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Ideas for 'fragments/reports', 'Explanation in Mathematics' and 'Intro to 'Communitarianism and Individualism''

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3 ideas

9. Objects / A. Existence of Objects / 6. Nihilism about Objects
There is no coming-to-be of anything, but only mixing and separating [Empedocles, by Aristotle]
     Full Idea: Empedocles says there is no coming-to-be of anything, but only a mingling and a divorce of what has been mingled.
     From: report of Empedocles (fragments/reports [c.453 BCE]) by Aristotle - Coming-to-be and Passing-away (Gen/Corr) 314b08
     A reaction: Aristotle comments that this prevents Empedocleans from distinguishing between superficial alteration and fundamental change of identity. Presumably, though, that wouldn't bother them.
9. Objects / D. Essence of Objects / 7. Essence and Necessity / b. Essence not necessities
Essences are no use in mathematics, if all mathematical truths are necessary [Mancosu]
     Full Idea: Essences and essential properties do not seem to be useful in mathematical contexts, since all mathematical truths are regarded as necessary (though Kit Fine distinguishes between essential and necessary properties).
     From: Paolo Mancosu (Explanation in Mathematics [2008], §6.1)
     A reaction: I take the proviso in brackets to be crucial. This represents a distortion of notion of an essence. There is a world of difference between the central facts about the nature of a square and the peripheral inferences derivable from it.
9. Objects / E. Objects over Time / 10. Beginning of an Object
Substance is not created or destroyed in mortals, but there is only mixing and exchange [Empedocles]
     Full Idea: There is no creation of substance in any one of mortal existence, nor any end in execrable death, but only mixing and exchange of what has been mixed.
     From: Empedocles (fragments/reports [c.453 BCE], B008), quoted by Plutarch - 74: Reply to Colotes 1111f
     A reaction: also Aristotle 314b08