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4 ideas
3907 | Could you be intellectually acquainted with numbers, but unable to count objects? [Scruton] |
Full Idea: Could someone have a perfect intellectual acquaintance with numbers, but be incapable of counting a flock of sheep? | |
From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 26.6) |
10529 | If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K] |
Full Idea: Neo-Fregeans have thought that Hume's Principle, and the like, might be definitive of number and therefore not subject to the usual epistemological worries over its truth. | |
From: Kit Fine (Precis of 'Limits of Abstraction' [2005], p.310) | |
A reaction: This seems to be the underlying dream of logicism - that arithmetic is actually brought into existence by definitions, rather than by truths derived from elsewhere. But we must be able to count physical objects, as well as just counting numbers. |
10530 | Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K] |
Full Idea: The fundamental difficulty facing the neo-Fregean is to either adopt the predicative reading of Hume's Principle, defining numbers, but inadequate, or the impredicative reading, which is adequate, but not really a definition. | |
From: Kit Fine (Precis of 'Limits of Abstraction' [2005], p.312) | |
A reaction: I'm not sure I understand this, but the general drift is the difficulty of building a system which has been brought into existence just by definition. |
3908 | If maths contains unprovable truths, then maths cannot be reduced to a set of proofs [Scruton] |
Full Idea: If there can be unprovable truths of mathematics, then mathematics cannot be reduced to the proofs whereby we construct it. | |
From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 26.7) |