TRUTH CONDITIONS OF TENSED SENTENCE TYPES

L. A. PAUL
TRUTH CONDITIONS OF TENSED SENTENCE TYPES
ABSTRACT. Quentin Smith has argued that the new tenseless theory of time is faced
with insurmountable problems and should be abandoned in favour of the tensed theory of
time. Smith’s main argument attacks the fundamental premise of the tenseless theory: that
tenseless truth conditions for tokens of tensed sentences adequately capture the meaning of
tensed sentences. His position is that tenseless truth conditions cannot explain the logical
relations between tensed sentences, thus the tensed theory must be accepted. Against Smith,
this paper adopts an alternative approach to the explanation of the entailment relations
between sentences which contain indexicals. The approach drops the reliance upon tokens
and instead relies on the evaluation of sentence types with respect to a context rather
than upon actual or possible utterances of tokens of the types. This (new) version of the
tenseless theory of time can adequately explain the relevant entailment relations between
tensed sentences.
1. INTRODUCTION
Quentin Smith (1993, 1994a, 1994b, 1994c, 1994d, 1994e) has initiated
a full frontal attack on the tenseless theory of time. The tenseless theory
holds that events sustain unchanging relations of earlier than, later than
and simultaneous with, and that tokens of tensed sentences have tenseless
truth conditions which capture the meaning of the tensed sentences. Smith
argues that the tenseless truth conditions of tokens of tensed sentences do
not explain the logical relations between the tensed sentences, and thus are
not able to adequately capture the meaning of tensed sentences. Proponents
of the tensed theory of time use these arguments to claim that the tenseless
theory is ‘in retreat’ (Craig 1996b, 249) or ‘false’ (Smith 1993, 12).
Against Smith, this paper will adopt an approach to the explanation
of the entailment relations between sentences which contain indexicals
that relies on the evaluation of sentence types with respect to a context
rather than upon actual or possible utterances of tokens of the types. This
will allow us to give a tenseless explanation of the entailment relations
between sentences which contain indexicals and rebut Smith’s arguments
against the tenseless theory of time. The paper will focus on the debate
on D.H. Mellor’s (1981, 1988) token-reflexive account, as this debate
characterises Smith’s position against the tenseless theory of time, and the
Synthese 111: 53–??, 1997.
c 1997 Kluwer Academic Publishers. Printed in the Netherlands.

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L. A. PAUL
solution suggested by the paper can be generalised as a response to Smith’s
central arguments. The discussion in Sections 5 and 6 applies to sentences
containing personal and spatial indexicals as well as temporal indexicals.
2. THE DEBATE ON THE NATURE OF TIME
The debate about the correct description of the nature of time centres
primarily around two incompatible theories: the tensed theory and the
tenseless theory. Those who hold the tensed theory of time (tensers) argue
that events possess the tensed properties of pastness, presentness and futu-
rity, and that a theory of time must incorporate tensed descriptions of event
properties.1 Those who espouse the tenseless theory (detensers) argue that
the properties of pastness, presentness and futurity do not exist, and that
events sustain unchanging relations of earlier than, later than and simul-
taneous with. Detensers argue that since reality is tenseless, a theory of
time need only incorporate tenseless descriptions of events, so ontologi-
cal descriptions including tensed event properties are incorrect or at best
superfluous.
Although ordinary language and folk intuition are normally charac-
terised in terms of tensed sentences, the original advocates of the tenseless
theory of time (the old tenseless theory of time) held that all tensed sen-
tences (and their tokens) could be translated by tenseless sentences. If
tenseless sentences can translate tensed sentences, the need for a tensed
theory of time is eliminated. Detensers held that their theory gave the
correct metaphysical description of time and that the characterisations of
tensed sentences given by tensers were incorrect.
However, as the result of developments in the philosophy of language
in the area of demonstratives and indexicals, it soon became apparent that
tenseless sentences could not translate all tensed sentences.2 Tensed sen-
tences containing the word ‘now’, such as ‘It is now 1980’, could not be
translated into tenseless sentences, even when using phrases like ‘simulta-
neously with this utterance’, etc. As a result, detensers have developed new
versions of the tenseless theory of time which they claim allow tenseless
sentences to give the meaning of the tensed sentences. Detensers now admit
that tensed sentences or their tokens are not translatable into tenseless sen-
tences but argue that, nevertheless, tenseless characterisations of the truth
conditions of tokens of tensed sentences can adequately capture the mean-
ing of tensed sentences. For detensers, these considerations, in conjunction
with McTaggart’s (1908) argument that the application of tensed properties
and the concept of temporal becoming to reality involves a contradiction,
are sufficient for the elimination of tensed properties.

