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Ideas for 'Structures and Structuralism in Phil of Maths', 'The Thought: a Logical Enquiry' and 'The Idea of the Brain'

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4 ideas

3. Truth / A. Truth Problems / 2. Defining Truth
The word 'true' seems to be unique and indefinable [Frege]
     Full Idea: It seems likely that the content of the word 'true' is sui generis and indefinable
     From: Gottlob Frege (The Thought: a Logical Enquiry [1918], p.327 (60))
     A reaction: This is the view I associate with Davidson, though fans of Axiomatic Truth give up defining it, and just describe how it behaves. Defining it is very elusive, but I don't accept that nothing can be said about the contents of the concept of truth.
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
There cannot be complete correspondence, because ideas and reality are quite different [Frege]
     Full Idea: It is essential that the reality shall be distinct from the idea. But then there can be no complete correspondence, no complete truth.
     From: Gottlob Frege (The Thought: a Logical Enquiry [1918], p.327 (60))
     A reaction: He thinks that logic can give a perfect account of truth, or at least the extension of truth, where ordinary language will always fail. I wonder what he would have thought of Tarski's theory?
3. Truth / F. Semantic Truth / 2. Semantic Truth
While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price]
     Full Idea: While truth can be defined in a relative way, as truth in one particular model, a non-relative notion of truth is implied, as truth in all models.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4)
     A reaction: [The article is actually discussing arithmetic] This idea strikes me as extremely important. True-in-all-models is usually taken to be tautological, but it does seem to give a more universal notion of truth. See semantic truth, Tarski, Davidson etc etc.
3. Truth / H. Deflationary Truth / 1. Redundant Truth
The property of truth in 'It is true that I smell violets' adds nothing to 'I smell violets' [Frege]
     Full Idea: The sentence 'I smell the scent of violets' has just the same content as 'It is true that I smell the scent of violets'. So it seems that nothing is added to the thought by my ascribing to it the property of truth.
     From: Gottlob Frege (The Thought: a Logical Enquiry [1918], p.328 (61))
     A reaction: This idea predates Ramsey's similar proposal, for which, oddly, Ramsey always seems to get the credit. To a logician they may have identical content, but pragmatically they are likely to differ in context. 'True' certainly doesn't add to the thought.