property of presentness, the proposition that 11 p.m., April 3 and Jane ‘s nightmares are present. (For a detailed explanation and critical discussion of the A-theorist’s account of structure and parts of propositions, see Graham Nerlich’s fine essay (1998).)

The sentence-type “Jane’s nightmares are presently occurring” is (present tense) false with respect to the context c’ that includes 11 p.m., April 2, Jane, and her nightmares, since this context does not include her nightmares having presentness. The sentence-type, “Jane’s nightmares are presently occurring”, Was true with respect to the context c’ which includes 11 p.m., April 2. The sentence-type “Jane’s nightmares are presently occurring”, was true with respect to c’ since c’ includes a time that meets all the conditions except for the fact that the time of the context is not present; the time is instead past or no longer present.

However, the different sentence-type, “Jane was having nightmares”, is (present tense) true with respect to the context c’ since c’ includes a

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time that is now past, viz., 11 p.m., April 2. The sentence-type, “Jane was having nightmares”, ascribes the A-property of pastness to an event-token of Jane having nightmares, and this sentence-type is now true with respect to the April 2nd context c’, since c’ includes a past event of this type.

3. POSSIBLE WAYS TO DEFEND THE SENTENCE-TYPE VERSION OF THE TENSELESS THEORY OF TIME

Perhaps a defender of Paul’s theory can explain these semantic facts in tenseless terms by saying that the truth-values of the tensed sentence-types are possessed tenselessly. The defender could say that “Jane’s nightmares are presently occurring” is (tenselessly) true with respect to 11 p.m., April 3 and also is (tenselessly) true with respect to 11 p.m., April 2.

The problem with this move is that Paul is giving a semantics of natural language, not the semantics of an artificial language, and natural language includes the tensed truth predicates “was true”, “is true” and “will be true”. Part of the linguistic data that Paul needs to explain is that there are complex, natural language sentence-types such as “The sentence ‘Jane’s nightmares are presently occurring’ is now true with respect to 11 p.m., April 3 and is not now true, but was true, with respect to 11 p.m., April 2.” Specifically, natural language includes tensed metasentence-types (tensed sentence-types about other tensed sentence-types) as well as other sorts of tensed sentence-types. Consequently, if Paul’s semantics for natural lan guage is inconsistent with some natural language metasentence-types, it is inconsistent with natural language.

Paul’s semantics for natural language need not be a part of natural language and may include only tenseless sentences and tenseless truth pre dications. But her sentences stating tenseless truth conditions for natural language sentences must have consequences for natural language that are consistent with the truth values and entailment relations that natural language sentences possess. Her sentences that state truth conditions cannot imply (for example) that “The storm is now occurring” is not logically equivalent to “The storm is occurring now”. Likewise, her tenseless truth condition sentences must preserve the right truth values for sentence-types such as “The sentence ‘Jane’s nightmares are presently occurring’ is now true with respect to 11 p.m., April 3 and is not now true, but was true, with respect to 11 p.m., April 2.”

Perhaps this could be done by saying that the sentence-type, “Jane’s nightmares are presently occurring”, is (tenselessly) true with respect to the context c (Jane having nightmares at 11 p.m., April 3) if and only if the time of evaluating this sentence-type is simultaneous with the time

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included in context c. The sentence-type “Jane’s nightmares are presently occurring” is (tenselessly) false with respect to the different context c’ (Jane having nightmares at 11 p.m., April 2) if the time of evaluating this sentence-type is later than the time included in c’. Further, “Jane’s nightmares are presently occurring” is (tenselessly) true with respect to c’ if the time of its evaluation is simultaneous with the time included in c’.

But now we have a different truth-conditional theory than Paul’s; we now have a theory of the truth conditions of the evaluation of a sentence- type with respect to contexts, not a theory of the truth conditions of the sentence-type that is evaluated with respect to contexts. An evaluation of a sentence-type is a mental event-token. I grasp a sentence-type, engage in the mental act of evaluating the sentence-type with respect to a context, and the result of this mental activity is an evaluation. The evaluation is a mental event-token (a belief) that has the truth value of true or false; this belief can be expressed by a sentence-token, such as the inscribed sentence-token “The sentence-type S is true with respect to the context c.”[5]

If Paul’s theory is changed in this manner to accommodate the problems I mentioned, then the original intent of her new and “third” version of the tenseless theory of time is lost. With this change to her theory, “the time of the evaluation of the sentence-type” plays the same logical role as “the time at which the token of the sentence-type occurs” and this not only vitiates Paul’s project of formulating truth condition sentences that do not refer to tokens (or their logical analogues, such as evaluations of a sentence- type), but also encounters the standard problems of the token-reflexive and date-analysis versions of the tenseless theory of time.

