The structure of truth is linked to its content. I will examine the views of Davidson on these issues and raise some questions.
Davidson cites Tarski (p. 291); Tarski holds that any semantic conception of truth must diverge from its meaning on a `meaning is use’ conception. That is because:
“the common meaning of the word “true” — as that of any other word of everyday language — is to some extent vague.”Tarski
We can question this in a variety of ways. Firstly, we may ask whether “true” really is vague in everyday use. Certainly that will be the case if by the claim we mean that ordinary speakers have not decided whether they prefer a correspondence, pragmatist or other theory of truth as they clearly will not have done. But presumably Tarksi means something more: that there will be indeterminate borderline cases where it is unclear to ordinary speakers whether what they say is true or not.
This may in fact be the case, but it will not appear so to speakers. They will know when they are unsure of something. But that will just represent, for example, epistemic uncertainty — not any belief on the part of the users of the term true that it is somehow fuzzy at the edges. Secondly, we may ask whether an examination of ordinary usage is really the best way to examine the notion of truth. Or would it be better to examine a more restricted and well-behaved formal language.
Tarski favours a “redundancy” model of truth. Viz. the assertion “It is true that A” does not say more than “A.” So he may not believe that attempt is worthwhile.
Structure Of Truth: Vagueness
Finally, Tarski assumes that if the vagueness he describes is really present, ineliminable, and a part of the most useful language to be analyzed, that such vagueness cannot be accommodated in the theory. And as Davidson points out (p. 294), Tarski himself claimed to have ` “caught the actual meaning” of the intuitive concept of truth’ — so either his theory accommodates this vagueness or it was not present to be accommodated.
Later (p. 298), Davidson criticizes both epistemic and realist views of truth — the former holding that truth is in some way mediated by finite human capacities, and the latter denying this. Davidson’s criticism is that both approaches `invite skepticism’. This should not be used as a criticism of theories, in the same way that Nozick was mistaken in presenting the main benefit of his tracking theory of truth as a defense against skepticism. His theory had value without that. Since few of us take the skeptical challenge seriously, avoiding or defeating it should count so much the less in assessing the merits of competing theories. As Nozick said, the real interest in skepticism is his formulation `how is knowledge possible?’ rather than `could we all really be brains in vats?’
Structure Of Truth: An Empirical Theory Of Truth
- Starting point: looking for a theory of meaning
- Motivation: cannot base theory of meaning on the form “s” means m’ because `means that’ is an intensional context → logically difficult to analyse
- Also difficult to find singular terms in “m” to refer to meaning
Davidson’s Approach To Theory Of Meaning
- Equivalent sentences: examine “s means p” → “p” is another sentence
- Seek “matching sentence” to replace “p” which “gives meaning” of “s”
- “Bold step:” make the “p” position extensional; make three changes
- Eliminate `means that’ because non-extensional
- Prefix “p” with sentential connective so we can analyse the logic
- Apply a predicate to “s”
- Result → (T): s is T if and only if p
- Also: require T predicate to entail all sentences when “s” becomes description of sentence and “p” becomes same sentence
- But this is just Tarski’s convention T!
Convention T In The Structure Of Truth
- T introduced by Tarski in “disquotational” theory of truth
- Example (E): “snow is white’ is true if and only if snow is white
- Use/mention distinction prevents circularity from multiple occurrences of e.g. `snow’
- Problem: also works with `grass is green’ on RHS since we are only interested in truth conditions
- Response: if this were part of a theory of truth also including `that is snow’; truth conditions would no longer match
- Also, T sentences are supposed to be law-like
- Theory of truth can be “foundation” of theory of meaning
- Theory of meaning empirical; account for natural languages
- Test theory by comparing predictions with facts
- Here, that means seeing whether E holds
- How do we verify a theory of truth empirically?
- Check that all the T sentences, or a sufficiently large sample, are true
- We only have access to behavior including utterances of speakers
- Adapt Quine’s notions of radical translation and matching to behavior/speech
- Find out what sentences speakers accept as true
- GE is evidence for T:
- (T) `Es regnet’ is true-in-German when spoken by x at time t if and only if it is raining near x at t
- (GE) (∀x)(∀t) (if x belongs to the German speech community then (x holds true `Es regnet’ at t if and only if it is raining near x at t’))
- Problems with extensive nature of (∀x)(∀t)
- Problems with error: speakers may be wrong about whether it is raining or not
- (GE) is only supposed to be a generalization: not always true
- Seek `best fit’; `maximize agreement’ making speakers right as much as possible
- Something like a Principle Of Charity — but based on the claim that if we cannot find agreement, then speakers are not rational
Liar Paradox And The Structure Of Truth
- Tarski’s analysis starts from the observation that the liar paradox is a feature of all sufficiently rich languages
- Addresses this by working in a metalanguage on a more restricted formal language
- This can be done in stages but will mean no adequate truth theory for natural languages is possible; the restricted target languages will just look like formal languages
- Gödel’s result on the non-coextensivity of provable and true statements in arithmetic derives from the liar paradox ultimately
- Arithmetic a simple formal language — shows Tarski’s concern genuine if Gödel’s result means there can be no theory of truth in arithmetic
- Tarski’s view described as a `redundancy’ theory of truth: there is no difference between asserting `It is true that A’ and simply `A’