9545
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Late in life Frege abandoned logicism, and saw the source of arithmetic as geometrical [Frege, by Chihara]
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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'.
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From:
report of Gottlob Frege (Sources of Knowledge of Mathematics [1922]) by Charles Chihara - A Structural Account of Mathematics Intro n3
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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.
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7399
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Even without religion, there are many guides to morality [Bacon]
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Full Idea:
Atheism leaves a man to sense, to philosophy, to natural piety, to laws, to reputation; all which may be guides to an outward moral virtue, though religion were not.
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From:
Francis Bacon (17: Of Superstition [1625], p.52)
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A reaction:
One might add to Bacon's list 'contracts', or 'rational consistency', or 'self-evident human excellence', or 'natural sympathy'. This is a striking idea, which clearly made churchmen uneasy when atheism began to spread.
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