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Ideas for 'Intensional Logic', 'Dialectic of Enlightenment' and 'Tractatus Logico-Philosophicus'

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5 ideas

6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / a. Defining numbers
18160 The concept of number is just what all numbers have in common [Wittgenstein]
     Full Idea: The concept of number is simply what is common to all numbers, the general form of number. The concept of number is the variable number.
     From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 6.022)
18153 A number is a repeated operation [Wittgenstein]
     Full Idea: A number is the index of an operation.
     From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 6.021)
     A reaction: Roughly, this means that a number indicates how many times some basic operation has been performed. Bostock 2009:286 expounds the idea.
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
18161 The theory of classes is superfluous in mathematics [Wittgenstein]
     Full Idea: The theory of classes is completely superfluous in mathematics. This is connected with the fact that the generality required in mathematics is not accidental generality.
     From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 6.031)
     A reaction: This fits Russell's no-class theory, which rests everything instead on propositional functions.
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
6849 Wittgenstein hated logicism, and described it as a cancerous growth [Wittgenstein, by Monk]
     Full Idea: Wittgenstein didn't just have an arguments against logicism; he hated logicism, and described is as a cancerous growth.
     From: report of Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921]) by Ray Monk - Interview with Baggini and Stangroom p.12
     A reaction: This appears to have been part of an inexplicable personal antipathy towards Russell. Wittgenstein appears to have developed a dislike of all reductionist ideas in philosophy.
23509 The logic of the world is shown by tautologies in logic, and by equations in mathematics [Wittgenstein]
     Full Idea: The logic of the world, which is shown in tautologies by the propositions of logic, is shown in equations by mathematics.
     From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 6.22)
     A reaction: White observes that this is Wittgenstein distinguishing logic from mathematics, and thus distancing himself from logicism. But see T 6.2.