Combining Texts

All the ideas for 'fragments/reports', 'Letters to Antoine Arnauld' and 'Reply to Foucher'

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3 ideas

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
I strongly believe in the actual infinite, which indicates the perfections of its author [Leibniz]
     Full Idea: I am so much for the actual infinite that instead of admitting that nature abhors it, as is commonly said, I hold that it affects nature everywhere in order to indicate the perfections of its author.
     From: Gottfried Leibniz (Reply to Foucher [1693], p.99)
     A reaction: I would have thought that, for Leibniz, while infinities indicate the perfections of their author, that is not the reason why they exist. God wasn't, presumably, showing off. Leibniz does not think we can actually know these infinities.
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
It is possible that an omnipotent God might make one and two fail to equal three [Descartes]
     Full Idea: Since every basic truth depends on God's omnipotence, I would not dare to say that God cannot make it....that one and two should not be three.
     From: René Descartes (Letters to Antoine Arnauld [1645]), quoted by A.W. Moore - The Evolution of Modern Metaphysics 01.3
     A reaction: An unusual view. Most people would say that if Descartes can doubt something that simple, he should also doubt his reasons for believing in God's existence.
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?