Lecture 5 — Making Sense of Relative Truth

John MacFarlane (jgm@berkeley.edu)

Context and Content Lectures, Paris, 2010

The task for today

Meiland’s dilemma

If “true” as it occurs in “true for X” is just the ordinary, nonrelative truth predicate, then it is unclear what “for X” (or “as assessed by X”) adds. On the other hand, if the occurrence of “true” in “true for X” is like the “cat” in “cattle”—an orthographic, not a semantic, part—then the relativist needs to explain what “true-for-X” means and what it has to do with truth, as ordinarily conceived.

Preview of our answer

Why not a definition?

Why not explain “true as used at c1 and assessed from c2” be giving a definition?

S is true as used at c1 and assessed from c2 iff …

We have a definition!

A relativist semantic theory for L will issue in a definition of “true as used at c1 and assessed from c2” that fixes its extension over a particular class of sentences and contexts. (We’ve seen how to write down such a theory.)

But such definition would not answer our question!

Dummett’s point

Winning at chess

White wins at chess just in case the current disposition of pieces on the board has been reached by a series of legal chess moves, with White and Black alternating, and Black’s king is in checkmate.

The martian anthropologist

A martian semanticist

Dummett summing up

If it was to be possible to explain the notion of meaning in terms of that of truth, if the meaning of an expression was to be regarded as a principle governing the contribution that it made to determining the truth-conditions of sentences containing it, then it must be possible to say more about the concept of truth than under which conditions it applied to given sentences. Since meaning depends, ultimately and exhaustively, on use, what was required was a uniform means of characterising the use of a sentence, given its truth-conditions.

An account of illocutionary forces

corresponding to each different kind of force will be a different uniform pattern of derivation of the use of a sentence from its sense, considered as determined by its truth-conditions.

What has to be added to a truth-definition for the sentences of a language, if the notion of truth is to be explained, is a description of the linguistic activity of making assertions…

Compare Lewis’s picture

Two observations

  1. If Dummett is right, then it is not just the relativist who owes an explication of her truth predicate. The absolutist owes one at well, at least if she is to use this predicate in semantics.

  2. Dummett proposes to illuminate “true (at c)” by describing its role in an account of assertion (and other illocutionary forces). We might try the same strategy with “true as used at c1 and assessed from c2.”

Our strategy

Start with an account that works with non-relativist theories (which use “true at c”), and tweak it to work with relativist theories (which use “true as used at c1 and assessed from c2”).

Meiland’s insight
Do not impose explanatory demands on the relativist beyond those we impose on the non-relativist!

Truth as the aim of assertion

The truth rule

Truth Rule
Assert that p (at a context c) only if p is true at c.

To say that the truth rule is constitutive of assertion is to say that nothing that (part of) what it is for a speech act to be an assertion is for it to be subject to this rule. (Not: for it to obey this rule.)

The Truth Rule is a semantic-pragmatic bridge principle.

Defending the Truth Rule

Williamson’s main criticisms:

  1. Truth Rule can’t explain why we shouldn’t assert of a lottery ticket that it won’t win.
  2. Truth Rule can’t explain why “How do you know?” is used to challenge assertions.
  3. Truth Rule can’t explain the paradoxicality of “P, but I don’t know that P” and the like.


All these things can be explained by the Truth Rule if we also assume:

Unreasonable Belief

If S knows that believing that p would be impermissible, then S would be unreasonable in believing that p.

Knowledge Rule for Belief

One must: believe that p only if one knows that p.

But if you’re not convinced, we’ll show later how to start with the Knowledge Rule instead.

Our question

The Truth Rule as formulated uses the standard “true at c.” Is there a natural way to revise it to use “true as used at c1 and assessed from c2”?

Three options

  1. Relativize the norm itself to contexts of assessment:

    Relative to context c2, an agent is permitted to assert that p at c1 only if p is true as used at c1 and assessed from c2.

  2. Quantify over contexts of assessment:

    An agent is permitted to assert that p at context c1 only if p is true as used at c1 and assessed from some/all/most contexts.

  3. Privilege one context of assessment:

    An agent is permitted to assert that p at context c1 only if p is true as used at c1 and assessed from c1.

Option 1

Truth Rule(s) v1
Relative to context c2, an agent is permitted to assert that p at c1 only if p is true as used at c1 and assessed from c2.

Option 2

Truth Rule v2
An agent is permitted to assert that p at context c1 only if p is true as used at c1 and assessed from some/all/most contexts.

Option 3

Truth Rule v3
An agent is permitted to assert that p at context c1 only if p is true as used at c1 and assessed from c1.

Two theories of “tasty”


p is true as used at c1 and assessed from c2 iff
p is true at  < wc1, gc2 > .


p is true as used at c1 and assessed from c2 iff
p is true at  < wc1, gc1 > .

No practical difference!

Licorice is tasty


Given any assessment-sensitive theory, we can construct a “normatively equivalent” theory that is not assessment-sensitive. The nonrelativist can say:

What you call “truth as used at and assessed from c,” and identify with the norm of assertion, is what I call “truth as used at c.” At any rate, they are identical in their normative and empirical import. But you have done nothing to explain what “truth as used at c1 and assessed from c2” means, when c1 ≠ c2. If you had, we would be able to see a difference in the consequences for language use between a relativist theory and a nonindexical contextualist theory that coincides with it “on the diagonal,” as T2 coincides with T1.


