display all the ideas for this combination of texts
3 ideas
19584 | Whoever first counted to two must have seen the possibility of infinite counting [Novalis] |
Full Idea: Whoever first understood how to count to two, even if he still found it difficult to keep on counting, saw nonetheless the possibility of infinite counting according to the same laws. | |
From: Novalis (Logological Fragments I [1798], 84) | |
A reaction: Presumably it is the discerning of the 'law' which triggers this. Is the key concept 'addition' or 'successor' (or are those the same?). |
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? |
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') |