display all the ideas for this combination of philosophers
3 ideas
10303 | Restricted Platonism is just an ideal projection of a domain of thought [Bernays] |
Full Idea: A restricted Platonism does not claim to be more than, so to speak, an ideal projection of a domain of thought. | |
From: Paul Bernays (On Platonism in Mathematics [1934], p.261) | |
A reaction: I have always found Platonism to be congenial when it talks of 'ideals', and ridiculous when it talks of a special form of 'existence'. Ideals only 'exist' because we idealise things. I may declare myself, after all, to be a Restricted Platonist. |
10306 | Mathematical abstraction just goes in a different direction from logic [Bernays] |
Full Idea: Mathematical abstraction does not have a lesser degree than logical abstraction, but rather another direction. | |
From: Paul Bernays (On Platonism in Mathematics [1934], p.268) | |
A reaction: His point is that the logicists seem to think that if you increasingly abstract from mathematics, you end up with pure logic. |
14248 | We could accept the integers as primitive, then use sets to construct the rest [Cohen] |
Full Idea: A very reasonable position would be to accept the integers as primitive entities and then use sets to form higher entities. | |
From: Paul J. Cohen (Set Theory and the Continuum Hypothesis [1966], 5.4), quoted by Oliver,A/Smiley,T - What are Sets and What are they For? | |
A reaction: I find this very appealing, and the authority of this major mathematician adds support. I would say, though, that the integers are not 'primitive', but pick out (in abstraction) consistent features of the natural world. |