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TRUTH CONDITIONS OF TENSED SENTENCE TYPES
55
Smith, in Language and Time and The New Theory of Time, challenges
the two main tenseless theories of time: the token-reflexive account and the
date-analysis version. The modern token-reflexive account has been given
by D. H. Mellor, one of the foremost proponents of the new tenseless theory
of time.3 Mellor’s book Real Time (1981) sets forth his token-reflexive
theory, which holds that untranslatable tensed sentences and their tokens
can be characterised using tenseless token-reflexive truth conditions. The
other main tenseless version, the date-analysis theory, holds that the truth
conditions of tensed sentence-tokens characterise the temporal relations of
the subject matters of the tokens to the dates on which the tokens occur.
The date-analysis version has been put forward by J. J. C. Smart (1980)
and Murray Macbeath (1983).
In his works, Smith argues that ‘
[T]he new tenseless theory of time
:
:
:
is faced with insurmountable problems, and that it ought to be abandoned
in favor of the tensed theory’ (1994a, 40).4 Smith bases a large part of his
argument on two theses: (1) the token-reflexive theory advanced by Mellor
is ‘in contradiction with its own assumptions’, and (2) the new tenseless
theories in general are unable to explain the entailment relations between
tensed sentences without relying upon his (new) version of the tensed
theory of time. If Smith is correct, tenseless sentences cannot explain
the logical relations between tensed sentences, and thus are not able to
adequately capture the meaning of tensed sentences. If versions of the new
tenseless theory of time must depend on the tensed theory of time in order
to explain entailment relations between tensed sentences, they cannot claim
that the tensed theory is false. Based on this, William Lane Craig claims
The B-Theory of tense and time [the tenseless theory of time], though still widely held, is
a theory in retreat. The [old tenseless theory of time], which held that tensed sentences can
be translated without meaning loss into canonical tenseless sentences, whether by means
of a date-sentence analysis (Frege, Russell) or a token-reflexive analysis (Reichenbach,
Smart) is today recognised even by [detensers] to have been a failure. The [new tenseless
theory of time], which attempts to escape the reality of tensed facts by means of a tenseless,
token-reflexive analysis of the truth-conditions of tensed sentences (Mellor, Oaklander),
turns out, upon reflection, to be inadequate and even incoherent (1996b, 249).
This paper will argue against the tensed theory of time adopted by
Smith, and in the process attempt to clarify and refine the tenseless
theory by developing an alternative account of the tenseless truth con-
ditions of tensed sentences, one which has antecedents in the work of
Richard Montague (1979a) on tense and indexicals. The version of the
tenseless theory will be developed through an examination of why Mellor
and his defenders are unable to respond successfully to Smith’s criticisms
of their token-reflexive theories. Smith’s first thesis shall be rejected by
showing that his interpretation of Mellor’s theory is incorrect and contains

