Combining Texts

All the ideas for 'Characteristics', 'What Numbers Are' and 'Meaning and Necessity'

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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]
19. Language / C. Assigning Meanings / 8. Possible Worlds Semantics
11968 The intension of a sentence is the set of all possible worlds in which it is true [Carnap, by Kaplan]
     Full Idea: Carnap's proposal is to understand the category of intensions appropriate to sentences (his 'propositions') as sets of possible worlds. The intension of the sentence is taken as the set of all possible worlds in which the sentence is true.
     From: report of Rudolph Carnap (Meaning and Necessity [1947]) by David Kaplan - Transworld Heir Lines p.90
     A reaction: [reference?] This extension of the truth-conditions view of meaning strikes me as being very attractive. Except that whole worlds hardly seem to be relevant to my remark about how lunch might have been improved.
21. Aesthetics / A. Aesthetic Experience / 2. Aesthetic Attitude
18545 The disinterested attitude of the judge is the hallmark of a judgement of beauty [Shaftesbury, by Scruton]
     Full Idea: Shaftesbury explained the peculiar features of the judgement of beauty in terms of the disinterested attitude of the judge.
     From: report of 3rd Earl of Shaftesbury (Characteristics [1711]) by Roger Scruton - Beauty: a very short introduction 1
     A reaction: Good. I take our vocabulary to mark a distinction between expressions of subjective preference, and expressions of what aspire to be objective facts. 'I love this' versus 'this is good or beautiful'.