4 ideas
| 9548 | A mathematical object exists if there is no contradiction in its definition [Waterfield] |
| Full Idea: A mathematical object exists provided there is no contradiction implied in its definition. | |
| From: Robin Waterfield (Introduction to 'Hippias Minor' [1987], p.44), quoted by Charles Chihara - A Structural Account of Mathematics 1.4 | |
| A reaction: A rather bizarre criterion for existence. Not one, for example, that you would consider applying to the existence of physical objects! But then Poincaré is the father of 'conventionalism', rather than being a platonist. |
| 8840 | There are five possible responses to the problem of infinite regress in justification [Cleve] |
| Full Idea: Sceptics respond to the regress problem by denying knowledge; Foundationalists accept justifications without reasons; Positists say reasons terminate is mere posits; Coherentists say mutual support is justification; Infinitists accept the regress. | |
| From: James Van Cleve (Why coherence is not enough [2005], I) | |
| A reaction: A nice map of the territory. The doubts of Scepticism are not strong enough for anyone to embrace the view; Foundationalist destroy knowledge (?), as do Positists; Infinitism is a version of Coherentism - which is the winner. |
| 8841 | Modern foundationalists say basic beliefs are fallible, and coherence is relevant [Cleve] |
| Full Idea: Contemporary foundationalists are seldom of the strong Cartesian variety: they do not insist that basic beliefs be absolutely certain. They also tend to allow that coherence can enhance justification. | |
| From: James Van Cleve (Why coherence is not enough [2005], III) | |
| A reaction: It strikes me that they have got onto a slippery slope. How certain are the basic beliefs? How do you evaluate their certainty? Could incoherence in their implications undermine them? Skyscrapers need perfect foundations. |
| 3061 | Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius] |
| Full Idea: Anaxarchus said that he was not even sure that he knew nothing. | |
| From: report of Anaxarchus (fragments/reports [c.340 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.10.1 |