Combining Texts

All the ideas for 'fragments/reports', 'What Numbers Are' and 'Model Theory for Modal Logic I'

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4 ideas

4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
9560 S5 provides the correct logic for necessity in the broadly logical sense [Fine,K]
     Full Idea: S5 provides the correct logic for necessity in the broadly logical sense.
     From: Kit Fine (Model Theory for Modal Logic I [1978], 151), quoted by Charles Chihara - A Structural Account of Mathematics
     A reaction: I have no view on this, but I am prejudiced in favour of the idea that there is a correct logic for such things, whichever one it may be. Presumably the fact that S5 has no restrictions on accessibility makes it more comprehensive and 'metaphysical'.
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]
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?