For example, suppose the time of the evaluation of “Jane’s nightmares are presently occurring” is 11 p.m., April 3, 1998. This is the time at which the act of evaluating occurs. Suppose further that this evaluation is an evaluation of “Jane’s nightmares are presently occurring” with respect to the time, 11 p.m., April 3, 1998. Let us call this particular evaluation “E”. The truth condition sentence would then be as follows. The evaluation E is (tenselessly) true if and only if Jane is (tenselessly) having nightmares at 11 p.m., April 3, 1998.

In general, the rule would be that (a) if an evaluation E is located at a certain time t (e.g., 11 p.m., April 3, 1998), and (b) if the evaluation E is an evaluation of a sentence-type with respect to the time at which E is located and (c) if the sentence-type is present tensed and says only that an event x “is present” or “is presently occurring”, etc., then (d) E is (tenselessly) true if and only if the event x is located at the time t.

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I shall show this theory of truth conditions is false. I shall use merely an example in which we assume the reductionist or relational theory of time, i.e., that a time is a set of simultaneous events. This example is analogous to the examples used to refute the date-analysis version of the tenseless theory of time, e.g., the date-analysis version in Mellor’s Real Time II. In the actual world w, let us suppose, Jane is having nightmares at the time or set of simultaneous events t; the evaluation E of “Jane’s nightmares are presently occurring” is also located at t. E is an evaluation of this sentence-type with respect to the time at which E is located. This makes the evaluation E true in the actual world w. But the location of the nightmares at the time t is not necessary for E‘s truth. There is a merely possible world w in which both E and Jane’s nightmares are occurring simultaneously, but in which E and Jane’s nightmares belong to some other set t* of simultaneous events, say a set t* that is just like the actual set t except that it does not include a leaf falling to the ground at a certain spot in Chapel Hill, North Carolina. Since E is located at t* and since E is an evaluation of “Jane’s nightmares are presently occurring” with respect to the time at which E is located, it follows that E is true. But this violates the above-stated truth conditions, which are that E is true if and only if Jane’s nightmares occur at t.

If we add a world-indexed condition to deal with this problem, we run into the same problems as does Oaklander’s revision of the date-analysis theory. Consider this truth condition sentence: The evaluation E is (tenselessly) true in world w if and only if Jane is (tenselessly) having nightmares at 11 p.m., April 3, 1998 in world w. Since we are talking about truths in a world w (world-indexed truths) the otherwise contingent truths are transformed into necessary truths. (It is contingently true that the world w containing Jane’s nightmares is actual, but it is necessarily true that w contains Jane’s nightmares.) Consider the following truth condition sentence: The evaluation E is (tenselessly) true in world w if and only if the Earth formed more than five billion years after the big bang in w. This truth condition sentence is necessarily true, even though it is merely a con tingent truth that our world w is actual. The following two world-indexed sentences are logically equivalent:

(2) The earth formed more than 5 billion years later than the big bang in world w.

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Since (2) can be substituted salva veritate for (1) in the truth-condition sentence “The evaluation E is (tenselessly) true in world w if and only if Jane has nightmares at 11 p.m., April 3, 1998 in world w”, it follows that world-indexed truth conditions of this sort are not truth conditions in the sense relevant to a semantics of natural language.

