Combining Texts

All the ideas for 'fragments/reports', 'On Platonism in Mathematics' and 'Against Method'

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6 ideas

1. Philosophy / G. Scientific Philosophy / 1. Aims of Science
Science rules the globe because of colonising power, not inherent rationality [Feyerabend]
     Full Idea: Science now reigns supreme all over the globe; but the reason was not insight in its 'inherent rationality' but power play (the colonising nations imposed their way of living) and the need for weapons.
     From: Paul Feyerabend (Against Method [1975], 3), quoted by Robert Fogelin - Walking the Tightrope of Reason Ch.5
     A reaction: A nice clear statement of ridiculous relativism about science. What gave the colonisers their power if it was not more accurate knowledge of how to manipulate nature?
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
Very few things in set theory remain valid in intuitionist mathematics [Bernays]
     Full Idea: Very few things in set theory remain valid in intuitionist mathematics.
     From: Paul Bernays (On Platonism in Mathematics [1934])
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
Restricted Platonism is just an ideal projection of a domain of thought [Bernays]
     Full Idea: A restricted Platonism does not claim to be more than, so to speak, an ideal projection of a domain of thought.
     From: Paul Bernays (On Platonism in Mathematics [1934], p.261)
     A reaction: I have always found Platonism to be congenial when it talks of 'ideals', and ridiculous when it talks of a special form of 'existence'. Ideals only 'exist' because we idealise things. I may declare myself, after all, to be a Restricted Platonist.
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Mathematical abstraction just goes in a different direction from logic [Bernays]
     Full Idea: Mathematical abstraction does not have a lesser degree than logical abstraction, but rather another direction.
     From: Paul Bernays (On Platonism in Mathematics [1934], p.268)
     A reaction: His point is that the logicists seem to think that if you increasingly abstract from mathematics, you end up with pure logic.
14. Science / B. Scientific Theories / 6. Theory Holism
For Feyerabend the meaning of a term depends on a whole theory [Feyerabend, by Rorty]
     Full Idea: For Feyerabend the meaning of a term depends on a whole theory containing the term.
     From: report of Paul Feyerabend (Against Method [1975]) by Richard Rorty - Philosophy and the Mirror of Nature 6.3
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
Musical performance can reveal a range of virtues [Damon of Ath.]
     Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice.
     From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where?