Combining Texts

All the ideas for 'The Gettier Problem', 'Letters to William Molyneux' and 'works'

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4 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
9565 Zermelo made 'set' and 'member' undefined axioms [Zermelo, by Chihara]
     Full Idea: The terms 'set' and 'is a member of' are primitives of Zermelo's 1908 axiomatization of set theory. They are not given model-theoretic analyses or definitions.
     From: report of Ernst Zermelo (works [1920]) by Charles Chihara - A Structural Account of Mathematics 7.5
     A reaction: This looks like good practice if you want to work with sets, but not so hot if you are interested in metaphysics.
3339 For Zermelo's set theory the empty set is zero and the successor of each number is its unit set [Zermelo, by Blackburn]
     Full Idea: For Zermelo's set theory the empty set is zero and the successor of each number is its unit set.
     From: report of Ernst Zermelo (works [1920]) by Simon Blackburn - Oxford Dictionary of Philosophy p.280
9. Objects / D. Essence of Objects / 13. Nominal Essence
12812 Things have real essences, but we categorise them according to the ideas we receive [Locke]
     Full Idea: This I do say, that there are real constitutions in things from whence simple ideas flow, which we observe combin'd in them. But we distinguish particular substances into sorts or genera not by real essences or constitutions, but by observed simple ideas.
     From: John Locke (Letters to William Molyneux [1692], 1693.01.20)
     A reaction: This is the clearest statement I can find of Locke's position on essences. He is totally committed to their reality, but strongly aware of the empirical constraints which keep us from direct knowledge of them. He would be amazed by modern discoveries.
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / b. Gettier problem
19699 A Gettier case is a belief which is true, and its fallible justification involves some luck [Hetherington]
     Full Idea: A Gettier case contains a belief which is true and well justified without being knowledge. Its justificatory support is also fallible, ...and there is considerable luck in how the belief combnes being true with being justified.
     From: Stephen Hetherington (The Gettier Problem [2011], 5)
     A reaction: This makes luck the key factor. 'Luck' is a rather vague concept, and so the sort of luck involved must first be spelled out. Or the varieties of luck that can produce this outcome.