18
Tense and Intension (2003)
The radical philosopher of flux, Cratylus of Athens, is said to have spurned the use of
language altogether in part because, like everything else, our words’ meanings are
continually changing, making it impossible to convey what we intend. Scholars in
the age of ‘publish or perish’ know that language has uses that do not require
successful communication, but this seems a weak answer to Cratylus. Whereas
diachronic change is inevitable, change in lexical meaning usually takes place over a
long enough period that we manage during the interim, now and then, to get our
thoughts across. I have come to believe, however, that any viable theory of the
semantic content of language—whether Fregean, Russellian, or neither, or both—
must accommodate the fact that, in a significant sense, the content or sense of most
terms (‘red’, ‘table’, ‘tree’, ‘walk’) is indeed different at different times. I present here
an account of semantic content that is philosophically neutral with respect to the
sorts of issues that dominated twentieth-century philosophy of semantics, but that
entails this kind of content shiftiness and other interesting consequences concerning
the relationship between content and the empire of Time.
SEMANTIC CONTENT
The primary presupposition of any philosophical theory of semantic content is
that the (or at least one) semantic function of declarative sentences is to express
a proposition.1 A declarative sentence may be said to contain the proposition it
Portions of my book Frege’s Puzzle (Atascadero, Calif.: Ridgeview, 1986, 1991) and of my chapter
‘Tense and Singular Propositions,’ in J. Almog, J. Perry, and H. Wettstein, eds., Themes from
Kaplan (Oxford: Oxford University Press, 1989), pp. 331–392, have been incorporated into the
present chapter. Where those presentations presuppose a Millian (or neo-Russellian) semantic
theory, this presentation, by contrast, is deliberately neutral regarding all such issues. I am grateful
to Steven Humphrey, Aleksandar Jokic, Takashi Yagisawa, and my audience at the Santa Barbara
City College conference ‘Time, Tense, and Reference’ for their comments.
1 Throughout this chapter, I am concerned with discrete units of information that are specifiable
by means of a ‘that’-clause—for example, that Socrates is wise. These discrete units are propositions.
Following the usual practice, I use the verb ‘express’ in such a way that an unambiguous declarative
sentence expresses (with respect to a given possible context c) a single proposition, which is referred
to (with respect to c) by the result of prefixing ‘the proposition that’ to the sentence. A declarative
sentence may express two or more propositions, but if it does so, it is ambiguous. Propositions
expressed by the proper logical consequences of an unambiguous sentence are not themselves
expressed, in this sense, by the sentence. The proposition that snow is white and grass is green is
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semantically expresses, and that proposition may be described as the semantic content,
or more simply as the content, of the sentence. Propositions are, like the sentences
that express them, abstract entities. Many of their properties can be ‘read off’ from
the containing sentences. Thus, for instance, it is evident that propositions are not
ontologically simple but complex. The proposition that Frege is ingenious and the
proposition that Frege is ingenuous are both, in the same way, propositions directly
about Frege; hence, they must have some component in common. Likewise, the
proposition that Frege is ingenious has some component in common with the
proposition that Russell is ingenious, and that component is different from what it
has in common with the proposition that Frege is ingenuous. Correspondingly, the
declarative sentence ‘Frege is ingenious’ shares certain syntactic components with the
sentences ‘Frege is ingenuous’ and ‘Russell is ingenious’. These syntactic components—
the name ‘Frege’ and the predicate ‘is ingenious’—are separately semantically correlated
with the corresponding component of the proposition contained by the sentence. Let
us call the proposition-component semantically correlated with an expression the
semantic content of the expression. The semantic content of the name ‘Frege’ is that
which the name contributes to the proposition contained by such sentences as ‘Frege is
ingenious’ and ‘Frege is ingenuous’; similarly, the semantic content of the predicate ‘is
ingenious’ is that entity which the predicate contributes to the proposition contained
by such sentences as ‘Frege is ingenious’ and ‘Russell is ingenious’. As a limiting case,
the semantic content of a declarative sentence is the proposition it contains, its proposition content.
Within the framework of so-called possible-worlds semantics, the extension of a
singular term with respect to a possible world w is simply its referent with respect to
w, that is, the object or individual to which the term refers with respect to w. The
extension of a sentence with respect to w is its truth value with respect to w—either
truth or falsehood. The extension of an n-place predicate with respect to w is the
class of n-tuples to which the predicate applies with respect to w, or rather the
characteristic function of the class, that is, the function that assigns either truth or
falsehood to an n-tuple of individuals, according as the predicate or its negation
applies with respect to w to the n-tuple. (Assuming bivalence, the extension of an
n-place predicate may simply be identified instead with the class of n-tuples to which
the predicate applies.) The content of an expression determines the intension of the
expression. The intension of a singular term, sentence, or predicate is a function
that assigns to any possible world w the extension that the expression takes on with
respect to w.
Since ordinary language includes so-called indexical expressions (such contextsensitive expression as ‘I’, ‘here’, ‘now’, ‘this’, ‘she’), the semantic content of an
expression, and hence also the semantic intension, may vary with the context in
which the expression is uttered. This means that content must in general be ‘indexed’
(i.e., relativized) to context. That is, strictly one should speak of the semantic content
of an expression with respect to this or that context of utterance, and similarly for the
different from the proposition that snow is white, though intuitively the latter is included as part of
the former. The sentence ‘Snow is white and grass is green’ expresses only the former, not the latter.
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367
corresponding semantic intension of an expression. This generates a higher-level,
nonrelativized semantic value for expressions, which Kaplan calls the character of an
expression. The character of an expression is a function or rule that determines for
any possible context of utterance c, the semantic content that the expression takes on
with respect to c.2 An indexical expression is then definable as one whose character is
not a constant function.
The systematic method by which it is secured which proposition is semantically
expressed by which sentence (with respect to a context) is, roughly, that a sentence
semantically contains that proposition whose components are the semantic
contents of the sentence-parts, with these semantic contents combined as the
sentence-parts are themselves combined to form the sentence.3 In order to analyze
2 Whereas Kaplan introduces his notion of character in connection with his version of a direct
reference theory, the general idea of relativizing content to context, and the resulting notion of the character of an expression, can easily fit within a Fregean (or ‘anti-direct reference’) conception of content.
Throughout this chapter, I use a quasi-technical notion of the context of an utterance which is
such tht for any particular actual utterance of an expression, if any facts had been different, even if
only facts entirely independent of and isolated from the utterance itself, then the context of the
utterance would, ipso facto, be a different context—even if the utterance is made by the very same
speaker in the very same way to the very same audience at the very same time in the very same place.
To put it another way, although a single utterance occurs in indefinitely many different possible
worlds, in every possible world in which the same utterance occurs it occurs in a new and different
context—even if the speakers, his or her manner of uttering, the time of the utterance, the location
of the speaker, the audience being addressed, and all other such features and aspects of the utterance
reamin exactly the same. Suppose, for example, that it will come to pass that a Democrat is elected
to the US presidency in the year 2000, and consider a possible world w that is exactly like the actual
world in every detail up to January 1, 1999, but in which a Republican is elected to the US
presidency in 2000. Suppose I here and now utter the sentence
(i) Actually, a Republican will be elected to the US presidency in 2000 ad.
In the actual world, I thereby assert a proposition that is necessarily false. In w, on the other hand,
I thereby assert a necessary truth. In uttering the very same sequence of words of English with the
very same English meanings in both possible worlds, I assert different things. If we were to use the
term ‘context’ in such a way that the context of my utterance remains the same in both worlds, we
would be forced to say, quite mysteriously, that the sentence I uttered is such that it would have
expressed a different proposition with respect to the context in which I uttered it if w had obtained,
even though both its meaning and its context of utterance would remain exactly the same. The
content of the sentence would emerge as a function not only of the meaning of the sentence and the
context of utterance but also of the apparently irrelevant question of which political party wins the
US presidency in the year 2000. Using the term ‘context’ as I do, we may say irtstead that although I
make the very same utterance both in w and in the actual world, the context of the utterance is
different in the two worlds. This allows us to say that the sentence I utter takes on different
information contents with respect to different contexts of utterance, thereby assimilating this
phenomenon to the sort of context sensitivity that is familiar in cases of such sentences as
‘A Republican is presently US president’.
3 The latter clause is needed in order to distinguish ‘Bill loves Mary’ from ‘Mary loves Bill’,
where the sequential order of composition is crucial. This succinct statement of the rule connecting
sentences and their contents is only an approximation to the truth. A complicated difficulty arises in
connection with the latter clause of the rule and with quantificational locutions. Grammatically the
sentence ‘Someone is wise’ is analogous to ‘Socrates is wise’, though logically and semantically
they are disanalogous. In ‘Socrates is wise’, the predicate ‘is wise’ attaches to the singular term
‘Socrates’. As Russell showed, this situation is reversed in ‘Someone is wise’, wherein the restricted
quantifier ‘someone’ attaches to the predicate ‘is wise’. Thus, whereas grammatically ‘someone’ is
combined with ‘is wise’ to form the first sentence in just the same way that ‘Socrates’ is combined
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the proposition contained by a sentence into its components, one simply decomposes the sentence into its contentful parts, and the semantic contents thereof are
the components of the contained proposition. In this way, declarative sentences not
only contain but also codify propositions. One may take it as a sort of general rule
or principle that the semantic content of any compound expression, with respect to
a given context of utterance, is made up of the semantic contents, with respect to
the given context, of the contentful components of the compound. This general rule
is subject to certain important qualifications, however, and must be construed more
as a general guide or rule of thumb. Exceptions arise in connection with quotation
marks and similar devices. The numeral ‘9’ is, in an ordinary sense, a component
part of the sentence ‘The numeral ‘‘9’’ is a singular term’, though the semantic
content of the former is no part of the proposition content of the latter. I shall
argue below that, in addition to quotation marks, there is another important though
often neglected class of operators that yield exceptions to the general rule in
something like the way quotation marks do. Still, it may be correctly said of any
English sentence free of any operators other than truth-functional connectives (e.g.,
‘If Frege is ingenious, then so is Russell’) that its proposition content is a complex
made up of the semantic contents of its contentful components.
THE SIMPLE THEORY
The simple theory is a theory of the semantic contents of some, but not all, sorts of
expressions. Specifically, the simple theory is tacit on the controversial question of
the semantic contents of proper names and similar sorts of singular terms. According
to the simple theory, the semantic content of a predicate (or common noun or verb),
as used in a particular context, is something like the attribute or concept semantically
associated with the predicate with respect to that context. For example, the content
of a monadic predicate may be identified with the corresponding property, while the
content of an n-adic predicate, n > 1, may be identified with the corresponding
n-ary relation. On the simple theory, the content of the sentence ‘Frege is ingenious’
is to be the proposition consisting of the semantic content of ‘Frege’—whatever that
may be (man, representational concept, or whatever)—and ingenuity (the property
of being ingenious). More generally, an atomic sentence consisting of an n-place
predicate p attached to an n-ary sequence of singular terms, a1,a2, . . . ,an, when
evaluated with respect to a particular possible context, is held to express the
proposition consisting of the attribute or concept referred to by p and the sequence
of semantic contents of the attached singular terms. A sentential connective may be
construed on the model of a predicate. The semantic content of a sentential
connective would thus be an attribute—not an attribute of individuals like Frege,
with ‘is wise’ to form the second sentence, the semantic contents of ‘someone’ and ‘is wise’ are
combined very differently from the way the contents of ‘Socrates’ and ‘is wise’ are combined.
A perhaps more important qualification to the general rule is noted in the next paragraph of the
text. Yet another important qualification concerns overlaid quantifiers. For details, see Frege’s
Puzzle, pp. 155–157.
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369
Top level:
character
þ context c
#
Middle level: content with respect to c ! intension with respect to c
þ possible world w and time t
#
Bottom level:
extension with respect to c, w, and t
Figure 18.1 Semantic values on the simple theory
but an attribute of propositions. Similarly, the semantic content of a quantifier
might be identified with a property of properties of individuals, and so on.
One may be tempted to hold that a sentence is a means for referring to its
proposition content by specifying the components that make it up. However, a
familiar argument due primarily to Alonzo Church and independently to Kurt
Gödel establishes that the closest theoretical analogue of singular-term reference for
any expression is its extension.4 Accordingly, the simple theory will be understood to
make room for the thesis that any expression refers to its extension, and for a
resulting distinction between reference and semantic content.