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L. A. PAUL
a logical fallacy, and that when the interpretation is refined so as to be log-
ically acceptable the ‘internal contradiction’ disappears. Smith’s second
thesis shall be rejected on the grounds that tenseless accounts of indexical-
containing sentences which depend upon truth conditions of tokens of
tensed sentences, such as token-reflexive (and date-analysis) theories, are
flawed. The criticisms directed against the tenseless theory of time may
be met if we instead evaluate the truth of the tensed sentence types with
respect to their contexts and construct tenseless truth conditions for these
types, for we may then use these tenseless truth conditions to explain the
entailment relations between tensed sentences.
3. MELLOR’S TOKEN-REFLEXIVE THEORY OF TIME
Smith’s attack on the new tenseless theory of time begins with the claim
that Mellor’s new token-reflexive theory reduces, on pain of contradiction,
to the old tenseless theory of time.5 He has further arguments against the
new tenseless theory, but in order to confront those arguments squarely, in
this section we will dispose of the charge of internal inconsistency.6 Since
we are making an internal critique of the argument attributing inconsistency
to Mellor, our discussion will employ Smith’s and Mellor’s terminology
(viz. ‘stating a fact’, ‘translate’ and ‘tenseless facts’), although the exact
meaning of these terms is somewhat unclear.
Smith (1994a) focuses on Mellor’s (1981) view that a tenseless explana-
tion of tokens of tensed sentences suffices to eliminate the need for tensed
descriptions even though tensed sentences are untranslatable by tenseless
sentences. Mellor argues that the truth conditions of tensed sentences can
be characterised tenselessly using the truth conditions of their tokens, and
that this characterisation allows the tenseless theory to explain the meaning
of tensed sentences without utilising tensed properties. Therefore, tensed
properties need not be assumed in a theory of time.
Smith argues that
Mellor’s theory is self-contradictory in a crucial respect. Mellor inconsistently holds
:
:
:
all five of these positions: (i) tensed sentences have different truth conditions than tenseless
sentences, and thus are untranslatable by them, (ii) tensed sentences have tenseless truth
conditions, viz., tenseless facts, (iii) these tenseless facts are the only facts needed to make
tensed sentences true, (iv) tensed sentences state the facts that are their truth conditions, and
(v) tensed sentences state the same facts that are stated by the tenseless sentences which
state the former sentences’ truth conditions
I will show that (i) is incompatible with (v)
:
:
:
(1994a, 41).7

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TRUTH CONDITIONS OF TENSED SENTENCE TYPES
57
He then argues that Mellor’s theory contains several assumptions which
entail what he calls the Principle of the Identity of Truth Conditions, or
PITC.
In order to show that points (i) and (v) are incompatible, certain more or less implicit
assumptions that Mellor makes must be made fully explicit. [These assumptions are] (a)
[F]acts correspond to true tokens of sentences, but not to false sentence-tokens
. (b)
:
:
:
[T]ruth conditions, conditions that are necessary and sufficient to make sentences true, are
facts
. (c) [I]f a sentence as tokened on some occasion states a fact 1, then the sentence
:
:
:
F
as tokened on that occasion is true iff
1 and every fact implied by
1 exists
Now
F
F
:
:
:
assumptions (a), (b) and (c) entail the principle of the identity of truth conditions (as I
choose to call it):
PITC: If two tokens of the same sentence or two tokens of different sentences state the same
fact,
1, they have the same truth conditions, i.e., are true iff
1 and every fact implied by
F
F
1 exists (1994a, 43).
F
Smith then claims that points (i) and (v), taken together with the PITC,
imply a contradiction. Consider tokens of the sentences
(1)
It is now 1980 (call any token of this sentence ‘ ’)
S
and
(2)
occurs in 1980 (call any token of this sentence ‘ ’).
S
U
Tokens of both (1) and (2) state the same fact, but their truth conditions
differ, and thus the PITC is violated. The fact that tokens of (1) and (2)
both state is the fact that S occurs in 1980, which is also the truth condition
of tokens of (1). However tokens of (2), which state the same fact as tokens
of (1) and thus have the same truth condition (S occurs in 1980), have
an additional truth condition (according to Smith’s characterisation) that
tokens of (1) do not have, that tokens of (2), if true, are true regardless of
when they are tokened.8 So, following Smith, tokens of (1) and (2) state
the same fact, but their truth conditions differ, which violates the PITC.
This is the reasoning Smith uses to claim that Mellor’s theory contains an
internal contradiction.
Smith then argues that in order for Mellor to resolve this contradiction
he must revert to the old tenseless theory of time with all its attendant
problems. But Smith makes an important oversight in his assessment of
Mellor, for the PITC itself is logically inconsistent, and this inconsistency
does not follow from anything peculiar to Mellor’s theory. To see the
inconsistency in the PITC, consider the possibility of two tokens of different
sentences, both which state fact 1, but also state different or incompatible
F
facts 2 and 3, respectively. What if tokens of sentence
state 1 and 2,
F
F
A
F
F