If we change Paul’s theory in a different way, along the lines of the token-reflexive version of the tenseless theory of time, then we will run into problems analogous to those that plague the token-reflexive theory. Suppose the evalution E occurs in the context c. We may say that the evaluation E of the sentence-type “Jane’s nightmares are presently occur ring” with respect to the context c is (tenselessly) true if and only if E is simultaneous with Jane‘s nightmares. Note that the sentence-type “Jane’s nightmares are presently occurring” is synonymous with the sentence-type “Jane’s nightmares are occurring presently”. Let E* be an evaluation of this second sentence-type, such that E* also occurs in context c. The relevant truth conditions for an evaluation E* of this second sentence-type would be: The evaluation E* of the sentence-type “Jane’s nightmares are occurring presently” with respect to the context c is (tenselessly) true if and only if E* is simultaneous with Jane ‘is’ nightmares. In this example, E and are simultaneous. The problem is that “E is simultaneous with Jane’s nightmares” is neither entailed nor entailed by E* is simultaneous with Jane’s nightmares”. (I can evaluate one sentence-type without evaluating the other.) However, these two clauses about E and E* allegedly give truth conditions for simultaneous evaluations of two synonymous sentence-types with respect to the same context c. An adequate truth condition semantics requires at a minimum that the two truth condition clauses be logically equivalent. (If we world-index the truth conditions, then we encounter the same problem we encountered with the date-analysis theory, viz., that the clauses after the biconditional become semantically irrelevant to the clauses before the biconditional.)

In summary, Paul’s sentence-type version of the tenseless theory of time faces unique problems of its own, and if it is altered to become similar to a date-analysis or token-reflexive version of the tenseless theory of time, it faces the problems these two versions face. This suggests that the detenser’s project of giving tenseless truth conditions for tensed sentence-types, tensed sentence-tokens, or the statements made (propositions expressed) by tensed sentence-tokens, has yet to meet with success

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4. CRAIG’S AND LE POIDEVIN’S CRITIQUE OF TENSED TOKEN-REFLEXIVE THEORIES

At this point, we need to make some clarifications based on some important criticisms Craig (1996a) and Le Poidevin (1995) have made of the account in Smith (1993, 98—105). Robin La Poidevin (1995) writes:

Smith spends some time demolishing the tenseless token-reflexive account, but he has to tread carefully, for it is actually part of his own analysis. I an not sure he always avoids inconsistency here. On page 83 he says that what is expressed by a true utterance such as ‘The forest is now burning’ would have been true even if the statement (sentence-token) had never been uttered. But on Smith’s own account, part of what is asserted concerns the utterance, and so cannot be true in a world where the utterance does not take place. (Le Poidevin 1995, 334)

I see the potential danger, but in the account I offered, part of what is asserted (part of what the expressed proposition includes or ascribes) does not refer to, ascribe, or in any way concern the utterance, so the proposi tion asserted by the utterance could be true in a possible world where the utterance does not take place. (See Smith 1993, 105-110).

Nonetheless, Le Poidevin is correct that I need to tread more carefully, for I did argue that tensed sentence-tokens (as distinct from the proposi tions they express) have tensed token-reflexive truth conditions. My tensed token-reflexive theory does run into problems. In (1993, 98—105), I argued that tensed sentence-tokens have token-reflexive tensed truth conditions; for example, I argued that the token U of “John is dead” is presently true if and only if U and John’s being dead are both present. William Lane Craig argues that this account succumbs to the very criticism I levelled at the tenseless token-reflexive theory in Chapter 3 of Smith (1993). Craig writes:

Smith’s own token-reflexive analysis falls prey to the same objection he urged against Mellor’s analysis. Let U and V be simultaneous tokens of ‘John is dead’. It follows from Smith’s analysis that

But while U and V state the same fact and are mutually entailing, it is not the case that the sentences (‘U’ and ‘V’) giving their truth conditions state the same fact and are materially equivalent. Therefore, they cannot be the truth conditions of U and V. (1996a, 18)

Craig’s criticism is not quite on the mark, since it is self-contradictory. If U and V occur simultaneously, ‘U’ and ‘V’ are materially equivalent. Craig is here assuming the biçonditional in truth condition sentences states

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a material equivalence. But the equivalence stated in truth condition sentences cannot be material, since it is a true material equivalence statement that a token T of “Aristotle is now dead” is true if and only if the radius of a proton is 10^-15 meters, and yet the latter clause has no semantic relevance to the token T. The biconditional in truth condition sentences states a logical equivalence. The reason my account in (1993, 98-105) is false is that the two simultaneous tokens U and V state identical or logically equivalent propositions and yet the sentences ‘U’ and ‘V’ giving their truth conditions state merely materially equivalent propositions.

