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All the ideas for 'works', 'Logic [1897]' and 'Set Theory and its Logic'

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3 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
21717 Reducibility undermines type ramification, and is committed to the existence of functions [Quine, by Linsky,B]
     Full Idea: Quine charges that the axiom of Reducibility both undoes the effect of the ramification, and commits the theory to a platonist view of propositional functions (which is a theory of sets, once use/mention confusions are cleared up).
     From: report of Willard Quine (Set Theory and its Logic [1963], p.249-58) by Bernard Linsky - Russell's Metaphysical Logic 6.1
5. Theory of Logic / D. Assumptions for Logic / 3. Contradiction
10121 Contradiction is not a sign of falsity, nor lack of contradiction a sign of truth [Pascal]
     Full Idea: Contradiction is not a sign of falsity, nor the lack of contradiction a sign of truth.
     From: Blaise Pascal (works [1660]), quoted by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6
     A reaction: [Quoted in Auden and Kronenberger's Book of Aphorisms] Presumably we would now say that contradiction is a purely formal, syntactic notion, and not a semantic one. If you hit a contradiction, something has certainly gone wrong.
13. Knowledge Criteria / C. External Justification / 2. Causal Justification
11052 Psychological logic can't distinguish justification from causes of a belief [Frege]
     Full Idea: With the psychological conception of logic we lose the distinction between the grounds that justify a conviction and the causes that actually produce it.
     From: Gottlob Frege (Logic [1897] [1897])
     A reaction: Thus Frege kicked the causal theory of justification well into touch long before it had even been properly formulated. That is not to say that there is no psychological aspect to logic, because there is.