Lecture 3 — Assessment Sensitivity

John MacFarlane (jgm@berkeley.edu)

Context and Content Lectures, Paris, 2010

The literature on truth relativism

Our question

Perhaps truth is relative; perhaps not. But I think that we cannot decide whether or not truth is relative until we first determine what “relative truth” might be. —J. Meiland

A simple but bad answer

A relativist about truth is anyone who uses a relativized truth predicate.

Truth at a context of use


Not a truth relativist

I have been to China.

This relativization simply registers a fact obvious to everyone—that in general, whether sentences express truths or falsehoods depends on the settings in which they are used.

Demands of compositionality

For all integers x, there exists an integer y such that x + y = 0.

Project: give a compositional account of the truth conditions of the whole sentence as a function of the truth conditions of the embedded open sentence:

there exists an integer y such that x + y = 0.

Problem: there are no “conditions” under which an open sentence is true.

Truth at an assignment


Not a truth relativist

Tarski’s solution: recursively define truth on an assignment of values to the variables rather than truth simpliciter.

⌜∀αφ⌝ is true on assignment a iff for every assignment aʹ that differs from a at most in the value it gives to α, φ is true on aʹ.

⌜¬φ⌝ is true on assignment a iff φ is not true on a.

Truth at an assignment and truth simpliciter

Truth at an assignment raises no philosophical eyebrows, because it is just a technical means for systematizing a definition of truth simpliciter.

At the end, we say:

If φ is a sentence, then φ is true iff φ is true on every/some assignment.

We could have just as well defined a function from assignments to {0,1} — or to {chair, beer mug}.

Truth at a context and utterance truth?

We could try a similar strategy for truth at a context, treating it as a device for systematizing a definition of truth for utterances (utterance-acts).

An utterance u is true iff there is a sentence S and a context c such that u is an utterance of S at c and S is true at c.

Utterance truth could then be taken to be absolute.

Relativism about utterance truth?

We could think of truth relativism as the view that truth for utterances must be relativized.

This is close, but still not completely satisfying as a characterization of truth relativism.

The objection from linguistic oddity

We do not characterize acts (even speech acts) as true or false (Strawson, Bar-Hillel).

His assertion was true.

Davidson’s response

Verbal felicity apart, there is no reason not to call the utterance of a sentence, under conditions that make the sentence true, a true utterance.

Kaplan’s objection

…it is important to distinguish an utterance from a sentence-in-context. The former notion is from the theory of speech acts, the latter from semantics. Utterances take time, and utterances of distinct sentences cannot be simultaneous (i.e., in the same context). But to develop a logic of demonstratives it seems most natural to be able to evaluate several premises and a conclusion all in the same context. Thus the notion of φ being true in c and A does not require an utterance of φ. In particular, cA need not be uttering φ in cW at cT.

Shouldn’t relativism about truth have significance for semantics, not just pragmatics or the theory of speech acts?

Zimmerman’s objection

Suppose that after Max drinks himself into unconsciousness, his buddies cover him in plaster and let it harden. The next day, Max relates the night’s events to his father and concludes his account by saying, “I really got plastered,” intending his statement to express a double entendre. What has Max said? One option is that he expresses the conjunctive proposition that he drank to the point of intoxication and was covered in plaster. Another option is that Max’s utterance is elliptical; what he really said was that he was plastered in more than one sense of ‘plastered’. But a third option is that Max produces a single token utterance that expresses two propositions: (1) that he got intoxicated, and (2) that he was covered in plaster. Suppose that (contrary to fact) Max has misremembered the incident, and though right in thinking he was covered in plaster, he is mistaken in thinking he got intoxicated. A common intuition is that what Max says is neither entirely false nor entirely true in such a circumstance. Rather, one of the things he says is true while the other is false. Of the three options here considered, only the third renders this verdict.

Utterances vs. assertions

Perhaps Max makes two distinct assertions by producing one utterance.

Propositions

Propositions = the contents of assertions/beliefs, the “primary bearers of truth values.”

Kölbel: non-tame relativism about truth is the view that “the truth of propositions (or contents) of some kind can be relative.”

What about truth at a world?

Relativization of propositional truth to worlds is compatible with the idea that particular assertions of propositions can be assigned absolute truth values.

an assertion that p is true (or false) simpliciter just in case p is true (or false) at the actual world (or, in some versions, the world in which the assertion is made).

Discrimination?

Nozick, Stanley, Zimmerman, Kölbel: it’s relativizing truth of propositions to parameters beyond worlds that makes one a truth relativist.

This classes temporalism — the view that propositions have truth values relative to times, as well as worlds — as a form of truth relativism. But why draw the line here?

More subtle discrimination?

Maybe relativizing to anything beyond worlds and times makes you a truth relativist?

Crazy vs. sane temporalism

Sane temporalism

An assertion of a tensed proposition is true just in case the proposition is true at the world and time of utterance.

