Truth Conditions and Entailment Relations of Tensed Sentences
An Examination of the Sentence-Type Theory
Institute for Logic, Language and Computation
University of Amsterdam
Farid Ahmed
January 2001
PREFACE
It has been said that the debate between the new tenseless theory of time and the
tensed theory of time is ongoing. There is no established solution. The debate appears
in the philosophical literature in the early 1980s with the publications of Smart’s
article ‘Time and Becoming,’ and Mellor’s Real Time. The new tenseless theory is
different from the old tenseless theory of time and even the debate between the new
tenseless theory of time and the tensed theory of time is different from the debate
between the old tenseless theory of time and the tensed theory of time. The debate
between the old tenseless theory of time and the tensed theory of time was focused on
the issue of whether or not tensed sentences are translatable in some sense into
tenseless sentences. The new tenseless theory of time rejects the claim that any tensed
sentences can be translated into a tenseless sentence, but argues for the claim that
tensed sentences are expressible in a tenseless metalanguage. Thus, this theory holds
that the truth conditions of tensed sentences can be given by tenseless sentences. The
tensed theory, on the other hand, claims that tenseless sentences are not sufficient to
account for the truth conditions of tensed sentences. Furthermore, the tensed theory
argues that the tenseless truth conditions of tensed sentences cannot explain the
entailment relations between tensed sentences. As a result, in the recent years, the
tensed theory argues against the new tenseless theory of time on two main issues: (a)
the issue of whether the truth conditions of tensed sentences can be expressed by
tenseless sentences, and (b) the explanation of the entailment relations between and
among tensed sentences.
The goal of this thesis is to explore this debate and to examine a solution to the
entailment relations between tensed sentence types within a framework of the
sentence-type theory of the new tenseless theory of time. In addition, I will examine
the arguments against the claim that tenseless sentences can give the truth conditions
of tensed sentences via the specification of tenseless facts. I will argue that the
arguments given by the two main versions of the new tenseless theory of time (the
token reflexive theory and the date analysis theory) for the tenseless truth conditions
of tensed sentences are conclusive.
This thesis is divided into four chapters. In chapter 1, I will discuss the development
of the new tenseless theory of time. In chapter 2, I will explain the two main versions
of the new tenseless theory of time. One is the token-reflexive theory and the other is
the date analysis theory. I will examine how each theory deals with the thesis that
tenseless truth conditions can be given for tensed sentences. In chapter 3, I will
analyze two major criticisms of these versions: firstly, that the token-reflexive theory
and the date analysis theory do not adequately explain the above-mentioned thesis,
and secondly, that neither of the two main versions of the new tenseless theory can
explain the entailment relations between tensed sentences. As for the first criticism, I
will argue for the claim of the token-reflexive and the date analysis versions that since
tensed sentences are expressible in a tenseless metalanguage, the truth conditions of
tensed sentences can be expressed in tenseless terms. As for the second, I will agree
with the claim that, on the token-reflexive theory, the explanation of the entailment
relations between tensed sentence tokens are problematic, but I will argue that on the
date analysis theory, such entailment relations can be obtained. In chapter 4, I will
examine a solution to the issue of the entailment relations within the framework of the
sentence-type theory of the new tenseless theory of time. I will argue that, within this
framework, the entailment relations of tensed sentences are properly captured. In
arguing for the above-mentioned claims, I will, in fact, be defending the position that
tenseless sentences can give the meaning of tensed sentences. Thus, tensed facts are
not needed in our temporal discourse. This position implies that I will defend the
basic claim of the old tenseless theory, albeit in a different way.
3
ACKNOWLEDGEMENT
I am gratefully indebted to my supervisor Dr. Frank Veltman for his generous cooperation. I believe that without his help, I would not have been able to finish this
thesis. I am thankful to Balder ten Cate, a Ph.D. student at the ILLC, for his helpful
suggestions and comments. Finally, I am deeply thankful to my friend Patrick (Clay)
Yancey for his helpful co-operation. I would also like to take this opportunity to thank
all of my teachers, Prof. Jeroen Groenendijk, Prof. Martin Stokhof, Dr. Paul Dekker,
Dr. Karen Kwast, and Dr. Herman Hendriks. By sharing lectures with them, I was
greatly helped.
4
CONTENTS
Preface
Acknowledgement
1
Introduction
6
1.1 The New Tenseless Theory of Time
1.2 The Failure of the Old Tenseless Theory of Time
7
7
1.2.1
1.2.2
The Failure of the Reducibility Thesis
The Failure of the Translatability Thesis
1.3 The Development of the New Tenseless Theory of Time
2.
The Two Versions of the New Tenseless Theory of Time
The Token-Reflexive Version of the New Tenseless
Theory of Time
2.2
The Date-Analysis Version of the New Tenseless Theory of Time
2.3
The Difference between the Token-Reflexive Version and the
Date Analysis Version
2.4 Summary and Conclusion of Chapter 2
9
11
12
14
2.1
3.
22
3.1 The Arguments against the New Tenseless Theory of Time
22
3.1.3
Tenseless Facts and Truth Conditions
Entailment Relations between Token-Reflexive
Tensed Sentences
Entailment Relations between Date Sentences
22
27
28
3.2 Summary and Conclusion of Chapter 3
31
Truth Conditions and Entailment Relations
33
4.1
4.2
5.
19
20
The Problem with Truth Conditions and Entailment Relations
3.1.1
3.1.2
4.
14
17
Paul’s Solution
Truth Conditions, Entailment Relations, and
Tensed Sentence Types
33
42
Conclusion
52
References
54
CHAPTER 1
INTRODUCTION
In the past few years, the debate between the new tenseless theory of time and the
tensed theory of time has focused on two questions: (a) Can the truth conditions of
tensed sentences be given in a tenseless sentence? (b) Can the new tenseless theory
explain the entailment relations between tensed sentences? These issues have
developed out of Mellor's token-reflexive version of the new tenseless theory of time.
Mellor argues that tensed sentences are not translatable into tenseless sentences, and
thus that these two do not have the same meaning. Nonetheless, he argues that the
truth conditions of tensed sentence tokens can be stated in a tenseless metalanguage.
Tenseless sentences can state the truth conditions of tensed sentence tokens without
employing tensed facts. Thus, tensed facts need not to be considered in order to
characterize the truth conditions of tensed sentence tokens. For example, any token S
of ‘It is now 1980’ is true if and only if S occurs in 1980 and any token T of ‘1980 is
present’ is true if and only if T occurs in 1980.
Smith (1993, 1994) and Craig (1996a, 1996b) argue that the token-reflexive version
of the new tenseless theory does not properly explain the idea that tenseless sentences
can provide the truth conditions of tensed sentence-tokens. The tenseless facts
expressed in ‘S occurs in 1980’ cannot characterize the truth conditions of the token S
of ‘It is now 1980’, because S’s occurrence in 1980 does not necessarily imply the
fact that it is now 1980. According to Smith and Craig, therefore, tenseless facts need
not to be considered in order to account for the truth conditions of tokens of ‘It is now
1980’. The only way to do this is to employ tensed facts.
Smith also criticizes Mellor's theory by pointing out that it cannot explain the
entailment relations between tensed sentences. Smith argues that token-reflexive
tenseless truth conditions cannot explain the entailment relations between ‘It is now
1980’ and ‘1980 is present’. He specifies that the truth conditions of ‘It is now 1980’
(viz., S occurs in 1980) neither implies nor is implied by the truth conditions of ‘1980
6
is present’ (viz., T occurs in 1980). Again, he suggests that the only way to explain
the entailment relations is to employ tensed facts.
I will argue, within a framework of the sentence-type theory that the tenseless theory
of time can adequately explain the entailment relations between tensed sentences and
accordingly, that by stating tenseless truth conditions of tensed sentences the tenseless
sentences can adequately give the meaning of tensed sentences. Thus, the new
tenseless theory does not require tensed facts in order to characterize the truth
conditions and entailment relations of tensed sentences.
1.1
THE NEW TENSELESS THEORY OF TIME
In this section, I will discuss the defining feature of the new tenseless theory of time.
In doing so, I will first explain the reasons why the old tenseless theory has failed. I
will explain that there are two main contributing factors. One is the failure of the
reducibility thesis and other is the failure of the translatability thesis. After explaining
the failures of the old tenseless theory of time, I will discuss the development of ‘The
new tenseless theory of time.’
1.2 THE FAILURE OF THE OLD TENSELESS THEORY OF TIME
McTaggart (1908, 1927) distinguishes ‘positions in time’ in two ways: A series and B
series. In the A series, time positions and events “runs from the far past through the
near past to the present, and from the present through the near future to the far
future.”1 In the B series, time positions and events are related to each other in a fixed
and unchanging way. Defenders of the old tenseless theory of time, which is based
on McTaggart’s B series, claim that reality consists of tenseless facts, and that all
tensed facts can be reduced to tenseless facts. Thus, tensed facts can be eliminated
from temporal discourse. The old tenseless theory further holds that events are
ordered by the unchanging relations ‘simultaneous with’, ‘earlier than’ and ‘later
1
McTaggart, 1927: p.10
7
than’, and that every tensed sentences is translatable into a tenseless sentence.
Therefore, tenseless and tensed sentences can have the same meaning. The defenders
of the old tenseless theory of time are B. Russell, H. Reichenbach, A .J. Ayer, M.
Fisk, N. Goodman, W. V.O. Quine, J.J.C. Smart, and C. Williams.
