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Ideas for 'Aristotle and Descartes on Matter', 'Higher-Order Logic' and 'Philosophy of Logic'

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5 ideas

5. Theory of Logic / A. Overview of Logic / 2. History of Logic

18954

Before the late 19th century logic was trivialised by not dealing with relations [Putnam]

5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic

18956

Asserting first-order validity implicitly involves second-order reference to classes [Putnam]

10588

First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro]

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

10298

Some say that second-order logic is mathematics, not logic [Shapiro]

10299

If the aim of logic is to codify inferences, second-order logic is useless [Shapiro]