Analyticity, Identity and Presupposition
(Lucas P. Halpin)
Introduction
First, I will sketch an account of identity sentences according to which identity is a device for achieving
semantic change. Specifically, it changes which sentences are analytic. Second, I will sketch an account
of presupposition according to which presupposition triggers are devices for logical change. More
precisely, they change the logic of the language (not the logical form of the sentences in which they
occur). The purpose is to sketch a general strategy of appealing to change within a language to handle
tricky cases.
Part One, Section One
Identity and Analyticity
Standardly, identities such as ‘Mark Twain = Mark Twain’1 are regarded as necessary. The thesis that
necessity = analyticity is reasonably attractive at first glance, for those inclined to flinch at robust/nonlinguistic notions of necessity anyway. Suppose we assume further that a priori = analytic. Then,
identity statements would be necessary, analytic, and a priori. Let’s go a bit further and assume that a
priori = cognitive insignificant. Then ‘Mark Twain = Mark Twain’ would then be analytic, necessary, a
priori, and cognitively insignificant.
Thesis 1: Analytic = necessary.
Thesis 2: Analytic = a priori.
Thesis 3: Analytic = cognitively insignificant.
Thesis 4: Identities are necessary.
Problems arise with the analytic conception of necessity when we consider cognitively significant
identity sentences such as ‘Hesperus = Phosphorus’, ‘Samuel Clemens = Mark Twain’, and ‘Water =
H2O’. An utterance of such a sentence would express the identity of a thing with itself, surely
necessary. Supposing necessity = analyticity, these are analytic. Supposing analyticity = a priori =
cognitively insignificant, these are then a priori and cognitively insignificant. Since they are not a priori
or cognitively insignificant, something is amiss.
Problem Thesis: Some identities are both necessary and cognitively significant.
1
If you don’t like the single quotes here, just bear with me.
1
Let’s term the trio of 1-3 Classic empiricism. We can summarize the dilemma for the classic empiricist as
follows. If she treats all identities as analytic, then she can treat them all as expressing necessary truths.
However, she must then reject the claim that some identities are cognitively significant. If she admits
that some identities are not analytic, then she may regard some identities as cognitively significant.
However, she must then reject the claim that all identities are necessary. But what she cannot do is
capture the wanted position; all identities are necessary and some are cognitively significant.
A common component of a common response to this Fregean/Kripkean dilemma is short and sweet.
Necessity is objective. It’s a feature of non-linguistic reality, not of our language or thought. It can be
teased apart from these linguistic and cognitive notions (analytic, a priori, cognitively significant)
because they are different things, not one thing.
In this essay, I’ll be endorsing theses 1, 4, and the problem thesis. Analyticity = necessity. Identities are
necessary. And some identities are cognitively significant. I will reject theses 2 and 3. Analyticity ≠ A
priori. Analyticity ≠ cognitively insignificant.
The thesis of Part One of this essay is, roughly, that if one changes her attitude towards an identity
sentence, one changes the language she speaks. Identities are always analytic and hence always
necessary in the language one speaks. But, one just isn’t always speaking the same language.
Section Two
LanguageN and Analyticity
Let’s start with the introduction of a technical term, languageN.
LanguageN: A languageN consists of a syntax, another syntax, and a map from the first to the second.
If you make any changes to any of the three components, you have a new language N (‘N’ for narrow).
With respect to the first syntax of a languageN, I’ll hand wave and say it’s the familiar sort of thing
comprised of sentences and what not, for which a reasonable science is up and running. The second
syntax, the one the first is mapped to, is just reality. I like to think of reality as a syntax and I’ll wave my
hand again and say that reality is the familiar sort of thing, comprised of electrons and what not, for
which a reasonable science is up and running. The relation between them, I’ll say, is a map.
Semantic maps are less well understood. Here, I will simply assume that the semantic map is
constituted by use. ‘Use’ is a rather vaguely used term. It shall remain so in this essay. Now for some
additional assumptions.
Endorsement: Endorsements and rejections of sentences are interpreted, not sentences themselves.
2
Negation: The rejection of a sentence is equivalent to the endorsement of its negation.
Endorsement will be indicated by T, rejection by F. To be clear, these are not semantic truth values.
They are psychological, and part of the syntactic apparatus which receives an interpretation. The
assumption about negation will simplify the present discussion, allowing us to treat S-F = ¬S-T, and will
bring rejection within the range of utterance. (I’ll assume utterance = endorsement)
Analyticity will be defined as follows.
Analyticity: S is analytic iff ¬S-T (the endorsement of the negation of S) is not interpreted, and S-T is
interpreted.2
So construed, a speaker of a languageN must endorse (assign T) an analytic statement.3 If she does not,
she shifts into another languageN. Let’s emphasize that analyticity entails syntactic endorsement, not
truth. It follows that a statement may be analytic and also semantically false. In that case, the speaker
ought to revise her language. So construed analyticity considered in isolation has no real epistemic
payout. Thus, we are rejecting theses 2 and 3.