On the other hand, the tensed theory of time, which is based on McTaggart’s A series
holds that reality consists of tensed facts, and that the tensed facts cannot be reduced
to tenseless facts. Thus, the tensed facts cannot be eliminated from temporal
discourse. This theory also holds that events or facts contained in temporal positions
refer to the non-relational properties of futurity, presentness and pastness, and that in
general, tensed sentences are not translatable into tenseless sentences. Therefore,
tenseless sentences and tensed sentences cannot have the same meaning. The
defenders of this theory are C.D. Broad, A.N. Prior, R. Taylor, R. Gale, F.
Chirstensen, G. Lloyd, G. Plumer, A.B. Levinson, E. Lowe, W. Sellars, and G.
Schlesinger.
Notice that, unlike the tenseless theory, the tensed theory is not divided into the old
version and the new version. I believe that the reason for this is that the tensed theory
argued (and is arguing) about one basic issue. The issue, which is based on a claim of
the tenseless theory, is the verity of the claim that since reality consists of tenseless
facts, tensed facts can be eliminated from our temporal discourse. Although there is a
recognizable difference between the old and new tenseless theory of time, their aim is
to give an account of the above-mentioned claim. It is true to say that, in recent years,
the new tenseless theory rejects the translatability thesis of the old tenseless theory of
time. However, their arguments do in fact support the basic claim of the old tenseless
theory of time, i.e., that reality consists of tenseless facts.
It has been argued, however, that the old tenseless theory has failed. Smith (1994)
points out that the development of the philosophy of language, particularly in the
areas of the theory of reference, indexicals, and demonstratives, makes it apparent that
the old tenseless theory has failed. Following Kaplan’s theory of indexicals and
demonstratives, Smith shows how the old tenseless theory is unsuccessful in the
8
explanation of its translatability and reducibility thesis. Kaplan argues that the
character of the indexical ‘now’ in a sentence refers directly to the time at which it is
uttered. It does not refer to a time via a sense. It is without doubt that Kaplan’s theory
does not approve the old tenseless theory of time. Consider the sentence ‘The event E
is occurring now’. Meaning, for Kaplan, is a function from contexts of utterance to
truth-conditions. The sentence, ‘The event E is occurring now’ is true if and only if
‘now’ refers to a time in which the event E is occurring. If we know that the time of
utterance is t0, then the sentence, ‘The event E is occurring now’ is true if and only if
the event E occurs at t0. However, in other contexts of utterance, ‘The event E is
occurring at t0’ has different truth conditions from ‘The event E is occurring now’.
Since these two sentences have different truth conditions in different contexts (hence
different meanings), one is not translatable into the other.2
I am now going to explain in detail why the old tenseless theory did not succeed in
defending its claims.
1.2.1
THE FAILURE OF THE REDUCIBILITY THESIS
The old tenseless theory holds that tensed sentences are reducible to tenseless
sentences. The reducibility thesis, which is based on a linguistic reduction claims that
a tensed sentence containing an indexical is identical with a non-indexical tenseless
sentence. However, this reducibility thesis has failed due to the fact that one can have
a propositional attitude toward the indexical sentence, but not toward the nonindexical tenseless sentence.3
Consider the following examples.
(a) John is playing now
2
Smith, 1994: p. 18
By following Michelle Beer (1994), I am going to examine two arguments as to the failure of the
reducibility thesis. See Beer, 1994: pp. 88-89.
3
9
If it is now t1, sentence (a) is identical with a non-indexical tenseless sentence,
(b) John is playing at t1.
However, the problem here is that one can believe that John is playing now, without
believing that John plays at t1. This means that our propositional attitude to the fact
that ‘John is playing now’ does not necessarily imply that the same propositional
attitude is applicable to the fact that John is playing at a certain time (t1). If this is the
case, then one cannot say that (a) and (b) are equivalent.
Another reason to reject the idea that every tensed sentence is identical with a
tenseless sentence is that, in some cases, the identity between tensed and tenseless
sentences violates Liebniz’s principle of the indiscernibility of identicals. This is
because the identity of tensed and tenseless sentences does not guarantee that they
both possess the same property.
Take the following examples.
(c) It is t7 now.
If it is now t7, sentence (c) is identical with a tenseless sentence,
(d) It is t7 at t7.
We notice here that sentence (d) is an a priori certitude, whereas sentence (c) is
merely an a posteriori contingency. Thus, these two sentences are not identical
according to Leibniz’s law because they have different properties.
10
1.2.2.
THE FAILURE OF THE TRANSLATABILITY THESIS
The translatability thesis of the old tenseless theory of time has failed due to the fact
that a tenseless translation of a tensed sentence does not preserve its meaning. When
tenseless sentences are uttered, they have different meanings from tensed sentences.
The meaning of a tenseless sentence is permanent in the sense that, if it is truly
(falsely) uttered in a context, it will be true (false) in any other context. Whereas the
meanings of tensed sentences are not permanent in that their meanings are determined
with respect to the context(s) in which they occur. If a tensed sentence is uttered, the
event it refers to is related to its temporal positions. Therefore, its meaning should be
determined by relating an event to the temporal positions. If this is indeed the case,
then it seems that a tenseless translation cannot capture the meaning of a tensed
sentence. For example,
If Susan utters the following sentence at t0,
(e) Ann was born today.
then the sentence will be true if and only if Ann was born at t0. Nonetheless,
according to the defining feature of the tensed sentence, this sentence will have a
different meaning if uttered at any other time than t0. For example, if it is uttered at t1,
it will have a different meaning. This is because the meaning of a tensed sentence
depends on the context in which it is uttered. This shows that tensed sentences are not
freely repeatable. Its meaning is always context dependent. Now, if we translate this
sentence into a tenseless sentence, then we will find that the tenseless sentence cannot
give the same meaning as the tensed one. The translated tenseless sentence of
sentence (e) is,
(e) Ann had been born before the time of Susan’s utterance.
11
Due to its tenseless nature, this sentence is freely repeatable. If it is true in one
context, it will be true in all other contexts. This is because its meaning is not context
dependent.
From the above analysis, we can say that due to the tensed nature, sentence (e) can be
uttered truly in context C, but it can be false in many other contexts C . On the other
hand, due to the tenseless nature if sentence (e) is truly uttered in a context C, it will
be true in any other context C. As a result, it can be the case that in context C:
sentence (e) is uttered, but is true and in the same context C, sentence (e) is uttered
and is false. Thus, they express different meanings in the same context C. Since they
cannot have the same meaning in the same context, (e) and (e) are not translatable
into each other.4
1.3
THE DEVELOPMENT OF THE NEW TENSELESS THEORY OF TIME
The failure of the reducibility and translatability theses had two main consequences
for the tenseless theories of time. First, they rejected the idea of the old tenseless
theory of time that tensed sentences are translatable into tenseless sentences. Second,
they influenced the defenders of the new tenseless theory of time to take a new
approach. The defenders of the new tenseless theory of time now hold that tensed
sentences are not translatable into tenseless ones. However, they add that the truth
conditions of tensed sentences can be stated in a tenseless sentence. Thus, the new
tenseless theory holds that tensed facts are not needed in our temporal discourse. J.J.C
Smart (1980) first formulates the new tenseless theory of time, but its later
development is due to D.H Mellor (1981), M. Macbeath (1983), M. Beer (1988), N.
Oaklander (1991), C. Williams (1994), L. A. Paul (1997), and J. M. Mozersky (2000).
4
A similar argument for the failure of the translatability thesis can be found in Seddon (1987), pp. 53-
54.
12
The proponents of the tensed theory of time, on the other hand, claim that the
tenseless account cannot adequately explain two points: first, that tenseless sentences
can specify the truth conditions of tensed sentences, and second, the nature of the
entailment relations between tensed sentences. In contrast, they claim that the only
way to state the truth conditions of tensed sentences and to explain their entailment
relations is to allow tensed facts. Thus, they conclude that tensed facts cannot be
eliminated from temporal discourse. The proponents of the tensed theory of time are
Smith (1993, 1994) and Craig (1996a, 1996b).
13
CHAPTER
2
THE TWO VERSIONS OF THE NEW TENSELESS THEORY OF TIME
In this chapter, I will discuss the two main versions of the new tenseless theory of
time. I will examine how each theory handles the idea that tenseless sentences can
stipulate the tenseless truth conditions of tensed sentences. In section 2.1, I will
discuss the token-reflexive version, in 2.2, the date-analysis version. In 2.3, I will
discuss the difference between the token-reflexive version and the date analysis
version. Finally, in section 2.4, I will conclude that since tensed sentences are
tenselessly expressible, their truth conditions can be given by tenseless sentences.
2.1
THE TOKEN-REFLEXIVE VERSION OF THE NEW TENSELESS
THEORY OF TIME
D.H Mellor (1981) developed the token-reflexive version of the new tenseless theory
of time. Mellor argues that truth and falsity are properties of tokens of tensed sentence
types. Tokens of tensed sentence types have tenseless truth conditions. Therefore,
tenseless truth conditions give the meaning of tensed sentences. However, he denies
the claim that all tokens of tensed sentences have a tenseless translation. Thus, tensed
sentences and tenseless sentences do not have the same meaning.
Mellor argues that truth and falsity are properties of the tokens of tensed sentence
types. They are not the properties of tensed sentence types. For example, any token of
the tensed sentence type, ‘The Queen is fifty-eight’, when uttered in May 1984, is true
with respect to the birthday of the Queen, which is May 1926. Any token of this
sentence type if uttered one year later must be false. Therefore, tokens of sentence
types may differ in their truth-values depending on the time at which the tokens are
uttered. However, in both cases (whether the token is true or false), tenseless
14
sentences suffice to give the objective truth and falsity of the tokens of tensed
sentence types.5
For example,
(a) A token of the sentence, ‘The Queen is fifty-eight’ if it occurs at time t is true if
and only if t is fifty-eight years later than the date of the Queen's birth.
