## Friday, June 04, 2010

### Deflationary theories of Truth

A common objection to deflationary theories of truth is sentences like 'Everything Tom says is true'. Analysing this as

(A) For all p, if he asserts p, then p.

results in incoherence when we attempt to substitute. If we substitute sentences like 'snow is white', we get

(B) If he asserts 'snow is white', then 'snow is white'.

which is nonsense. If we substitute propositional content, signified by a 'that' clause, we get

(C) If he asserts that snow is white, then that snow is white.

which is also nonsense. However, we can evade this difficulty along the lines I have suggested in earlier posts. The first insight is that 'it is true that' is a complex operator built from 'it is true', which operates on 'that' clauses to form declarative sentences, and 'that' which operates on sentences to form 'that' clauses. Then it is coherent to hold that the semantics of any declarative sentence can be represented formally as

(D) |- c

where the operator |- corresponds to the 'it is true' part, and 'c' to a that-clause. I.e. we parse 'it is true that Tom runs' as 'it is true / that Tom runs'. Then the problem sentence 'He is always right' can be analysed as

(E) If he says c, |- c

Suppose for example that he says that Tom runs. then c = that Tom runs (note I substitute a 'that' clause, not a sentence), and |- = 'it is true', as above. This yields

(F) If he says that Tom runs, it is true that Tom runs = if he says that Tom runs, Tom runs

which makes perfect sense.