If we substitute “logically equivalent” for “materially equivalent”, then the passage quoted from Craig’s article is more nearly on the mark. Craig concludes that “tokens as such are not truth-bearers and can be called true or false only insofar as what they express is true or false” (1996a, 18). This seems to be the correct conclusion of my reformulation of Craig’s criticism of the tensed token-reflexive theory I presented in (1993, 98-105). The correct theory should be that what is stated by the tokens U and V, the proposition John is dead, is presently true if and only if John’s being dead is present. Accordingly, the internal, tenseless criticisms of the date- analysis and token-reflexive tenseless theories of time I offered in (1993) need to be reformulated in terms of what tokens state (the propositions they express). This can easily be done. For example, the sentence “In both of these worlds, U is true, since U is simultaneous with Henry’s illness” (Smith 1993, 35, my italics) should be rephrased as “In both of these worlds, U states something true, since U is simultaneous with Henry’s illness”. In fact, this reformulation has already been done. I presented the criticism of the token-reflexive and date-analysis tenseless theories in Section 2 of this paper in terms of the truth value of what the tokens stated (the propositions they expressed), rather than in terms of the truth value of the tokens.

If we make this modification, then it seems we have in hand sound arguments against the three versions of the tenseless theory of time, the token-reflexive version, the date analysis version and the sentence-type version. We could agree with Craig that “The B-theory of tense and time, though still widely held, is a theory in retreat” (Craig 1996, 249).

Nonetheless, we need to acknowledge that B-theorists such as Oak lander (forthcoming) and Le Poidevin (forthcoming) are continuing to develop novel defenses of “the new tenseless theory of time” and novel cri ticisms of the tensed theory, and their new arguments need to be addressed by A-theorists. Furthermore, some already published criticisms of the tensed theory of time, such as Graham Nerlich’s penetrating essay “Time as Space Time” (1998) and Oaklander’s equally forceful “McTaggart’s

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Paradox and Smith’s Tensed Theory of Time” (1996) require responses before the A-theorist can say the tensed theory of time is fully justified as it stands.[6]

REFERENCES

Craig, W. L.: 1996a, ‘Tense and the New B-Theory of Language’, Philosophy 71, 5—26.

Craig, W. L.: 1996b, ‘The New B-Theory’s Tu Quoque Argument’, Synthese 107, 249—269.

Craig, W. L.: 1997, ‘Is Presentness a Property?’, American Philosophical Quarterly 34, 27—40.

Craig, W. L.: forthcoming, ‘Presentism: An Account and Defence’, in A. Jokic and Q. Smith (eds.), Time, Tense and Reference.

Dyke, H.: forthcoming, ‘Time, Tense and Meaning: A Tenseless Account’, in A. Jokic and Q. Smith (eds.), Time, Tense and Reference.

Le Poidevin, R.: 1991, Change, Cause and Contradiction. Macmillan, London. Le Poidevin, R.: 1995, ‘Review of Quentin Smith’s Language and Time’, in The Philosophical Review 104, 333—335.

Le Poidevin, R.: 1998, ‘Review of Michael Tooley’s Time, Tense and Causation’, British Journal for the Philosophy of Science 49, 365—3 69.

Le Poidevin, R.: forthcoming, ‘Why Tenses Need Real Times’, in A. Jokic and Q. Smith (eds.), Time, Tense and Reference.

Nerlich, G.: 1998, ‘Time As Spacetime’, in Robin Le Poidevin (ed.), Questions of Time and Tense. Clarendon Press, Oxford, pp. 119—34.

Oaklander, L. N.: 1984, Temporal Relations and Temporal Becoming. University Press of America, Lanham.

Oaklander, L. N.: 1994, ‘A Defence of the New Tenseless Theory of Time’, in L. Nathan Oaklander and Quentin Smith (eds.), The New Theory of Time. Yale University Press, New Haven.

Oaldander, L. N.: 1996, ‘McTaggart’s Paradox and Smith’s Tensed Theory of Time’, Synthese 107, 205—221.

Oaklander, L. N.: 1999, ‘Review of Michael Tooley’s Time, Tense and Causation’, Mind 108, 407—13.