Therefore, if it occurs in May 1984, the token is true, and if it occurs in May 1985, it
is false.
As we have seen above, for Mellor, the truth-values of these tokens are derived
directly from their time positions in which the events (which the tokens refer to) are
related to their time positions. Thus, the truth-values of tokens can be given by
relating events to their temporal positions. Mellor states that “the truth-values of
tokens of any particular tensed type are - so far as time is concerned - a definite
function of how much later or earlier the tokens are than the events they are about.”6
However, facts stated in the truth conditions are completely tenseless. For this reason,
Mellor accepts the idea of the old tenseless theory that “… the tenseless facts that fix
the truth-values of tokens of simple tensed sentences and judgements. Since they
include facts about the tokens themselves - their relative whereabouts in the time
positions” 7 (my italics). This is called a ‘token–reflexive’ account.
However, Mellor denies that a token of a tensed sentence has a tenseless translation.
He argues that the truth-values of tokens of tensed sentence types vary with respect to
their temporal and spatial positions and therefore that their tenseless truth conditions
vary with respect to temporal and spatial positions. The truth conditions of spatially
tenseless tokens, on the other hand, are the same in all places, and the truth conditions
of temporally tenseless tokens are the same at all times. This is because if tenseless
5
Mellor, 1981: p. 40.
Ibid., p. 41.
7
Ibid., p. 42.
6
15
tokens are truly (or falsely) uttered, they are true (or false) everywhere regardless of
when and where they are uttered. The truth conditions of tensed sentence tokens, on
the other hand, depend on the circumstances of utterances (i.e. where or when the
tokens were uttered). Therefore, as Mellor argues, since the truth conditions of tensed
tokens and tenseless tokens are different, they are not translatable. Mellor
characterizes the tenseless truth conditions of tensed tokens as token-reflexive truth
conditions and the tenseless truth conditions of tenseless tokens as non-tokenreflexive truth conditions. Thus, he claims that “… no tenseless sentence can mean
the same as a tensed one does: tenseless token-reflexive and non-token-reflexive truth
conditions are bound to differ. Far from the tenseless translatability of tensed
sentences following from the tenseless view of space and time, it follows that they are
not thus translatable.”8 What follows from Mellor’s untranslatability thesis is that
since tenseless tokens have different truth conditions from tensed tokens, these two
are not inter-translatable. For this reason, they do not have the same meaning.
However, we will see by examining two sample sentences that tensed tokens have
tenseless truth conditions. Therefore, by stating the truth conditions of tensed tokens,
tenseless truth conditions can provide the meaning of tensed tokens.
Let us examine Mellor’s view by considering the following sample sentences:
(a) Cambridge is here
(b) It is now 1980
Further, let R be any token of ‘Cambridge is here’ and S be any token of ‘It is now
1980’.
The truth conditions of R and S are:
(b)
8
R is true if and only if R occurs in Cambridge.
Ibid., p.78.
16
(c)
S is true if and only if S occurs in 1980.
Now, given this truth conditional account one might think that R and S should mean
‘R occurs in Cambridge’ and ‘S occurs in 1980’. But according to Mellor, this
account does not mean that sentences, which give each other’s truth conditions
necessarily, have the same meaning. This is because the two tenseless sentences,
namely ‘S occurs in 1980’ and ‘R occurs in Cambridge’, and the two tensed sentence
types, namely ‘It is now 1980’ and ‘Cambridge is here’, have different truth
conditions. To see why this is so, Mellor argues that if any token of the sentence, ‘R
occurs in Cambridge’ is truthfully uttered in one place, then the token of this sentence
is always true in all places. Similarly, if any token of the sentence ‘S occurs in 1980’
is truthfully uttered at one time, then the token of this sentence is always true at all
times. In order to know whether the token of ‘R occurs in Cambridge’ and ‘S occurs
in 1980’ are true or not, we do not have to be in Cambridge in 1980. However,
because the true tokens of R and S can only occur in Cambridge in 1980, we would
have to be in Cambridge in 1980 in order to meet them.9
What follows from the above analysis is that tensed sentence tokens and their
tenseless truth conditions can vary with respect to the places and times at which the
tokens occur. But in any case, since a tensed sentence is expressible in a tenseless
sentence, its truth conditions can be given by a tenseless sentence.
2.2
THE DATE-ANALYSIS VERSION OF THE NEW TENSELESS
THEORY OF TIME
Smart (1980) introduces the date-analysis version of the new tenseless theory of time.
He agrees with the claim of the tensed theory that tensed sentences are not translatable
into tenseless sentences, but he challenges its metaphysical significance. He
challenges this claim by claiming that tensed sentences containing dates have
9
Ibid., p. 74
17
tenseless truth conditions, and that the semantics of indexical expressions are
expressible in a tenseless metalanguage. For example,
(d) Event E is present
The truth conditions of the tensed sentence are that:
(d) ‘Event E is present’ if uttered at a time t is true if and only if E occurs at t.
Smart states that
When a person P utters at a time t the sentence ‘Event E is present’ his assertion
is true if and only if E is at t. More trivially, when P says at t ‘time t is now’ his
assertion is true if and only if t is at t, so that if P says at t ‘t is now’ his assertion
is thereby true.10
Let us examine this point by means of two simple examples,
(e) When John says in 1980, ‘It is now 1980,’ his assertion is true if and only
if 1980 is at 1980.
(f) When John says in 1980, ‘1980 is present,’ his assertion is true if and only
if 1980 is at 1980.11
In both examples, we see that the two-tensed date sentences have the same
tenseless truth conditions in 1980. This does not imply, however, that these
tensed sentences are translatable into tenseless sentences; rather it implies that
since date tensed sentences are expressible in a tenseless metalanguage, the
truth conditions of tensed sentences can be given by tenseless sentences.
10
11
Smart, 1980: p. 5.
These sorts of examples can be found in Smith 1994, p. 50.
18
2.3
THE DIFFERENCE BETWEEN TOKEN REFLEXIVE VERSION AND
DATE ANALYSIS THEORY OF TIME
Although the token-reflexive version and the date analysis version are concerned with
the same problem, viz., the problem of how to employ tenseless sentences in order to
give the truth conditions of tensed sentences, their respective approaches are
somewhat different.
The token reflexive version of time is concerned with the tenseless truth conditions of
token-reflexive tensed sentences. Thus, a token of a tensed sentence type is true
(false) if and only if the token is uttered at certain times and places. For example,
Let S be a token of the sentence type, ‘John left home one hour ago’. The truth
conditions of the token S are that
The token S of ‘John left home one hour ago’ is true if and only if John’s leaving at
home is one hour earlier than S (the occurrence of the token).
The date analysis version, on the other hand, is concerned with the tenseless truth
conditions of dated tensed sentence types. This version gives the truth conditions
relative to the dates at which tensed sentence types occur, not by relating the
occurrences of its tokens. 12
Thus, we get for example,
12
There is a debate on the issue of whether the date analysis theory gives the truth conditions of tensed
sentence types or not. Paul (1997) states that ‘the date-analysis theory holds that the truth conditions of
tensed sentence-tokens characterize the temporal relations of the subject matter of the tokens to the
dates on which the tokens occur’ (Paul 1997, p. 55). Mozersky (2000), on the other hand, holds that
‘Rather than casting the truth conditions of tensed sentences in token reflexive terms, date sentence’s
truth conditions are relations between dates’ (Mozersky 2000, p. 204, my italics). It is clear that on
Paul’s characterization of the date analysis theory; this theory gives the truth conditions of dated tensed
sentence tokens, whereas Mozersky is not clear on this issue. However, it seems to me that the date
analysis theory characterizes the truth conditions of dated tensed sentence types in the sense that, in a
context (in which the tensed sentence type occurs) the theory is concerned with the truth conditions of
19
The sentence type ‘John left home one hour ago’ uttered at t, is true if and only if
John’s leaving home is one hour earlier than t (The time of the occurrence of the dated
sentence type).
2.4
SUMMARY AND CONCLUSION OF CHAPTER 2
My aim in this chapter was to outline the two main versions of the new tenseless
theory of time and to show how they handle the idea that tenseless sentences suffice
to state the truth conditions of tensed sentences. These two versions are similar in that
since tensed sentences are expressible in a tenseless metalanguage, the truth
conditions of any tokens and types of tensed sentences can be stated by tenseless
sentences.
Token-reflexive theorists often argue that tensed sentence types do not have truthvalues. They hold that only utterances of tensed sentence-types have truth-values.
This means that the tokens of tensed sentence types have the truth-values. Therefore,
the truth-values of tensed sentence types are taken into consideration when their
tokens occur in a certain time and place. Based on this consideration, the tokenreflexive theorists argue that when a tensed token occurs, its truth-value can be given
by tenseless sentences. The basic reason behind this idea is that when a tensed token
occurs, its occurrence can be stated in a tenseless metalanguage. Since the occurrence
of the token can be stated in a tenseless metalanguage, tenseless sentences are
adequate to give the truth conditions of tensed sentences.
On the other hand, as for the date analysis version, it can be said that tensed sentence
types containing indexicals can have truth-values depending on their context of
utterance. They can be true with respect to one context of utterance, but false with
respect to others. If we know the context in which a dated tensed sentence type
occurs, then it is possible to say that the dated tensed sentence type is true (false) in
an occurrence of a tensed sentence type, not with the truth conditions of an occurrence of a token of a
tensed sentence type.
