Full Idea
The sentence 'A cat is on a mat' can be reinterpreted so that in the actual world 'cat' refers to cherries and 'mat' refers to trees, without affecting the truth-value of the sentence in any possible world.
Gist of Idea
The sentence 'A cat is on a mat' remains always true when 'cat' means cherry and 'mat' means tree
Source
Hilary Putnam (Reason, Truth and History [1981], Ch.2)
Book Reference
Putnam,Hilary: 'Reason, Truth and History' [CUP 1998], p.33
A Reaction
This simple suggestion is the basis of a notorious argument in favour of anti-realism. See D.Lewis's 'Putnam's Paradox'. It tracks back to Skolem's doubts about whether infinitary mathematics is possible. Putnam's conclusion sounds daft.
Related Ideas
Idea 14206 There are infinitely many interpretations of a sentence which can all seem to be 'correct' [Putnam]
Idea 14207 If cats equal cherries, model theory allows reinterpretation of the whole language preserving truth [Putnam]