One might conclude, pessimistically, that relative truth is incoherent after all.

Or, optimistically, that we simply haven’t given enough semantic-pragmatic bridge principles yet.



“takes back” an assertion you have made, indicating that you want the assertion “taken off the books,” and no longer take responsibility for it

Two relevant contexts

Retraction rule

Retraction Rule
An agent in context c2 is required to retract an (unretracted) assertion of p made at c1 if p is not true as used at c1 and assessed from c2.

The difference between T1 and T2

Given the Retraction Rule, T1 predicts that an assertion of p at c1 ought to be retracted by the asserter in c3, while T2 predicts that it need not be retracted.

An objection

According to the Truth Rule v3 and the Retraction Rule, someone who asserts that p in c1 might be compelled to retract this assertion in a later context c2, even though the assertion was permissible for her to make at c1. (Suppose that p is true as used at and assessed from c1, but not true as used at c1 and assessed from c2.)

How can I believe both that the aims given A, for him, by the language he employs were successfully pursued, and that I have every right to force him to withdraw his utterance?
—Philip Percival


Withdrawing an assertion (or other speech act) is not tantamount to conceding that one was at fault in making it. Consider this scenario:

All of one’s evidence all strongly suggests that Uncle Jack is coming to lunch, and on the strength of that evidence you assert that Uncle Jack is coming. A bit later, Aunt Sally calls to say that Uncle Jack has broken his leg. This makes it quite unlikely that he is coming, so you retract your assertion.

Nonetheless, you were perfectly reasonable in making it, and cannot be criticized for having done so. Retracting it is not admitting fault.


But surely it’s irrational to assert something that you might have to retract just because you come to be in a relevantly different context!


This is not obvious (and even if it were, it wouldn’t follow that we don’t engage in this practice).

The rationality of actions depends on many factors, and speech acts are no exception. In deciding whether it is rational to assert an assessment-sensitive proposition, one would have to consider:

The Knowledge Rule

What if you think that the constitutive norm governing assertion is not the Truth Rule but the

Knowledge Rule
An agent is permitted to assert that p only if she knows that p.

Can we make room for assessment sensitivity starting from this idea?



But this objection is faulty.

Factivity is best understood as the claim that instances of the following schema are analytically true:

If α knows that φ, then φ.

What we can conclude from this is that if φ is assessment-sensitive, so is ⌜α knows that φ⌝, and so is the predicate “knows” (since its extension varies as we shift the context of assessment).

Restating the Knowledge Rule

If “knows” is assessment-sensitive, we need to restate the Knowledge Rule in non-assessment-sensitive language.

Knowledge Rule v2
An agent is permitted to assert that p (at a context c) only if the proposition that she knows (at tc) that p is true as used at c and assessed from c.

A corresponding Retraction Rule

Retraction Rule
An agent at c2 is required to retract an assertion that p (made in c1) if the proposition that she knows (at tc1) that p is not true as used at c1 and assessed from c2.

From the agent’s standpoint, this amounts to saying that you should retract an earlier assertion that p if, from your present perspective, you did not know that p.

“Making sense” again

“Making sense” again

Believing relative truths

Why this focus on assertion? Why not make sense of relative truth by explaining the practical difference between believing an assessment-sensitive proposition and believing an assessment-invariant one?

Why not?

There is nothing corresponding to the retraction of a belief, and so nothing to give a job to both the context of use and the context of assessment. One can give up believing something, but that is different from retraction.

An assertion is an action (hence also an event); a belief is a state that an agent can be in.

When one gives up a belief that p, one transitions from being in the state of believing that p to being in the state of not believing that p, but this transition is not directed towards any particular past event. Retraction, by contrast, is always retraction of some particular dated act.

The story of Jim



The Italian garden

Two men, A and B, are walking around an Italian garden.

A carries with him a supply of stakes with flags on them. He stops periodically, drives a stake into the ground, and writes on the flag, “Viola is the loveliest woman on earth.”

B is also an admirer of Viola, but instead of planting flags in the ground, he simply carries his flag reading “Viola is the loveliest woman on earth.”

The Italian garden

Halfway through the garden, A and B both spot Cynthia and are immediately smitten.

The Italian garden

A begins to plant flags reading “Cynthia is the loveliest woman on earth.”

B repaints his flag to read the same.

At this point, A must go back and pick up all the flags declaring Viola to be the loveliest woman on earth. B faces no comparable task; it is enough for him to simply change his flag.

Aiming at truth

The point is not that the relativist can’t make sense of the idea that belief “aims at the truth.”

The point is that if this is all we say, we can’t distinguish relativist from nonindexical contextualist views.


What makes relative truth intelligible is the potential difference between the context at which an assertion is made and the contexts at which challenges to it will have to be met and retractions considered.

Thus, even though assessment-sensitive propositions can be believed, judged, doubted, supposed, and so on, there would be no theoretical need for relative truth if we did not also make assertions.

Our progress

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

A neutral framework

Accepting the norms linking the assessment-relative truth predicate with assertion and retraction does not commit one to relativism. One could accept this framework and deny that anything is assessment-sensitive.

So these norms can serve as a neutral framework for discussion, one that gives a sense to relativist semantic proposals, and allows us to evaluate them, without presupposing their truth.