Combining Texts

All the ideas for 'fragments/reports', 'The Rationalists' and 'Science and Hypothesis'

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5 ideas

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism

10180	Mathematicians do not study objects, but relations between objects [Poincaré]
	Full Idea: Mathematicians do not study objects, but relations between objects; it is a matter of indifference if the objects are replaced by others, provided the relations do not change. They are interested in form alone, not matter.
	From: Henri Poincaré (Science and Hypothesis [1902], p.20), quoted by E Reck / M Price - Structures and Structuralism in Phil of Maths §6
	A reaction: This connects modern structuralism with Aritotle's interest in the 'form' of things. Contrary to the views of the likes of Frege, it is hard to see that the number '7' has any properties at all, apart from its relations. A daffodil would do just as well.

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?

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.

21. Aesthetics / C. Artistic Issues / 7. Art and Morality

468	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?

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.