Draft of a paper that appeared in Synthese 129 (2001) 405-411
Smith on Times and Tokens
By Joshua M. Mozersky
Department of Philosophy
University of Toronto
Toronto, Ontario, Canada M5S 1A1
e-mail: mozersky@chass.utoronto.ca
Tel.: (416) 531-7384
Fax: (416) 978-8703
ABSTRACT
In this essay I respond to Quentin Smith’s charge that ‘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’ (Smith 1999, 236). His argument is based
on an analysis of certain counterfactual situations that is at odds with the date-analysis
account of language and hence succeeds only in begging the question against that theory.
To anticipate: his argument fails if one allows that temporal indexicals such as ‘now’
rigidly designate their time of utterance, something the date-analyst can happily admit
whether she holds an absolute or relational metaphysics of time.
Times, Types and Tokens
0. INTRODUCTION
In my (2000) I defend a version of the date-analysis theory of time. This is a tenseless or
B-theory of time according to which the truth conditions of tensed sentences consist of
tenseless B-series relations between events and times. So, for example, when one says, at
t, ‘the movie starts now’, one’s utterance is true if and only if the movie referred to starts
at t. Besides avoiding tensed or A-series properties this theory combines nicely with
recent work on indexicals (Perry 1977, Kaplan 1989) that suggests ‘now’, ‘then’ and
other tensed expressions are terms whose contribution to propositional content is purely
referential (i.e. they contribute only a time not a sense to a proposition). I also argued
that this view has the resources to respond to the thoughtful and subtle criticisms raised
by Quentin Smith (see Smith 1987).
Smith has, however, renewed his attack on the date-analysis view, arguing that
‘the date-analysis version of the tenseless theory of time is equally as unsalvageable as
the token-reflexive version’ (Smith 1999, 236). This recent article raises some objections
that any defender of the date-analysis theory ought to consider. In particular, Smith
argues that the date-analysis theory is semantically implausible:
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 (Smith 1999, 236).
I think that Smith’s arguments are unconvincing in both cases. I will take them up in
turn.
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1. REDUCTIONIST TIME AND THE DATE-ANALYSIS THEORY
‘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’
(Smith 1999, 236). Smith asks us to consider an utterance, U, of ‘Beth is waking up’ that
occurs at some time, t. U is true, according to the date-analysis view, if and only if
Beth’s waking up is simultaneous with t. But according to reductionist time, t is the set
of events simultaneous with Beth’s waking up (this set, of course, includes her waking
up). This is, needless to say, a very large set, including, to use Smith’s example, ‘a
certain ultraviolet ray, x, hitting the top of the Empire State Building’ (Smith 1999, 236).
However:
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 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 (Smith 1999, 236-7).
This argument, persuasive as it may seem at first glance, misses the mark.
To see why, let us more closely analyze Smith’s reasoning. I offer the following
reconstruction of the argument in the passage above:
(1) Sets have their members essentially;
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(2) Set t consists of all the events simultaneous with Beth’s waking up in our world
(including her waking up and the utterance, U, of ‘Beth is waking up’);
(3) Some merely possible world, w, has no set identical to t. However, w does
contain a set just like t except that it lacks the event of x hitting the Empire State
Building;
(4) Therefore, in w, t does not exist (from 1-3);
(5) Since the utterance, U, in w of ‘Beth is waking up’ is simultaneous with Beth’s
waking up, U is true in w;
(6) Therefore, it is false that U is true if and only if Beth wakes at t (from 4 and 5).
Let t’ denote the set in w that is identical to t except for the absence of x’s collision with
the Empire State Building. Smith’s argument can be put succinctly: since U is true if
Beth’s waking up is simultaneous with t or if Beth’s waking up is simultaneous with t’, U
cannot be true if and only if Beth’s waking up is simultaneous with t. Therefore, the dateanalysis theory is false.
It seems to me that premises (1)-(3) above are unassailable. At the very least,
there is no harm in accepting them and severe implausibility attaches to any attempts to
deny them within the confines of relational time. Accordingly, I accept Smith’s subconclusion, (4), that there is no time t in w. I do, however, wish to take issue with
premise (5), though not because I think it is false that the simultaneity of the utterance
‘Beth is waking up’ and Beth’s waking up is sufficient for the truth of the utterance in w.
Rather, I disagree that the utterance in w is identical to U.
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U is, let us recall, a token, that occurs in our world at t and is simultaneous with
Beth’s awakening. One of the obvious semantic properties of U is that it is in the present
tense. Now consider the following bicondtionals:
(7) ‘Beth is waking up’ said at t is true iff Beth’s waking up is simultaneous with t.
