Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'Identity over Time' and 'Sources of Knowledge of Mathematics'

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5 ideas

6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Late in life Frege abandoned logicism, and saw the source of arithmetic as geometrical [Frege, by Chihara]
     Full Idea: Near the end of his life, Frege completely abandoned his logicism, and came to the conclusion that the source of our arithmetical knowledge is what he called 'the Geometrical Source of Knowledge'.
     From: report of Gottlob Frege (Sources of Knowledge of Mathematics [1922]) by Charles Chihara - A Structural Account of Mathematics Intro n3
     A reaction: We have, rather crucially, lost touch with the geometrical origins of arithmetic (such as 'square' numbers), which is good news for the practice of mathematics, but probably a disaster for the philosophy of the subject.
9. Objects / E. Objects over Time / 1. Objects over Time
If things change they become different - but then no one thing undergoes the change! [Gallois]
     Full Idea: If things really change, there can't literally be one thing before and after the change. However, if there isn't one thing before and after the change, then no thing has really undergone any change.
     From: André Gallois (Identity over Time [2011], Intro)
     A reaction: [He cites Copi for this way of expressing the problem of identity through change] There is an obvious simple ambiguity about 'change' in ordinary English. A change of property isn't a change of object. Painting a red ball blue isn't swapping it.
9. Objects / E. Objects over Time / 4. Four-Dimensionalism
4D: time is space-like; a thing is its history; past and future are real; or things extend in time [Gallois]
     Full Idea: We have four versions of Four-Dimensionalism: the relativistic view that time is space-like; a persisting thing is identical with its history (so objects are events); past and future are equally real; or (Lewis) things extend in time, with temporal parts.
     From: André Gallois (Identity over Time [2011], §2.5)
     A reaction: Broad proposed the second one. I prefer 3-D: at any given time a thing is wholly present. At another time it is wholly present despite having changed. It is ridiculous to think that small changes destroy identity. We acquire identity by dying??
9. Objects / F. Identity among Objects / 6. Identity between Objects
If two things are equal, each side involves a necessity, so the equality is necessary [Gallois]
     Full Idea: The necessity of identity: a=b; □(a=a); so something necessarily = a; so something necessarily must equal b; so □(a=b). [A summary of the argument of Marcus and Kripke]
     From: André Gallois (Identity over Time [2011], §3)
     A reaction: [Lowe 1982 offered a response] The conclusion seems reasonable. If two things are mistakenly thought to be different, but turn out to be one thing, that one thing could not possibly be two things. In no world is one thing two things!
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
     Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom.
     From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88)
     A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate').