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All the ideas for 'reports', 'The Rationalists' and 'Introduction to 'Hippias Minor''

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5 ideas

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
9548 A mathematical object exists if there is no contradiction in its definition [Waterfield]
     Full Idea: A mathematical object exists provided there is no contradiction implied in its definition.
     From: Robin Waterfield (Introduction to 'Hippias Minor' [1987], p.44), quoted by Charles Chihara - A Structural Account of Mathematics 1.4
     A reaction: A rather bizarre criterion for existence. Not one, for example, that you would consider applying to the existence of physical objects! But then Poincaré is the father of 'conventionalism', rather than being a platonist.
9. Objects / B. Unity of Objects / 2. Substance / c. Types of substance
4304 Descartes says there are two substance, Spinoza one, and Leibniz infinitely many [Cottingham]
     Full Idea: Descartes was a dualist about substance, Spinoza was a monist, and Leibniz was a pluralist (an infinity of substances).
     From: John Cottingham (The Rationalists [1988], p.76)
     A reaction: Spinoza is appealing. We posit a substance, as the necessary basis for existence, but it is unclear how more than one substance can be differentiated. If mind is a separate substance, why isn't iron? Why aren't numbers?
10. Modality / A. Necessity / 8. Transcendental Necessity
3016 Even the gods cannot strive against necessity [Pittacus, by Diog. Laertius]
     Full Idea: Even the gods cannot strive against necessity.
     From: report of Pittacus (reports [c.610 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 01.5.4
12. Knowledge Sources / C. Rationalism / 1. Rationalism
4303 The notion of substance lies at the heart of rationalist metaphysics [Cottingham]
     Full Idea: The notion of substance lies at the heart of rationalist metaphysics.
     From: John Cottingham (The Rationalists [1988], p.75)
     A reaction: The idea of 'substance' has had an interesting revival in modern philosophy (though not, obviously, in physics). Maybe physics and philosophy have views of reality which are not complementary, but are rivals.
26. Natural Theory / C. Causation / 9. General Causation / d. Causal necessity
4306 For rationalists, it is necessary that effects be deducible from their causes [Cottingham]
     Full Idea: The rationalist view of causation takes it that to make effects intelligible, it must be shown that they are in principle deducible from their causes.
     From: John Cottingham (The Rationalists [1988], p.92)
     A reaction: This has intuitive appeal, but deduction is only possible with further premises, such as the laws of physics. The effects of human behaviour look a bit tricky, even if we cause them.