Combining Texts

All the ideas for 'Frege's Theory of Numbers', 'The Inference to the Best Explanation' and 'Amphitheatrum'

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3 ideas

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck]
     Full Idea: In Parsons's demonstrative model of counting, '1' means the first, and counting says 'the first, the second, the third', where one is supposed to 'tag' each object exactly once, and report how many by converting the last ordinal into a cardinal.
     From: report of Charles Parsons (Frege's Theory of Numbers [1965]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 3
     A reaction: This sounds good. Counting seems to rely on that fact that numbers can be both ordinals and cardinals. You don't 'convert' at the end, though, because all the way you mean 'this cardinality in this order'.
14. Science / D. Explanation / 3. Best Explanation / a. Best explanation
Best Explanation is the core notion of epistemology [Harman, by Smart]
     Full Idea: Gilbert Harman introduced the term 'inference to the best explanation', and argued that it is the core notion of epistemology.
     From: report of Gilbert Harman (The Inference to the Best Explanation [1974]) by J.J.C. Smart - Explanation - Opening Address p. 01
     A reaction: Hard to assess that, but it sounds right. I'm a fan of coherence theories of justification, and also coherence theories of explanation, and there is a neat package there somewhere.
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / b. Prime matter
Prime matter is nothing but its parts [Vanini]
     Full Idea: The whole of prime matter, considered as prime matter, is nothing other than its parts.
     From: Julio Cesare Vanini (Amphitheatrum [1615], Ex 5:p.28), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 03.2
     A reaction: This is a late scholastic writer rejecting the traditional (and obscure) prime matter with the new corpuscularian approach. It signals the end of the Greek concept of matter.