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L. A. PAUL
while tokens of sentence
state 1 and 3? For example, sentence
could
B
F
F
A
be ‘It is now 1997, and Cicero is dead’, while sentence
could be ‘It is
B
now 1997, and Virginia Woolf is dead’. Clearly, tokens of
and
do not
A
B
have identical truth conditions, and so the PITC is not valid. Fortunately,
the PITC is not the Principle that follows from Smith’s characterisation of
Mellor’s theory. We may revise the PITC to read:
PITC (revised): If two tokens of the same sentence or two tokens of different
sentences state all and only the same facts, 1
, they have the same truth
F
:::
n
conditions, i.e., are true iff 1
exists.
F
:::
n
This is the Principle that follows from Smith’s (a), (b) and (c). According
to the revised PITC, only when tokens of two sentences state all and only
the same facts would they then have identical truth conditions. And this is
exactly what we see with Smith’s characterisation of Mellor’s new theory
of time: tokens of the tenseless sentence (2) state the same fact as tokens
of (1), yet the truth conditions of the tokens differ. Tokens of (1) state the
fact 1, that S occurs in 1980. Tokens of (2) also state 1. But we may say
F
F
that tokens of (2) state an additional fact 2 (following the spirit of Smith’s
F
presentation of Mellor’s argument) because of their tenseless nature; they
state the fact that tokens of (2), if true, are true regardless of when they
are tokened. So, tokens of (1) and (2) would both state
1, but would
F
not both state
2, and so their truth conditions would not be the same.
F
But this conclusion does not violate the revised PITC! Hence, Mellor’s
new tenseless theory of time is not forced to reduce to the old theory of
time, as it is not in contradiction with its own assumptions, and Smith is
unable to use this argument to claim that there can be no such thing as a
token-reflexive theory of time (1993, 71).
4. LOGICAL RELATIONS BETWEEN TENSED SENTENCES
After claiming that Mellor’s theory is inconsistent, Smith goes on to argue
that the logical relation between the tensed sentences
(1)
It is now 1980 (as before, call tokens ‘ ’)
S
and
(3)
1980 is present (any token of this sentence shall be called ‘ ’)
V
cannot be explained by the tenseless theory of time, and that as a result
both the new and the old tenseless theories are false. This paper will agree

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TRUTH CONDITIONS OF TENSED SENTENCE TYPES
59
with Smith that the new tenseless theory of time must be modified in order
to respond to his argument, but it will be argued that this modification does
not require acceptance of the tensed theory of time.
Smith’s argument is based on the entailment of It is now 1980 by 1980
is present and vice versa. He argues that if two sentences are logically
equivalent, it is necessary that the truth conditions of those sentences entail
one another.9 If the truth conditions of two sentences entail one another,
then an explanation of the equivalence of the two sentences is achieved.
(Alternatively, if one sentence entails another, then the truth condition of the
first sentence must entail the truth condition of the second sentence in order
to explain the entailment.) However, the token-reflexive truth conditions of
tokens of ‘It is now 1980’ and ‘1980 is present’ do not entail one another,
because the token-reflexive truth condition of a token
of ‘It is now 1980’
S
is that S occurs in 1980, while the token-reflexive truth condition of a token
of ‘1980 is present’ is that V occurs in 1980. The problem is that the
V
tenseless truth condition S occurs in 1980 does not entail the tenseless truth
condition V occurs in 1980, since it is not necessary for
to be produced
V
simply because
is produced. Therefore, Mellor’s theory cannot explain
S
the logical equivalence of ‘It is now 1980’ and ‘1980 is present’.
Smith argues that the only way to explain the logical equivalence is to
introduce ‘tensed facts’.10
There must be
other facts statable by
and
that explain this entailment, namely
:
:
:
S
V
tensed facts. The tensed fact statable by
is that it is now 1980 and the tensed fact statable
S
by
is 1980 is present, and these two facts imply each other. Alternatively, one could
V
argue that these two facts are really one and the same fact, and that (1) and [3] entail each
other because the same tensed fact is statable by tokens of each (1994a, 45–6).
Smith’s tensed facts allow the logical equivalence of ‘It is now 1980’
and ‘1980 is present’ to be explained. For him, unless the tenseless truth
conditions of tokens of ‘It is now 1980’ and ‘1980 is present’ can be shown
to entail one another, tensed facts are necessary for an adequate theory of
time.
L. Nathan Oaklander disagrees. Oaklander (1994a) defends Mellor’s
theory, accepting the premise that truth conditions of sentences that are
logically equivalent must entail one another.11 In his defence of Mellor,
Oaklander relies upon the discussion of the meaning of tensed sentence
types and tokens in Mellor (1988), where Mellor claims to be following
Kaplan’s (1989) theory of demonstratives and indexicals and states that a
meaning of a tensed sentence token is a semantic function from the time
when the token occurs to its truth condition (Mellor, 1988, 81).12 Oaklander
suggests that if Mellor can rely on his interpretation of Kaplan’s theory to
evaluate the meaning of tensed sentences, he can employ these views to