(8) ‘Beth is now waking up’ said at t is true iff Beth’s waking up is simultaneous with
t.
I think that each of these is obviously correct. They certainly follow from the dateanalysis view of time. If (7) and (8) are both true, then utterances of ‘Beth is waking up’
(where ‘is’ is in the present tense) and ‘Beth is now waking up’ are logically equivalent.
This is, as I (2000) argue, a strength of the date-analysis theory for it reveals that
sentences such as U designate their time of utterance which is important for otherwise
there would be no way for the hearer of U to conclude that the speaker is referring to the
awakening of Beth that is simultaneous with U rather than her awakening the day before,
or after.1
So, according to the date-analysis theory of time, uses of the present tense copula
refer to their time of utterance (this is why the truth conditions of present tense sentences
are relations between times and events). Moreover, since ‘is’ (present tense) and ‘is now’
are semantically equivalent, and since ‘now’ directly refers to its time of utterance, it
follows that uses of the present tense copula rigidly designate their time of utterance.
After all, if the only function of ‘now’ is to introduce a time into a proposition,2 then
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‘now’ in effect names a time and as Kripke (1980) demonstrates, names are rigid
designators. Therefore, U in part rigidly designates its time of utterance.
But how, then, can U, a particular token that occurs at t, exist in w if t doesn’t
exist in w? A sentence token that rigidly designates its time of occurrence cannot be
identified with a token, in w, that occurs at, and hence rigidly designates, another time.
There might very well be a token of sentence type U that occurs at t’ and that refers to
Beth’s awakening at t’. But this token occurs at a difference time than U and hence is a
different utterance. Consider a similar case in which we consider not two worlds but two
times, t and t*, in our own world. A token of ‘Beth is waking up’ that occurs at t is
simply not the same token as that which occurs at t*. Why should we conclude, as Smith
does, that when we move to the trans-world case that the token, U, that occurs at t is the
same as the token that occurs at t’? We shouldn’t.
The reason why U and its w counterpart, call it U’, are each true is that they in
fact make different claims. U, since it occurs at t, is true if and only if Beth awakens at t.
U’, since it occurs at t’, is true if and only if Beth awakens at t’. So it is clear that the two
utterances have different truth conditions. Therefore, each utterance expresses a different
proposition; in short, they differ in semantic content. That is why U and U’ are different
tokens. I conclude that the date-analysis theory of temporal language is consistent with a
relational metaphysics of time. Reductionist time can be tenseless time; at least Smith
hasn’t given us any reason to think otherwise.
2. SUBSTANTIVALIST TIME AND THE DATE-ANALYSIS THEORY
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I will follow Smith’s definition of absolute time, according to which ‘a time t is a
particular that is logically independent of any events that occupy that time’ (Smith 1999,
237). He argues that
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, 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 than an utterance of ‘Beth is
waking up’ at time t states a truth if and only if Beth’s waking up occurs at
t (Smith 1999, 237).
This argument is formally similar to that considered in section 1 above, so there is no
need to reconstruct it here. It is worth taking a moment to indicate how it falls prey to a
similar rebuttal.
In w, Smith argues, Beth’s awakening and U both occur at t’ rather than t. Let e
denote Beth’s awakening in our world. Therefore, e occurs at t. But in w, e occurs at t’,
as does U. But of course, according to the date-analysis theory, it is not in fact U that
occurs at t’ but some other token, U’, of the same sentence type. Therefore, the token
under consideration in our world has the simultaneity of e and t as its truth conditions, the
token in w has the simultaneity of e and t’ as its truth conditions and there is no reason to
suppose that there is one and the same token under consideration here.
Moreover, one could plausibly deny that e exists in w. After all, in w Beth wakes
up at a different time than she does in our world. Why, then, conclude that this is the
same event as that in the actual world? If we limit ourselves to our world, we know that
Beth waking up at t and Beth waking up at a later time, t*, are not the same event. It is
hard to see why Beth’s waking up at t in our world and at t’ in w should be considered
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one event rather than two. If this is correct, then w contains neither U nor e and so can
hardly be used to show that it is incorrect to say that U is true if and only if e is
simultaneous with t.