With this explication at hand, and assuming analyticity = necessity, we can now assert the following.
Necessity: S is necessary iff ¬S-T is not interpreted, and S-T is interpreted.
So construed, we can extend the problematic issues for the empiricist. Suppose ‘Samuel Clemens =
Mark Twain’ is analytic and therefore necessary. It would then follow that ‘¬(Samuel Clemens = Mark
Twain)’ has no interpretation. Supposing this has no interpretation, competent English speakers do not
endorse it. “They just don’t say that,” we might say. But, sometimes competent English speakers do
endorse it (or some other relevant sentence).
In the next section, we’ll make use of these notions, analyticity and languageN, to address the two
problems that concern us presently. First, how can identity statements be cognitively significant (or a
posteriori), if analytic? Second, how is it, supposing P is analytic, that speakers endorse ¬P (or vice
versa).
Thus, I must explain how identities can be cognitively significant, given that they are analytic. And, I
must explain why speakers of a language have endorsed the negations of identities that are analytic (or
endorsed identities whose negations are analytic), given that the language assigns them no
interpretation.
Section Three
2
This constitutes a version of the Grice/Strawson conception of analyticity. See Analyticity and Substantive Inquiry
for a more detailed presentation of this version of analyticity. Chalmers offers a similar account in “Revisability and
Conceptual Change.”
3
This is similar in some respects to views according to which there is an understanding-assent guarantee. For a
reasonably quick, but broad discussion of understanding-assent guarantees, see “Understanding and Philosophical
Methodlogy,” Magdalena and Brendan Balecerak-Jackson.
3
Identity and LanguageN Change
How can analytic identities be cognitively significant?
endorsed?
How can negations of analytic identities be
We’ll make quick work of the second issue. There are a number of ways it might be framed. Here’s one:
We are all competent speakers of the same language. Competent speakers sometimes endorse the
relevant identity statements (X = Y), or the relevant negation perhaps, ‘Hesperus ≠ Phosphorus’.
Competent speakers do not violate the semantic boundaries (analyticities) of their language. So, the
relevant identities are not analytic.
As was noted, ‘languageN’ is a technical term. A language, our natural endowment, would be a
collection of languageNs, perhaps. Let’s assume that for now.
Language: A language = a collection of languageNs.
Now we can say that a competent speaker remains with the bounds of her language. Since a language is
comprised of a collection of languageNs, she can do so while shifting languageNs. In addressing the first
issue, I’ll use two more technical terms.
A Theory: A theory = a distribution of Ts and Fs over the sentences of a languageN.
Cognitive significance: Cognitive significance = theory change.
Trivially, theory change comes in two kinds. One can change her attitude (endorsement or rejection)
towards sentences in the languageN she speaks. If she does, that is theory change and is cognitively
significant. Second, she can change the language she speaks. If she does, that is theory change and is
cognitively significant.
On the present view, T/F changes with respect to identities always involve languageN change. Thus, they
always involve theory change, and are always cognitively significant.4 Identity sentences (and their
negations) are analytic, if endorsed. Thus, the negations must be un-interpreted. Speakers don’t say
things that aren’t interpreted. So, if someone utters the relevant sentence, they must be speaking a
languageN in which it is interpreted, i.e, they must be speaking another languageN.
Consider a toy example. Zeus rejects ‘Hesperus = Phosphorus’, and endorses ‘Hesperus ≠ Phosphorus’.
Regardless of the time of day, Zeus says “Hesporus ≠ Phosphorus.” In the morning he says, “There’s
Phosphorus,” but never, “There’s Hesperus.” These identities are analytic in the languageN which Zues
speaks, and hence necessary. He’d have to use a distinct languageN to change his theory with regard to
them.
4
We might have associated cognitive significance with having an interpretation, a notion that applies to sentences
(with a T/F value), rather than changes. However, it seems to me that the interpreted/un-interpreted distinction
simply doesn’t track Frege’s concern very cleanly.
4
Then, something causes Zeus to change his theory. We’ll leave it open how such changes occur. But,
Zeus now says, “Hesperus = Phosphorus,” regardless of the time of day. In the morning he says,
“There’s Phosphorus” or “There’s Hesperus” depending on who he is speaking with. His patterns of
speech have changed in relation to the world around him. In the terms of this essay, his semantic map
has changed.
The only self-consistent motivation for the view above would involve two components. First, we would
need to finish constructing the theory. Second, we would need to show that the finished project
“handles” the data. Finishing the theory would require, among other things, a more detailed theory of
use. There is a familiar problem for theories according to which maps = use, especially salient to the
present view. Whenever one changes her patterns of endorsement, she changes her patterns of
speech. If we, following Quine, identify use with actual patterns of factual speech, we will have erased
the wanted distinction between changes in patterns of endorsement within a language, and changes in
the language itself.5 We need that distinction. So then, what is the difference between shifting from
endorsement to rejection of a sentence within a single languageN, and shifting to a new languageN
entirely? A theory of use is called for here. None will be forthcoming in this essay.
