Combining Texts

Ideas for 'Material Constitution', 'Frege Philosophy of Language (2nd ed)' and 'Impossible Objects: interviews'

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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic

10554	Intuitionists find the Incompleteness Theorem unsurprising, since proof is intuitive, not formal [Dummett]
	Full Idea: In the intuitionist view, the notion of an intuitive proof cannot be expected to coincide with that of a proof in a formal system, and Gödel's incompleteness theorem is thus unsurprising from an intuitionist point of view.
	From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14)

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism

10552	Intuitionism says that totality of numbers is only potential, but is still determinate [Dummett]
	Full Idea: From the intuitionist point of view natural numbers are mental constructions, so their totality is only potential, but it is neverthless a fully determinate totality.
	From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14)
	A reaction: This could only be if the means of constructing the numbers was fully determinate, so how does that situation come about?