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Ideas for 'The Evolution of Logic', 'Much Ado About Nothing' and 'On Body and Force, Against the Cartesians'

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4 ideas

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

13513	Models are ways the world might be from a first-order point of view [Hart,WD]
	Full Idea: Models are ways the world might be from a first-order point of view.
	From: William D. Hart (The Evolution of Logic [2010], 9)

13512	Modern model theory begins with the proof of Los's Conjecture in 1962 [Hart,WD]
	Full Idea: The beginning of modern model theory was when Morley proved Los's Conjecture in 1962 - that a complete theory in a countable language categorical in one uncountable cardinal is categorical in all.
	From: William D. Hart (The Evolution of Logic [2010], 9)

13505	Model theory studies how set theory can model sets of sentences [Hart,WD]
	Full Idea: Modern model theory investigates which set theoretic structures are models for which collections of sentences.
	From: William D. Hart (The Evolution of Logic [2010], 4)
	A reaction: So first you must choose your set theory (see Idea 13497). Then you presumably look at how to formalise sentences, and then look at the really tricky ones, many of which will involve various degrees of infinity.

13511	Model theory is mostly confined to first-order theories [Hart,WD]
	Full Idea: There is no developed methematics of models for second-order theories, so for the most part, model theory is about models for first-order theories.
	From: William D. Hart (The Evolution of Logic [2010], 9)