However, we can construct a bit more theory which should be insightful with respect to our present
issues. Closely associated with the notion, “a map,” is the notion, “representation.” As a first take, we
might say that X represents Y iff X is mapped to Y. These are related notions for sure. Let’s treat that as
an implicit definition.
It is commonly said that representation is arbitrary and conventional. More care is wanted here. More
precisely, mapping is arbitrary. Ignoring compositionality, nothing prevents one thing (some bit) from
being mapped to another (some other bit). There are no restrictions. Communication, on the other
hand, is not arbitrary. It is, however, conventional. There are restrictions (conventions) which are
necessary for well-functioning communication. If you would like to exchange information with another,
then you may not map your linguistic bits to whatever you like. Rather, you must use those bits in
accordance with your speech community. So then, if Z is arbitrary, certain restrictions are absent. If Z is
conventional, certain other restrictions are present. Best to keep these notions separate.
Semantic change implies semantic distinctness. Semantic distinctness violates conventions. Semantic
conventions are enforced by communication failure. Since there is variation with respect to attitudes
towards identity statements, there is semantic distinctness, and there is communication failure.
Communication failure, like use, needs to be more carefully described. I will not argue here that
divergences in attitude towards identity statements do in fact result in communication failure. My
purpose here is merely to sketch. But I will tell a suggestive little story.
Zues and Zina both believe that Hesperus is a meteorite. Only Zues believes that Hesperus =
Phosphorus. At 4 am, Zues calls Zina and tells her that Hesperus will strike the earth! She believes him.
The both endorse ‘Hesperus will strike the earth’. Zues immediately descends into his underground
5
Two Dogmas, Word and Object.
5
bunker and survives the catastrophe. Zina begins preparations for an evening disaster and is incinerated
that morning.
Something went wrong. They were operating with different theories. Presently, I am suggesting that
human behavior will be included in our theory of language, specifically of semantic maps. And, a good
way to parse (predict) cases such as this will involve attributing different semantic maps to the agents.6
The Frege scholar may be feeling a bit queasy. There is a difference between the two identities, H = H
and H = P. Inwardly, they certainly feel different. And, ordinary English speakers never switch to a
language in which ¬(X = X) is analytic. What’s the difference? That’s what concerned Frege, and it
hasn’t really been addressed. I’ll use another technical term.
Logical: S is logical iff S-T is part of the syntax and ¬S-T is not.7
Analytic sentences are those whose negations are merely un-interpreted. Logical sentences are those
whose negations8 are absent from the syntax entirely. We are supposing that there is semantic
(map/interpretation) variation among the languageNs comprising a language. In contrast, let us suppose
that there is no variation in the linguistic syntax belonging to a language. For a given language, each
languageN belonging to it shares a logical syntax. So, if ¬S-T is not part of languageN-x, it is not part of
any languageN belonging to the language.
We can now account for the difference between the two identity sentences. Identity sentences
(endorsements of them) of the form ¬(X = X) are not part of the English linguistic syntax. Those of the
form ¬(X = Y) are. Thus, identities of the form X = X, are logical, those of the form X = Y are merely
analytic.
Identity has been construed as a map changing device. It seems plain that a language could have
devices that facilitate semantic change. Would nature, or God, select a language with such devices for
us? Suppose all languages are not created equal, that we are not gifted with a uniquely best language
from the outset, are imperfectly placed and/or equipped to judge which is best, but capable of progress.
A language that comes equipped with devices to facilitate semantic change would be useful. They
would save us a great deal of pain and difficulty in cases in which semantic change is wanted. And, they
would allow us an option between two types of theory change in the event that either type will do,
whichever is most economical or aesthetically pleasing in the case at hand. The cost is a regular
communication failure.
6
For something similar in spirit to what I have in mind, see Brandom, Between Saying and Doing: Towards an
Analytic Pragmatism.
7
I’m just leaving it as an open question here how implicit definitions of this form should be treated.
8
More precisely, it is endorsements of the negations that are absent from the syntax.
6
Part Two, Section One
Presupposition
Here, in Part Two, sketch an account of presupposition that involves changes in the logical syntax of a
language. 9 We’ll start with a quotation from Stalnaker.
“The principle criterion that has been used to identify presuppositions can be stated in the
following way: Q is presupposed by an assertion that P just in case under normal conditions
one can reasonably infer that a speaker believes that Q from either his assertion or his denial
that P.” (Stalnaker, Pragmatic Presuppositions)
The most familiar cases of presupposition involve the definite article ‘the’. When one says, “The
king is bald,” or “The king is not bald,” we suppose that they believe there is a king.
Speaker-Presupposition: Q is speaker-presupposed by an assertion that P just in case under normal
conditions one can reasonably infer that a speaker believes that Q from either her assertion or her
denial that P.
The statement above focuses on the hearer’s beliefs (what we can reasonably infer) about the speaker’s
beliefs. Rather than assuming that the hearer’s inferences are reasonable, we will assume that her
beliefs are accurate. Thus, we can say that a speaker believes Q if she believes either P or ¬P.