Crazy temporalism

An assertion of a tensed proposition is true, as assessed from time t, just in case the proposition is true at the world of utterance and t.

Crazy temporalism is not at all plausible, but it does seem to be a form of truth relativism.

Upshot so far

Relativization to nonstandard parameters is not necessary for relativism about truth. In Lecture 4 we will see that it is also not sufficient.

Slogan
It is not the kind of parameters to which one relativizes propositional truth that makes one a relativist, but what one does with them.

A new start: assessment sensitivity

Proposal: What makes one a relativist about truth is a commitment to the assessment sensitivity of some sentences or propositions.

Our next task is to get clear about what assessment sensitivity is. We will work within a semantic framework in the style of David Lewis’s “Index, Context, and Content.”

The task of a semantic theory

The task of a semantic theory for a language L, as Lewis conceives it, is to define truth at a context of use for arbitrary sentences of L: to say, given any sentence S of L, what a context must be like in order for an utterance of S at that context to express a truth.

For example, we want a semantic theory of English to tell us that

I am six feet tall

is true at a context if the agent of that context is six feet in height at the time and world of the context.

What is a context of use?

Why is truth-at-a-context the target?

Truth-at-a-context has direct relevance to our use of sentences.

The foremost thing we do with words is to impart information, and this is how we do it. Suppose (1) that you do not know whether A or B or …; and (2) that I do know; and (3) that I want you to know; and (4) that no extraneous reasons much constrain my choice of words; and (5) that we both know that the conditions (1)–(5) obtain. Then I will be truthful and you will be trusting and thereby you will come to share my knowledge. I will find something to say that depends for its truth on whether A or B or … and that I take to be true. I will say it and you will hear it. You, trusting me to be willing and able to tell the truth, will then be in a position to infer whether A or B or …

Point of contact between semantics and pragmatics

So the condition for a sentence to be true at a context is the central semantic fact we need to know if we are to use the sentence and understand others’ uses of it.

The need for indices

The need for indices

The solution: indices

Introduce an artificial index, a sequence of parameters (Lewis: “features of context”) that can be shifted independently.

It has always been the case that φ⌝ is true at c,  < w, t >  iff for every time tʹ ≤ t, φ is true at c,  < w, tʹ > .

We recursively define truth at a context and index.

Postsemantics

But our target was truth at a context? How do we get that from truth at a context and index?

Let us say that sentence s is true at context c iff s is true at c at the index of the context c. —Lewis

I call this step “postsemantics” to distinguish it from the recursive definition itself. (Compare Tarski’s definition of truth in terms of truth at an assignment.)

The modified picture

Neither relativization makes us “truth relativists”

Contexts of assessment

Changing the target

The output of our semantic theory will be a definition of “true as used at c1 and assessed from c2.”

Global vs local relevance

Two ways for a feature of context to be semantically relevant:

locally

plays a role in the semantics proper (in the recursive clause for a particular construction)

globally

plays a role in the postsemantics

Global vs local relevance

A toy example

Two flavors of context sensitivity

Use sensitivity

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.

Assessment sensitivity

An expression is assessment-sensitive if its extension (relative to a context of use and context of assessment) depends on features of the context of assessment.

Parameterized versions

P use sensitivity

An expression is P-use-sensitive if its extension (relative to a context of use and context of assessment) depends on the P of the context of use.

P assessment sensitivity

An expression is P-assessment-sensitive if its extension (relative to a context of use and context of assessment) depends on the P of the context of assessment.

Relativism about truth

Truth relativism
To be a relativist about truth is to hold that languages with assessment-sensitive expressions are at least conceptually possible.

This is a philosophical thesis. For each natural language L there is a related empirical thesis:

Truth relativism in L
To be a relativist about truth for a language L is to hold that L in fact contains assessment-sensitive expressions.

Advantages of this characterization

Three kinds of relativity to F

We said before that it’s not what you relativize to that matters. We can now see why. There are three ways in which the truth of a sentence S might be relative to some feature F:

  1. S’s truth might vary with the F coordinate of the index.

  2. S might be F-use-sensitive.

  3. S might be F-assessment-sensitive.

For example…

Socrates is sitting

For example…

Socrates is sitting now

For example…

Socrates is sitting noy

Aesthetic standards

Objectivist postsemantics

Objectivist postsemantics
A sentence S is true at a context c iff for all assignments a, S is true at  < wc, sG, a > , where wc is the world of c and sG is God’s aesthetic standard.

Contextualist postsemantics

Contextualist postsemantics
A sentence S is true at a context c iff for all assignments a, S is true at  < wc, sc, a > , where wc is the world of c and sc is the aesthetic standard of the agent at c.

Relativist postsemantics

Relativist postsemantics
A sentence S is true as used at a context c1 and assessed from a context c2 iff for all assignments a, S is true at  < wc1, sc2, a > , where wc1 is the world of c1 and sc2 is the aesthetic standard of the agent at c2.