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60
L. A. PAUL
fashion truth conditions of tokens of tensed sentences that will allow him
to rebut Smith’s arguments.
If we simply follow Kaplan in order to determine the truth conditions
of tokens (produced in 1980) of ‘It is now 1980’ and ‘1980 is present’, we
see that they are indeed the same, namely, that 1980 is at 1980 [or 1980
(is) 1980], and it would seem that Smith’s argument is refuted. However,
if Mellor simply follows Kaplan’s theory in order to determine the truth
conditions, he contradicts his own characterisation of the token-reflexive
truth conditions for tokens of tensed sentences that he presents in (Mellor
1981) and again in (Mellor 1988).
To see this, recall that for Mellor, the tenseless truth conditions of
tokens of tensed sentences give the meaning of the tensed sentences, and
his definition of the truth conditions of tensed sentences and tokens, as
characterised (1981, 1988), is a token-reflexive definition: ‘[A]ny token of
a past tense sentence, to the effect that some event happened
years (days,
N
or whatever) ago, will be true if its date is
years (days, or whatever)
N
later than the date of that event
. They are what we may conveniently
:
:
:
call the tenseless “truth conditions” of these tokens’ (1981, 41). The truth
conditions of future and present tense tokens are of the same form, mutatis
mutandis. For Mellor, ‘To get one definite and unchanging truth-value [a
tenseless truth condition] for a thing token of a particular tensed sentence
type, we must in general specify not only the token but also a particular B
series instant within its lifetime’ (1981, 36).
Thus, Mellor states: ‘[L]et
be any token of “Cambridge is here” and
R
be any token of “It is now 1980”
. Then
is true iff it occurs in
S
:
:
:
R
Cambridge, and
is true iff it occurs in 1980’ (1981, 74). He presents
S
the same characterisation later (Mellor 1988), in his discussion of a token
(KN) of
(KN), where
(KN) is the sentence ‘K faces food now’: ‘[A
s
S
S
token] (KN) is true if and only if it occurs while K faces food, [since]
s
(KN) is temporally token-reflexive’ (80).
S
The token-reflexive account of truth conditions for tokens of tensed
sentences is the centrepiece of Mellor’s contribution to the contemporary
debate on time, and provides an account of how tensed sentences are
indispensable for timely action and communication, yet dispensable in
the account of the ontological nature of time. ‘So, far from the tenseless
view of time, with its token-reflexive analysis of tensed belief, implying
that tensed beliefs are dispensable, it alone explains exactly why they are
not’ (1981, 88).13 The truth conditions of tokens (produced in 1980) of
‘It is now 1980’ and ‘1980 is present’ as defined under Kaplan’s theory,
that 1980 is at 1980, are not token-reflexive truth conditions and so are

