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2 ideas
9641 | Definitions should be replaceable by primitives, and should not be creative [Brown,JR] |
Full Idea: The standard requirement of definitions involves 'eliminability' (any defined terms must be replaceable by primitives) and 'non-creativity' (proofs of theorems should not depend on the definition). | |
From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 7) | |
A reaction: [He cites Russell and Whitehead as a source for this view] This is the austere view of the mathematician or logician. But almost every abstract concept that we use was actually defined in a creative way. |
18889 | Ostensive definitions needn't involve pointing, but must refer to something specific [Salmon,N] |
Full Idea: So-called ostensive definitions need not literally involve ostension, e.g. pointing, but they must involve genuine reference of some sort (in this case reference to a sample of water). | |
From: Nathan Salmon (Reference and Essence (1st edn) [1981], 4.11.2) |