Henceforth, we will take speaker beliefs as our data.
Data:
1. If a speaker believes P, she believes Q.
2. If a speaker believes ¬P, she believes Q.
It should be emphasized that we have not, as yet, said anything about what P, ¬P and Q themselves are
like. We have only mentioned speakers’ attitudes (belief) towards them.
“The criterion, and many of the examples, are relatively clear and uncontroversial; it is clear
that there is a phenomenon to be explained. But it is much less clear what kind of explanation
of it should be given.” (Stalnaker, Pragmatic Presuppositions)
In contrast to speaker-presupposition, semantic presupposition is a thesis about P and Q themselves. A
semantic theory of presupposition appeals to facts pertaining to the interpretations (semantics) of P and
Q to explain facts about agents’ beliefs. Consider the following version of semantic presupposition.
9
This is just a sketch. As such, only a small sample of cases will be considered. It is also not part of the purpose of
this essay to engage in substantial exegesis. For an extensive, introductory discussion of cases and issues, together
with extensive citations, see the S.E.P. entry “Presupposition,” Beaver and Geurts.
7
Semantic-Presupposition One: Q (a statement) is semantically-presupposed by P just in case: if either P
is true or ¬P is true, then Q is true.
Suppose that “The king is bald” (P) and “The king isn’t bald” (¬P) both entail “there is a king” (Q). It
would follow from the assumption that a speaker is rational that she believes either P or ¬P only if she
believes Q. We can mimic the proposal above in syntactic terms.
Syntactic-Presupposition-1: Q (a sentence) is syntactically-presupposed by P just in case if either P is T
(endorsed) or ¬P is T, then Q is T.
Both the syntactic and the semantic proposals appeal to logical entailment to explain speaker
presupposition. They differ in the account of logical entailment they appeal to. The semantic proposal
involves a semantic, truth preserving account of logical entailment. The syntactic account involves a
syntactic, endorsement preserving account of logical entailment. The definition of logical is repeated
below.
Logical: S is logical iff S-T is part of the syntax and ¬S-T is not.
On the syntactic view, if P logically entails Q and ¬P logically entails Q, then the syntax contains neither
{P-T, ¬Q-T}, nor {¬P-T, ¬Q-T} (no rows in the T-table contain those pairs), but does contain {P-T, Q-T} and
{¬P-T, Q-T}.
Here, I’ll be pursuing a syntactic account of presupposition. I’ll assume that presupposition has the
following three features, and tailor the theory accordingly. First, presupposed sentences, e.g., ‘There is
a king’, are not necessary. Second, presuppositions can be cancelled. ‘The king isn’t bald’ presupposes
‘There is a king’. But, ‘The king isn’t bald. There is no king.’ is a logically acceptable English monolog.
Third, presuppositions sometimes fail to project. ‘The king is bald’ presupposes that there is a king’, but
‘If there is a king, then the king is bald’ does not presuppose there is a king.
Non-Necessity: P, which is speaker presupposed by Q, isn’t necessary or logical.
Cancellation: ¬P presupposes Q. But (¬P, ¬Q) is a logically acceptable monolog.
Projection failure: P presupposes Q. But S, containing P, does not.
I’ll proceed as follows. First, I’ll revise the logic of the language to accommodate non-necessity. Second,
I’ll revise the logic again (more drastically) to accommodate cancellation. The second revision will allow
us to draw syntactic distinctions relevant to projection failure.
8
Section Two
Non-Necessity and Cancellation
We’ll start with non-necessity. Suppose P presupposes Q, and assume the following.
Assumption: The logic ensures that either P is T, or ¬P is T.
It would follow that Q is logical, i.e., ¬Q-T is not in the syntax. Logicality entails analyticity, what isn’t in
the syntax also isn’t interpreted. Analyticity = necessity. So, it follows that Q is necessary. Clearly, Q
(e.g., there is a king) is not necessary. So, we must revise. Consider the following.
Syntactic-Presupposition-2: P syntactically presupposes Q iff the following conditions are met.
1.
2.
3.
4.
If P is T, Q is T.
If ¬P is T, Q is T.
If ¬Q is T, then P is not T (nor F).(neither endorsed nor rejected)
If ¬Q is T, then ¬P is not T (nor F).
The syntactic proposal above is reminiscent of familiar three valued semantic theories of
presupposition. We are violating the assumption that either P is T, or ¬P is T. In so doing, we have not
merely assigned the sentence a different logical form. We have revised the logic itself. In a certain
sense, we have contracted the logic. Consider the following notions.
A Distribution: a distribution = a set of ordered pairs: <sentence, T/F value>. (a row in a table)
A Logic: A logic = a set of distributions. (a table)
One can think of the three valued logic as replacing some distributions in the set of distributions with
smaller distributions. Ordered pairs containing sentences whose T/F switch has been turned Off are
removed from some distributions.
