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Ideas for 'Logicism and Ontological Commits. of Arithmetic', 'The Concept of Logical Consequence' and 'The Decline of the West'

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6 ideas

5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic

10015

Higher-order logic may be unintelligible, but it isn't set theory [Hodes]

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 / D. Assumptions for Logic / 4. Identity in Logic

10011

Identity is a level one relation with a second-order definition [Hodes]

5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic

10016

When an 'interpretation' creates a model based on truth, this doesn't include Fregean 'sense' [Hodes]

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]