### Single Idea 14212

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

Full Idea

A consistent theory is, by definition, one satisfied by some model; an isomorphic image of a model satisfies the same theories as the original model; to provide the making of an isomorphic image of any given model, a domain need only be large enough.

Gist of Idea

A consistent theory just needs one model; isomorphic versions will do too, and large domains provide those

Source

David Lewis (Putnam's Paradox [1984], 'Why Model')

Book Reference

Lewis,David: 'Papers in Metaphysics and Epistemology' [CUP 1999], p.68

A Reaction

This is laying out the ground for Putnam's model theory argument in favour of anti-realism. If you are chasing the one true model of reality, then formal model theory doesn't seem to offer much encouragement.

Related Idea

Idea 14207
If cats equal cherries, model theory allows reinterpretation of the whole language preserving truth **[Putnam]**