I’ll use tables to visually illustrate how the theory accommodates non-necessity. Rows that are
inadmissible (either illogical (not part of the syntax) or un-interpreted (analytically F)) will either be
darkened or left out of the table entirely. If a speaker endorses a sentence (assigns it T) by uttering it,
we will highlight the relevant rows with light grey. This indicates what we might call the speaker’s
“psychological location.” The tables represent the speaker’s psychological/syntactic space.
As a warm up, consider a table for the non-presupposing sentence, ¬P, ‘A king isn’t bald.’ Suppose the
speaker utters this. In that case, she locates herself somewhere in rows 3/4. Row 2 is illogical and has
been darkened.
9
Row 1
Row 2
Row 3
Row 4
A king is bald.
A king isn’t bald.
There is a king.
There isn’t a king.
P
T
T
F
F
¬P
F
F
T
T
Q
T
F
T
F
¬Q
F
T
F
T
Now, let’s look at candidate tables for a presupposing sentence. Below, ‘A king is bald’ is replaced with
‘The king is bald’, which contains the “presupposition trigger,” ‘the’. Two tables are presented, one
illustrating the logic of syntactic-presupposition-1, the other the logic of syntactic-presupposition-2.
Syntactic-Presupposition-1
Row 1
Row 2
Row 3
Row 4
The king is bald.
The king isn’t bald.
There is a king.
There isn’t a king.
P
T
T
F
F
¬P
F
F
T
T
Q
T
F
T
F
¬Q
F
T
F
T
The king is bald.
The king isn’t bald.
There is a king.
There isn’t a king.
P
T
T
F
F
¬P
F
F
T
T
Q
T
F
T
F
¬Q
F
T
F
T
Syntactic-Presupposition-2
Row 1
Row 2
Row 3
Row 4
According to syntactic-presupposition-1, both P and ¬P logically entail Q. Since both are in the syntax
and one must be marked with T, ‘There is a king’ is necessary and non-necessity is violated.
Syntactic-presupposition-2, however, does not violate non-necessity. ‘There is a king’ may be assigned
F, so long as neither P nor ¬P are assigned a T/F value. The relevant psychological possibility is
illustrated in row 4, which is only a partial row. The ‘the’ sentences are simply absent, receiving no
value, in those rows. It is the presence of partial rows (contracted distributions) that makes the logic
different(“smaller parts”), and allows us to avoid necessity.
Let’s turn to cancellation, and assume the following monolog acceptable
Monologue: ‘The king isn’t bald. There is no king.’
It contains the presupposing sentence. However, that sentence is followed by an explicit rejection of
the presupposition. And, it sounds fine. Problematically, this monolog cannot be accommodated in the
10
psychological syntax of syntactic-presupposition-2. In the wanted row, T would be assigned to ¬P and
¬Q. No such row is available in that syntax.
Sometimes, it’s best to work with the easiest cases available. In some respects, ‘the’ is not the easiest
case.10 Let’s turn our attention to easier but analogous case. Consider the following.(Prince)
1) It wasn’t George who stole the tarts.
2) The tarts were stolen.
1 typically presupposes 2. Let’s suppose, however, that the following monolog is acceptable English.
Monologue: ‘It wasn’t George who stole the tarts. The tarts weren’t stolen.’
Now, we have an analogous case. The table for P and its presupposition, Q, is presented below.
Syntactic-Presupposition-2
Row 1
Row 2
Row 3
Row 4
It was George who. . .
It wasn’t George who . . .
The tarts were stolen.
The tarts weren’t stolen.
P
T
T
F
F
¬P
F
F
T
T
Q
T
F
T
F
¬Q
F
T
F
T
Again, we’ve avoided non-necessity, but the syntax cannot accommodate cancellation. Thus, the cases
appear to be analogous.
There’s something interesting about the sentence, ‘It was George who stole the tarts’. It seems to be, in
one respect or another, identical to ‘George stole the tarts’. For example, it’s natural to regard them as
having identical meanings. ‘George stole the tarts’, however, does not carry a presupposition. Consider
the table below which illustrates this.
Row 1
Row 2
Row 3
Row 4
George stole the tarts.
George didn’t steal the tarts.
The tarts were stolen.
The tarts weren’t stolen.
P
T
T
F
F
¬P
F
F
T
T
Q
T
F
T
F
¬Q
F
T
F
T
Since a row which assigns T to both ¬P and ¬Q is available, there is no presupposition. Notice further
that we can represent the wanted monolog (presupposition with cancellation) in the table above, on the
assumption that ‘It was George who stole the tarts’ = ‘George stole the tarts’.
10
I have uniqueness in mind here.
11
This is a bit strange. We want different tables illustrating the relationship between P and Q for the
following pair of sentences.
1. It wasn’t George who stole the tarts. (Three valued)
2. George didn’t steal the tarts.(Two valued)
But we want the same table for the following monologs.
1. It wasn’t George who stole the tarts. No one stole them. (Two Valued)
2. George didn’t steal the tarts. No one stole them. (Two Valued)
I suggest we follow the evidence were it leads, and use both tables. In short, presupposition triggers are
not parts of the logical form of the sentence. They change the logic of the language. Cancellation
changes it back.
