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Single Idea 14207

[filed under theme 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 Ref

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]

The 22 ideas from 'Reason, Truth and History'

4714 Putnam's epistemic notion of truth replaces the realism of correspondence with ontological relativism [Putnam, by O'Grady]
4716 The correspondence theory is wrong, because there is no one correspondence between reality and fact [Putnam, by O'Grady]
14214 If we try to cure the abundance of theories with causal links, this is 'just more theory' [Putnam, by Lewis]
4718 If necessity is always relative to a description in a language, then there is only 'de dicto' necessity [Putnam, by O'Grady]
7624 The word 'inconsiderate' nicely shows the blurring of facts and values [Putnam]
7610 A fact is simply what it is rational to accept [Putnam]
7611 Rationality is one part of our conception of human flourishing [Putnam]
7612 Reference is social not individual, because we defer to experts when referring to elm trees [Putnam]
7613 Concepts are (at least in part) abilities and not occurrences [Putnam]
14202 Neither individual nor community mental states fix reference [Putnam]
14201 Maybe the total mental state of a language community fixes the reference of a term [Putnam]
14206 There are infinitely many interpretations of a sentence which can all seem to be 'correct' [Putnam]
14200 'Water' on Twin Earth doesn't refer to water, but no mental difference can account for this [Putnam]
14204 Naïve operationalism would have meanings change every time the tests change [Putnam]
14205 The sentence 'A cat is on a mat' remains always true when 'cat' means cherry and 'mat' means tree [Putnam]
14203 Intension is not meaning, as 'cube' and 'square-faced polyhedron' are intensionally the same [Putnam]
14207 If cats equal cherries, model theory allows reinterpretation of the whole language preserving truth [Putnam]
7616 Truth is an idealisation of rational acceptability [Putnam]
7617 Before Kant, all philosophers had a correspondence theory of truth [Putnam]
7618 Very nominalistic philosophers deny properties, though scientists accept them [Putnam]
7620 Some kind of objective 'rightness' is a presupposition of thought itself [Putnam]
7623 For ancient Greeks being wise was an ethical value [Putnam]