display all the ideas for this combination of texts
5 ideas
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. |
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. |
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. |