Think of a logical syntax as involving two components. First, a horizontal component, which is
comprised of the well-formed formula. Second, a vertical component which is comprised of
distributions of Ts and Fs over the formula (a T-table). Presupposition triggers change the vertical
component of the logical syntax. They are ldistribution contracting devices. That is the thesis of Part
Two of this essay.
Section Three
The Theory
I’ll start by invoking an identity thesis. ‘George stole the tarts’ and ‘It was George who stole the tarts’
are the very same sentence. And, I’ll generalize.
Thesis One: For any sentence P that speaker presupposes Q, there is some sentence that R that does
not speaker presuppose Q, and Q horizontally = R (they are the same sentence).
Perhaps it would be better to abandon the term ‘sentence’ here. I’ll keep it because it’s familiar.
Furthermore, claims of this sort are not without precedence. The logical forms of X and Y are
(numerically) identical. These two phones are the same phoneme. These have identical meanings, etc.
Next, some technical terms.
SyntaxN: A syntaxN is characterized by a set of well-formed formula and a table (a logic). Any changes to
the either result in a new syntaxN.
Syntax: A syntax is a collection of syntaxNs.
12
We will suppose that all syntaxNs in a syntax share the same horizontal component. That will facilitate
our identity claim. They will not, on the present view, share the same vertical component (logic) (a brief
return to identity)11 Now for the machinery. . .
Each sentence has a switch that is in either the T or the F position exclusively. In addition, each
sentence has an On/Off switch which is in either the On or the Off position exclusively. That’s two
switches per sentence. The On/Off switch turns the T/F switch on and off.12 When a T/F switch is on, its
position is psychological active. When a T/F switch is turned Off, it is psychological inactive. The agent
can neither endorse nor reject the sentence if the T/F switch has been turned Off.
Recall that a syntactic item, e.g., S-T, is illogical iff ¬S-T is not part of the syntax. When a T/F switch has
been turned off, it’s as if (loosely) the sentence just isn’t there. But we don’t (given our working
assumptions about negation) render a new sentence logical. Rather, we are getting rid of both S-T and
¬S-T, and anything constructed from them. In essence, we are shrinking the language.
Turning a sentence’s T/F switch Off removes distributions from the logic and replaces them with other
(smaller) distributions, thereby changing the logic. So construed, it is not helpful to think of On and Off
as values akin to the T/F values.13 There’s an old cliché, that you make a statue of an elephant by
carving away everything that isn’t an elephant. Distributions of Ts and Fs, their presence or absence in
the syntax, are a logical elephant. On and Off switches are elephant carving devices.
Now, we need to describe how On/Off switches operate.
Presupposition Trigger: A presupposition trigger is a logic (syntaxN) changing device which functions as
follows: If a presupposition trigger is attached to P, then there is some sentence Q, such that if Q is in
the F position, then P and ¬P are in the Off position.
Cleft-Triggers: If ‘Someone [Y]’ is in the F position, ‘It was [X] who [Y]’ and its negation are in the off
position.
The pair of tables below illustrates change in logic for the cleft construction.
Row 1
Row 2
Row 3
Row 4
George stole the tarts.
George didn’t steal the tarts.
Someone stole the tarts.
No one stole the tarts.
P
On-T
On-T
On-F
On-F
¬P
On-F
On-F
On-T
On-T
Q
On-T
On-F
On-T
On-F
¬Q
On-F
On-T
On-F
On-T
11
Earlier, we distinguished between X = X, and X = Y, on the grounds that one is logical and one merely analytic.
To explain why speakers of language never endorse ¬(X = X), it was suggested that all language Ns in a language
share the same linguistic syntax. We are now supposing that the logical syntax changes. Let’s say then that that
¬(X = X) is illogical in all syntaxNs belonging to the syntax.
12
I’ll suppose that the default position is On.
13
My knowledge of multi-valued logic is very thin. I make no claim to originality, only ignorance.
13
Row 1
Row 2
Row 3
Row 4
It was George who stole...
It wasn’t George who stole …
Someone stole the tarts.
No one stole the tarts.
P
On-T
Off
On-F
Off
¬P
On-F
Off
On-T
Off
Q
On-T
On-F
On-T
On-F
¬Q
On-F
On-T
On-F
On-T
[-T]
[-F]
[-F]
[-T]
So construed, the cleft-construction changes the logical syntaxN of the relevant language. The table
below illustrates the change in logic of the ‘the’ triggers.
The-Triggers: If ‘There is an [X]’ is in the F position, then ‘The [X] is [Y]’ and its negation on the Off
position.
Row 1
Row 2
Row 3
Row 4
Row 1
Row 2
Row 3
Row 4
A king is bald.
No king is bald.
There is a king.
There isn’t a king.
P
On-T
On-T
On-F
On-F
¬P
On-F
On-F
On-T
On-T
Q
On-T
On-F
On-T
On-F
¬Q
On-F
On-T
On-F
On-T
The (unique) king is bald.
The (unique) king isn’t bald.
