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2 ideas
| 10775 | The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp] |
| Full Idea: The main objection to the axiom of choice was that it had to be given by some law or definition, but since sets are arbitrary this seems irrelevant. Formalists consider it meaningless, but set-theorists consider it as true, and practically obvious. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §3) |
| 7548 | Classes, grouped by a convenient property, are logical constructions [Russell] |
| Full Idea: Classes or series of particulars, collected together on account of some property which makes it convenient to be able to speak of them as wholes, are what I call logical constructions or symbolic fictions. | |
| From: Bertrand Russell (The Ultimate Constituents of Matter [1915], p.125) | |
| A reaction: When does a construction become 'logical' instead of arbitrary? What is it about a property that makes it 'convenient'? At this point Russell seems to have built his ontology on classes, and the edifice was crumbling, thanks to Wittgenstein. |