Oaklander, L. N.: forthcoming, ‘The Metaphysics of Time and Tense’, in A. Jokic and Q. Smith (eds.), Time, Tense and Reference.

Oaklander, L. N. and Smith, Q. (eds.): 1994, The New Theory of Time. Yale University Press, New Haven.

Paul, L. A.: 1997, ‘Truth Conditions of Tensed Sentence Types’, Synthese 111, 53—71. Smart, J. J. C.: 1980, ‘Time and Becoming’, in Peter van Inwegen (ed., Time and Cause. Reidel, Boston.

Smart, J. J. C.: 1993, Private communication reproduced in part in (Smith 1993). Smith, Q.: 1986, ‘The Infinite Regress of Temporal Attributions’, The Southern Journal of Philosophy 24, 383—96. Reprinted in L. Nathan Oaklander and Quentin Smith (eds.), The New Theory of Time. Yale University Press, New Haven, 1994.

Smith, Q.: 1987, ‘Problems with the New Tenseless Theory of Time’, Philosophical Studies 52, 371—92. Reprinted in L. Nathan Oaklander and Quentin Smith (eds.), The New Theory of Time. Yale University Press, New Haven, 1994.

Smith, Q.: 1998, ‘Absolute Simultaneity and the Infinity of Time’, in Robin Le Poidevin (ed), Questions of Time and Tense. Clarendon Press, Oxford, pp. 135—83.

Smith, Q.: 1999, ‘Review of Michael Tooley’s Time, Tense and Causation’, The Philosophical Review 108, 123—7.

Smith, Q.: forthcoming, ‘Reference to the Past and Future’, in A. Jokic and Q. Smith (eds.), Time, Tense and Reference.

Stone, A.: 1997, ‘A Program Model of Becoming’, Physics Essays 10, 150—63.

Tooley, M.: forthcoming, ‘Basic Tensed Sentences and their Analyses’, in A. Jokic and Q. Smith (eds.), Time, Tense and Reference.

[1] In (1958, 34), MelIor writes that “A-theorists too need times-A-times-to give A- propositions A-truthmakers. Thus, if we let t be either an A- or a B-time, we can all agree to replace the token-reflexive theory of #2 with:

any A-proposition ‘P’ about any event e is made true at any t by t’s being as much earlier or later than e as ‘P’ says the present is than e.”

In response to Mellor’s theory, I would note that one problem is that the token-reflexive theory discussed In section #2 of Mellor (1998) was a theory of truth conditions (and thus used a biconditional, “if and only if”, (Mellor, 1998, 31)), and it is invalid to conclude that a theory stating merely a sufficient condition (“is made true by”) can “replace” a theory of truth conditions. Secondly, the mention of any time t in Mellor’s above-quoted “sufficient condition statement” renders Mellor’s theory inadequate as a theory of sufficient conditions for truth, as indicated on pages 33—63 of Smith (1993).

[2] It should be added that Tooley has since responded at length to some of these argu ments in a Philosophy of Time Society session in Chicago, 1998. I am not convinced these responses are sound, but this debate will take us beyond the proper subject-matter of the present paper. For a general indication of how Tooley might respond to my criticisms, see my review of his Time, Tense and Causation in (Smith 1998c). I think, however, it is worth reiterating my point at the Philosophy of Time Society session that there is a more important feature of Tooley’s book than this particular area of disagreement between us, namely, Tooley’s plausible and well-argued development of a “modification of STR” that takes into account the EPR correlations and argues for absolute simultaneity relations, that obtain in absolute, substantial space. Tooley is able to establish by purely physical means what I endeavoured to establish by means of the metaphysical assumption that abstract objects exist in time (Smith 1998). I believe a metaphysical argument is sufficient, but I welcome the news from Anthony Stone: In a well-argued essay in Physics Letters, Stone derives my “metaphysical time” from purely physical premises; he concludes: “If desired, kairos [ could therefore be identified with Smith’s metaphysical time” (Stone 1997, 159). William Lane Craig, Craig Callender, Robert Weingard, Richard Swinburne, John Lucas and an increasing number of other philosophers are advocating post-Einsteinian theories of absolute simultaneity. One of the best versions to date is Tooley’s (1997, chapter eleven).