The simple theory thus recognizes three distinct levels of semantic value. The
three primary semantic values are extension, content, and character. On the same level
as, and fully determined by, content is intension. Semantic values on the simple
theory, and their levels and interrelations, are diagrammed in Figure 18.1.
(Of course, these are not the only semantic values available on the simple theory, but
they are the significant ones.) Within the framework of the simple theory, the
meaning of an expression might be identified with the expression’s character, that is,
the semantically correlated function from possible contexts of utterance to semantic
contents. For example, the meaning of the sentence
(1) I am writing
may be thought of as a function that assigns to any context of utterance c the proposition composed of the semantic content of ‘I’ with respect to c (whether that content
may be the agent of c, a Fregean sense, or something else) and the property of writing.
PROPOSITIONS AND PROPOSITION MATRICES
Compelling though it is, the simple theory is fundamentally defective and must be
modified if it is to yield a viable theory of semantic content. The flaw is illustrated by
the following example: Suppose that at some time in 1890 Frege utters sentence
4 See A. Church, ‘Review of Carnap’s Introduction to Semantics,’ The Philosophical Review, 52
(1943), pp. 298–304, at pp. 299–301; K. Gödel, ‘Russell’s Mathematical Logic,’ in P. A. Schilpp,
ed., The Philosophy of Bertrand Russell, (New York: Tudor, 1944), pp. 125–153, at pp. 128–129.
The general argument is applied to the special case of monadic predicates in my Frege’s Puzzle,
pp. 22–23, and in greater detail to the special case of common nouns in my Reference and Essence
(Princeton, N.J.: Princeton University Press, and Oxford: Basil Blackwell, 1981), pp. 48–52.
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Theory of Meaning and Reference
(1) (or its German equivalent). Consider the proposition that Frege asserts in
uttering this sentence. This is the proposition content of the sentence with respect to
the context of Frege’s uttering it. Let us call this proposition ‘p’ and the context in
which Frege asserts it ‘c ’. The proposition p is made up of the semantic content of
the indexical term ‘I’ with respect to c and the semantic content of the predicate
‘writing’ with respect to c . According to the simple theory, the latter semantic
content is the property of writing. Thus, p (the semantic content of the whole
sentence with respect to c ) is a complex abstract entity made up of the semantic
content of ‘Frege’ and the property of writing. Let us call this complex ‘Frege
writing’, or ‘fw’ for short. Thus, according to the simple theory, p ¼ fw. But this
cannot be correct. If fw is thought of as having a truth value, then it is true if and
when Frege is writing and false if and when he is not writing. Thus, fw vacillated
in truth value over time, becoming true whenever Frege began writing and false
whenever he ceased writing.5 But p , being a proposition, has in any possible world
(or at least in any possible world in which something is determined by the semantic
content of ‘Frege’) a fixed and unchanging truth value throughout its existence, and
never takes on the opposite truth value. In effect, a present-tensed sentence like
(1) expresses the same eternal proposition on any occasion of utterance as does its
temporally modified cousin
(2) I am writing now.
In this sense, propositions are eternal.
Not just some; all propositions are eternal. The eternalness of a proposition is
central and fundamental to the very idea of a proposition, and is part and parcel of a
philosophically entrenched conception of proposition content. For example, Frege,
identifying the cognitive proposition content (Erkenntniswerte) of a sentence with
what he called the ‘thought’ (Gedanke) expressed by the sentence, wrote:
Now is a thought changeable or is it timeless? The thought we express by the Pythagorean
Theorem is surely timeless, eternal, unvarying. ‘But are there not thoughts which are true
today but false in six months’ time? The thought, for example, that the tree there is covered
with green leaves, will surely be false in six months’ time.’ No, for it is not the same thought at
all. The words ‘This tree is covered with green leaves’ are not sufficient by themselves to
constitute the expression of thought, for the time of utterance is involved as well. Without the
time-specification thus given we have not a complete thought, i.e., we have no thought at all.
Only a sentence with the time-specification filled out, a sentence complete in every respect,
expresses a thought. But this thought, if it is true, is true not only today or tomorrow but
timelessly. (‘Thoughts,’ in Frege’s Logical Investigations, P. T. Geach, ed., New Haven, Conn.:
Yale University Press, 1977, pp. 1–30, at pp. 27–28)
The same sort of consideration is used by Richard Cartwright to show that the
meaning of a present-tensed sentence is not its proposition content when uttered
with assertive intent, or what is asserted by someone who utters the sentence.
5 This forces a misconstrual of the intension of sentence (1) with respect to Frege’s context c as
a two-place function that assigns to the ordered pair of both a possible world w and a time t a truth
value, either truth or falsehood, according as the individual determined by the semantic content of
‘Frege’ is writing in w at t or not.
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371
Cartwright’s argument exploits the further fact that the truth value of a proposition
is constant over space as well as time:
Consider, for this purpose, the words ‘It’s raining’. These are words, in the uttering of which,
people often (though not always) assert something. But of course what is asserted varies from
one occasion of their utterance to another. A person who utters them one day does not
(normally) make the same statement as one who utters them the next; and one who utters
them in Oberlin does not usually assert what is asserted by one who utters them in Detroit.
But these variations in what is asserted are not accompanied by corresponding changes in
meaning. The words ‘It’s raining’ retain the same meaning throughout . . . [One] who utters
[these words] speaks correctly only if he [talks about] the weather at the time of his utterance
and in his (more or less) immediate vicinity. It is this general fact about what the words mean
which makes it possible for distinct utterances of them to vary as to statement made . . . They
are used, without any alteration in meaning, to assert now one thing, now another.
(‘Propositions,’ in R. Butler, ed., Analytical Philosophy, Oxford: Basil Blackwell, 1968,
pp. 81–103, at pp. 92–94)
Similar remarks by G. E. Moore make essentially the same point about propositions expressed using the past tense:
As a general rule, whenever we use a past tense to express a proposition, the fact that we use it
is a sign that the proposition expressed is about the time at which we use it; so that if I say twice
over ‘Caesar was murdered,’ the proposition which I express on each occasion is a different
one—the first being a proposition with regard to the earlier of the two times at which I use the
words, to the effect that Caesar was murdered before that time, and the second a proposition
with regard to the latter of the two, to the effect that he was murdered before that time. So
much seems to me hardly open to question. (‘Facts and Propositions,’ in Philosophical Papers,
New York: Collier, 1966, pp. 60–88, at p. 71)
Consider again Frege’s ‘thought’ that a particular tree is covered with green leaves.
Six months from now, when the tree in question is no longer covered with green
leaves, the sentence
(3) This tree is covered with green leaves,
uttered with reference to the tree in question, will express the proposition that the
tree is then covered with green leaves. This will be false. But that proposition is false
even now. What is true now is the proposition that the tree is covered with green
leaves, in other words, the proposition that the tree is now covered with green leaves.
This is the proposition that one would currently express by uttering sentence (3). It
is eternally true—or at least true throughout the entire lifetime of the tree and never
false. There is no proposition concerning the tree’s foliage that is true now but will
be false in six months. Similarly, if the proposition p that Frege asserts in c is true,
it is eternally true. There is no noneternal proposition concerning Frege that
vacillates in truth value as he shifts from writing to not writing. The complex fw is
noneternal, neutral with respect to time. Hence, it is not a complete proposition;
that is, it is no proposition at all, properly so-called.
The truths truthsayers say and the sooths soothsayers soothsay—these all are
propositions fixed, eternal, and unvarying. Eternal are the things asserters assert, the
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things believers believe, the things dreamers dream. Eternal also are the principles we
defend, the doctrines we abhor, the things we doubt, the things we cannot doubt.
The truths that are necessarily true and those that are not, the falsehoods that are
necessarily false and those that are not—these are one and all eternal propositions.
None of this is to say that the noneternal complex fw is not a semantic value of the
sentence Frege utters, or that fw has nothing to do with proposition content. Indeed,
fw is directly obtained from the sentence Frege utters in the context c by taking the
semantic content of ‘I’ with respect to c and the property associated with ‘writing’
with respect to c . Moreover, fw can be converted into a proposition simply by
eternalizing it, that is, by infusing a particular time (moment or interval) t into the
complex to get a new abstract entity consisting of the semantic content of ‘Frege’, the
property of writing, and the particular time t. One may think of the noneternal
complex fw as the matrix of the proposition p that Frege asserts in c . Each time he
utters sentence (1), Frege asserts a different proposition, expresses a different
‘thought,’ but always one having the same matrix fw. Similarly, in some cases it may
be necessary to incorporate a location as well as a time in order to obtain a genuine
proposition, for example, ‘It is raining’ or ‘It is noon’. A proposition does not
have different truth values at different locations in the universe, any more than it
has different truth values at different times. A proposition is fixed, eternal, and
unvarying in truth value over both time and space.
To each proposition matrix there corresponds a particular property of times (or,
where necessary, a binary relation between times and places). For example, the time
property corresponding to the proposition matrix fw is the property of being a time
at which Frege is writing. It is often helpful in considering the role of proposition
matrices in the semantics of sentences to think of a proposition matrix as if it were its
corresponding property of times.
It has been noted by William and Martha Kneale, and more recently and in more
detail by Mark Richard, that this traditional conception of semantic content is
reflected in our ordinary ascriptions of belief and other propositional attitudes.6 As
Richard points out, if what is asserted or believed were something temporally neutral
or noneternal, then from the conjunction
(4) In 1990, Mary believed that Bush was president, and she has not changed her
mind about that,
it would be legitimate to infer
(5) Mary still believes that Bush is president.
Such an inference is an insult not only to Mary but also to the logic of English, as it is
ordinarily spoken. Rather, what we might infer is
(6) There is some time t in 1990 such that Mary still believes that Bush was
president at t.
6 See W. Kneale and M. Kneale, ‘Propositions and Time,’ in A. Ambrose and M. Lazerowitz,
eds., G. E. Moore: Essays in Retrospect (New York: Humanities Press, 1970), pp. 228–241, at p. 235;
Mark Richard, ‘Temporalism and Eternalism,’ Philosophical Studies 39 (1981), pp. 1–13.
Tense and Intention
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The reason for this is that what Mary is said by sentence (4) to have believed in 1990
is not the noneternal proposition matrix, Bush being president, but the eternal
proposition that Bush is president throughout a particular time period. The point is
bolstered if ‘know’ is substituted for ‘believe’.
The length of the time period is a vague matter. For many purposes, it may be
taken to be the entire year of 1990. When the time interval involved in a proposition
is significantly long, the proposition may mimic its noneternal matrix—for example,
in contexts like ‘Mary once believed that Bush was a Republican, and she still believes
that’—as long as one stays within the boundaries of the time interval in question.
Relatively stable properties (like being a Republican, as opposed to being US
president) tend to lengthen the time interval in question.7 (They need not invariably
do so.) This point is crucial to the proper analysis of inferences that seem to tell
against the argument just considered. Mark Aronszajn, for example, objects to the
argument by citing formally similar but evidently valid inferences like the following:
(7) In 1976, experts doubted that AIDS was transmitted through unprotected
heterosexual intercourse, but no experts doubt that today.
Therefore, today no experts doubt that AIDS is transmitted through
unprotected heterosexual intercourse.
(8) In 1990, Mary believed that Bush was president, and in 1992, she still
believed that.
Therefore, in 1992, Mary still believed that Bush was president.8
The modes by which AIDS is transmitted among humans are presumed to be
invariant over a very long period of time (perhaps for eternity). Likewise, a natural
interpretation of the second inference has its author ascribing to Mary the belief that
7 This is similar to a point made by Kneale and Kneale, ‘Propositions and Time,’ pp. 232–233.
Compare my Frege’s Puzzle, p. 157 n. 3. On the most natural interpretation of past-tensed belief
attribution sentences a believed that j , such a sentence is true with respect to a particular time t if
and only if there is a salient time t 0 earlier than t and a salient interval t00 including t 0 such that the
referent of a with respect to t 0 believed at t 0 the proposition expressed by j with respect to t00 . (This
semantics involves a slight departure from that proposed by Richard.)
