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All the ideas for 'Remarks on the definition and nature of mathematics', 'fragments/reports' and 'talk'

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5 ideas

5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic

17807	To study formal systems, look at the whole thing, and not just how it is constructed in steps [Curry]
	Full Idea: In the study of formal systems we do not confine ourselves to the derivation of elementary propositions step by step. Rather we take the system, defined by its primitive frame, as datum, and then study it by any means at our command.
	From: Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'The formalist')
	A reaction: This is what may potentially lead to an essentialist view of such things. Focusing on bricks gives formalism, focusing on buildings gives essentialism.

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism

17806	It is untenable that mathematics is general physical truths, because it needs infinity [Curry]
	Full Idea: According to realism, mathematical propositions express the most general properties of our physical environment. This is the primitive view of mathematics, yet on account of the essential role played by infinity in mathematics, it is untenable today.
	From: Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'The problem')
	A reaction: I resist this view, because Curry's view seems to imply a mad metaphysics. Hilbert resisted the role of the infinite in essential mathematics. If the physical world includes its possibilities, that might do the job. Hellman on structuralism?

6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique

17808	Saying mathematics is logic is merely replacing one undefined term by another [Curry]
	Full Idea: To say that mathematics is logic is merely to replace one undefined term by another.
	From: Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'Mathematics')

15. Nature of Minds / B. Features of Minds / 1. Consciousness / d. Purpose of consciousness

4741	A very powerful computer might have its operations restricted by the addition of consciousness [Clark,T]
	Full Idea: It seems possible that if a powerful multi-tasking computer was then given consciousness, this might restrict its operations instead of enhancing them.
	From: Tom Clark (talk [2003]), quoted by PG - Db (ideas)
	A reaction: A nice thought, because it challenges the usual view - that consciousness brings huge intellectual liberty to a mind, and that a mind without it is necessarily restricted. Maybe consciousness is a bottleneck.

20. Action / B. Preliminaries of Action / 2. Willed Action / d. Weakness of will

22511	Some reasonings are stronger than we are [Philolaus]
	Full Idea: Some reasonings are stronger than we are.
	From: Philolaus (fragments/reports [c.425 BCE]), quoted by Aristotle - Eudemian Ethics 1225a33
	A reaction: This endorses the Aristotle view of akrasia (as opposed to the Socratic view). This isolated remark seems to imply that we are more clearly embodiments of will than of reason.