Lecture 4 — Propositions

John MacFarlane (jgm@berkeley.edu)

Context and Content Lectures, Paris, 2010

Objectives

Propositions

Propositions

Two-stage semantics

Content and character

Context vs circumstance

Kaplan wants to say that a directly referential expression, like the indexical “here”, “designates the same object in all circumstances.”

But this can lead to confusion. Surely, you might say, there are circumstances in which “here” denotes Paris, and circumstances in which “here” denotes Berkeley!

Context vs circumstance

We need a distinction:

We do not mean that the expression could not have been used to designate a different object. We mean rather that given a use of the expression, we may ask of what has been said whether it would have been true or false in various counterfactual circumstances, and in such counterfactual circumstances, which are the individuals relevant to determining truth-value. Thus we must distinguish possible occasions of use—which I call contexts—from possible circumstances of evaluation of what was said on a given occasion of use.

Context vs circumstance

I do not exist

Consider

I do not exist.

There is no context at which this sentence expresses a truth.

Yet the falsehood it expresses is one that is true at some counterfactual circumstances.

Two-stage semantics again

What is a “circumstance”?

By [“circumstances”] I mean both actual and counterfactual situations with respect to which it is appropriate to ask for the extensions of a given well-formed expression. A circumstance will usually include a possible state or history of the world, a time, and perhaps other features as well. The amount of information we require from a circumstance is linked to the degree of specificity of contents, and thus to the kinds of operators in the language.

Why include times?

Independent considerations?

Kaplan is sometimes taken to hold that the presence of an operator that shifts X is both necessary and sufficient for the inclusion of X in circumstances.

But I only see a clear commitment to sufficiency.

Might there be other considerations, independent of operators, for including X in circumstances?

Ordinary language arguments

we may ask of what has been said whether it would have been true or false in various counterfactual circumstances

  1. Sam is the tallest man in his town.
    Would that have been true if his legs had been amputated?

  2. Sam is the tallest man in his town.
    Was that true last year?

But we might worry about overgeneration:

  1. Sam is the tallest man in his town.
    Is that true in your imagination?

  2. Sam is the tallest man in his town.
    Is that true for Harry too?

Content individuation

A language without modals

Suppose we are considering people whose language originally lacked modal operators (world-shifters), but evolved to contain them.

Neither option seems attractive, but the idea that only world-shifting operators can justify relativizing propositional truth to worlds forces us to choose between them.

What can count as a circumstance?

Could the circumstances of evaluation to which propositional truth is relative include coordinates besides worlds and perhaps times—for example, tastes, standards of precision, information states, moral codes, or epistemic standards?

Kaplan himself takes a fairly permissive stance:

What sorts of intensional operators to admit seems to me largely a matter of language engineering. It is a question of which features of what we intuitively think of as possible circumstances can be sufficiently well defined and isolated. If we wish to isolate location and regard it as a feature of possible circumstances we can introduce locational operators: ‘Two miles north it is the case that’, etc. … However, to make such operators interesting we must have contents which are locationally neutral. That is, it must be appropriate to ask if what is said would be true in Pakistan. (For example, ‘It is raining’ seems to be locationally as well as temporally and modally neutral.)

Why not, then, contents that are taste-neutral?

The analytic argument

Let’s dismiss an argument that I have sometimes encountered:

By ‘proposition’ we just mean something that partitions the possible world-states into those at which it is true and those at which it is not true. So if your ‘propositions’ do not do that, they are not propositions properly so-called.

There is a real issue here that verbal stipulation can’t settle: do the contents of assertions, beliefs, and other so-called “propositional attitudes” have truth values relative to worlds only, or relative to worlds and something else?

The incompleteness objection

If someone wished to cite, say, ‘The total number of inhabitants of the German Empire is 52 000 000’, as a counter-example to the timelessness of thoughts, I should reply: This sentence is not a complete expression of a thought at all, since it lacks a time-determination. If we add such a determination, for example, ‘at noon on 1 January 1897 by central European time’, then the thought is either true, in which case it is always, or better, timelessly, true, or it is false and in that case it is false without qualification.
—Frege, “Logic”

By “thought” here, Frege means essentially what we mean by “proposition.” So this might seem to support opposition to time-neutral (taste-neutral, etc.) propositions. But that is doubtful.