8 See M. Aronszajn, ‘A Defense of Temporalism,’ Philosophical Studies, 81 (1996), pp. 71–95.
Aronszajn’s actual examples invoke the past progressive in place of the simple past tense (specifically,
‘AIDS was spreading among heterosexuals’ in place of ‘AIDS was transmitted through unprotected
heterosexual intercourse’), and the attribute of being up to no good as president in place of merely
being president. Aronszajn’s examples strike me as significantly less plausible than the ones provided
here. If experts in 1976 believed that AIDS was not spreading among heterosexuals, but they have
since changed their minds about that, then what they no longer believe is that AIDS was not spreading
in 1976 among heterosexuals. It is logically possible, and even consistent (albeit irrational), for such
experts to believe that AIDS was spreading among heterosexuals in 1976 (having changed their minds
in exactly the manner described) and at the same time to believe that as a result of recent educational
efforts AIDS is no longer spreading among heterosexuals. Likewise, though Mary in 1990 believed
Bush to be up to no good, and though she held fast about that two years later, she may well have
believed by then that Bush was no longer up to no good. Imagine, for example, Mary saying the
following: ‘In 1990, I believed on the basis of reliable sources that Bush was abusing the power of
his office through illegal wiretaps, directing the IRS to persecute his enemies, and more. Two years
later, I received confirmation of that very same abuse in the 1990 White House and so continued to
believe that, though I also believed that Bush had cleaned up his act by then and was finally behaving
properly. I have just received evidence that such abuse in fact continued through 1992.’
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Theory of Meaning and Reference
Bush was president during the presidential term encompassing the years 1990–1992
(as he in fact was). Indeed, if the attributed belief is presumed instead to be merely
that Bush was president throughout some shorter period of time (e.g., the year
1990), the inference becomes obviously invalid. In each case, insofar as the inference
receives an interpretation on which it is clearly valid, the proposition attributed
incorporates a time interval encompassing the indicated passage of time.
CONTENT AND CONTENT BASE
Let us call the proposition matrix that a sentence like (1) takes on with respect to a
particular context c the content base of the sentence with respect to c. More generally,
we may speak of the content base with respect to a context of any meaningful
expression (a singular term, a predicate, a connective, a quantifier, etc.). The content
base of an expression is the entity that the expression contributes to the proposition
matrix taken on by (i.e., the content base of) typical sentences containing the
expression (where a ‘typical’ sentence containing an expression does not include
additional occurrences of such devices as quotation marks or the ‘that’-operator).
The content base of a simple predicate, such as ‘writes’, with respect to a context c,
is the attribute semantically associated with the predicate with respect to c (the
property of writing). The content base of a compound expression, like a sentence, is
(typically) a complex made up of the content bases of the simple parts of the
compound expression. In particular, the content base of a definite description is a
complex made up partly of the property associated with the description’s constitutive
predicate. Since ordinary language includes indexical expressions such as ‘this tree’,
not only the semantic content but also the content base of an expression is to be
relativized to the context of utterance. An expression may take on one content base
with respect to one context, and another content base with respect to a different
context. An indexical expression is properly defined as one that takes on different
content bases with respect to different possible contexts.
The simple theory is at odds with the eternalness of propositions. There remains a
question of how best to accommodate this feature of propositions within a framework like that of the simple theory. While alternative accounts are available, what is
perhaps the path of minimal mutilation from the simple theory centers on its notion
of character.9 As defined by Kaplan, the character of an expression is the function or
It should be noted that the anaphoric pronoun ‘that’ in examples like those under consideration
here need not always refer to the proposition referred to by its antecedent. In some uses, it may refer
instead to another proposition related to the antecedently referred to proposition by having the
same matrix. Analogously, the conjunction ‘Johnny believes that he is the strongest boy in the class
and so does Billy’ may be used to report agreement between Johnny and Billy concerning who is
strongest, or alternatively to report a disagreement between them. On the latter reading, the anaphoric
pronoun ‘so’ does not refer to the act of believing the particular proposition referred to in the first
disjunct, but to the act of believing the proposition expressed by ‘I am strongest’. (Compare ‘Naturally,
Johnny believes that he is the strongest boy in the class. At that age, nearly every boy believes that’.)
9 A somewhat different approach is adopted in my Frege’s Puzzle, pp. 24–43, and in ‘Tense and
Singular Propositions.’ Compare M. Richard, ‘Tense, Propositions, and Meanings,’ Philosophical
Tense and Intention
375
rule that takes one from an arbitrary context of utterance to the expression’s semantic
content with respect to that context. This may be identified with the expression’s
meaning only insofar as the content is misidentified with its noneternal matrix. Let
us now reconstrue character as the function or rule that determines for any possible
context c the content base (rather than the content) that the expression takes on with
respect to c. This transmutation of the old notion of character forms the heart of a
corrected version of the simple theory. An indexical expression is now redefined as
one whose character, as here reconstrued, is not a constant function; it is one whose
content base varies with context.
The content base of an expression with respect to a context c determines a corresponding function that assigns to any time t (and location l, if necessary) an
appropriate content for the expression. (In fact, the function also determines the
corresponding content base.) For example, the proposition matrix fw (the content
base of ‘Frege is writing’) determines a function that assigns to any time t the
proposition that Frege is writing at t. (This is the propositional function corresponding to the property of being a time at which Frege is writing.) Let us call the
function from times (and locations) to contents thus determined by the content base
of an expression with respect to a given context c the schedule of the expression with
respect to c. Since the semantic content of an expression determines its intension, the
content base of an expression with respect to a context c also determines a corresponding function that assigns to any time t (and location l, if necessary) the resulting
intension for the expression. Let us call this function from times (and locations) to
intensions the superintension of the expression with respect to c. Accordingly, we
should speak of the semantic content, and the corresponding intension, of an
expression with respect to a context c and a time t (and a location l, if necessary). The
simple theory must be modified accordingly. Specifically, the notion of semantic
content, by contrast with that of content base, is doubly relativized (in some cases,
triply relativized). Significantly, the time to which the content of an expression
is relativized need not be the time of the context, although of course it can be.
Thus, for example, the expression ‘my car’ refers with respect to my present context
and the year 1989 to the Honda that is formerly mine. The same expression
refers with respect to my present context and the year 1996 to the Toyota that is
presently mine.
We should also like to speak (as we already have) of the content of an expression
(e.g., of the proposition expressed by a sentence) with respect to a context simpliciter,
without having to speak of the content with respect to both a context and a time.
Studies, 41 (1982), pp. 337–351. The burden of this chapter is to show that one can consistently
hold that propositions are eternal while temporal sentential operators operate on noneternal
semantic values of sentences, by holding that temporal sentential operators operate on two-place
functions from contexts and times to eternal propositions. These two-place functions are similar to
(and determined by) sentence characters. Indeed, Richard calls his two-place functions the
‘meanings’ of sentences. The claim that temporal operators operate on the ‘meanings’ of expressions, however, is at best misleading. When each of Richard’s two-place functions is replaced by its
corresponding one-place function from contexts to one-place functions from times to eternal
propositions, it emerges that temporal operators operate on something at a level other than that of
character.
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Theory of Meaning and Reference
This is implicit in the notion of the character of an expression, as defined earlier.
How do we get from the content base of an expression with respect to a given context
to the content with respect to the same context simpliciter without further indexing,
or relativization, to a time (and location)?
In the passage quoted above, Frege seems to suggest that the words making up a
tensed but otherwise temporally unmodified sentence, taken together with contextual factors that secure contents for indexical expressions such as ‘this tree’, at most
yield only something like what we are calling a ‘proposition matrix’, that is, the
content base of the sentence with respect to the context of utterance, which is ‘not a
complete thought, i.e., . . . no thought at all.’ He suggests further that we must rely
on the very time of the context of utterance to provide a ‘time-specification’ or ‘timeindication’—presumably a specification or indication of the very time itself—which
supplements the words to eternalize their content base, thereby yielding a genuine
proposition or ‘thought.’ Earlier in the same article, Frege writes:
[It often happens that] the mere wording, which can be made permanent by writing or the
gramophone, does not suffice for the expression of the thought. The present tense is [typically]
used . . . in order to indicate a time. . . . If a time-indication is conveyed by the present tense
one must know when the sentence was uttered in order to grasp the thought correctly.
Therefore the time of utterance is part of the expression of the thought (‘Thoughts,’ in Logical
Investigations, p. 10)
On Frege’s view, strictly speaking, the sequence of words making up a tensed but
otherwise temporally unmodified sentence like (3), even when taken together with a
contextual indication of which tree is intended, does not yet bear genuine cognitive
content. Its content is incomplete. Presumably, on Frege’s view, the sequence of
words together with a contextual indication of which tree is intended has the logicosemantic status of a predicate true of certain times—something like the predicate
‘is a time at which this tree is covered with green leaves’ accompanied by a pointing
to the tree in question—except that (3) thus accompanied may be completed by a
time, serving as a specification or indication of itself, rather than by something
syntactic, like the term ‘now’. Accordingly, on Frege’s theory, the content, or ‘sense’
(Sinn), of (3) together with an indication of the intended tree but in abstraction
from any time would be a function whose values are propositions, or ‘thoughts’
(Gedanken).10 Only the sequence of words making up the sentence together with an
Richard also apparently misconstrues to some extent what Kaplan (and others) mean in saying
that an operator ‘operates on’ such-and-such’s. In general, to say that a given operator operates on
the such-and-such of its operand is to say that an appropriate extension for the operator would be a
function from such-and-such’s appropriate to expressions that may serve as its operand to extensions appropriate to the compounds formed from the operator together with the operand. For
example, to say that a modal sentential operator operates on the content or on the intension of its
operand sentence is to say that an appropriate extension for a modal operator would be a function
from propositions or from sentence intensions (functions from possible worlds to truth values) to
truth values.
10 On Frege’s theory, the domain of this function would consist of senses that determine times,
rather than the times themselves.
There is no reason on Frege’s theory why the time-indication or time-specification that
supplements the incomplete present-tensed sentence could not be verbal, as in ‘At 12:00 noon on
Tense and Intention
377
indication of which tree is intended and together with a time-indication or timespecification, as may be provided by the time of utterance itself, is ‘a sentence
complete in every respect’ and has cognitive content.
It is not necessary to view the situation by Frege’s lights. Whereas Frege speaks of
the cognitive thought content (or Erkenntniswerte) of the words supplemented by both
a contextual indication of which tree is intended and a ‘time-indication,’ one may
speak instead (as I already have) of the content of the sequence of words themselves
with respect to a context of utterance and a time. The content of sentence (3) with
respect to a context c and a time t is simply the result of applying the schedule, with
respect to c, of the sequence of words to t. This is a proposition about the tree
contextually indicated in c, to the effect that it is covered with green leaves at t. In the
general case, instead of speaking of the content of an expression supplemented by
both a contextual indication of the referents of the demonstratives or other indexicals
contained therein and a ‘time-indication,’ as may be provided by the time of
utterance, one may speak of the content of the expression with respect to a context
and a time (and a location, if necessary). Still, Frege’s conception strongly suggests a
way of constructing a singly indexed notion of the content of an expression with
respect to (or supplemented by) a context of utterance c simpliciter, without further
relativization to (or supplementation by) a time, in terms of the doubly indexed
locution: we may define the singly relativized notion of the content of an expression
with respect to a context c as the content with respect both to c and the very time of c
(and with respect to the very location of c, if necessary).
In particular, then, the semantic content of a sentence with respect to a given
context c is its content with respect to c and the time of c (and the location of c, if
necessary). Consequently, any temporally unmodified sentence or clause expresses
different propositions with respect to different contexts of utterance (simpliciter). For
example, sentence (3) (more accurately, the untensed clause ‘this tree be covered
July 4, 1983, this tree is covered with green leaves’. This aspect of Frege’s theory allows for a
solution to the problem of failure of substitutivity of coreferential singular terms in temporal
contexts—a solution very different from Frege’s solution to the parallel problem of failure of
substitutivity in propositional attitude contexts. Consider the following example. The expressions
‘the US president’ and ‘Bill Clinton’ refer to the same individual with respect to the time of my
writing these wods, but the former cannot be substituted salva veritate for the latter in the true
sentence ‘In 1991, Bill Clinton was a Democrat’. The result of such substitution is ‘In 1991, the US
president was a Democrat’, which is false on the relevant reading (the Russellian secondary
occurrence or narrow scope reading). Frege may solve this problem, not implausibly, by noting
that the expression ‘the US president’ is incomplete and requires supplementation by a timespecification, such as may be provided by the time of utterance, before it can refer to an individual.
