Combining Philosophers

Ideas for H.Putnam/P.Oppenheim, Steven Weinberg and Ludwig Wittgenstein

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3 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.