The point concerning trans-world identity of events is, however, weaker than the
argument against identifying U and U’. After all, one might want to follow Davidson
(1969) and individuate events causally. In that case, it could be argued that e exists in
both w and our world since it has the same cause and effect(s) in each world. Of course,
for this to work, e must have the same token cause and effect(s) in both worlds. For if an
event in w is caused by an event token of the same type as the cause of e, and has as
effect an event token of the same type as the effect of e, then this is insufficient for transworld identity (again, consider the case of two tokens of the same event type happening
at different times in our world; they each have the same type of cause and effect but are
distinct events). Nonetheless, it certainly seems possible to argue that e can occur at a
different time in w so long as the causal criterion of event individuation is sound.3
It is worth emphasizing, however, that the same cannot be said for U and U’ for
they each in part rigidly designate their time of occurrence. Since these utterances are
semantic entities, they must be individuated differently than other sorts of events: if they
differ in content, then they must be differentiated. It is for this reason that Smith’s
arguments against the date-analysis version of the tenseless theory of time are
inconclusive, whether or not one adopts a reductionist or substantivalist metaphysics.
3. CONCLUSION
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William Lane Craig credits Smith (1993) with delivering ‘the mortal blow to the new Btheory of language’ (Craig 1999, 265). I have argued that Smith’s attacks do not succeed
against the date-analysis version (though I concede—see my (2000)—that the token
reflexive account fails). The biggest challenge facing the date-analysis theory is not
semantic but epistemological, i.e. explaining how tensed sentences that have tenseless
and, therefore, unchanging truth conditions can nonetheless be cognitively useful in
timing actions (something that requires beliefs with changing truth values). Some very
good theories are out there (see, for example, Mellor 1998, Price 1996). Therefore,
though work remains to be done, there is good reason to be optimistic.
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References
Craig, W. L.: 1999, ‘On Truth Conditions of Tensed Sentence Types’, Synthese 120, 26570.
Davidson, D.: 1969, ‘The Individuation of Events’, in N. Rescher (ed.), Essays in Honor
of Carl G. Hempel. D. Reidel, Boston, 216-34.
Horwich, P.: 1987, Asymmetries in Time. MIT Press, Cambridge.
Kaplan, D.: 1989, ‘Demonstratives’, in J. Almog, J. Perry and H. Wettstein (eds.),
Themes from Kaplan. Oxford University Press, New York.
Kripke, S.: 1980, Naming and Necessity. Harvard University Press, Cambridge.
Mellor, D. H.: 1998, Real Time II. Routledge, London.
Perry, J.: 1977, ‘Frege on Demonstratives’, The Philosophical Review 86, 474-497.
Price, H.: 1996, Time's Arrow and Archimedes' Point: New Directions for the Physics
of time. Oxford University Press, New York.
Smith, Q.: 1999, ‘The “Sentence-Type Version” of the Tenseless Theory of Time’,
Synthese 119, 233-51
Smith, Q.: 1993, Language and Time. Oxford University Press, New York.
Smith, Q.: 1990, ‘Temporal Indexicals’, Erkenntnis 32, 5-25.
Smith, Q.: 1987, ‘Problems with the New Tenseless Theory of Time’, Philosophical
Studies 52, 371-92.
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NOTES
1
Smith (1990) argues that ‘is’ and ‘is now’ are not in fact equivalent so that the present
tense ‘is’ does not refer to its time of utterance. My (2000) argues that Smith’s position
is unconvincing. I needn’t rehearse the argument here because Smith’s (1999) attack
takes the date-analysis theory as given. I can, therefore, help myself here to its
consequences.
2
See my (2000) for an argument to the effect that Smith’s (1990) arguments against the
direct theory of reference fail. That the present tense copula is a rigid designator can be
seen more clearly if we consider sentences such as ‘It is now 2000’. Such a sentence,
uttered at t clearly designates t and equates it with the year 2000. If the direct theory of
indexical reference is correct, then this designation is rigid.
3
A possible rejoinder is as follows. The natural language term ‘event’ denotes a
heterogeneous rather than a natural kind. Therefore, upon investigation it will turn out
that an ‘event’ such as Beth’s awakening is in fact composed of many natural kind
events. These latter events are micro-level interactions amongst elementary particles and
are individuated according to their spacetime location because causation is not a
legitimate relation at the micro-level (see Price 1996); causation is, in other words, a
macro-phenomenon (see also Horwich 1987). Hence genuine events have their
spatiotemporal properties essentially and cannot be identified with otherwise similar
events that occur at different times in other worlds. So Beth’s waking up at t’ in w will
necessarily be a different set of events than Beth’s waking up at t in our world.
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Fortunately, for the purposes of this essay it is not necessary for me to settle this dispute
because the events under consideration are sentence tokens that have semantic properties
that trump causal considerations (see below). I do want to point out, however, that it
remains plausible to argue that at least natural kind events cannot be identified with
events at different spacetime locations.
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