Combining Texts

All the ideas for 'fragments/reports', 'Chapters on Scepticism' and 'What Numbers Are'

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4 ideas

5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems

17813	Löwenheim-Skolem says any theory with a true interpretation has a model in the natural numbers [White,NP]
	Full Idea: The Löwenheim-Skolem theorem tells us that any theory with a true interpretation has a model in the natural numbers.
	From: Nicholas P. White (What Numbers Are [1974], V)

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure

17812	Finite cardinalities don't need numbers as objects; numerical quantifiers will do [White,NP]
	Full Idea: Statements involving finite cardinalities can be made without treating numbers as objects at all, simply by using quantification and identity to define numerically definite quantifiers in the manner of Frege.
	From: Nicholas P. White (What Numbers Are [1974], IV)
	A reaction: [He adds Quine 1960:268 as a reference]

15. Nature of Minds / A. Nature of Mind / 4. Other Minds / b. Scepticism of other minds

1799	If we can't know minds, we can't know if Pyrrho was a sceptic [Theodosius, by Diog. Laertius]
	Full Idea: We can't say the school of Pyrrho is sceptical, because the motion of the mind in each individual is incomprehensible to others, so we don't know Pyrrho's disposition.
	From: report of Theodosius (Chapters on Scepticism [c.100 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.Py.8

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?