more from Hilary Putnam

### Single Idea 14207

#### [catalogued under 5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms]

Full Idea

If the number of cats happens to equal the cherries, then it follows from the theory of models that there is a reinterpretation of the entire language that leaves all sentences unchanged in truth value while permuting the extensions of 'cat' and 'cherry'.

Gist of Idea

If cats equal cherries, model theory allows reinterpretation of the whole language preserving truth

Source

Hilary Putnam (Reason, Truth and History [1981], Ch.2)

Book Reference

Putnam,Hilary: 'Reason, Truth and History' [CUP 1998], p.44

A Reaction

This horrifying result seems to come simply from the fact that there is an isomorphism between two models, which in turn seems to rest largely on the cardinality of the models. There seems to be something wrong with model theory here (?).

Related Ideas

Idea 14205
The sentence 'A cat is on a mat' remains always true when 'cat' means cherry and 'mat' means tree **[Putnam]**

Idea 14206
There are infinitely many interpretations of a sentence which can all seem to be 'correct' **[Putnam]**

Idea 14212
A consistent theory just needs one model; isomorphic versions will do too, and large domains provide those **[Lewis]**