Combining Philosophers

All the ideas for Paul Bernays, Kretzmann/Stump and Timon

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5 ideas

4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
10304 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
10303 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
10306 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.
13. Knowledge Criteria / E. Relativism / 3. Subjectivism
2975 That honey is sweet I do not affirm, but I agree that it appears so [Timon]
     Full Idea: That honey is sweet I do not affirm, but I agree that it appears so.
     From: Timon (On Sensations (frags) [c.285 BCE]), quoted by Diogenes Laertius - Lives of Eminent Philosophers 09.104-5
14. Science / A. Basis of Science / 2. Demonstration
22110 Demonstration provides depth of understanding and explanation (rather than foundations) [Kretzmann/Stump]
     Full Idea: According to Aquinas, what demonstration provides is not so much knowledge as conceived by foundationalists as depth of understanding and explanatory insight.
     From: Kretzmann/Stump (Aquinas, Thomas [2005]), quoted by Kretzmann/Stump - Aquinas, Thomas 11
     A reaction: It was noticeable that Aristotle didn't make clear what demonstration aims to achieve, and he didn't employ it elsewhere in his writings. We aim for understanding, not for well grounded propositions. Understanding needs implications and mechanisms.