Combining Texts

All the ideas for 'fragments/reports', 'On the True Doctrine (Against Christians)' and 'Remarks on the definition and nature of mathematics'

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6 ideas

5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic

17807	To study formal systems, look at the whole thing, and not just how it is constructed in steps [Curry]
	Full Idea: In the study of formal systems we do not confine ourselves to the derivation of elementary propositions step by step. Rather we take the system, defined by its primitive frame, as datum, and then study it by any means at our command.
	From: Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'The formalist')
	A reaction: This is what may potentially lead to an essentialist view of such things. Focusing on bricks gives formalism, focusing on buildings gives essentialism.

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism

17806	It is untenable that mathematics is general physical truths, because it needs infinity [Curry]
	Full Idea: According to realism, mathematical propositions express the most general properties of our physical environment. This is the primitive view of mathematics, yet on account of the essential role played by infinity in mathematics, it is untenable today.
	From: Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'The problem')
	A reaction: I resist this view, because Curry's view seems to imply a mad metaphysics. Hilbert resisted the role of the infinite in essential mathematics. If the physical world includes its possibilities, that might do the job. Hellman on structuralism?

6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique

17808	Saying mathematics is logic is merely replacing one undefined term by another [Curry]
	Full Idea: To say that mathematics is logic is merely to replace one undefined term by another.
	From: Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'Mathematics')

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?

25. Social Practice / F. Life Issues / 6. Animal Rights

1868	The world was made as much for animals as for man [Celsus]
	Full Idea: The world was made as much for the irrational animals as for men.
	From: Celsus (On the True Doctrine (Against Christians) [c.178], §V)
	A reaction: A good remark. It seems to be a classic distortion of European Christianity that the world is made for us, and that animals only exist to fill our sandwiches.

29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity

1867	Christians presented Jesus as a new kind of logos to oppose that of the philosophers [Celsus]
	Full Idea: Christians put forth this Jesus not only as the son of God, but as the very Logos - not the pure and holy Logos known to the philosophers, but a new kind of Logos.
	From: Celsus (On the True Doctrine (Against Christians) [c.178], III)