Combining Texts

All the ideas for 'fragments/reports', 'The Concept of Logical Consequence' and 'The Philosophy of Logic'

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8 ideas

5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence

18812

Split out the logical vocabulary, make an assignment to the rest. It's logical if premises and conclusion match [Tarski, by Rumfitt]

5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=

13344

X follows from sentences K iff every model of K also models X [Tarski]

5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models

13343

A 'model' is a sequence of objects which satisfies a complete set of sentential functions [Tarski]

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity

18200

Very large sets should be studied in an 'if-then' spirit [Putnam]

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics

18199

Indispensability strongly supports predicative sets, and somewhat supports impredicative sets [Putnam]

8857	We must quantify over numbers for science; but that commits us to their existence [Putnam]

19. Language / E. Analyticity / 1. Analytic Propositions

13345

Sentences are 'analytical' if every sequence of objects models them [Tarski]

21. Aesthetics / C. Artistic Issues / 7. Art and Morality

468	Musical performance can reveal a range of virtues [Damon of Ath.]