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TRUTH CONDITIONS OF TENSED SENTENCE TYPES
61
inconsistent with Mellor’ token-reflexive account of the truth conditions
for tokens of tensed sentences.14
In his defence of Mellor, perhaps realising that the truth conditions
according to Kaplan are not token-reflexive, Oaklander does not argue that
Mellor would accept 1980 is at 1980 as the truth conditions for tokens of
‘It is now 1980’ and ‘1980 is present’.15 Instead he argues that the truth
conditions should be revised from S occurs in 1980 and V occurs in 1980
to (4) and (5):
(4)
Any token S of (1) is true with respect to the context in which
it is produced iff the year of its context is 1980,
and
(5)
Any token
of [3] is true with respect to the context in which
V
it is produced iff the year of its context is 1980.
Oaklander argues that the tenseless truth conditions of tokens of ‘It is now
1980’ and ‘1980 is present’ are identical, because they depend on the same
context for their truth, and so the token-reflexive theory can meet Smith’s
challenge (1994a, 63).
However, although at first glance it seems as though the truth conditions
of tokens of ‘It is now 1980’ and ‘1980 is present’ are identical (i.e., the
token is true iff the year of its context is 1980), when we recognise that in
(4) the pronoun ‘its’ refers to the token , and in (5) the pronoun ‘its’ refers
S
to the token
, it is revealed that the truth conditions are not the same.
V
Smith makes exactly this point in (1994b), where he shows that Oaklander
can only make the truth conditions (4) and (5) appear to be the same by
equivocating upon ‘it’:
‘But once we replace the occurrences of “it” by names of the relevant tokens, this appearance
of similar truth conditions vanishes. The tenseless truth conditions [of tokens
of ‘It is
S
now 1980’ and tokens
of ‘1980 is present’] are these:
V
(6)
Any token
of (1) is true with respect to the context of
’s utterance [pro-
S
S
duction] iff the year of
’s context of utterance [production] is 1980.
S
(7)
Any token
of [3] is true with respect to the context of
’s utterance
V
V
[production] iff the year of
’s context of utterance [production] is 1980’
V
(1994b, 73).
Since the sentences ‘It is now 1980’ and ‘1980 is present’ are logical-
ly equivalent, but the token-reflexive truth conditions of their tokens do
not entail one another, Smith argues that Mellor’s token-reflexive account
must be rejected and that tensed facts are required in order to explain the
entailment relation.

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L. A. PAUL
Smith then claims that we must return to the original issue he put
forth regarding how the tenseless theory of time is to explain the logical
entailment. As it stands, Smith is able to argue effectively against the token-
reflexive account, for it seems to be the case that Mellor and others claim
to be able to capture the meaning of ordinary tensed sentences, and that
the token-reflexive truth conditions of tokens of ‘It is now 1980’ and ‘1980
is present’ do not entail each other when we rely on the usual rules for
entailment relations between the truth conditions of logically equivalent
sentences (namely, that when P iff Q and R iff S, then if P iff R, then Q iff
S).16 Since, as Oaklander notes, ‘
. [I]f one sentence logically implies a
:
:
:
second, then we should be able to justify the inference on the basis of truth
conditions’ (1994a, 62), must we accept that we cannot demonstrate that
tensed properties are reducible to tenseless relations, and admit the tensed
theory of time in order to explain the logical relation?
5. TRUTH CONDITIONS AND ENTAILMENT RELATIONS
Although mutual entailment of the tenseless truth conditions of tokens of
tensed sentences seems to be a sufficient condition for the explanation of
a logical equivalence between tensed sentences, it is not clear that this
condition is necessary. Smith’s argument that we require the tensed theory
of time in order to explain the entailment relation survives only on the basis
of his assumption that it is a necessary condition for a tenseless explanation
of the entailment between two tensed sentences that the truth conditions of
their tokens entail each other.
In this section, a different and more direct approach will be adopted
towards the explanation of entailment relations between tensed sentences.
The emphasis upon tokens will be dropped. To explain the equivalence
of ‘It is now 1980’ and ‘1980 is present’, I will argue that sentences
which contain indexicals are unusual because their truth depends upon
the context in which they are produced.17 Thus, an explanation of the
entailment relations between sentences which contain indexicals may not
follow the same rules as those for sentences which do not. Since the truth
of a sentence which contains indexicals varies according to the context at
which it is evaluated, it 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). Truth of tokens is not lost on this analysis: a
token is true in a context just on condition that its type is true with respect
to its context.

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