The description ‘the US president’, supplemented by the time of my writing these worlds, refers
to the same individual as the name ‘Bill Clinton’. Supplemented by the year 1991, or by a verbal
specification thereof, it refers to George Bush. The result of the substitution includes a verbal timespecification, ‘in 1991’, which, we may assume, supersedes the time of utterance in completing
any expression occurring within its scope in need of completion by a time-specification. Compare
Frege’s treatment of substitutivity failure in propositional attitude contexts. On Frege’s theory, a
propositional attitude operator such as ‘Jones believes that’ creates an oblique context in which
expressions refer to their customary contents (‘senses’) instead of their customary referents. On the
Fregean solution to substitutivity failure in temporal contexts presented here, by contrast, the
referent of ‘the US president’, as occurring within the context ‘in 1991, __’, is just its customary
referent.
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Theory of Meaning and Reference
with green leaves’) contains different propositions with respect to different times of
utterance even though the speaker is pointing to the same tree. Uttered six months
from now, it expresses the proposition about the tree in question that it is then
covered with green leaves. Uttered today, it contains the proposition that the tree
is covered with green leaves, that is, that it is now covered with green leaves. The
existence of this linguistic phenomenon is precisely the point made by Frege and
echoed by Moore and Cartwright in the passages quoted in the section on Propositions and Proposition Matrices.
Let us call this adjusted version of the simple theory the corrected theory. The
corrected theory is the simple theory adjusted to accommodate the eternalness of
semantic content. The adjustment involves only the temporal nature of content. The
corrected theory remains neutral with respect to the dispute among Fregeans,
Millians, and others concerning the question of what constitutes the semantic
content of indexicals and similar expressions.
Within the framework of the corrected theory, the meaning of an expression is
identified with its character, now construed as a function from contexts to content
bases. This allows one to distinguish pairs of expressions like ‘the US president’ and
‘the present US president’ as having different meanings, even though they take on
the same contents (or at least trivially equivalent contents) with respect to the same
contexts. Their difference in meaning is highlighted by the fact that the latter is
indexical while the former is not. More accurately, the character of an expression is
the primary component of what is ordinarily called the ‘meaning’ of the expression,
though an expression’s meaning may have additional components that supplement
the character.11
The corrected theory’s notion of the content base of an expression with respect to
a given context, and the resulting reconstrual of the character of an expression, impose
a fourth level of semantic value, intermediate between the level of character and the
level of content. The four primary semantic values, from the bottom up, are extension,
content (construed now as necessarily eternal), content base, and character. There are
also two additional subordinate semantic values. Besides intension (construed now as
a one-place function from possible worlds) there are schedule and superintension,
both of which are on the same level as, and fully determined by, the content base.
Semantic values on the corrected theory, and their levels and interrelations, are
diagrammed in Figure 18.2. (Notice that character now takes one from a context c to
a content base, which still needs a time t in order to generate a content.)
The referent of a complex definite description like ‘the wife of the present US
president’ with respect to a context of utterance c, a time t, and a possible world w is
semantically determined in a sequence of steps. First, the character of the expression
is applied to the context c to yield the content base of the expression with respect to c.
11 For example, the meaning of the term ‘table’ might include, in addition to its character, some
sort of conceptual content, such as a specification of the function of a table. If so, it does not follow
that this sort of conceptual entity is any part of the semantic content of the term. Nor does it
follow that it is analytic, in the classical sense, that tables have such and such a function. What does
follow is that in order to know fully the meaning of ‘table’, one would have to know that the things
called ‘tables’ are conventionally believed to have such and such a function.
Tense and Intention
Level 4:
(Top level)
Level 3:
Level 2:
character
þ context c
#
context base with $ schedule with
respect to c
respect to c
þ time t
#
content with respect
to c and t
Level 1:
(Bottom level)
379
! superintension with
respect to c
þ time t
#
! intension with respect to
c and t
þ possible world w
#
extension with respect
to c, t, and w
Figure 18.2 Semantic values on the corrected theory
The latter is something like the time-neutral concept of uniquely being a wife of
whoever is uniquely US president at cT, where cT is the particular time of the context
c. (The temporal indexing to cT is provided for by the term ‘present’, which is
interpreted here in its indexical sense.) This yields the schedule of the expression
with respect to c, which assigns to any time t 0 the concept of uniquely being at t 0 a
wife of whoever is uniquely US president at cT. This schedule is applied to the
particular time t to give the eternal semantic content of the expression with respect to
both c and t. This semantic content, in turn, yields the expression’s intension with
respect to c and t, which assigns to any possible world w 0 the individual who is
uniquely a wife at t in w 0 of whoever is uniquely US president at cT in w 0 . (Since this
is not a constant function, the description is not a rigid designator.) Finally, this
intension is applied to the particular world w to yield the wife at t in w of the US
president at cT in w. On the corrected theory, the extension of an expression with
respect simply to a given context of utterance, without further relativization to a time
or a possible world, is the result of applying the intension of the expression with
respect to that context (which in turn is the result of applying the super-intension of
the expression with respect to that context to the very time of the context) to the very
possible world of the context. Thus, where cW is the possible world of c, the referent
of ‘the wife of the present US president’ with respect to c itself is none other than the
wife at cT in cW of the US president at cT in cW.
TENSE VERSUS INDEXICALITY
It may appear that I have been spinning out semantic values in excess of what is
needed. We need a singly indexed notion of the semantic content of an expression
with respect to a context and, as a special case, a notion of the content of a sentence
with respect to a context. This led to the simple theory’s identification of
meaning with a function from contexts to contents. But we have just seen that this
function has no special role to play in determining the semantics for an expression
like ‘the wife of the actual US president’. In getting to the content, and ultimately to
the extension, we are now going by way of the content base instead of the content.
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Theory of Meaning and Reference
With regard to ‘the wife of the actual US president’, and similarly with regard to an
entire sentence like (1) or (3), the content base with respect to a context is neutral with
respect to time whereas the, content with respect to the same context is eternal,
somehow incorporating the time (and location, if necessary) of the context. If the rule
of content composition is that the content of a complex expression, like a sentence, is
constructed from the contents of the simple contentful components together with the
time (and location, if necessary) of utterance, then why bother mentioning those
partially constructed propositions I am calling ‘proposition matrices’? Singling out
content bases as separate semantic values generates the doubly indexed notion of the
content of a sentence with respect to both a context c and a time t, and thereby the
new construal of character. What is the point of this doubly indexed notion, and of
the resulting reconstrual of character? Are we not interested only in the case where
the time t is the time of the context of utterance c? Why separate out the time as an
independent semantic parameter that may differ from the time of utterance?
Semantic theorists heretofore have gotten along fine by indexing the notion of
content once, and only once, to the context of utterance, without relativizing further
and independently to times. For example, in discussing the phenomenon of tense,
Frege also considers various indexicals—‘today’, ‘yesterday’, ‘here’, ‘there’, and ‘I’—
and suggests a uniform treatment for sentences involving either tense or indexicals:
In all such cases the mere wording, as it can be preserved in writing, is not the complete
expression of the thought; the knowledge of certain conditions accompanying the utterance,
which are used as a means of expressing the thought, is needed for us to grasp the thought
correctly. Pointing the finger, hand gestures, glances may belong here too. (‘Thoughts,’
in Logical Investigations, pp. 10–11)
Following Frege, it would seem that we can handle the phenomena of tense and
indexicality together in one fell swoop, with tense as a special case of indexicality, by
simply relativizing the notion of semantic content once and for all to the complete
context of utterance—including the time and location of the utterance as well as the
speaker and his or her accompanying pointings, hand gestures, and glances. Any
aspect of the complete context of utterance may conceivably form ‘part of the
expression of the thought’ or contribute to the content. Once content is relativized
to the complete context, including the time of utterance, gestures, and so on, there
seems to be no need to relativize further and independently to times.
It has been known since the mid-1970s that the phenomenon of tense cannot be
fully assimilated to temporal indexicality and that the presence of indexical temporal
operators necessitates ‘double indexing,’ that is, relativization of the extensions of
expressions—the reference of a singular term, the truth value of a sentence, the class
of application of a predicate—to utterance times independently of the relativization
to times already required by the presence of tense or other temporal operators.12
(Something similar is true in the presence of an indexical modal operator such as
‘actually’ and in the presence of indexical locational operators such as ‘it is the case
12 The need for double indexing was apparently first noted in 1967 by Hans Kamp in
unpublished material distributed to a graduate seminar while Kamp was a graduate student at
UCLA See his ‘Formal Properties of ‘‘Now’’,’ Theoria 37 (1972), pp. 227–273. Kamp’s results were
reported in A. N. Prior, ‘ ‘‘Now’’,’ Noûs 2 (1968), pp. 101–119.
Tense and Intention
381
here that’.) Here is an illustration: The present perfect tense operator functions in
such a way that for any untensed clause S (e.g., ‘Frege be writing’), the result of
applying the present perfect tense operator to S (‘Frege has been writing’) is true with
respect to a time t (roughly) if and only if S is true with respect to some time t 0 earlier
than t. Similarly, the nonindexical operator ‘on the next day’ þ future tense functions in such a way that the result of applying this operator to any untensed clause S
is true with respect to a time t if and only if S is true with respect to the day next after
the day of t. For example, suppose that instead of uttering sentence (1), Frege speaks
the following words (perhaps as part of a larger utterance) in his context c :
(9) I will be writing on the next day.
This sentence, in Frege’s mouth, is true with respect to a time t if and only if Frege
writes on the day after the day of t—whether or not t is the time of c . Indeed, our
primary interest may be in some time t other than that of c —for example, if Frege’s
complete utterance in c is of the sentence
(10) Regarding December 24, 1891, I will be writing on the next day.
On the other hand, the indexical operator ‘tomorrow’ þ future tense functions in
such a way that the result of applying it to any untensed clause S is true with respect
to a context c and a time t if and only if S is true with respect to c and the day after c,
forgetting about the time t altogether. If in c Frege had uttered the sentence
(11) I will be writing tomorrow,
the sentence, in Frege’s mouth, would be true with respect to any time if and only if
Frege writes on the day after c .
To illustrate the need for double indexing, consider how one might attempt to
accommodate ‘on the next day’ þ future tense using relativization only to possible
contexts of utterance, without independent relativization to times. Let us try this:
Say that the result of applying this operator to S is true with respect to a context c if
and only if S is true with respect to some possible context c 0 just like c in every respect
(agent, location, etc.) except that the time of c 0 is one day later than that of c. For
example, ‘I will be writing on the next day’ will be regarded as being true with respect
to a context c if and only if its untensed operand
(1 0 ) I be writing
is true with respect to a possible context c 0 whose day is the day after c, but which
involves the same agent as c to preserve the referent of ‘I’. (We assume for the time being
that an untensed clause such as (1 0 ) is a mere surface grammar variation of its presenttensed counterpart, so that (1) and (1 0 ) share the same semantics.) This singly indexed
account seems to yield the correct results until we consider sentences that embed one
temporal operator within the scope of another. Consider the following sentences:
(12)
(13)
(14)
(15)
The US president is a Republican,
The present US president is a Republican,
Sometimes, the US president is a Republican,
Sometimes, the present US president is a Republican.
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Theory of Meaning and Reference
Sentences (14) and (15) result from applying the temporal operator ‘sometimes’
to sentences (12) and (13), respectively. According to the singly relativized account,
(15) is true with respect to a context of utterance c (roughly) if and only if there is
some time t 0 , which need not be cT (the time of c), such that the US president at t 0 is
a Republican at t 0 (in the possible world of c). But this is the wrong truth condition
for the sentence. In fact, it is the correct truth condition for the wrong sentence, to
wit, the nonindexical sentence (14).