Separating the issues

Frege’s discussion seems to confuse two very different issues:

  1. whether propositions themselves are unchanging or mutable
  2. whether their truth is relative to times

Before and after the passage just quoted, Frege is mainly concerned with (1).

Whereas ideas (in the psychological sense of the word) have no fixed boundaries, but are constantly changing and, Proteus-like, assume different forms, thoughts always remain the same. It is of the essence of a thought to be non-temporal and non-spatial.

But (2) is orthogonal to (1). A temporalist can accept that propositions are abstract, timeless entities, and endorse (1).

Moreover, Frege doesn’t really give a reason for thinking that a complete expression of a thought must include a time determination.

Was Frege confused?

Sense determines reference

Frege held that sense determines reference. On a strong (and I think correct) way of reading the claim, it implies that in any case where you have the same sense, it has the same reference — reference is entirely determined by sense.

Since the sense of a sentence is a thought, and the reference is a truth value, this implies that thoughts have their truth values intrinsically.

So Frege is no friend to those who want to drive a wedge between worlds and times. (Indeed, he never took alethic modality seriously.)

The incompleteness objection II

Response

Bringing the world into the content

The incompleteness objection III

Postsemantics

How can we get sentence truth at a context out of a two-stage semantics?

If c is a context, then an occurrence of [a sentence] φ in c is true iff the content expressed by φ in this context is true when evaluated with respect to the circumstance of the context.

Dropping the assumption that there will always be a unique “circumstance of the assumption,” we can generalize:

A sentence S is true at context c iff the proposition expressed by S in c is true at all circumstances of evaluation compatible with c.

What “compatibility” amounts to must be worked out in detail for each semantic theory.

Propositional truth at a context

It is also useful to define propositional truth relative to a context:

A proposition p is true at a context of use c iff p is true at all circumstances of evaluation compatible with c.

We can now rephrase our definition of sentence truth at a context as follows:

A sentence S is true at context c iff the proposition expressed by S in c is true at c.

Two roles for context

The context of use plays two distinct roles in the definition of truth at a context:

A sentence S is true at context c iff the proposition expressed by S in c is true at c.

content-determining role

determining which proposition a sentence expresses

circumstance-determining role

selecting which circumstances of evaluation are relevant to the truth of an occurrence of a sentence at the context.

Context sensitivity vs indexicality

So there are two distinct ways in which a sentence can be context-sensitive. It can be sensitive to a feature of context because that feature plays a content-determining role, or because it plays a circumstance-determining role.

use-sensitive
An expression is use-sensitive if its extension (relative to a context of use and context of assessment) depends on features of the context of use.
use-indexical
An expression is use-indexical iff it expresses different contents at different contexts of use.
F-use-sensitive
An expression is F-use-sensitive if its extension (relative to a context of use and context of assessment) depends on the F of the context of use.
F-use-indexical
An expression is F-use-indexical iff the content it expresses at a context depends on the F of that context.

Examples

  1. I am over five feet tall. [agent-use-indexical, agent-use-sensitive]
  2. If it is raining now, it is raining. [time-use-indexical, but not time-use-sensitive]
  3. Socrates is sitting.
    • for the temporalist: [time-use-sensitive, not time-use-indexical]
    • for the eternalist: [time-use-sensitive, time-use-indexical]
  4. Dulce de leche is tasty.
    • indexical contextualist: [taste-use-sensitive, taste-use-indexical]
    • nonindexical contextualist: [taste-use-sensitive, not taste-use-indexical]

Nonindexical contextualism

A nonindexical contextualist about “tasty” holds that

Implementation:

No assessment sensitivity here.

Relativism

To make room for asssessment sensitivity in our two-stage semantic framework, we need truth to be relative to both a context of use and a context of assessment:

A proposition p is true at as used at c1 and assessed from c2 iff p is true all circumstances of evaluation compatible with  < c1, c2 > .

A sentence S is true as used at c1 and assessed from c2 iff the proposition expressed by S in c1 as assessed from c2 is true as used at c1 and assessed from c2.

The relation of “compatibility” now holds between circumstances and a pair of contexts—a context of use and context of assessment. As before, it must be defined on a per-application basis. Example:

A circumstance  < w, s >  is compatible with  < c1, c2 >  iff w is the world of c1 and s is the aesthetic standard relevant at c2.

