Combining Texts

Ideas for 'Frege's Theory of Numbers', 'Truth by Convention' and 'Rationality and Virtue'

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5 ideas

5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
Quine quickly dismisses If-thenism [Quine, by Musgrave]
     Full Idea: Quine quickly dismisses If-thenism.
     From: report of Willard Quine (Truth by Convention [1935], p.327) by Alan Musgrave - Logicism Revisited §5
     A reaction: [Musgrave quotes a long chunk of Quine which is hard to compress!] Effectively, he says If-thenism is cheating, or begs the question, by eliminating whole sections of perfectly good mathematics, because they cannot be derived from axioms.
5. Theory of Logic / C. Ontology of Logic / 4. Logic by Convention
Logic needs general conventions, but that needs logic to apply them to individual cases [Quine, by Rey]
     Full Idea: Quine argues that logic could not be established by conventions, since the logical truths, being infinite in number, must be given by general conventions rather than singly; and logic is needed in the meta-theory, to apply to individual cases.
     From: report of Willard Quine (Truth by Convention [1935]) by Georges Rey - The Analytic/Synthetic Distinction 3.4
     A reaction: A helpful insight into Quine's claim. If only someone would print these one sentence summaries at the top of classic papers, we would all get far more out of them at first reading. Assuming Rey is right!
Claims that logic and mathematics are conventional are either empty, uninteresting, or false [Quine]
     Full Idea: If logic and mathematics being true by convention says the primitives can be conventionally described, that works for anything, and is empty; if the conventions are only for those fields, that's uninteresting; if a general practice, that is false.
     From: Willard Quine (Truth by Convention [1935], p.102)
     A reaction: This is Quine's famous denial of the traditional platonist view, and the new Wittgensteinian conventional view, preparing the ground for a more naturalistic and empirical view. I feel more sympathy with Quine than with the other two.
Logic isn't conventional, because logic is needed to infer logic from conventions [Quine]
     Full Idea: If logic is to proceed mediately from conventions, logic is needed for inferring logic from the conventions. Conventions for adopting logical primitives can only be communicated by free use of those very idioms.
     From: Willard Quine (Truth by Convention [1935], p.104)
     A reaction: A common pattern of modern argument, which always seems to imply that nothing can ever get off the ground. I suspect that there are far more benign circles in the world of thought than most philosophers imagine.
If a convention cannot be communicated until after its adoption, what is its role? [Quine]
     Full Idea: When a convention is incapable of being communicated until after its adoption, its role is not clear.
     From: Willard Quine (Truth by Convention [1935], p.106)
     A reaction: Quine is discussing the basis of logic, but the point applies to morality - that if there is said to be a convention at work, the concepts of morality must already exist to get the conventional framework off the ground. What is it that comes first?