Sentences (14) and (15) differ in their truth conditions. Suppose both sentences
are uttered in 1996, when the US president is a lifelong Democrat though previously
the presidency had been held by the Republicans. Sentence (14) is then true whereas
sentence (15) is false. Sentence (15) is true with respect to a context of utterance c
(roughly) if and only if there is some time t 0 such that the US president at cT (the
time of the context c) is a Republican at t 0 (in the possible world of c). The temporal
operator ‘sometimes’ directs us to evaluate its operand clause with respect to all times
t 0 . The operand clause (13) is true with respect to the same context c and a time t 0 if
and only if the description ‘the present US president’ refers to something with
respect to c and t 0 to which the predicate ‘is a Republican’ applies with respect to c
and t 0 . In computing the referent of the description with respect to c and t 0 , the
indexical operator ‘present’ directs us to seek an object to which its operand phrase
‘US president’ applies with respect to cT, the very time of the context of utterance
itself, forgetting about the time t 0 . Thus, in evaluating sentence (15) with respect to a
time of utterance cT, we are concerned simultaneously with the extension of ‘US
president’ with respect to cT and the extension of ‘is a Republican’ with respect to a
second time t 0 . The truth value of the whole depends entirely and solely on whether
the unique object to which the phrase ‘US president’ applies with respect to cT is
something to which the predicate is a Republican’ applies with respect to t 0 . It is for
this reason that a systematic theory of the extensions of the expressions of a language
containing indexical temporal operators requires double indexing; that is, in general
the notion of the extension of an expression (e.g., the truth value of a sentence) is
relativized to both a context and a time, treated as independent semantic parameters.
A systematic singly indexed theory gives the wrong results. Frege’s theory, for
example, must regard the indexical description ‘the present US president’ as
extensionally semantically equivalent to the non-indexical ‘the US president’. Both
would be regarded as expressions that are incomplete by themselves (hence, refer by
themselves, in abstraction from any context, to functions), but that when completed
by a ‘time-specification’ or ‘time-indication’ (as may be provided by the time of
utterance) refer to the individual who is US president at the specified or indicated
time. Using extensional semantic considerations alone, Frege’s theory is unable to
find any difference with respect to truth or even with respect to truth conditions
between the indexical sentence (15), taken as uttered at a certain time, and the
nonindexical (14), taken as uttered at the very same time.13
13 This is partly a result of Frege’s principle of compositionality (or interchange) for reference.
(See note 1.) On Frege’s theory of tense and indexicality, both ‘the US president’ and ‘the present
US president’ refer, in abstraction from context, to the function that assigns to any time t the
individual who is US president at t—like the functor ‘the US president at time__’—except that the
Tense and Intention
383
This example illustrates that where an indexical temporal operator occurs within
the scope of another temporal operator within a single sentence, the extensions of
expressions are to be indexed both to the time of utterance and to a second time
parameter, which may be other than the time of utterance and not even significantly
related to the time of utterance. Temporal operators determine which time or times
the extension of their operands are determined with respect to. In the special case of
indexical temporal operators, the time so determined is a function of the time of the
context of utterance. What is distinctive about indexical expressions (‘I’, ‘this tree’,
or ‘the present US president’) is not merely that the extension with respect to a
context c varies with the context c, or even that the intension or semantic content
with respect to a context c varies with c. That much may be true of even a nonindexical expression, such as ‘the US president’ or ‘Frege is writing’. What makes an
expression indexical is that its extension with respect to a context c and a time t and a
possible world w varies with the context c even when the other parameters are held
fixed. This is to say that its superintension, and hence its content base, with respect
to a context c varies with c. It is precisely this that separates ‘the present US president’
from its non-indexical cousin ‘the US president’.
Though it is less often noted,14 it is equally important that double indexing to
contexts and times (or triple indexing to contexts, times, and locations, if necessary)
is required at the level of semantic content as well as at the level of extension. For
illustration, consider first the sentence
(16) At t , I believed that Frege was writing.
By the ordinary laws of temporal semantics, this sentence is true with respect to a
context of utterance c if and only if the sentence
(17) I believe that Frege is writing
is true with respect to both c and the time t . This, in turn, is so if and only if the
binary predicate ‘believe’ applies with respect to c and t to the ordered pair of the
referent of ‘I’ with respect to c and t and the referent of the ‘that’-clause ‘that Frege
is writing’ with respect to c and t . Hence, sentence (16) is true with respect to c if
and only if the agent of c believes at t the proposition referred to by the ‘that’-clause
with respect to c and t . The ‘that’-clause in (16) refers with respect to c and t to the
proposition that is the content of the operand sentence ‘Frege is writing’. But which
proposition is that?
If content is to be singly indexed to context alone, it would seem that the ‘that’clause ‘that Frege is writing’ refers with respect to c and t to the content of ‘Frege is
writing’ with respect to c, forgetting about t altogether. This is the proposition that
expression may be completed by a time rather than by a verbal time-specification (the time of
utterance acting as a self-referential singular term). By Frege’s compositionality principle for reference, it follows that any complete sentence built from ‘the US president’, without using oblique
devices (e.g., ‘In 1996, the US president was a Republican’), has the same truth conditions, and
therefore the same truth value, as the corresponding sentence built from ‘the present US president’.
14 But see Richard, ‘Tense, Propositions, and Meanings,’ pp. 346–349. The idea of double
indexing content to both contexts and times is Richard’s.
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Theory of Meaning and Reference
Frege is writing at cT, where cT is the time of c. However, this yields the wrong truth
condition for (16). This would be the correct truth condition for the sentence
(18) At t , I believed that Frege would be writing now.
Sentence (16) ascribes a belief at t that Frege is writing at t . Assuming that
content is singly indexed to context alone, we are apparently
forced to construe the
d
e
‘that’-operator in such a way that a ‘that’-clause that S refers with respect to a
context c and a time t 0 not to the content of S with respect to c but to the content of S
with respect to a (typically different) context c 0 exactly like c in every respect (agent,
location, etc.) except that its time is t 0 . (The contexts c and c 0 would be the same if
and only if t 0 were the time of c.)
This account appears to yield exactly the right results until we consider a sentence
that embeds an indexical temporal operator within the ‘that’-operator and embeds
the result within another temporal operator. Consider the following:
(19) In 2001, Jones will believe that the present US president is the best of all the
former US presidents.
This sentence is true with respect to a context c if and only if Jones believes in 2001
the proposition referred to by the words ‘that the present US president is the best of
all the former US presidents’ with respect to c and the year 2001. On the singly
indexed account of content, sentence (19) comes out true if and only if Jones believes
in 2001 that the US president in 2001 is the best of all the US presidents before
2001. But this is the truth condition for the wrong sentence, namely,
(20) In 2001, Jones will believe that the then US president is the best of all the
former US presidents.
Sentence (19) ascribes, with respect to c, a belief that the US president at cT is the
best of all the US presidents before 2001. In order to obtain this result, the ‘that’clause in (19) must be taken as referring with respect to c and the year 2001 to the
proposition that the US president at cT is the best of all the US presidents prior to
2001 (or to some proposition trivially equivalent to this). This cannot be accommodated by a singly indexed account. It requires seeing content as doubly indexed:
to the original context c and to the year 2001.
TEMPORAL OPERATORS
Two sorts of operators are familiar to philosophers of language. An extensional
operator is one that operates on the extensions of its operands, in the sense that an
appropriate extension for the operator itself would be a function from extensions
appropriate to the operands (as opposed to some other aspect of the operands) to
extensions appropriate to the compounds formed by attaching the operator to an
appropriate operand. An extensional sentential connective (such as ‘not’ or ‘if . . . ,
then . . .’) is truth functional; an appropriate extension would be a function from
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385
(n-tuples of ) truth values to truth values, and hence an appropriate semantic content
would be an attribute of truth values. An intensional or modal operator is one that
operates, on the intensions of its operands. An appropriate extension for a modal
connective like ‘it is necessarily the case that’ would be a function from (n-tuples of )
sentence intensions (functions from possible worlds to truth values) or propositions
to truth values, and an appropriate semantic content would be an attribute of
intensions or propositions—for example, the property of being a necessary truth.
David Kaplan forcefully raises an objection to the conventional conception of
propositions as eternal in connection with the applicability of intensional operators.
He writes:
Operators of the familiar kind treated in intensional logic (modal, temporal, etc.) operate on
contents. . . . A modal operator when applied to an intension will look at the behavior of the
intension with respect to [possible worlds]. A temporal operator will, similarly, be concerned
with the time. . . . If we build the time of evaluation into the contents (thus . . . making contents specific as to time), it would make no sense to have temporal operators. To put the point
another way, if what is said [i.e., if the proposition asserted by a speaker] is thought of as
incorporating reference to a specific time, . . . it is otiose to ask whether what is said [the
proposition] would have been true at another time . . . (‘Demonstratives,’ pp. 502–503)
He elaborates in a footnote:
Technically, we must note that [temporal] operators must, if they are not to be vacuous,
operate on contents which are neutral with respect to [time]. Thus, for example, if we take the
content of [(1)] to be [an eternal, time-specific proposition rather than its noneternal, temporally neutral matrix], the application of a temporal operator to such a content would have
no effect; the operator would be vacuous. (‘Demonstratives,’ pp.503–504 n.)
Continuing this line of thought in the text, he writes:
This functional notion of the content of a sentence in a context may not, because of the
neutrality of content with respect to time and place, say, exactly correspond to the classical
conception of a proposition. But the classical conception can be introduced by adding the
demonstratives ‘now’ and ‘here’ to the sentence and taking the content of the result.
(‘Demonstratives,’ p. 504)
It is not otiose in the least to modify a sentence like (1) by applying a temporal
operator, like ‘yesterday’ þ past tense. The attached operator is anything but
vacuous. It does not follow, however, that the content of (1), with respect to a given
context, is something temporally neutral. Claiming that temporal operators operate
on contents, and having defined the content of a sentence as the proposition asserted
by someone in uttering the sentence, or what is said, Kaplan is forced to construe the
proposition expressed by a sentence like (1) as something that may change in truth
value at different times and in some cases even at different places. But this yields an
incorrect account of propositions. Propositions, qua objects of assertion and belief,
are eternal. As Frege, Moore, and Cartwright pointed out—and as Kaplan seems to
acknowledge—propositions do not vacillate in truth value over time or space.
Consider the temporal operator ‘sometimes’—or more accurately, ‘sometimes’ þ
present tense, which applies to an untensed clause S to form a new sentence. Is this
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Theory of Meaning and Reference
an extensional operator? Certainly not. With respect to my actual present context,
the sentences ‘It is cloudy’ and ‘2 þ 2 ¼ 5’ are equally false, though ‘Sometimes, it is
cloudy’ is true whereas ‘Sometimes, 2 þ 2 ¼ 5’ is false. Nor is the ‘sometimes’
operator intensional, in the above sense. As with (1) and (2), sentences (12) and (13),
uttered simultaneously, have precisely the same intension—indeed, they share the
same proposition content (or at least trivially equivalent contents that are very nearly
the same). But their temporal existential generalizations, (14) and (15), uttered
simultaneously, have different contents, even different truth values. On the relevant
reading (the Russellian secondary occurrence or narrow scope reading), (14) is true
whereas (15) is false. (In fact, (15) is false on both the narrow scope and wide scope
readings.) Thus, ’sometimes’ is not a content operator either. As Kaplan points out,
a temporal operator, if it is not to be vacuous, must operate on something that is
temporally neutral. Contrary to Kaplan, what follows from this is that temporal
operators do not operate on propositions. When a temporal operator is applied to
(12), it is the matrix of the proposition expressed by (12), not the proposition itself,
that is the proper object upon which the operator operates. In short, temporal
operators like ‘sometimes’ are superintensional operators.15 An appropriate extension for ‘sometimes’ with respect to a context c, a time t, and a possible world w
would be the function that assigns truth to a proposition matrix (or to its corresponding schedule or superintension) if its value for at least one time (the resulting
proposition or sentence intension) itself yields truth for the world w, and that
otherwise assigns falsehood to the proposition matrix.
Kaplan comes close to recognizing that the objects of assertion and propositional
attitude are eternal propositions when he shows (‘Demonstratives,’ p. 500) that what
is said in uttering a temporally indexical sentence like (2) at different times is
different. His argument for this is that if such a sentence is uttered by me today and
by you tomorrow, then
[if] what we say differs in truth value, that is enough to show that we say different things. But
even if the truth values were the same, it is clear that there are possible circumstances in which
what I said would be true but what you said would be false. Thus we say different things.
This is indeed correct. But the same argument can be made with equal force for a
nonindexical tensed sentence. Thus, it is not surprising to find the following analogous argument given earlier by G. E. Moore:
It seems at first sight obvious that, if you have a number of judgements [i.e., utterances] with
the same content, if one is true the rest must be.
But if you take a set of judgements [i.e., utterances] with regard to a given event A, [using
words to the effect] either that it is happening, or that it is past, or that it is future, some of
each set will be true and some false, which are true and which false depending on the time
when the judgement [i.e., utterance] is made.