Assessment indexicality

assessment-indexical

An expression is assessment-indexical iff it expresses different contents relative to different contexts of assessment.

F-assessment-indexical

An expression is F-assessment-indexical iff the content it expresses as assessed from c depends on the F of c.

Assessment sensitivity for propositions

assessment-sensitive

A proposition is assessment-sensitive if its truth value as used at c1 and assessed from c2 depends on features of c2.

F-assessment-sensitive

A proposition is F-assessment-sensitive if its truth value as used at c1 and assessed from c2 depends on the F of c2.

Content relativism vs truth-value relativism

Content relativism

There are assessment-indexical sentences.

Truth-value relativism

There are assessment-sensitive propositions.

Truth-value relativism and “tasty”

A truth-value relativist about “tasty” holds that

Implementation:

“About” and “concerns”

Three positions can be usefully compared using the terminology of “about” and “concerns”:

Indexical contextualist
The proposition that DDL is tasty is partly about the speaker’s taste.
Nonindexical contextualist
The proposition that DDL is tasty is not about the speaker’s taste, but an assertion of this proposition will concern the speaker’s taste.
Truth relativist
The proposition that DDL is tasty is not about the speaker’s taste, and an assertion of this proposition does not concern the speaker’s taste, either.

Monadic “true”

Semantics for “true”

The extension of “true” at a circumstance of evaluation e is the set of propositions that are true at e.

Given this clause, every instance of the Equivalence Schema will be true at every circumstance of evaluation, and hence also at every context of use and context of assessment.

Equivalence Schema
The proposition that Φ  is true iff Φ .

Newton-Smith’s argument reconsidered

  1. Suppose S1 is true in Ψ and S2 is false in Θ . And suppose that S1 and S2 express the same proposition, p.

  2. S1 and S2 differ in truth value (by 1).

  3. If two sentences differ in truth value, they differ in truth conditions.

  4. If two sentences express the same proposition, then they have the same truth conditions.

  5. So if two sentences differ in truth value, they do not express the same proposition (by 3, 4).

  6. So S1 and S2 do not express the same proposition, contrary to our supposition (by 2, 5).

Ambiguities in the supposition

1. Suppose S1 is true in Ψ and S2 is false in Θ . And suppose that S1 and S2 express the same proposition, p.

We’re talking about sentences being “true in Ψ” and “false in Θ ,” so presumably we should think of Ψ and Θ  as contexts. (N-S says: theories or social groups.) But are we to think of these as contexts of use or contexts of assessment?

Do they express the same proposition in some single context? Or the same proposition in their respective contexts?

Perhaps we can pin this down by looking at what the argument requires.

Clarifying (3)

Like Socrates, Newton-Smith seems to have dropped the relativizing qualifiers (“in Ψ”). So we’d better restore these.

3. If two sentences have different truth values at (possibly) different contexts, they differ in truth conditions.

This means that we must construe (5) as:

5. If two sentences have different truth values at (possibly) different contexts, they do not express the same proposition.

Assessing (5)

Two versions

(5a) If two sentences have different truth values as used at (possibly) different contexts, they do not express the same proposition.

(5b) If two sentences have different truth values as assessed from (possibly) different contexts, they do not express the same proposition.

Neither is true.

Counterexample to (5a)

“It snows in Germany” as used in contexts in different worlds; or (on temporalist account) “Socrates is sitting” as used at different times.

Counterexample to (5b)

“This chile is tasty” as assessed by people with different tastes.

No non-question-begging reason has been given to accept (5b), and (5a) is false even in non-relativist frameworks.

General assessment

Newton-Smith’s argument exemplifies a general tendency in much of the literature on relative truth. Terms like “true in,” “true for,” and “truth-conditions” are deployed without any sensitivity to the various kinds of relativization of truth that can be used in semantics.

As we have seen, proper statement of a relativist position requires some care. A general argument against relative truth needs to take the same care.

Taking stock

At the end of Lecture 2, we had this list of tasks:

  • completed
Provide an account of propositions that
allows them to be merely “relatively true.”
  • completed
Explain how the ordinary monadic truth predicate
is related to the relativized truth predicate.
  • to do
Explain what one is doing in asserting
propositions, if not putting them forward as true
absolutely.
  • partly done
Explain what the relativized “true for/at” means.