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2 ideas
8956 | What is a singleton set, if a set is meant to be a collection of objects? [Szabó] |
Full Idea: The relationship between an object and its singleton is puzzling. Our intuitive conception of a set is a collection of objects - what are we to make of a collection of a single object? | |
From: Zoltán Gendler Szabó (Nominalism [2003], 4.1) | |
A reaction: The ontological problem seems to be the same as that of the empty set, and indeed the claim that a pair of entities is three things. For logicians the empty set is as real as a pet dog, but not for me. |
10196 | The Axiom of Choice needs a criterion of choice [Black] |
Full Idea: Some mathematicians seem to think that talk of an Axiom of Choice allows them to choose a single member of a collection when there is no criterion of choice. | |
From: Max Black (The Identity of Indiscernibles [1952], p.68) |