20
that context. In such cases, the truth conditions of these occurrences of the dated
tensed sentence type are tenselessly expressible, since its occurrences are expressible
in tenseless sentences.
Therefore, according to the above analysis; on the token-reflexive version, the
meaning of a tensed token is a function from the utterances of its types to its tenseless
truth conditions. On the date analysis version, the meaning of a tensed sentence type
is a function from the occurrences of types to its tenseless truth conditions. 13 But both
ideas explicate the same fact, namely, that the truth conditions of the tensed sentence
types (tokens) are always tenseless.
By ‘the utterance of a sentence type’ and ‘the occurrence of a sentence type’, I mean two different
things. By ‘the utterance of a sentence’, I mean a token of the sentence type, and by ‘the occurrence of
a sentence type’; I mean the context in which a sentence type occurs.
13
21
CHAPTER 3
THE
PROBLEM
WITH
TENSELESS
TRUTH
CONDITIONS
AND
ENTAILMENT RELATIONS
In this chapter, I will analyze Smith’s two major criticisms of the two main versions:
firstly, that Mellor’s token reflexive theory and Smart’s date analysis theory fail to
explain the meaning of tensed sentences. I will argue that Smith’s criticisms to this
claim are unconvincing. Secondly, concerning the way in which Mellor and Smart
propound their theories does not explain the entailment relations between tensed
sentences. I will agree with Smith that the explanation of the entailment relations
within the framework of Mellor’s token-reflexive version is problematic, but disagree
with his claim that within the framework of the Smart’s date-analysis version such
entailment relations cannot be obtained.14
3.1
THE ARGUMENTS AGAINST THE NEW TENSELESS THEORY OF
TIME
3.1.1 TENSELESS FACTS AND TRUTH CONDITIONS: THE ARGUMENTS AGAINST
MELLOR’S TOKEN-REFLEXIVE VERSION
Quinton Smith (1987, 1993) argues against the new tenseless theory of time. One of
his criticisms against Mellor's token-reflexive version is that tenseless sentences are
not sufficient for stating the truth conditions of tensed sentence tokens and that the
14
A similar line of arguing can be found in Paul (1997) and Mozersky (2000). Paul and Mozerskay
both agree with Smith that the entailment relations within Mellor’s token-reflexive account are
indefensible. Paul works the problem out by introducing a new theory, which is called ‘The SentenceType Theory. Mozersky, on the other hand, hits upon a solution by proposing a schema within the
framework of Smart’s date-analysis version and the direct theory of indexical reference. Nevertheless,
they both disagree with Smith’s claim that the truth conditional analysis of tensed sentence tokens
given by Mellor’s token- reflexive version is questionable. I concur in that Smith’s attack against the
truth conditional analysis is unsatisfactory, but his arguments as to the entailment relations within
Mellor’s theory are successful. I further argue that Smith’s position regarding the entailment relations
within the framework of the date-analysis version is not conclusive. My position in this thesis
respecting the problem of the entailment relations within Mellor’s theory is that this problem can be
resolved within the framework of the truth conditional analysis that is introduced by the sentence-type
theory.
22
tenseless truth conditions of tokens of tensed sentence types fail to account for the
entailment relations between and among tensed sentences.
Smith argues that, on Mellor’s theory, tensed sentences and tenseless sentences state
the same facts, whereas they differ in their truth conditions. Therefore, Mellor’s
theory contains a fundamental inconsistency, since it violates the Principle of the
Identity of Truth Conditions (hereafter PITC). Smith states:
Mellor inconsistently holds all five of these positions: (1) tensed sentences have
different truth conditions from tenseless sentences and thus are untranslatable by
them; (2) tensed sentences have tenseless truth conditions, namely, tenseless facts;
(3) these tenseless facts are the only facts needed to make tensed sentences true; (4)
tensed sentences state the facts that are their truth conditions; and (5) tensed
sentences state the same facts that are stated by the tenseless sentences that state the
former sentences’ truth conditions. 15
He argues that (1) is incompatible with (5), since tensed sentences and tenseless
sentences state the same fact and yet they do have different truth conditions.
Moreover, as Smith argues, the conjunction of (1) and (5) contradicts the Principle of
the Identity of Truth Conditions. In order to show how the conjunction of (1) and (5)
contradicts the PITC, Smith develops an internal critique of Mellor's theory. He
argues that the notion of ‘fact’, as Mellor uses it, holds several assumptions. Smith
states these assumptions are that:
(a) facts correspond to true tokens of sentences, but not to false sentence-tokens. ...
(b) truth conditions, conditions that are necessary and sufficient to make sentence
true, are facts. ... (c) if a sentence as tokened on some occasion states a fact F1, then
the sentence as tokened on that occasion is true iff F1 and every fact implied by F1
exists. ...16
Smith contends that the conjunction of these assumptions entails the following
theory of the PITC.
15
16
Smith, 1994: p. 41
Ibid., p.42-43
23
PITC
If two tokens of the same sentence or two tokens of different sentences
state the same fact, F1, they have the same truth conditions; that is, are
true iff F1 and every fact implied by F1 exist.17
In order to show how the conjunction of points (1) and (5) contradicts the PITC,
consider the following examples.
(1) It is now 1980
Let S be any token of this sentence uttered in 1980.
(2) S occurs in 1980
Let T be any token of this sentence uttered in 1980.
Smith argues that, according to Mellor’s theory, tokens of (1) and (2) state the same
fact, yet they differ in their truth conditions. They state the same fact, because
sentence (1) states a fact that is the same fact, which is stated by sentence (2). Their
truth conditions differ, because the token of sentence (1) is true only when tokened in
1980, but if the token of sentence (2) is true, it is always true regardless of when it is
tokened. Therefore, Smith concludes that since tokens of (1) and (2) state the same
fact, but they differ in their truth conditions, the PITC is violated.
Paul (1997) proposes a different explanation to this matter. She argues that if tokens
of (1) occur in 1980, tokens of (1) and tokens of (2) would both state the same fact,
but if tokens of (1) occur in a different time, tokens of (1) and (2) would not both state
the same fact. Thus, Paul concludes that tokens of (1) and (2) have different truth
conditions.
17
Ibid., p.43.
24
Paul writes:
Tokens of (1) state the fact F1, that S occurs in 1980. Tokens of (2) also state F1. But
we may say that tokens of (2) state an additional fact F2 (following the sprit of
Smith’s presentation of Mellor’s argument) [18] 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 F1, but would not both state F2, and so their
truth conditions would not be the same. 19
The explanation given by Paul and the above examination of Mellor’s version do not
imply that Mellor’s version is self-contradictory or it violates the PITC. I will
consider two arguments below and argue that on one consideration, Mellor’s version
is not subject to criticisms via Smith’s PITC. Thus, I will conclude that Smith
criticisms to the fact that tenseless sentences do not suffice to give the truth conditions
of tensed sentence tokens, are not satisfactory.
Mozersky (2000) raises a question that: “…what does it mean to claim that a token of
(1) can be uttered truly only at one time while tokens of (2) can be uttered truly at any
time?”20 For Mozersky, it means two things.
(a) Tokens of (1) are true only in 1980, but false at any other time. But if tokens of (2)
are true in 1980, they are true at any time.
What follows from (a) is that:
(b) If a token of (1) occurs in 1980, it states a fact F1 (when it is true), but at any other
time it states F2 (when it is false). On the other hand, if a token of (2) occurs in
1980, states F1, and all other times it states the same fact F1.
18
I do not think Smith shares the idea that tokens of (2) state an additional fact F 2. It seems to me that
Paul mischaracterizes Smith’s argument. Craig has pointed out the same objection. , See Craig 1999,
p.266.
19
Paul, 1997: p. 58.
20
Mozersky, 2000: p. 261.
25
Therefore, tokens of (1) occurring in 1980 have the same truth conditions as tokens of
(2), but at any other time tokens of (1) have different truth conditions than tokens of
(2). Thus, as Mozersky states that “… if a dated, particular utterance of (1) shares a
truth condition with all utterances of (2), then that token of (1) when conjoined with
any of the tokens of (2) forms a pair that satisfies (PITC).”21
What follows from the above analysis is that in one case, tokens of (1) and tokens of
(2) have the same truth conditions, namely when they both occur in 1980, and in the
other case, they have different truth conditions, namely, when tokens of (1) occur at
any other time. This sort of characterization of Mellor’s theory cannot be solved by
Smith’s PITC. I think, therefore, that Smith’s characterization of the PITC is
inadequate to judge Mellor’s theory.
If our above analysis is successful, then there would be no reason to accept Smith’s
additional claim that, in order to resolve the contradiction, Mellor has to concede that
tokens of (1) and tokens of (2) have the same truth conditions. Let us see why Smith
is claiming this point.
Smith argues that four points need to be considered concerning the sample sentences,
‘It is now 1980’ and its tenseless truth condition ‘S occurs in 1980.’ He states:
(a) ‘S occurs in 1980’ is the fact, which is stated by any token of the tenseless
sentence, ‘S occurs in1980’, (b) The fact stated by any token S of ‘It is now 1980’, is
the tenseless truth condition of the token S, (c) This is the only tenseless fact stated by
the token S, and (d) tokens of ‘It is now 1980’, and ‘S occurs in 1980’ have different
truth conditions.22
In considering point (d), Smith argues that, on Mellor theory, since a token of ‘It is
now 1980’ is true if and only if it occurs in 1980 and since a token of ‘S occurs in 1980’
is true at all times, these two sentences have different truth conditions even though
21
22
Ibid., p. 261.
Smith, 1994: pp.43-44.
