Combining Texts

All the ideas for 'The Concept of Logical Consequence', 'Sentences' and 'Structuralism Reconsidered'

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9 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 / 3. Nature of Numbers / d. Natural numbers
8923 Numbers are identified by their main properties and relations, involving the successor function [MacBride]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
8926 For mathematical objects to be positions, positions themselves must exist first [MacBride]
8. Modes of Existence / A. Relations / 1. Nature of Relations
18528 The single imagined 'interval' between things only exists in the intellect [Auriol]
19. Language / E. Analyticity / 1. Analytic Propositions
13345 Sentences are 'analytical' if every sequence of objects models them [Tarski]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / b. Prime matter
16589 Prime matter lacks essence, but is only potentially and indeterminately a physical thing [Auriol]
28. God / A. Divine Nature / 4. Divine Contradictions
16651 God can do anything non-contradictory, as making straightness with no line, or lightness with no parts [Auriol]