It seems a sufficient answer to say that a judgement [i.e., an utterance of a sentence of the
form] ‘A is happening’ made at one time never has the same content as the judgement [i.e.,
an utterance of the sentence] ‘A is happening’ made at another. (‘The Present,’ Notebook ii.
15 Modal operators on the so-called branching worlds (or ‘unpreventability’) interpretation
emerge as superintensional operators.
Tense and Intention
387
[c. 1926], in The Commonplace Book 1919–1953, Casimir Lewy, ed., New York: Macmillan,
1962, p. 89)
Consider again sentence (1). Mimicking Kaplan, and following Moore, one may
argue that if Frege utters it at t and again on the next day, and if what he asserted on
the two occasions of utterance differ in truth value (across time), as indeed they may,
that is enough to show that he asserted different things. This is precisely because it is
known that what is asserted is not the sort of thing that can switch back and forth in
truth value from one moment to the next. Since what is asserted on the one occasion
is different from what is asserted on the other, it is not this content but its matrix, fw,
upon which temporal operators operate.
In order to obtain the correct results, one must regard a sentential temporal
operator such as ‘sometimes’ as operating on some aspect of its operand clause that is
fixed relative to a context of utterance (in order to give a correct treatment of
temporally modified indexical sentences like (15)) but whose truth value typically
varies with respect to time (so that it makes sense to say that it is sometimes true, or
true at such and such time). Once it is acknowledged that content is eternal, there
simply is no such semantic value of a sentence on the simple theory’s three-tiered
array of semantic values. Nothing that is fixed relative to a context is also time
sensitive in the required way. In order to find an appropriate semantic value for
temporal operators such as ‘sometimes’ þ present tense to operate on, one must posit
a fourth level of semantic value.
The result of applying ‘sometimes’ to a sentence S may be regarded as expressing,
with respect to a given context c, a proposition concerning the content base of the
operand sentence S with respect to c. For example, the sentence
(21) Sometimes, I am writing
contains, with respect to Frege’s context c (or any other context in which Frege is
the agent), the proposition about the proposition matrix fw that it is sometimes true.
Accordingly, an appropriate semantic content for a temporal operator such as
‘sometimes’ would be a property of proposition matrices—in this case, the property
of being true at some time(s).
PREDICATES AND QUANTIFIERS
An important point about predicates, quantifiers, and certain other operators
emerges from the four-tiered corrected theory, and from the distinction between
semantic content and content base in particular. The content base of a predicate with
respect to a given context of utterance c is a concept or attribute (property or
relation). This, together with a time t, determines the semantic content of the
predicate with respect to c and t. In turn, the semantic content of a predicate with
respect to c and t, together with a possible world w, determines the extension of the
predicate with respect to c, t, and w. It follows that the semantic content of a
predicate such as ‘writes’ (or ‘be writing’) with respect to a context c and a time t is
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Theory of Meaning and Reference
not just the concept or property of writing (or anything similar, such as the function
that assigns to any individual x the proposition matrix x writing). The concept or
property of writing, together with a possible world w, cannot determine the
extension of ‘writes’ with respect to both the world w and the time t, that is, the class
of possible individuals who are writing at t in w. The property of writing, together
with a possible world w, determines only the class of possible individuals who are
writing at some time or other in w (or at most, the function that assigns to any time t
the class of possible individuals who are writing at t in w). The semantic content of
‘writes’ with respect to a time t must be such as to determine for any possible world
w the class of (possible) individuals who are writing at the given time t in w. Only
some sort of complex consisting of the concept or property of writing together with
the given time t will suffice to determine for any possible world w the extension of
‘writes’ with respect to both w and t. The semantic content of ‘writes’ with respect to
a given time t is not merely the concept or property of writing but a temporally
indexed concept or property: the concept or property of writing at t.
In general, the semantic content of a predicate with respect to a time t (and a
location l, if necessary) is not the same attribute as the content base of the predicate
but is the temporally indexed attribute that results from taking the content base of
the predicate together with the time t (and location l, if necessary). Semantic content
for predicates like ‘writes’ thus varies with time. Exactly analogous remarks apply to
quantifiers, other second-order predicates, the definite-description operator ‘the’,
and a variety of other operators.
This usually unrecognized fact about predicates allows us to retain, at least as a
sort of general guide or rule of thumb, the principle that the semantic content of a
compound expression, such as a sentence or phrase, is a complex made up solely and
entirely of the semantic contents of the contentful components that make up the
compound. In particular, the content of sentence (1) with respect to a context of
utterance c may be thought of as made up of the semantic contents of ‘I’ and ‘am
writing’ with respect to c. There is no need to introduce the time of the context as a
third and separate component, for it is already built into the semantic content of the
predicate (the property or concept of writing-at-cT, where cT is the time of c).
Since the semantic content of an expression with respect to a context c simpliciter
is the semantic content with respect to both c and the time of c (and the location of c,
if necessary), it follows that the semantic content of a typical predicate varies with
context—even the content of non-indexicals like ‘writes’, ‘red’, ‘table’, ‘tree’. To this
extent, Cratylus was right on the money. It is this usually unnoticed feature of
predicates that accounts for the fact that the sentence ‘Frege is writing’ takes on not
only different truth values but also different contents when uttered at different times,
even though the sentence contains no indexicals and is not itself indexical. It is also
this feature of predicates that accounts for the fact that certain noneternal (i.e.,
temporally nonrigid) definite descriptions, such as ‘the US president’, take on not
only different referents but also different semantic contents when uttered at different
times even though the description is not indexical. Recall that the distinctive feature
of an indexical like ‘I’ or ‘the present US president’ is that it takes on different
content bases in different contexts. The semantic contents of the definite description
‘the US president’, of the word ‘writes’, and of the sentence ‘The US president is
Tense and Intention
389
writing’ each varies with context. Yet none of these expressions is indexical; each
retains the same content base in all contexts.16
The account of the semantic contents of temporal operators as properties of
proposition matrices (or other content bases) makes for an important but usually
unrecognized class of exceptions to the general principle that the semantic content of
a compound expression is made up of the contents of its contentful components.
Where T is a monadic temporal sentential operator (e.g., ‘sometimes’ þ present
tense or ‘on July 4, 1968’ þ past tense), the content of the result of applying T to a
clause S is made up of the content of T together with the content base rather than
the content of S. In general, if T is a temporal operator, the content of the result of
applying T to an expression is a complex made up of the semantic content of T and
the content base rather than the content of the operand expression. Ordinarily, the
content of an expression containing as a part the result of applying a temporal
operator T to an operand expression is made up, in part, of the content base of the
operand expression rather than its semantic content. (For complete accuracy, the
notion of semantic content with respect to a context, a time, and a location, for a
language L should be defined recursively over the complexity of expressions of L.)17
It is instructive to look at how the four-tiered corrected theory treats a simple,
untensed clause, such as (1 0 ) and various complex sentences built from it. The
character of (1 0 ) is given by the following rule:
(22) For any context c, the content base of (1 0 ) with respect to c is the proposition
matrix cA writing, where cA is the agent of c. This proposition matrix is made
up of the content bases of ‘I’ and of ‘be writing’ with respect to c. The latter
may be taken to be the property or concept of writing.
16 On this account, the sentence ‘Rain is falling’ typically expresses, with respect to a context
of utterance c, the proposition that rain is falling at cL at cT, where cL is the location of c and cT is
the time of c. (An exception arises if, for example, the sentence is used as a shorthand for ‘Rain is
falling there’, with implicit reference to some location other than that of the context.) No actual
reference is made, however, either explicitly or implicitly, to either cL, or cT. Instead, assuming that
the sentence is subject-predicate, the predicate ‘is falling’ expresses as its semantic content the
spatially and temporally indexed concept or property of falling at cL at cT, and the extension
determined is the class of things that are falling at cL at cT in the world of the context. This contrasts
with the account proposed by Mark Crimmins and John Perry. See their ‘The Prince and
the Phone Booth: Reporting Puzzling Beliefs,’ Journal of Philosophy 86 (December 1989),
pp. 685–711, at pp. 699–700; and Crimmins’s Talk about Beliefs (Cambridge, Mass.: MIT Press,
1992), pp. 16–18.
17 The content base of the result of attaching a content operator (such as ‘necessarily’ or the
‘that’-operator) to a sentence is a complex made up of the content base of the operator and
the content base of the sentence, rather than its content. Thus, for example, the content base of the
‘that’-clause ‘that Frege is writing’ with respect to any context c does not involve the content of
‘Frege is writing’ with respect to c (which is the proposition that Frege is writing at cT). Instead, it is
something like the ordered pair of two elements: (a) a certain abstract entity, analogous to a
property, which is the operation of assigning any proposition to itself (this operation—call it ‘Op’—
is the content base of the ‘that’-operator); and (b) the proposition matrix fw. Thus, the content base
of ‘that Frege is writing’ has the structure hOp, hFrege, writingii. The content of ‘Sometimes, Frege
believes that he is writing’ has the following structure, where ‘Stimes’ designates the property of
proposition matrices of being true at some time(s):
(i) hhFrege, Op, hFrege, writingi, believingi, Stimesi.
(For further details, see appendix C of Frege’s Puzzle.)
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Theory of Meaning and Reference
The schedule of (1 0 ) with respect to a given context c is thus given by the
following rule:
(23) For any time t, the semantic content of (1 0 ) with respect to c and t is the
proposition made up of the content of ‘I’ with respect to c and t (i.e., the
result of applying the schedule of ‘I’ with respect to c to the particular time t)
and the property of writing-at-t (the result of applying the schedule of ‘be
writing’ to t). This may be taken to be the proposition that cA is writing at t,
where cA is the agent of c.
The semantic content of (1 0 ) with respect to a context c simpliciter is therefore the
proposition that cA is writing at cT, where cT is the time of c.
We may contrast this with the indexical sentence (2). Its character is given by
something like the following rule:
(24) For any context c, the content base of (2) with respect to c is the higher-order
proposition made up of the content bases of (1 0 ) and of ‘now’ þ present tense
with respect to c. The former may be taken to be the proposition matrix cA
writing, and the latter the property of proposition matrices of obtaining (or
being true) at cT, where cA is the agent of c and cT is the time of c.
This rule reveals the fact that the content base, of the eternal sentence (2) is in fact
already a full-fledged, eternal proposition, rather than a non-eternal proposition
matrix. The schedule of (2) with respect to a context c is thus a constant function
from times to the, higher-order proposition about the proposition matrix cA writing
that it obtains at cT. The content of (2) with respect to a context c simpliciter is this
same higher-order singular proposition, whereas the semantic content of the simpler
(1 0 ) with respect to c is the proposition that cA is writing at cT. Since, cA is writing
at cT if and only if the proposition matrix cA writing obtains at cT, the semantic
contents of (1 0 ) and (2) with respect to any context of utterance are trivially
equivalent. If we assume that sentence (1) is merely a surface transformation of (1 0 ),
then what is said by a speaker uttering either (1) or (2) at the same time is very nearly
the same, as long as the speaker is the same. Still, the content bases are very different.
With respect to any context c, the content base of (1) is noneternal, neutral with
respect to time, whereas the content base of (2) is eternal. As Kaplan notes, only the
former can be felicitously operated upon by temporal operators.
Contrary to Kaplan, since the contents, what is said, are trivially equivalent, the
function of ‘now’ cannot be primarily to affect what is said in context. Its effect on
content is in fact nil (or virtually so). Rather, the function of ‘now’ is primarily to
affect the content base of its operand, eternalizing it and thereby sealing it off from
the influence of external occurrences of temporal operators. For example, attaching
‘sometimes’ to sentence (1), whose content base with respect to any context is
noneternal, aptly yields sentence (21), whose content base is eternal. By contrast,
‘sometimes’ is at best superfluous in
(25) Sometimes, I am writing now.
Compare also the role of ‘present’ in (15).
Tense and Intention
391
Analogously, the schedule of a sentence like ‘I will be writing tomorrow’, as
uttered by a speaker cT at time cA, is the constant function that assigns to any time t
the eternal proposition that cT writing obtains on d þ , where d þ is the day after the
day of cT. The schedule of the sentence ‘I will be writing on the next day’, with
respect to the same context, is a nonconstant function that assigns to any time t the
proposition that cA writing obtains on the day next after tD, where tD is the day of t.