There is a king.
There isn’t a king.
P
On-T
Off
On-F
Off
¬P
On-F
Off
On-T
Off
Q
On-T
On-F
On-T
On-F
¬Q
On-F
On-T
On-F
On-T
[-T]
[-F]
[-F]
[-T]
The move from the default logic (every T/F switch is On) to the contracted logics (some T/F switches are
Off) is enacted by the attachment of a presupposition trigger to a sentence.
Let’s turn to cancellation. Suppose the speaker utters: ‘It wasn’t George who stole the tarts’ (¬P). Note
that no cancellation has occurred yet. Here’s the table.
Row 1
Row 2
Row 3
Row 4
It was George who stole...
It wasn’t George who stole …
Someone stole the tarts.
No one stole the tarts.
P
On-T
Off
On-F
Off
¬P
On-F
Off
On-T
Off
Q
On-T
On-F
On-T
On-F
¬Q
On-F
On-T
On-F
On-T
[-T]
[-F]
[-F]
[-T]
She goes on to utter, ‘No one stole the tarts’, cancelling the presupposition. There is no row in the table
above which will accommodate this. However, if we construe her as occupying a table in which P does
not contain a presupposition trigger, we can construe her as occupying row 4.
14
Row 1
Row 2
Row 3
Row 4
George stole the tarts.
George didn’t steal the tarts.
Someone stole the tarts.
No one stole the tarts.
P
On-T
On-T
On-F
On-F
¬P
On-F
On-F
On-T
On-T
Q
On-T
On-F
On-T
On-F
¬Q
On-F
On-T
On-F
On-T
This suggests the following principle.
Cancellation Principle: If a speaker’s monolog is illogical supposing that the presupposition trigger is in
force, but logical supposing it is not, the presupposition is cancelled.14 (Brief note on dynamic
semantics15)
Section Four
Productivity and Projection Failure
In a moment, we’ll consider some cases of projection failure. First, let’s introduce a new notion,
productivity.
Productivity: A trigger contained in some sentence, P, is productive in an endorsement of S (where S
contains P) iff the trigger forces an assignment (On) T to an atomic sentence (or it’s negation) that would
not be forced without the trigger.
The productivity of a trigger is seen in the effect an utterance has on one’s location in a psychological
space. Consider a simple example. Suppose the speaker utters ¬P and consider the two tables below.
The first table represents the default state (no trigger). The second represents the modified logic (cleft).
Row 1
Row 2
Row 3
Row 4
George stole the tarts.
George didn’t steal the tarts.
Someone stole the tarts.
No one stole the tarts.
P
On-T
On-T
On-F
On-F
¬P
On-F
On-F
On-T
On-T
Q
On-T
On-F
On-T
On-F
¬Q
On-F
On-T
On-F
On-T
14
Appeals to consistency to explain cancellation are common, though the details vary. See Gazdar for an early
example.
15
I have only just recently started to look at the literature for dynamic semantics (Heim, etc). It is unclear to me
how exactly the present proposal relates to what is going on there. Construing possible worlds syntactically, and Off
as undefined, it may be that the accounts are very similar. However, it appears, from what I can tell, that those
accounts involve 1) no shift in logic and 2) a crucial temporal element, or ordering of commitments, which is absent
from the present account. So, on the present proposal, there is no need for “accommodation.” You endorse what the
speaker utters, and move into the relevant syntax/language/theory, or you don’t and don’t.
15
Row 1
Row 2
Row 3
Row 4
It was George who stole...
It wasn’t George who stole …
Someone stole the tarts.
No one stole the tarts.
P
On-T
Off
On-F
Off
¬P
On-F
Off
On-T
Off
Q
On-T
On-F
On-T
On-F
¬Q
On-F
On-T
On-F
On-T
[-T]
[-F]
[-F]
[-T]
In the second table, the speaker who endorses ¬P is forced to endorse Q with the trigger in place, but
not if the trigger is absent. So, in this case, the presupposition trigger is productive with respect to the
presupposed sentence, Q.
We are now in a good position to grasp the nature and purpose of the On/Off switch. As I am conceiving
of things, a speaker never locates herself in a row in which a sentence has the value Off. Consider the
following monologs.
1. ‘There is no king.’
2. ‘There is no king. So, the king isn’t bald.’ (or reverse)16
3. ‘The king isn’t bald.’
In 1, the speaker would not be located in a table with Off values. One actually has to insert the trigger
into a sentence to “trigger” that. On is the default value, we might say. 2 constitutes a case of
cancellation. In 3, there are Off values in the table, but one isn’t located there. This makes the purpose
of Off a bit mysterious.
The purpose of Off is to force a more precise psychological location. Typically, a precise location within
a psychological space is achieved by endorsement, i.e., by assigning T’s to sentences. Presupposition
achieves precision in a different way. It shuts down portions of the psychological syntax. T and F values
partition psychological/syntactic spaces. On and Off values expand and shrink spaces. This is where Off
does it work. One never locates herself in a row in which a sentence has that “value.” Rather, she is
forced out of such rows by that value.