26
they state the same fact. Therefore, (d) contradicts the conjunction of (a), (b), and (c).
For this reason, Smith claims that by rejecting (d) we can resolve this contradiction.
This means that we need to accept the claim that tokens of ‘It is now 1980’ and ‘S
occurs in 1980’ have different truth conditions.23
We have seen above that in a particular case (when we are concerned with giving the
tenseless truth conditions of tokens of ‘It is now 1980’), tokens of ‘It is now 1980’
and tokens of ‘S occurs in 1980’ are both true. They are true, since they occur in
1980. Apart from this particular case, tokens of ‘It is now 1980’ can be false. Thus, it
seems that they differ in their truth conditions for a different reason. This reason has
no role when they are both true in 1980 and when a tenseless sentence gives the truth
conditions of a token that occurs in 1980. Therefore, I do not think that the point (d)
needs to be rejected.
3.1.2 ENTAIMENT RELATIONS BETWEEN TENSED SENTENCES
After arguing for the claim that Mellor’s token-reflexive version is self-contradictory,
Smith goes on to show that the sample sentences, ‘It is now 1980’ and ‘1980 is present’
cannot entail each other. According to him, in order for these sentences to entail each
other, truth conditions of these sentences would have to entail each other. He argues
that within Mellor’s version, this is not the case.
Consider the following two sentences,
(1)
It is now 1980.
Let S be any token of this sentence. The truth conditions of S are:
S occurs in 1980.
23
Ibid., p.44.
27
(2)
1980 is present
Let V be any token of this sentence. The truth conditions of V are:
V occurs in 1980
The truth conditions of the tokens of these sentences ‘S occurs in 1980’ and ‘V occurs
in 1980’ do not imply each other. This is because it is possible for the sentence (1) to
be produced, whereas the sentence (2) is not produced. This is the reason why Smith
claims that Mellor’s token-reflexive version cannot account for the fact that these two
tensed sentences entail each other.
Since tenseless facts stated by tokens of (1) and (2) fail to imply each other, according
to Smith, the only way to account for the entailment relations between tensed
sentences and that is to employ tensed facts. If (1) and (2) state the same tensed fact,
namely ‘It is now 1980’ and ‘1980 is present’, and then the tokens of (1) and (2) entail
each other. Smith states that this entailment can also be explained in terms of tensed
facts, which are statable by (1) and (2). S states the tensed fact ‘it is now 1980’, and V
states the tensed fact ‘1980 is present. These two facts do imply each other, but one
could also argue that these two facts are actually one in the same fact. Thus, since the
same tensed fact is statable by tokens of (1) and (2), they actually entail each other.24
Thus, Smith concludes that only tensed facts are necessary and sufficient to explain
the entailment relations. Hence, tenseless facts are not necessary to explain a theory of
time.
3.1.3 ENTAILMENT RELATIONS BETWEEN DATE SENTENCES
Smith raises the same problem of logical entailment relations between date sentences.
He argues that, according to Smart’s version, tensed sentence types, ‘It is now 1980’
and ‘1980 is present’ do not entail each other. He points out that since a date sentence
type is a contingent sentence, the truth conditions of its tokens must also be
24
Ibid., pp.45-46
28
contingent. However, Smith argues that this is not the case in Smart’s truth
conditional framework. Consider his two examples.
(1) When P says in 1980, ‘It is now 1980,’ his assertion is true if and only if
1980 is at 1980.
(2) When P says in 1980, ‘1980 is present,’ his assertion is true if and only if
1980 is at 1980.
Smith’s explains the entailment relations of dated tensed sentences in terms of the
same tenseless fact that is stated as the truth conditions of these sentences. He claims
that the truth conditional analysis of the two examples imply the idea that since the
same tenseless fact, namely ‘1980 is at 1980’ has stated as the truth conditions of
tokens of the two sentences, they must entail each other. But Smith argues that (1) and
(2) are not real truth-condition sentences. He arrives at this conclusion by the
following example.
(3) When P says in the presence of white snow, “This snow is white,” his assertion is true
iff the white snow is in the same place as the white snow.25
On one consideration, Smith argues that (1), (2), and (3) are not the real truthcondition sentences. Because the real truth conditions of the sentence-tokens has
already been stated before the biconditional. He claims that “the sentence-tokens are
made true by their occurrence in 1980 or in the presence of white snow, and the
conditions specified after the biconditional are therefore redundant, being but some of
the many tautologies implied by the real truth conditions (other of these tautologies
being that the 1980 tokens occur when they occur and that the tokens occurring near
the snow occur where they occur).”26
25
Ibid., p.50.
26
Ibid., pp.50-51
29
Smith clarifies the meaning of ‘the real truth conditions of the sentence-tokens
have already been stated before the biconditional’ with the following example.
He states:
(2) “Henry is ill” is true as spoken by John on July 28, 1940 if and if Henry (is) ill on
July 28, 1940.
The truth condition clause following the biconditional is exactly the same as the
clause following the biconditional in the statement of the truth conditions of the
corresponding tenseless date-sentence:
(3) “Henry (is) ill on July 28, 1940” is true if and only if Henry (is) is ill on July 28,
1940.27
On the second consideration, (1) and (2) are not truth conditions of the 1980 tokens of
‘It is now 1980’ and ‘1980 is present’. The 1980 tokens are contingent sentences and
their respective truth conditions; namely, ‘1980 is at 1980’ are tautologies. Therefore,
Smith claims that “… no tautological fact can make two logically contingent
sentences or tokens true in all and only the same circumstances.”28 The only way to
make a contingent sentence true, for him, is to introduce a logically contingent fact;
the fact that is stated by the tensed sentence type ‘It is now 1980’.
One important point needs to be clear here. Smith assumes that the date analysis
version gives the truth conditions of tokens of tensed sentence types. This is not quite
true. Because, when a person P utters at t that it is now 1980, the time of his assertion,
in fact, refers to a time in which the sentence type occurs. This is not the case that it
refers to the time in which its tokens occur.
However, the problem here is that the truth conditions, ‘1980 is at 1980’, are not the
real truth conditions of ‘It is now 1980’ and ‘1980 is present’. Smith’s argument rests
on confusion. It is a specific instantiation, not the general case. The truth conditions of
27
28
Smith, 1993: p. 35.
Smith, 1994: p. 51.
30
these sentences are that when P says at t ‘It is now 1980’ his assertion is true if and
only if t occurs in 1980. Similarly, when P says at t ‘1980 is present’ his assertion is
true if and only if t occurs in 1980. If this were the case, then there would be no reason
for arguing that ‘It is now 1980’ and ‘1980 is present’ do not logically entail each other.
Since their truth conditions are the same, it must be the case that one must entail the
other.
3.2
SUMMARY AND CONCLUSION OF CHAPTER
3
In this chapter, I have argued that Smith’s arguments that tenseless sentences are not
sufficient for giving the truth conditions of tensed sentence tokens, are unsatisfactory.
Smith’s main argument against the token-reflexive version is that since tokens of
tensed sentences and tenseless sentences have different truth conditions, the facts they
state in their truth condition sentences must be different. Therefore, no tenseless facts
can be sufficient to give the truth conditions of tensed sentence tokens.
We have argued that on the token-reflexive version and the date analysis version that
the truth-values of tensed sentence tokens depend on their occurrences. This means
that a tensed sentence token can be true (false) if it occurs at a certain time and place.
This implies that an occurrence of a token makes a tensed sentence token true (false).
Correspondingly, by taking the truth conditional analysis of the token-reflexive
version, we can say that a token of tenseless sentence types can also be true if it
occurs at a certain time and place. Thus, an occurrence of a token can also make a
tenseless sentence token true.
In both cases, if the occurrences of a tensed and tenseless sentence token state the
same fact, there would be no reason to argue that they would state different facts. We
have already seen that occurrences of tokens of ‘It is now 1980’ and ‘S occurs in
1980’ state the same fact if their tokens occur in 1980, namely that ‘S occurs in
31
1980’.They state the same fact because they are true with respect to their same
occurrence (i.e., the occurrences of 1980).
Given this account, if a 1980 occurrence makes a tenseless sentence true by stating a
tenseless fact, then there would be sufficient reason to say that the same fact is
responsible for making the tensed sentence token true. Thus, tenseless facts are
sufficient to give the truth conditions of tensed sentence tokens.
On the other hand, Smith’s arguments on the entailment relations between tensed
sentences seem very strong. In analyzing Mellor’s version, he maintains that since the
respective tenseless truth conditions of tokens of ‘It is now 1980’ and ‘1980 is
present’ do not entail each other, the tensed sentences ‘It is now 1980’ and ‘1980 is
present’ cannot entail each other. As for the date analysis version, the entailment
relations cannot be explained due to the fact that the alleged tenseless truth conditions
of the two contingent sentences, namely ‘It is now 1980’ and ‘1980 is present’, are
tautologies. Thus, according to him, tautological truth conditions are not necessary
and sufficient to make the tokens of a tensed contingent sentence true. Nevertheless,
we refuted his argument by arguing that the truth conditions of ‘It is now 1980’ and
‘1980 is present’ are not tautological. This is because the real truth conditions of the
tenseless sentence type (it occurs in 1980) can vary with respect to time. This implies
that the truth-value of this tenseless sentence type is true relative to one time, but false
relative to other time. Thus, the real truth conditions are not tautological sentences in
any meaningful sense.