Despite the close similarity between the contents of the two sentences with respect to
any context (what are said), the schedules are very different, and only the latter
sentence may be felicitously operated upon by temporal operators. Compare ‘On
December 24, 2001, I will be writing on the next day’ with ‘On December 24, 2001,
1 will be writing tomorrow’.
PURE TENSES
A considerably richer semantic theory of temporal operators may be obtained by
drawing a three-way distinction among quantificational or general temporal operators, specific or singular temporal operators, and pure tense operators such as simple
past or future tense. Quantificational or general temporal operators include such
operators as ‘sometimes’, ‘always’, present perfect tense (as in ‘I have been writing’
in the sense of ‘I have sometimes been writing’), ‘it will always be that’ þ present
tense, ‘twice before’ þ past tense, and so on. Specific or singular temporal operators
include ‘it is now the case that’, ‘on December 24, 2001’ þ future tense, ‘when Frege
wrote ‘‘Thoughts’’ ’ þ past tense, and so on. (Compare ‘possibly’ with ‘actually’.)
The difference between these two sorts of temporal operators lies in their accompanying semantics. Roughly, a specific sentential temporal operator T is one such
that there is some specific time t semantically associated with T, with respect to a
context (and a time and a possible world), in such way that the result of applying T
to a sentence S is true with respect to a time t 0 if and only if S is true with respect
to t, and t stands in some appropriate temporal-order relation to t 0 . For example,
‘On December 24, 2001, I will be writing’ is true with respect to a context c and the
year 1996 if and only if both of the following conditions obtain: (a) clause (1 0 ) (or
sentence (1)) is true with respect to c and December 24, 2001; and (b) 2001 is later
than 1996. A general sentential temporal operator T is a nonspecific temporal
operator such that there is some specific property P of classes of times semantically
associated with T (with respect to semantic parameters) in such a way that the result
of applying T to a sentence S is true with respect to a time t 0 if and only if the class of
times with respect to which S is true and that stand in some appropriate temporalorder relation to t 0 has P. For example, in the case of the present perfect tense, the
property P is that of being nonempty, and the appropriate temporal-order relation is
the earlier-than relation.18
18 These explications of the notions of specific and general temporal operators cannot be
regarded as strict definitions and are intended only to convey a general idea. The operator ‘when
Frege wrote ‘‘Thoughts’’ ’ þ past tense is to count as a specific temporal operator even if it should
turn out that Frege did not write ‘Thoughts.’ Also, given a sufficiently liberal notion of a property
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Theory of Meaning and Reference
Now consider ordinary past or future tense, as in ‘Frege was writing’ or ‘Frege will
be writing’. Past tense is often treated as though it were a quantificational temporal
operator, so that the displayed sentence is regarded as being true with respect to a
time t if and only if ‘Frege is writing’ is true with respect to some time or other earlier
than t. (See, for example, the quotation from G. E. Moore in section 2.3.) While a
simple past-tensed sentence is sometimes used in this way (roughly, as equivalent to
the corresponding present-perfect-tensed sentence), it generally is not. Ordinarily, a
simple past-tensed sentence like ‘Frege was writing’ is used with implicit reference to
a specific (though perhaps vaguely delineated) time, so that if Frege was not writing
at the relevant time, then what is said is false even if Frege was writing at some time
or other prior to the utterance. Compare ‘I asked Frege to come along, but he was
writing’ with ‘I have sometimes asked Frege to come along, but he has sometimes
been writing’. Analogous remarks apply to future tense.
Most simple sentential temporal operators require, in idiomatic English, an
appropriate adjustment in the tense of the operand. For example, if I wished to apply
the temporal operator ‘at 3:00 p.m. on August 24, 1996’ to sentence (1), at the time
of my writing these words—which happens to be 2:55 p.m. on August 24, 1996—I
must accompany it with a shift from present to future tense. If I wait six minutes and
forever thereafter, I must instead use past tense. It is not sufficient to say when my
writing occurs; I must also specify whether the time of my writing is now, or
previously, or still to come. The content base of each sentence is eternal, and the
same proposition (or at least very nearly the same propositions) would be asserted at
each time, and yet grammar compels me to indicate besides the indicated time, the
temporal direction of that time—either earlier or later—from the time of utterance.
What I say is that (a) my writing occurs at 3:00 p.m. on August 24, 1996; and (b)
3:00 p.m. on August 24, 1996, is future (or present or past, depending on the
tense used). It is not enough simply to date the described state of affairs. One is
linguistically required also to place the state of affairs described within what
J. M. E. McTaggart called the A-series—the everchanging manifold divided into
past, present, and future, in which each element in the third of these three categories
eventually finds itself temporarily in the second before coming to rest in the first. In
this sense, the specific temporal operator ‘at 3:00 p.m. on August 24, 1996’ is
incomplete. Simple past tense and simple future tense are complementary incomplete
temporal operators, which modify an untensed, temporally unmodified clause like
(1 0 ) to form a sentence that may now be modified by an incomplete specific or
incomplete general temporal operator. The tense operator primes the atomic clause
for the application of a specific or general (incomplete) temporal operator. An
of a class, some precaution must be taken if a specific temporal operator is to be precluded from
being a general temporal operator. It may be appropriate to define a general temporal operator as a
nonspecific temporal operator of a certain sort. (A similar difficulty is encountered in defining
ordinary quantifiers in such a way as to preclude ordinary singular terms.) More importantly, the
explications provided here are appropriate for what I shall call complete temporal operators below,
although the terminology of ‘specific’ or ‘singular’ and ‘quantificational’ or ‘general’ temporal
operators will be used also for the components of these, which I shall call ‘incomplete’ temporal
operators below (e.g., ‘when Frege wrote ‘‘Thoughts’’ ’ without an accompanying tense operator).
These various notions can be made precise, though it is preferable to leave them at an intuitive,
informal level in motivating the account under consideration here.
Tense and Intention
393
incomplete specific or general temporal operator combines with a pure tense
operator to form a complete temporal operator. The complete temporal operator
applied to (1 0 ) is ‘at 3:00 p.m. on August 24, 1996’ þ future tense. The extension of
a complete temporal operator is a function from proposition matrices (or minimally,
from sentence superintensions) to truth values, and the content of a complete
temporal operator is accordingly a concept or property of proposition matrices.
It is instructive to regard ordinary past tense as a superintensional operator with
the following distinguishing property: its extension with respect to a time t and a
possible world w is the function that assigns to any proposition matrix m (alternatively, to any sentence schedule or superintension—i.e., any function from times
to sentence intensions) not a truth value, but the class of times t 0 earlier than t at
which m obtains in w (or equivalently, the characteristic function of this class of
times). An analogous construal is possible for the future tense operator, replacing
‘earlier’ by ‘later’. A past-tensed or future-tensed but otherwise temporally unmodified sentence would thus have as its extension not a truth value, but a class of times.
For example, the extension of the simple past-tensed sentence
(26) I was writing,
with respect to a context c, a time t, and a possible world w, would be the class of
times t 0 earlier than t such that the component untensed clause (1 0 ) is true with
respect to c, t 0 , and w. An unmodified past-tensed sentence like (26) may be
represented formally as
(27) Past Tense[Be Writing(I )].19
Such a sentence essentially stands in need of completion by an incomplete temporal operator, either specific or general, in order to achieve truth value. The
extension (with respect to a context, a time, and a possible world) of an incomplete
specific temporal operator, like ‘at 3:00 p.m. on August 24, 1996’, may be taken to
be simply the indicated time, rather than the corresponding function from
proposition matrices (or sentence schedules or superintensions) to truth values.
Where T is any incomplete specific temporal operator without an accompanying
tense operator, the result of applying T to a past-tensed sentence such as (26) is
representable as
(28) T(Past Tense[Be Writing(I )]).
This is a complete sentence, whose extension is a truth value. The sentence is true
(with respect to semantic parameters) if and only if the extension of T is an element
of the extension of the operand past-tensed clause Past Tense[Be Writing(I )]. It is
thus as if the past tense operator in
(26) transformed its operand clause (1 0 ) into the corresponding predicate
(29) is a past time at which I be writing.
19
The naked infinitive phrase ‘be writing’ might be represented further as
(i) Progressive Tense (Write).
The word ‘writing’ itself is functioning here adjectivally.
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Theory of Meaning and Reference
An incomplete specific temporal operator such as ‘at 3:00 p.m. on August 24,
1996’ attaches to the tensed sentence as if the operator were a singular term to which
a monadic predicate attaches. The complete temporal operator ‘at 3:00 p.m. on
August 24, 1996’ þ past tense is a one-place connective. Its extension may be
regarded as a function from proposition matrices to truth values.
In ordinary use, a past-tensed but otherwise temporally unmodified sentence like
(26), standing alone as a declarative sentence in a piece of discourse, may be regarded
as involving an implicit, specific, demonstrative temporal operator ‘then’, or ‘at that
time’, in order to obtain a complete sentence, ‘I was writing then’. This ordinary sort
of use of (26) would thus be represented formally as
(30) Then(Past Tense[Be Writing(I )])
and would be taken to mean something like That time is a past time at which I be
writing. If the time implicitly designated in an utterance of (26) (standing alone as a
declarative sentence in a piece of discourse) is not one at which the speaker writes,
what is said is false even if the speaker has written at other times prior to the
utterance. Analogous remarks apply to ‘I will be writing’.20
Taking the extension of an incomplete specific temporal operator like ‘at
3:00 p.m. on August 24, 1996’ without an accompanying tense operator to be
simply the indicated time, in order to obtain a complete sentence whose extension is
a truth value from an incomplete specific temporal operator and an untensed clause
like (1 0 ) as operand, a tense operator must be supplied as a bridge connecting the
content base of the operand clause with respect to a context c to the extension with
respect to c of the temporal operator, thereby achieving truth value. Which tense
operator is appropriate will depend on the direction of the indicated time, earlier or
later, relative to the time of c. This account thus accommodates the fact that the
appropriate complete temporal operator typically shifts its constitutive tense from
future to past with the passage of time.
On a Fregean approach, incomplete specific temporal operators like ‘now’ and ‘at
3:00 p.m. on August 24, 1996’ would be taken as expressing as the operator’s
semantic content (Sinn), a certain concept or property of the time so designated. On
a Millian approach, by contrast, the semantic contents of these operators may again
be regarded as simply the indicated time. On either approach, the content of a
specific temporal operator like ‘when Frege wrote ‘‘Thoughts’’ ’ may plausibly be
regarded as analogous to that of the corresponding definite description ‘the past time
at which Frege writes ‘‘Thoughts’’ ’. (The word ‘when’ in such constructions is the
temporal analogue of the definite-description operator ‘the’.) To repeat, the corrected theory is completely neutral regarding such issues and is consistent with either
approach.
In earlier work, I have advocated a Millian version of the corrected theory, on
which the semantic content of ‘now’ with respect to a context is taken to be the time
of the context itself rather than a concept or property ( presentness) of that time (see
Frege’s Puzzle and ‘Tense and Singular Propositions’). It does not follow, contrary to
20
See W. V. O. Quine, Word and Object (Cambridge, Mass.: MIT Press, 1960), pp. 170–171.
Tense and Intention
395
an argument of Quentin Smith,21 that my nonneutral approach is committed to a
rejection of McTaggart’s A-series of time in favor of the B-series—in which any
element is past, present, or future not per se but only relative to some (another or the
same) element of the series—and hence to a ‘tenseless’ theory of time, according to
which the distinction among past, present, and future is unreal, illusory, relational
(to a particular speech act or thought act), merely subjective, or carries no special
metaphysical or cosmological significance.22 Nor does it follow that tensed sentences
like (1), (2), and (26), on my approach, locate particular states of affairs within the
B-series but not within the A-series. On the contrary, even the corrected theory,
which is itself neutral with regard to the contents of specific temporal operators—
and of which my Millian account is a special version—explicitly recognizes, for
example, that (26) places the speaker’s writing in the past. On a Millian version of
the corrected theory, this is not accomplished by the implicit ‘then’ in (26). On any
version of the corrected theory, it is accomplished by the explicit ‘was’. The
A-property of pastness is overtly expressed in (26), by the very presence of past tense.
Similarly, futurity is expressed by future tense.23
Just as an incomplete specific temporal operator may be plausibly treated as a
singular term, so an incomplete quantificational temporal operator may be plausibly
21 See Q. Smith, Language and Time (Oxford: Oxford University Press, 1993), especially pp.
44–48; L. N. Oaklander and Q. Smith, eds., The New Theory of Time (New Haven, Conn.: Yale
University Press; 1994), especially pp. 12–19, 51–54, 136–153.