[3] Some defenders of the tensed theory of time deny that the ontological correlates of tenses are A-properties of pastness, presentness and futurity. However, these defenders of the tensed theory, who typically follow Prior, have made no attempt to specify the ontological correlates of tenses. Since they also reject the tenseless theory of time, it seems that they leave us with a universe that is devoid of temporal features or structures, i.e., is timeless. These disciples of Prior have offered no positive ontological theory that is designed to replace the B-relation theory or A-property theory. Until they do so, why should B-theorists and A-property theorists pay attention to their so-called “alternatives” to the B-relation theory and the A-property theory? When these Priorities write that tenses do not refer to B-times or ascribe A-properties but instead “tell us when substances possess their properties”, one may respond that vague slogans belong to political campaigns, not philosophy. In fact, a close examination of these Prior-based philosophies indicate their statements have at least one of three characteristics: they are either vacuous, unintelligible or self-contradictory. This problem of the “lack of ontology” of Prior-based theories was originally noted by Oaklander (1984, 90—92), and later elaborated by Smith (1986; 1993, 158—169; forthcoming) and Tooley (1997, 165—70, 232—8). Craig (1997) is sympathetic with these Prior-based theories but makes an advance over the standard Prior-based theories by arguing that the present tense has a “mode of exemplification”, viz, presently exem plifies, for its ontic correlate, which he (forthcoming) allows may be called an “unusual property”. Craig seems to be the first tenser to make some progress with supplying the Prior-type theories with an ontology.

[4] Tooley (1997) bravely argues that “Event E is present at 11 p.m.” is not equivalent to “Event B occurs simultaneously with 11 p.m.” but instead expresses the proposition that Event E is actual as of]] p.m., where E’s being actual as of]] p.m., is a tenseless fact or state of affairs. However, I argue in Smith (1 998b) that Tooley’s primitive, unanalyzable concept of actuality as of a time is not coherent. Robin Le Poidevin (1998), L. Nathan Oaklander (1999; forthcoming), D. H. Mellor (1998, 81—83) and William Lane Craig (forthcoming) also argue that Tooley’s primitive concept of äötuality as of a time is in coherent. For example, Le Poidevin writes of Tooley’s concept: “Actually, I find the notion of actuality-at-a-time somewhat baffling” (Le Poidevin, 1999, 368). And Oaklander writes that Tooley’s assertion that there is a primitive distinction between actuality simpliciter and actuality as of a time “strikes me as obfuscating” (Oaklander 1999, 412). While Tooley should be conm for his bravery and originality, it would be interesting to see how he can respond to all these criticisms. (Note that a partial response to a few of the criticisms is made in Tooley (forthcoming).)

[5] This ontological characterization of evaluations is mine, not Paul’s. Paul’s theory of tensed sentences and indexicals, like Kaplan’s, seems heavy on the formal side and light on the metaphysical side. I would ask Paul these questions: Are sentence-types universals, as conceived in the platonic realist tradition (e.g., of Butchvarov, Oaklander, Bealer and Tooley)? Paul cannot conceive sentence-types nominalistically as n-tuples of sentence- tokens, for then Paul’s theory implies some of the problems with the token-reflexive tenseless theory of time that she is endeavouring to escape. Accordingly, Paul seems to be committed implicitly to the thesis that the tenseless theory of time is true only if platonic realism is true. (I am not troubled by platonic realism; I argued for platonic realism in (Smith 1993)).

A second question concerns Paul’s “contexts”. What is a context? For example, is it a possible world in the Adams-Plantinga sense, a possible world in David Lewis’ sense, a possible world in Gideon Rosen’s sense, or is it something else altogether?

A third question is about “evaluations”. Paul leaves the notion of evaluation undefined, much as it is treated in formal semantics. But in a metaphysical theory of time, we need this notion to be ontically clarified. Is an evaluation a mental event? Or is it a timelessly existing triad consisting of a sentence-type T, a context C, and a truth value V(T, C, V)? Or does it have some other ontological status? In this paper, I treat evaluations as mental events, since I find other ways of analyzing them metaphysically suspect.

[6] I thank a referee for Synthese for helpful suggestions about how to improve this paper.