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Ideas for 'Internalism Exposed', 'Understanding' and 'Philosophical Logic: Intro to Advanced Topics'

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4 ideas

5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
13850 In modern logic all formal validity can be characterised syntactically [Engelbretsen/Sayward]
     Full Idea: One of the key ideas of modern formal logic is that all formally valid inferences can be specified in strictly syntactic terms.
     From: Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], Ch.2)
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
13849 Classical logic rests on truth and models, where constructivist logic rests on defence and refutation [Engelbretsen/Sayward]
     Full Idea: Classical logic rests on the concepts of truth and falsity (and usually makes use of a semantic theory based on models), whereas constructivist logic accounts for inference in terms of defense and refutation.
     From: Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], Intro)
     A reaction: My instincts go with the classical view, which is that inferences do not depend on the human capacity to defend them, but sit there awaiting revelation. My view isn't platonist, because I take the inferences to be rooted in the physical world.
5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
13851 Unlike most other signs, = cannot be eliminated [Engelbretsen/Sayward]
     Full Idea: Unlike ∨, →, ↔, and ∀, the sign = is not eliminable from a logic.
     From: Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], Ch.3)
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
13852 Axioms are ω-incomplete if the instances are all derivable, but the universal quantification isn't [Engelbretsen/Sayward]
     Full Idea: A set of axioms is said to be ω-incomplete if, for some universal quantification, each of its instances is derivable from those axioms but the quantification is not thus derivable.
     From: Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], 7)