22 Those (such as myself ) who accept the A-series as veridical need not deny that the dating of an
event or state of affairs within the series, or indeed that the whole series itself, is relativized to a
‘frame of reference.’ They may hold that, relative to one’s frame of reference, the division among
past, present, and future is real, with the present enjoying a special metaphysical status and each
time eventually having its turn at it.
23 Furthermore, even if the particular word ‘now’ does not express any concept as its semantic
content, a relevant concept of presentness may be semantically contained elsewhere in other
expressions. In my ‘Existence,’ in J. Tomberlin, ed., Philosophical Perspectives. Vol. 1, Metaphysics
(Atascadero, Calif.: Ridgeview, 1987), pp. 49–108, I suggest that the English word ‘current’, as in
‘the current US president’, exemplifies an ambiguity analogous to David Lewis’s distinction
between the primary (indexical) and secondary (nonindexical) English senses of ‘actual’. (Consider
‘In 1989, current interest rates were higher than present rates’.) The secondary sense of ‘current’ is a
concept of precisely the sort that Smith misinterprets me as rejecting (note 21 above).
On the other hand, on the corrected theory a tensed sentence is translatable, in some relevant
sense, into an untensed sentence that places the described state of affairs in the B-series. According
to the corrected theory, in uttering the sentence ‘At t , Frege was writing’, one asserts that (a) fw
obtains at t , and (b) t is past. This is an A-determination, rather than a B-determination, in virtue
of the second conjunct. But since propositions are eternal, the second conjunct is not the proposition matrix t being past (which obtains only after t , not at t itself or at any earlier time), but
the eternal proposition that t is past at cT, where cT is the time of utterance. And this proposition is
tantamount to the B-determination that t is earlier than cT. For this reason, it is a conceptual
mistake to pose the question of whether ‘time is tensed’ (i.e., whether the A-series is cosmologically
veridical or objective, etc.) in terms of the untranslatability of tensed A-statements into tenseless
B-statements. And indeed, it is a philosophical mistake to infer from the translatability (in this
sense) of A-statements into B-statements that the A-properties of pastness, presentness, and futurity
are somehow unreal or illusory, and so on. Doing so is analogous to claiming to have discovered a
cure for baldness, which consists in paraphrasing any statement ascribing baldness to Jones into a
statement asserting the binary relation of being bald at—not a property—to hold between Jones and
the time of utterance. Though Jones may rejoice in his loss of the property of baldness, he still has
no need of shampoo. (Hegelians, who love a synthesis, will probably conclude that he wears a wig.)
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Theory of Meaning and Reference
treated as a corresponding quantifier. The extension of ‘sometimes’, for example, may
be taken to be the class of all nonempty classes of times (or equivalently, the characteristic function of this class), and its semantic content may likewise be taken to be
the corresponding higher-order property of being a nonempty class of times. A
quantificational temporal operator thus also requires an accompanying tense as a bridge
connecting the superintension of its operand clause to its own extension. The result of
applying a quantificational temporal operator to a tensed sentence is true if and only if
the extension of the tensed sentence (which is not a truth value but a class of times) is an
element of the extension of the quantificational temporal operator. Thus, for example,
the sentence ‘Sometimes, Frege was writing’ is true with respect to a time t if and only if
the class of times earlier than t at which Frege is writing (the extension of ‘Frege was
writing’ with respect to t) is nonempty—that is, if and only if some time t 0 is a time
earlier than t at which Frege is writing. (The complete quantificational temporal
operator ‘sometimes’ þ past tense provides a roughly correct, albeit somewhat strained,
definition of one use of the present perfect tense, as in ‘Frege has been writing’, as well
as of language theorists’ alternative use of simple past tense.) Incomplete quantificational temporal sentential operators such as ‘sometimes’, ‘always’, and ‘twice before’ are
thus regarded as attaching to tensed sentences in the way that quantifiers such as
‘something’, ‘everything’, and ‘exactly two smaller things’ attach to monadic predicates,
whereas incomplete specific temporal operators such as ‘on August 24, 1996’ and
‘when Frege wrote ‘‘Thoughts’’ ’ are regarded as attaching to tensed sentences in the
way that singular terms are attached to by monadic predicates.24
There are complications involved in extending this account of temporal operators
to cases in which temporal operators such as ‘sometimes’, ‘always’, ‘now’, and ‘today’
are applied directly to present-tensed sentences, as in any of the examples (2), (14),
(15), and (21). The account would suggest that such instances of present tense be
regarded as instances of a pure tense operator, analogous to past or future tense
except that its extension with respect to a time t and a possible world w is the
function that assigns to any proposition matrix m the class of times t 0 —whether
earlier than, later than, or overlapping with t—at which m obtains in w. Such an
operator is required, on the account being considered here, in order to prime a
temporally unmodified clause such as (1 0 ) for an operator such as ‘sometimes’ or
‘today’, to bridge the super-intension of the unmodified clause with the extension of
the incomplete specific or general temporal operator.
Strictly speaking, (1) probably should not be regarded as the atomic sentence
formed by attaching the temporally unmodified predicate corresponding to the
naked infinitive phrase ‘be writing’ to the term ‘I’, as represented formally by
(31) Be Writing (I ).
24 A problem for this account arises in connection with such constructions as ‘Frege always was
busy’, which does not mean that every time is a past time at which Frege is busy. The sentence seems
to mean instead that every past time is a time at which Frege is busy. But on the account proposed
here, the past tense operator operates on the value base of the untensed clause ‘Frege be busy’ and
the incomplete operator ‘always’ attaches to the result (i.e., to the past-tensed ‘Frege was busy’),
apparently resulting in the incorrect former reading for the sentence. The alternative reading would
seem to require seeing the past tense operator as somehow modifying the ‘always’ rather than the
untensed clause.
Tense and Intention
397
What this represents is not (1) but (1 0 ). Although (1 0 ) is not a grammatical sentence
of English, it is complete in itself. Its extension (with respect to appropriate semantic
parameters) is a truth value; it is true with respect to a context c, a world w, and a
time t if and only if the agent of c is writing at t in w. What, then, becomes of (1)?
On the account of temporal operators under consideration, the result of applying
present tense to (1 0 ), represented formally as
(32) Present Tense[Be Writing(I )],
is not a complete sentence of English, capable of truth value standing alone. Its extension is a class of times rather than a truth value. Yet surely one who wishes to assert
what is encoded by a simple, atomic clause like (1 0 ) uses a tensed sentence, namely,
(1). How are we to accommodate the fact that (1) is capable of achieving truth value
when standing alone as a declarative sentence without an additional temporal operator?
On this theory, such uses are regarded as involving an implicit specific, indexical
temporal operator such as ‘now’. For example, sentence (1) standing alone would be
seen as elliptical for (2), represented formally as
(33) Now(Present Tense[Be Writing(I )]).
This account of simple present tense is exactly analogous to the treatment suggested above of simple past tense according to which a simple past-tensed sentence
such as (26) or ‘Frege was writing’, standing alone as a declarative sentence in a piece
of discourse, is elliptical for a temporally indexical completion, for example, ‘Frege
was writing then’. We may call this the ellipsis theory of present tense.25 It is not my
Whereas the latter reading of the sentence is closer to the actual meaning than the former (clearly
a misreading), it also does not seem exactly correct. The sentence in question generally is not used
with this meaning (although, of course, it can be so used). As with a simple past-tensed sentence,
a sentence such as ‘Frege always was busy’ is ordinarily used with implicit reference to a particular
(perhaps vaguely delineated) period or interval of time in mind, so that what is said is true as long
as Frege is busy throughout that period even if at some other times he is not busy. This feature
of such constructions can be accommodated on the present account by taking incomplete quantificational temporal operators, such as ‘always’, to involve implicit reference to a particular period
or interval—very much in the manner of implicitly relativized uses of quantificational constructions
in English (such as, the ‘everything’ in ‘Everything is in order’ or the ‘everyone’ in ‘Is everyone
here?’). A sentence such as ‘Frege always was busy’, standing alone as a declarative sentence in a
piece of discourse, may thus be taken to mean something like the following: Every time during
that period is an earlier time at which Frege is busy (with reference to a contextually indicated
period of time).
25 One alternative to the ellipsis theory is the theory that the English construction represented by
‘Writing(I)’ is simply sentence (1). Indeed, it is commonplace in most discussions concerning
logical form to assume that (1) is, at least as typically intended, an atomic sentence constructed from
the singular term ‘I’ and the simple predicate ‘am writing’, while regarding the present tense of the
latter not as a separate component of the sentence but as somehow built into the predicate. In an
effort to facilitate understanding of the general theory of temporal operators presented here, much
of the preceding discussion was based on the presumption of some such theory. However, if verb
tenses are to be taken seriously in accordance with the general theory of temporal operators presented here—as semantically significant contributions to sentences in themselves—this alternative
theory ultimately requires the postulation of a systematic semantic ambiguity in the present tense,
so that a simple, present-tensed sentence like (1) is ambiguous between the complete
(i) Writing(I)
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Theory of Meaning and Reference
purpose here to fill out the details of the ellipsis theory or to cite linguistic evidence
either in favor of or against this general account of the simple tenses. It is adequate to
my purpose merely to indicate the richness of the apparatus of the corrected theory
for dealing with complete and incomplete temporal operators.26
It is interesting to note that on the ellipsis theory, a present-tensed sentence such
as (3) is taken to be an incomplete sentence standing in need of completion, much as
if it were the corresponding predicate ‘is a time at which this tree be covered with
green leaves’. At the level of semantic content, the present tense operator thus
converts the content base of its untensed operand clause into something like its
corresponding property of being a time at which the tree in question is covered with
green leaves. This theory of the pure tenses thus mimics Frege’s construal of a
present-tensed sentence as standing in need of completion or supplementation,
typically provided by the time of utterance. Frege’s theory works remarkably well as
a theory of tense. Unfortunately, as we saw in sections 2.5 and 2.6, it fails as an
account of temporal indexicality.
and the incomplete (in need of supplementation by an incomplete specific or general temporal
operator)
(ii) Present Tense[Writing(I)].
The first would be an instance of the tenseless use of present tense, the second of the tensed use. The
tenseless (1) has a truth value for its extension and would be an appropriate operand for any
complete temporal operator, whereas the tensed (1) would be the result of applying, a certain tense
operator (viz., present tense qua tense operator) to the tenseless (1). The more complex logical form
of the latter would have to be regarded on this theory as going entirely unrepresented in the surface
grammar. We may call this the ambiguity theory of present tense.
Certain general considerations tend to favor the ellipsis theory over the ambiguity theory of
present tense. In general, when attempting to explain apparently divergent uses of a single
expression or locution, if an ellipsis account is available, it is to be preferred over the postulation of a
systematic semantic ambiguity—although, of course, some third alternative may be preferable to it.
See S. Kripke, ‘Speaker’s Reference and Semantic Reference,’ in P. French, T. Uehling, and
H. Wettstein, eds., Contemporary Perspectives in the Philosophy of Language (Minneapolis: University
of Minnesota Press, 1979), pp. 6–27, especially p. 19.
26 It is important for a full theory of the simple tenses to take account of the fact that the proper
operands of tenses in English seem to be not whole clauses but simple predicates (or, more
accurately, verbs). It is largely a simple problem of formal engineering to transform the theory of
pure tenses presented here into a theory of tenses as operators on the content bases of simple
predicates rather than on the value bases of whole clauses. For example, in accordance with the
spirit of the general theory of tenses presented here, a past-tensed predicate such as ‘was writing’—
which results from applying the past tense operation to the simple predicate (naked infinitive)
‘be writing’—may be regarded as having for its extension, with respect to a possible world w and a
time t, not a class of individuals (or its corresponding characteristic function from individuals to
truth values), but the function that assigns to each (possible, past, present, or future) individual i the
class of times before t at which i is writing in w.
It may also be important to recognize that the ‘that’-operator, which transforms a sentence into a
singular term (typically) referring to the sentence’s semantic content, may be attached in English to
a tensed but apparently otherwise temporally unmodified sentence, for example, ‘When Frege wrote
‘‘Thoughts,’’ he knew that he was writing’. It may be necessary to regard such ‘that’-clauses as
involving an implicit ‘then’ or ‘now’ operator. See note 17.