32
CHAPTER 4
TRUTH CONDITIONS AND ENTAILMENT RELATIONS
In order to solve the problem of the entailment relations within Mellor’s token
reflexive version, Laurie Paul (1997) proposes a different schema for the entailment
relations between tensed sentence types. Although she gives the schema for the
entailment relations between tensed sentence types, this does not mean that her
schema cannot explain the truth of tensed sentence tokens. She maintains that her
analysis of this schema for the truth of tensed sentence types provides a condition that
if a tensed sentence type is true with respect to its context, then its alleged tokens can
be true with respect to that context. In this chapter, I will introduce her solution. I will
argue that, within Paul’s theory, Smith’s criticisms to the entailment relations of
tensed sentences do not apply. In section 4.1, I will introduce the solution, and in 4.2,
I will examine this solution.
4.1
PAUL’S SOLUTION
One of the crucial arguments against Mellor's token-reflexive version is that it cannot
explain the entailment relations between tensed sentences. Smith argues that the
tenseless truth conditions of tokens of tensed sentence types do not adequately entail
the meaning of tensed sentences. In her article ‘Truth conditions of tensed sentence
types’, L. A. Paul (1997) states that:
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.29
29
Paul, 1997: p. 62.
33
Paul, in fact, agrees with Smith that Mellor's token-reflexive version is in some
respect problematic, but that this problem of the token-reflexive version could be
solved if we took a different approach. Her new approach is called a sentence-type
theory. She claims that her new approach is able to explain the entailment relations
between tensed sentences. Thus, it will save the token-reflexive version from Smith’s
criticisms.
One crucial point of the sentence-type theory is that this theory is about the truth
conditions of tensed sentence types containing indexicals. Paul argues that truth of
sentences containing indexicals depends on the context in which they are produced.
She writes:
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). 30
She rejects the idea of a token-reflexive version in which the truth conditions of the
tokens of tensed sentence types are given by the truth conditional analysis. Instead of
this, she favors giving truth conditions for tensed sentence-types that maintain an
evaluation of context for the tensed sentence-type. She notes, however, that this type
of explanation implies that “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.”31
Paul’s proposed schema for the truth conditional analysis makes clear that her theory
is distinct from the token-reflexive version. This theory is different since it gives the
truth conditions of the tensed sentence types with respect to the contexts in which they
are produced. The token-reflexive version, on the other hand, gives the truth
conditions of the tensed sentence types by evaluating its tokens with respect to the
contexts in which the tokens are produced. Therefore, the key difference between
30
31
Ibid., 62
Ibid., p.62
34
them is that the truth conditions of tensed types on the sentence-types theory depends
on the evaluation of the occurrences of sentence types, but on the token-reflexive
theory it depends on the evaluation of the occurrence of sentence tokens. But the
sentence-types theory is not distinct from the date analysis version since they both
characterize the truth conditions of tensed sentence types, not tokens. Someone might
argue that they are distinct in that the date analysis version is concerned with the truth
conditions of indexical and non-indexical tensed sentence types, whereas the
sentence-type theory is only concerned with indexical tensed sentence types. But this
does not make a sharp distinction between them in the sense that they both, at least,
deal with the truth conditions of indexical tensed sentence types and the sentence-type
theory is easy to generalize.
In order to show how the tensed sentence-types are evaluated with respect to tenseless
truth conditions she modifies the standard (or non-indexical) notion of logical
implication. The standard (or non-indexical) notion of logical implication holds that A
logically implies B iff when A is true, B must also be true. She modifies it in the
following form:
For sentences (which contain indexicals) A and B, A logically implies B ‘iff for any
context of evaluation C, where A is true with respect to C, B is true with respect to
C.32
By using this modified form, as she states, we may define sentences containing
indexicals A and B as logically equivalent if and only if they entail each other. Thus,
she argues that “these definitions may be used in conjunction with the truth conditions
of sentence types that contain indexicals in order to explain entailment relations.”33
However, she drops the requirement that two logical equivalent sentences entail each
other if and only if their truth conditions entail each other. She claims that logical
equivalence of truth conditions is sufficient for the explanation of entailment
32
33
Ibid., p. 63.
Ibid., p. 63.
35
relations, but it is not necessary. In fact, she wants to explain the entailment relations
in terms of the truth of two-tensed sentence types in the same context. This means that
if two tensed sentence types are true in the same context, then they must entail each
other.
Furthermore, she argues that the production of tokens of tensed sentence types in a
context C, is not necessary for the evaluation of tensed sentence types. This implies
that tokens of sentence types need not be involved in the context of evaluation C in
order to evaluate the truth of the sentence types with respect to context of evaluation
C. For example, she argues, the sentence type ‘No tokens are being produced now’
should not be necessarily false with respect to the context C. But if we evaluate this
sentence by employing any of its tokens, it will be necessarily false.
It seems that Paul is correct in saying that, within her new theory, the sentence type,
‘No tokens are being produced now’ will be possibly true. I do not think that in order
to solve the problem of the entailment relations of the token-reflexive version, her
sentence type theory needs to solve a different problem. A very well established
criticism against the token-reflexive version is that if no tokens are produced, then it
will not be possible to determine the truth-values of a sentence type. For example, if a
token of the sentence type, ‘No tokens are being produced now’ is not occurring now,
then it is not possible to determine its truth-value. However, let us see in what sense
Paul claims that the evaluation of this sentence by its tokens can be necessarily false.
As we know, the evaluation of this sentence type with respect to its tokens depends on
the evaluation of its tokens. If this is the case, then a token of the sentence type, which
is uttered now, is false. This is because the token of this sentence type, which is
uttered now, implies the fact that there is a token of this sentence, whereas the
sentence type implies the fact that there are no tokens those are being produced now.
Thus, if we say that this sentence type is simply true now, then its evaluation with
respect to its tokens at any time must be false. Thus, the evaluation of this sentence
with respect to its tokens will make this sentence necessarily false.
36
On the other hand, according to the sentence-types theory, every sentence type
containing indexicals has a truth-value with respect to its context of evaluation. This
is because sentence types containing indexicals are special and therefore, their truthvalues depend on the context in which they are produced. This means that a sentence
type containing an indexical can be true (or false) depending on its context of
evaluation.
Given this account it seems that the evaluation of the sentence type containing an
indexical, ‘No tokens are being produced now’ can be possibly true. Because,
according to the sentence-types theory, the evaluation of this sentence type depends
on the evaluation of its production with respect to a context. If this is the case, then
any production of the sentence type in a context is true. This is because the production
of the sentence type in a context implies that a true occurrence of this sentence type
has been produced in that context.34 Nevertheless, it can also be the case that this
occurrence of the sentence type can be false with respect to a different context. What
follows from this is that the evaluation of occurrences of this sentence can be true (or
false) with respect the contexts in which they are produced. Therefore, the evaluation
of this sentence type with respect to contexts cannot be necessarily falsehood.
Following the aforementioned analysis, it can be argued that the production of a
sentence type in a context is actually a token of the sentence. If this idea stands, then
what the production of a true token of the sentence type ‘No tokens are being
produced now’ makes is nothing but one like a liar sentence. As a result, if this
sentence type is true in terms of its true tokens, then it is false and thus, it is false if
and only if it is true. This means that the account of giving truth of the sentence type
with respect to its true tokens results in a paradox. Nevertheless, Paul could avoid the
paradox by maintaining a recognizable condition that she employs in order to give the
truth of sentence types. The condition states that a sentence type can be true with
34
By production of a sentence type, I mean an occurrence of a sentence type. The notion of an
occurrence of a sentence type and the notion of a token of the sentence type do not hold the same
meaning. For example, ‘the letter ‘x’ (the very same letter type) occurs three times in the formula
(type) ‘(x) (FxGx)’. Thus, the notion of an occurrence of ‘x’ must not be confused with the notion
of a token of ‘x’ (although it often is so confused). The notion of ‘an occurrence of x in y’ involves not
only x and y, but also how x is situated in y’. (See for detail, Wetzel, 1998).
37
respect to a context without requiring whether or not a token of it is truly produced in
that context. It follows that a sentence type can be true in a context without taking
account of its true tokens.
Paul points out that we have a recognizable condition under which the production of a
true token of a sentence type does not require to give the truth of a sentence type.
Given this condition, now it is evident, as stated above, that the sentence type ‘No
tokens are being produced now’ is a possibly true sentence. But if we give its truth in
terms of the truth of its tokens, then the truth conditional analysis of this sentence type
would be paradoxical. Therefore, the condition that characterizes the way of giving
the truth of sentence type avoids the paradox by maintaining that the production of a
token is not necessary for giving the truth of a sentence type.
According to the formulation of the standard (or non-indexical) notion of implication
(or logical equivalence), Paul examines a sentence type with respect to a context of
evaluation. She believes by interpreting a sentence type with respect to a context, the
problem of the token-reflexive version can be solved and the entailment relations
between tensed sentence types can be explained. We will see now how she explains
the logical equivalence between the tensed sentence types (a) and (b).
(a)
It is now 1980.
(b)
1980 is present.
By the definition of the logical equivalence provided by the standard (or nonindexical) notion of implication the truth conditions of the two sentences are:
(a)
‘It is now 1980’ is true in the context of evaluation C if and only if the time of
its context of evaluation C is 1980.
38
(b)
‘1980 is present’ is true in the context of evaluation C if and only if the time of
its context of evaluation C is 1980.
Paul argues that the truth conditional analysis of these sentences shows that they are
logically equivalent, since they are both true in the same context. She states:
Therefore, for the context of evaluation C, when ‘It is now 1980’ is true with respect
to C, ‘1980 is present’ is true with respect to C, and when ‘1980 is present’ is true
with respect to C, ‘It is now 1980’ is true with respect to C. This, by our definition,
means that ‘It is now 1980’ and ‘1980 is present’ are logically equivalent.35
Paul further examines why tokens of two tensed sentences are not logically
equivalent.
