Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'What is innate and why' and 'Sources of Knowledge of Mathematics'

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4 ideas

6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
9545 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.
18. Thought / B. Mechanics of Thought / 4. Language of Thought
2605 If everything uses mentalese, ALL concepts must be innate! [Putnam]
     Full Idea: Fodor concludes that every predicate that a brain could learn to use must have a translation into the computer language of that brain. So no "new" concepts can be acquired: all concepts are innate!
     From: Hilary Putnam (What is innate and why [1980], p.407)
     A reaction: Some misunderstanding, surely? No one could be so daft as to think that everyone has an innate idea of an iPod. More basic innate building blocks for thought are quite plausible.
2606 No machine language can express generalisations [Putnam]
     Full Idea: Computers have a built-in language, but not a language that contains quantifiers (that is, the words "all" and "some"). …So generalizations (containing "all") cannot ever be stated in machine language.
     From: Hilary Putnam (What is innate and why [1980], p.408)
     A reaction: Computers are too sophisticated to need quantification (which is crude). Computers can work with very precise and complex specifications of the domain of a given variable.
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
7903 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').