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4 ideas
15879 | The Square of Opposition has two contradictory pairs, one contrary pair, and one sub-contrary pair [Harré] |
Full Idea: Square of Opposition: 'all A are B' and 'no A are B' are contraries; 'some A are B' and 'some A are not B' are sub-contraries; the pairs 'all A are B'/'some A are B' and 'no A are B'/'some A are B' are contradictories. | |
From: Rom Harré (Laws of Nature [1993], 3) | |
A reaction: [the reader may construct his own diagram from this description!] The contraries are at the extremes of contradiction, but the sub-contraries are actual compatible. You could add possible worlds to this picture. |
23623 | Predicativism says only predicated sets exist [Hossack] |
Full Idea: Predicativists doubt the existence of sets with no predicative definition. | |
From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 02.3) | |
A reaction: This would imply that sets which encounter paradoxes when they try to be predicative do not therefore exist. Surely you can have a set of random objects which don't fall under a single predicate? |
23624 | The iterative conception has to appropriate Replacement, to justify the ordinals [Hossack] |
Full Idea: The iterative conception justifies Power Set, but cannot justify a satisfactory theory of von Neumann ordinals, so ZFC appropriates Replacement from NBG set theory. | |
From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 09.9) | |
A reaction: The modern approach to axioms, where we want to prove something so we just add an axiom that does the job. |
23625 | Limitation of Size justifies Replacement, but then has to appropriate Power Set [Hossack] |
Full Idea: The limitation of size conception of sets justifies the axiom of Replacement, but cannot justify Power Set, so NBG set theory appropriates the Power Set axiom from ZFC. | |
From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 09.9) | |
A reaction: Which suggests that the Power Set axiom is not as indispensable as it at first appears to be. |