Take two tensed sentences,
(c)
It is now 1997.
(d)
1996 is past.
It simply appears that (c) entails (d), but (d) does not entail (c). In order to examine
the entailment relations of (c) and (d) by using tenseless token-reflexive truth
conditions, let S be any token of (c) and T be any token of (d). Thus, according to
Mellor's token reflexive version, the truth conditions of S and T are that:
(c’) S is true if and only if S occurs in 1997.
(d’) T is true if and only if T occurs later than 1996.
Paul argues that the truth conditions of a token of (c) do not entail the truth conditions
of a token of (d), because the production of a token of (c) does not entail the
35
Paul, 1997: p.63
39
production of a token of (d). Therefore, on token-reflexive account, the truth
conditions of tokens of the tensed sentences do not logically entail each other.36
Now, let us examine the two sentences in order to show how Paul's modified theory
works in these examples.
(c)
‘It is now 1997’ is true in the context of evaluation if and only if the time of its
context of evaluation is 1997.
(d)
‘1996 is past’ is true in the context of evaluation if and only if the time of its
context of evaluation is later than 1996.
The truth conditions of the two sentences have been evaluated here with respect to the
context with a time (that is 1997). The time of context of evaluation here is 1997,
because, as Paul claims, a context with time of 1997 by definition implies a context
with a time that is later than 1996. For this reason, when ‘It is now 1997’ is true,
‘1996 is past’ must be true.37
In order to show how the definition of equivalence is applicable to the indexical
sentences involving places; Paul further considers two concrete examples.
(e) Princeton is here
entails
(f) Princeton is at this location
The truth conditions of tokens of these sentences do not entail each other, for the
production of tokens of (e) does not entail the production of tokens of (f). However,
36
37
Ibid., 64
Ibid., 64
40
Paul’s new definition of logical equivalence shows that these two sentence types are
logical equivalent.
(e)
‘Princeton is here’ is true in the context of evaluation C if and only if its
context of evaluation is Princeton.
(f)
‘Princeton is at this location’ is true in the context of evaluation C if and only
if the place its context of evaluation is Princeton.
So, now it is clear that the truth conditions of these sentences entail each other with
respect to the same context of evaluation. The context of evaluation of the two
sentences is Princeton.
Paul agrees with Smith's contention that Mellor's token-reflexive version does not
adequately explain the entailment relations between the two sentences: ‘It is now
1980’ and ‘1980 is present.’ However, Paul argues that if we are able to evaluate
these two sentences with respect to the evaluation of context C, at least we can say
that they are logically equivalent. Paul states that “using the truth conditions of
sentence types with respect to a context of evaluation seems reasonable, for it is
because we recognize that sentences containing indexicals like ‘It is now 1980’ and
‘1980 is present’ are true with respect to all and only the same contexts that we want
to say they are logically equivalent.” 38
38
Ibid., p. 64.
41
4.2
TRUTH CONDITIONS, ENTAILMENT RELATIONS, AND TENSED
SENTENCES TYPES
Smith (1999) critically examines Paul's solution to the entailment relations between
tensed sentence types. He argues that although her solution solves the problems of
Mellor’s token-reflexive version, this solution is not successful.
Smith points out some conceptual and terminological problems of Paul's solution.
Firstly, Smith argues that Paul is not explicit in her characterization of the notion,
‘true with respect to a context C’. According to Paul, since a sentence type containing
indexical is special, it must be evaluated with respect to its context C in which it is
true. Therefore, by the notion of ‘with respect to its context C’ she means that the
truth of a sentence type can be given with respect to its context C. Smith argues that
Paul’s characterization of ‘with respect to its context C’ cannot allow us to believe
that a true token of the type exists in the context C, or that the sentence-type is true
simpliciter. Rather, as he states, a sentence type can be true with respect to some
contexts, but false with respect to others. Instead of this account of giving truth
conditions of sentence types, as Smith states, it seems that Paul’s characterization of
‘true with respect to a context C’ gives a condition under which a sentence type is
true, but this condition cannot provide an account of giving truth conditional analysis
in which a sentence type can be false. So, Smith concludes that, in fact, Paul does not
give the truth conditions for the sentence types, but rather that she gives conditions for
truth-with-respect-to-a-context.39
One problem with Smith’s argument is that he does not consider the idea that a tensed
sentence type containing indexicals is special- it should be evaluated with respect to a
context C. It seems that Smith critique of Paul’s characterization of the truth
conditions of tensed sentence is based on the non-indexical view, which was
advanced by A.N. Prior (1967). This view holds that the proposition a tensed sentence
42
type expresses is the same proposition expressed at all times and its truth-value can be
obtained with respect to the time positions in which it occurs. Thus, it can be true with
respect to some times, but false with respect to others. Paul’s characterization of ‘with
respect to a context C’ is not comparable with this view. She points out that “tensed
sentence types which contain indexicals, are special because their truth depends upon
the context in which they are true. … 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 contexts…” (my italics).40 Thus, it seems that her characterization
of the truth conditions of a tensed sentence type with respect to context C is similar to
the mixed indexical view of the tensed theory - the view, which has been developed
by Dummett (1981). This view holds that a tensed sentence type “expresses different
propositions at different times, but the proposition it expresses at a given time has (or
rather, can have) a temporally variable truth-value- say, in that it is truth-valueless at
one time, and true at some other (future) time.”41 Since Paul’s characterization of the
truth conditions of tensed sentence types containing indexicals is different from the
characterization given by the non-indexical view, Smith is not correct in criticizing
Paul’s characterization of the ‘with respect to context C’ by distinguishing these two
phenomena.
Secondly, Smith examines Paul's characterization of ‘context of evaluation’, which
includes a possible world, a time, a place, and an agent. Smith argues that some
tensed sentences do not require the contexts of evaluation, which include ‘agents’,
‘times’, and ‘places’. Therefore, for him, in order to determine their truth-values Paul
needs to exclude ‘agents’, ‘times’ and ‘places’ from her characterization of contexts.
To see why this is so, Smith asks us to consider the following two tensed sentence
types.
(a) There are no agents.
39
Smith, 1999: p. 239
Paul, 1997: p. 62
41
P. Percival (1989) classifies three types of times as indices of truth. See for detail, P. Percival,
‘Indices of Truth and Temporal Propositions’, Philosophical Quarterly, vol. 39, 155: 1989, p. 192).
40
43
Since Paul includes in her definition of 'contexts': indexes that include agents,
sentence (a) would be a logically necessary falsehood under her theory. Thus, because
sentence (a) is a possibly true sentence, Paul's theory is thereby falsified.
(b) Only timeless abstract objects exist.
This sentence type is true with respect to a context in which there is neither time nor
place. Truth conditions of this sentence do not require the existence of times and
places. Thus, this sentence is true within a context of evaluation that lacks times,
places.
Smith’s arguments are not quite satisfactory. The proposition expressed by ‘There are
no agents’ when it is uttered now, is not a tautology. Because it is not the case that it
is true in every world. Rather, this proposition expresses that when it is uttered at a
given time, it is true in a world, but can be false in another world. Thus, neither this
sentence is necessarily true nor necessarily false i.e., this sentence is a possibly true
sentence. Therefore, Smith’s argument that sentence (a) would be logically necessary
falsehood under Paul’s theory seems unsatisfactory. The problem of sentence (b) can
be handled accordingly.
Apart from these terminological and conceptual problems, Smith also argues against
Paul’s claim that a sentence type must be evaluated with respect to its contexts in
order to determine its truth-value. According to Smith, this claim is not correct
because,
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
44
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). 42
What follows from the above quotation is that a sentence type can be true or false
only if it is tokened in a certain time. It seems that Smith assumes the general idea that
a sentence type does not have a truth-value due to the fact that it does not have its own
context of evaluation. For this reason, it may be the case that, for Smith, a sentence
type can be evaluated by the evaluation of its token with respect to a context. In fact,
he characterizes the ‘context of evaluation’ as a context in which a token of a sentence
type can be evaluated. This means- at a time in which a token of this sentence types
occurs. Thus, a token of the sentence type can be evaluated in a context (which
includes a time) in which a token-event (Jane having nightmares) occurs. Smith
explains this by examining an example.
Consider the sentence-type, “Jane’s nightmares are presently occurring”. Suppose it
is now 11 p.m., April 3, 1998 and that Jane is now having nightmares. The sentencetype “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.43
Thus, for Smith, in order to evaluate the truth-value of this sentence type, its context
must include a present time and a token of event-type.
Furthermore, Smith argues that even the sentence-type ‘Jane's nightmares are
presently occurring’ cannot be true with respect to each context in which its eventtokens (Jane’s having nightmares) occur. He argues that
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
42
Smith, 1999: p. 240
Ibid., 240.
44
Ibid., 240
43
45
to last night, since last night is no longer presently occurring, and thus this context fails to
include a condition (presently occurring) specified by the sentence-type.44
What follows from the above truth conditional analysis is that in order to evaluate a
tensed sentence type it needs a context and it has own context only if it tokens in a
context. Thus, it seems that without any occurrence of a token of a sentence type, the
sentence type does not have its own context. Furthermore, when a token of sentence
type occurs in a context, it must occur at a certain time. Thus, in order to evaluate a
sentence type with respect to the context, a sentence type needs a token and some
irreducible tensed conditions. Smith writes: “… 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.”45
In order to defend the above-mentioned claim, Smith turns to Paul’s definition of
‘contexts’. He writes: ‘Paul says the context of evaluation includes “a time” and
anything else necessary to give the present tense sentence-type a truth value.’46 He
argues that since a sentence-type is evaluated with respect to a context that includes a
time, and since the token of the sentence type, ‘Jane's nightmares are presently
occurring’ is evaluated with respect to temporal positions, the ‘anything else’ seems
to be referring to the time positions. Smith writes:
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,…47
For the sake of argument if we agree with Smith that in order to evaluate a sentence
type its context needs a token and some irreducibility tensed conditions, then the
phrase ‘presently occurring’ in the sentence type ‘Jane’s nightmares are presently
45
Ibid., p. 241.
Ibid., p.240
47
Ibid., p. 241
46
46
occurring’, for Smith, must refer to a context that includes a time. Let us assume that
the time is t0. Now, an event token of the sentence type ‘Jane’s nightmare’s are
presently occurring’ is true with respect to a context if and only if the context is t 0.
This truth conditional analysis means that the truth conditions of this sentence type,
which are evaluated by the truth conditions of tokens, are tenselessly expressible. But
Smith argues that if Paul gives the truth of the sentence type in this way, then it seems
that Paul is not giving semantics of natural language. This is because, as he states, ‘…
natural language includes the tensed truth predications “was true”, “is true”, and “will
be true”.’48 But Paul’s way of giving truth conditions for the semantics of natural
language does not include the tensed predications. However, Smith claims that
without considering the tensed truth predications, Paul can give the truth conditions of
tensed sentence type by using only tenseless sentences and tenseless truth
predications. In such case, her theory should give tenseless truth conditions for natural
language sentences in such a way that her giving tenseless truth conditions of tensed
sentences is consistent with the truth-values and entailment relations of natural
language sentences. Smith states:
Paul’s semantics for natural language need not be a part of natural language and may
include only tenseless sentences and tenseless truth predications. 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.” 49
The problem here is that Smith does not explain the reason why these two sentences
are not logically equivalent in the natural language. However, from the viewpoint of
Paul’s semantics, Smith’s contention seems to be unsound. Against Smith claims, it
can be argued that within the Paul’s semantic framework, these two sentences (‘The
storm is now occurring’ and ‘The storm is occurring now’) can be shown as logically
48
49
Ibid p.242
Ibid., p. 242.
47
non-equivalent sentences. In order to show how these are not logically equivalent, let
us analyze the following two sentences.50
(g)
It is 12 o’clock exactly now.
The referents of ‘Now’ in the above form of sentences depend on the different time
moments in which the sentences containing them are uttered. In the case of this
sentence, ‘Now’ is referred to 12 o’clock (if this sentence is uttered at 12 o’clock.),
but it can also be referred to other time moments in which they are produced. If so,
then, according to Paul’s semantic analysis, we are in a position to give the truth
condition of this sentence.
The truth condition of this sentence is:
(g’) ‘It is 12 o’clock exactly now’ is true in the context of evaluation if and only if
the time of its context of evaluation is 12 o’clock. Since ‘Now’ can also refer to
different time moments, this sentence can be true with respect to a different context of
evaluation if and only if the time of its context of evaluation is other than 12 o’clock.
However, this truth conditional analysis cannot hold as to the following sentence. Let
us consider the sentence.
(h)
It is now exactly 12 o’clock.
Due to the position of the adverb ‘Now’ in this sentence, ‘Now’ refers to a time
moment that is exactly 12 o’clock.
Given this account, we can give the truth
condition of this sentence in accordance with Paul’s analysis.
The truth condition of this sentence is:
50
For these two sentences, I am indebted to Professor Dick de Jongh.
48
(h’) ‘It is now exactly 12 o’clock’ is true in the context of evaluation if and only if
the time of its context of evaluation is exactly 12 o’clock. Nevertheless, if we give the
truth condition of this sentence with respect to any time moments other than 12
o’clock, then this sentence must be false.
What follows from the above truth conditional analysis is that the two sentences are
true with respect to a time i.e., 12 O’clock. But this does not imply that the truth of (g)
can necessarily entail the truth of (h). Because the truth of (g) can vary relative to
other time of contexts. As a result, when (g) is true, it cannot be the case that (h) will
be true. Since the truth of (g) does not guarantee the truth of (h) and vice versa, one
cannot entail the other. Since they do not entail each other, they cannot be logically
equivalent sentences.
If the above truth conditional analysis is satisfactory, then it will be applicable to the
sentences given by Smith, and thus, according to Paul’s semantics, these sentences
can not be shown to be logically equivalent.
Furthermore, Smith argues that Paul’s tenseless truth conditions sentences should give
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 it is not now
true, but was true with respect to 11 p.m., April 2.” ’51 Smith claims that it is possible
to give the truth conditions of this sentence by employing tenseless predications. In
such case, then we will get different truth conditions than Paul’s truth conditional
analysis. Because, for him, the truth conditions of this sentence imply the fact that we
are giving the truth conditions of the evaluation of a sentence type with respect to
contexts. We are not giving the truth conditions of the sentence type that is evaluated
with respect to contexts. Let us see how Smith gives the tenseless truth conditions of
this sentence. The truth conditions of this sentence type by using tenseless
predications, according to Smith, are as follows:
51
Ibid., p.243
49
“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 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’. 52
In giving these kinds of truth conditions, Smith assumes that tensed sentence types can
only be evaluated with respect to the contexts of occurrences of its tokens. Because,
the phrase the time of evaluating this sentence-type expressed in the truth condition
sentences refers to the time at which a token of this type occurs. One might argue that
this phrase also refers to the time at which an occurrence of this sentence type
produces. But this is not consistent with Smith’s characterization of the evaluation of
the sentence type, since he disagrees with the claim that a tensed sentence type can be
evaluated with respect to the occurrences of tensed sentence types. Thus, it seems that
by the notion ‘the evaluation of a sentence type’, Smith means ‘the evaluation of token
of a sentence type’. In such case, then, it is true that we will get the truth conditions of
the evaluation of a sentence type with respect to contexts, not the truth conditions of a
sentence type that is evaluated with respect to contexts. Nevertheless, the problem here
is that if the truth conditions of tensed sentence types containing indexicals are
evaluated with respect to contexts, does it imply that its truth should be evaluated with
respect to the contexts of occurrences of its tokens? It does not seem so. According to
Paul’s theory, since the truth-values of tensed sentence types containing indexicals
vary with respect to their time of production, the functions of an indexical expressed in
a tensed sentence type shows that the truth-values of a tensed sentence type should be
evaluated with respect to a context in which it occurrences are produced. If this idea is
plausible, then the truth conditions of this sentence can be given as follows:
The occurrence of the tensed sentence type “Jane’s nightmares are presently
occurring” is (tenselessly) true in the context of evaluation C (Jane having nightmares
52
Ibid., p. 243
50
at 11 p.m., April 3), if and only if the context of evaluation C is a time that is
simultaneous with the time of occurrence of the sentence type. The occurrence of the
tensed sentence type “Jane’s nightmares are presently occurring” is (tenselessly) false
with respect to the different context of evaluation C’ (Jane having nightmares at 11
p.m., April 2) if and only if the context of evaluation C is a time that is earlier than the
time of occurrence of the sentence type. Further, the occurrence of the tensed sentence
type “Jane’s nightmares are presently occurring” is true with respect to C’ if and only
if the context of evaluation C’ is a time that is simultaneous with the time of
occurrence of the sentence type.
What follows from the truth conditional analysis is that by evaluating the truth
conditions of an occurrence of a tensed sentence type with respect to contexts, we are,
in fact, getting the truth conditions of a tensed sentence type. This is because in giving
the truth conditions of the occurrences of a tensed sentence type we are, in fact, giving
the truth conditions of a tensed sentence type. This way of giving truth conditions,
thus, does not contradict Paul’s truth conditional analysis.
51
CHAPTER
5
CONCLUSION
Two basic points have been discussed in this thesis. First, by considering the token
reflexive theory and the date analysis theory, I have analyzed the idea that tenseless
sentences are sufficient to give an account of the truth conditions of tensed sentences.
I have argued that since tokens and occurrences of tensed sentence types are
tenselessly expressible, their truth conditions can be given by stating tenseless
sentences. I argued for this claim by examining Smith’s criticisms. I argued that the
tenseless truth conditions of tensed sentences imply that a fact stated by a tensed
sentence is the same fact as the one stated by a tenseless sentence. It is true that
sentences with tenseless truth conditions state different facts than tensed ones, but this
is not the case when tenseless sentences are involved in giving the truth conditions of
tensed sentences. In fact, I pointed out that a tenseless sentence states a different fact
for a different reason. This reason cannot be considered when they are involved in
giving the truth conditions of tensed sentences. This argument, thus, implies that
tenseless sentences are sufficient to give an account of the truth conditions of tensed
sentences.
Second, within the framework of the sentence-type theory, I argued that the
explanation of the entailment relations between tensed sentence types is satisfactory.
By examining Smith’s criticisms, it has been argued that a tensed sentence type must
not be evaluated with respect to the evaluation of its tokens. I claimed, according to
the characterization of tensed sentence types given by Paul, that since tensed
sentences containing indexicals are specific kinds of sentences, their truth should be
given with respect to their contexts of evaluation, which include the time of their
production (which I prefer to call the occurrence of the tensed sentence type instead of
the production of the tensed sentence type). Thus, by evaluating the truth conditions
of the occurrences of tensed sentence types, the truth conditions of the occurrences of
52
tensed sentence types must yield the truth conditions of the tensed sentence types.
Therefore, it is not necessary to evaluate the truth conditions of tokens in order to
evaluate the truth conditions of tensed sentence types.
53
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