Using the notion “productivity,” we can differentiate the logical/syntactic behavior of sentences
containing triggers which are embedded in larger sentences.
Well behaved Trigger: A trigger contained in P is well-behaved in an endorsement of S (containing P) iff
it is productive with respect to Q, and only Q.
Good behavior can help us parse projection failure. Let’s suppose that ‘stopped’ is a presupposition
trigger, and that ‘George stopped smoking’ presupposes ‘George was smoking’. We will suppose further
One might wish to reject the monolog ‘No one stole the tarts. Thus, it wasn’t George who stole the tarts.’ To
distinguish this from cancellation, we would need to appeal to some kind of ordering. None will be introduced.
16
16
that ‘George stopped smoking’ = ‘George was and isn’t smoking.’
conditionals.
Now consider the following
Conditional: If George was smoking, then George stopped smoking.
Conditional: If George was running, then George stopped smoking.
The first conditional does not generate the presupposition, the second does. The first is not wellbehaved, the second is. The following pair of tables illustrates the productivity of the trigger for the
first, poorly behaved, conditional.
Row 1
Row 2
Row 3
Row 4
G was
G wasn’t
G is
G isn’t
G was and isn’t
G was and isn’t
Q
T
T
F
F
¬Q
F
F
T
T
P
T
F
T
F
¬P
F
T
F
T
(Q and ¬P)
F
T
F
F
Q→ (Q and ¬P)
F
T
T
T
Trigger/stopped
Row 1
Row 2
Row 3
Row 4
Q
T
T
F
F
¬Q
F
F
T
T
P
T
F
T
F
¬P
F
T
F
T
(Q and ¬P)
F
T
Off-F
Off-F
Q→ (Q and ¬P)
F
T
Off-T
Off-T
It is the conditional that is endorsed. So, we highlight those rows in which the conditional is On and
assigned T with light grey. If the trigger is active (second table), we are forced to endorse ¬P. If the
trigger is not active, we are not forced to endorse ¬P. ¬P is neither the sentence uttered (Q→ (Q and
¬P)), nor the sentence presupposed (Q). So, in this case, the trigger is forcing the endorsement of a
sentence (the negation of an atomic sentence), other than the presupposed sentence, Q. Hence, the
trigger is not well-behaved. This suggests the following principle.
Projection Failure: A trigger does not take effect if it is not well behaved in the endorsed sentence.
Consider another pair of conditionals.
Conditional: If George stopped smoking, then George was drinking.
Conditional: If George stopped smoking, then George was smoking.
The first conditional generates a presupposition and is well behaved. However, the second is wellbehaved, but does not generate a presupposition. So, the second conditional violates our rule for
projection failure. The tables for the second conditional are presented below.
17
Row 1
Row 2
Row 3
Row 4
Row 1
Row 2
Row 3
Row 4
Q
T
T
F
F
Q
T
T
F
F
P
T
F
T
F
P
T
F
T
F
¬P
F
T
F
T
¬P
F
T
F
T
No Trigger
No Trigger
(Q and ¬P)
F
T
F
F
(Q and ¬P) → Q
T
T
T
T
Q-Trigger
Q-Trigger
(Q and ¬P)
F
T
Off - F
Off - F
(Q and ¬P) → Q
T
T
Off - T
Off - T
The most salient thing about the pair of tables above is an endorsement of the sentence in the default
logic isn’t productive at all. It is logical. There is no psychological space for an endorsement of that
sentence to partition. Let’s modify our definition of good-behavior so as to exclude this case.
Well behaved Trigger: A trigger contained in P is well behaved in an endorsement of S (containing P) iff
P isn’t logical and the trigger is productive with respect to Q, and only Q.17
Conclusion
In this essay I have tried to sketch a strategy. I hope I have given the reader the gist of how appeals to
syntactic and semantic change within a language might help handle tricky cases. I’ll finish by briefly
trying to motivate the idea of syntax change, assuming that syntactic items are meant to be interpreted.
The view that logical syntax changes predicts, as with semantic change, a certain amount of
communication failure between speakers of the same language. If the speaker is using a syntax N with
Off values, and the hearer is not, then it may be that the hearer simply cannot locate herself in the
speaker’s syntax. In that case, we should expect communication failure (or some sort of failure). This
might be indicated by the response “Huh?”, or the refusal to either endorse or reject the relevant
utterance.(Strawson)
Communication failure isn’t good. Why would we have a language that’s so tolerant of regular
communication failure? Grant for the sake of argument that bees can exchange infinitely many distinct
bits of information about direction and distance, but nothing else. Why has God, or nature, been so
stingy with the bees? A speculative answer: it wouldn’t be worth it. A language of the sort we operate,
17
Appeals to redundancy, or triviality, are similar in spirit to what I have here. See Van der Sandt for an example.
18
cool as it is, is costly, and the bees just don’t need it. What’s even cooler than a language with a huge
amount of expressive power? A language with adjustable expressive power! Use what you need and
not more.
19