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Ideas for 'fragments/reports', 'Philosophical Logic: Intro to Advanced Topics' and 'On Body and Force, Against the Cartesians'

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6 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 / B. Logical Consequence / 5. Modus Ponens

8078	Modus ponens is one of five inference rules identified by the Stoics [Chrysippus, by Devlin]
	Full Idea: Modus ponens is just one of the five different inference rules identified by the Stoics.
	From: report of Chrysippus (fragments/reports [c.240 BCE]) by Keith Devlin - Goodbye Descartes Ch.2
	A reaction: Modus ponens strikes me as being more like a definition of implication than a 'rule'. Implication is what gets you from one truth to another. All the implications of a truth must also be true.

5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle

6023	Every proposition is either true or false [Chrysippus, by Cicero]
	Full Idea: We hold fast to the position, defended by Chrysippus, that every proposition is either true or false.
	From: report of Chrysippus (fragments/reports [c.240 BCE]) by M. Tullius Cicero - On Fate ('De fato') 38
	A reaction: I am intrigued to know exactly how you defend this claim. It may depend what you mean by a proposition. A badly expressed proposition may have indeterminate truth, quite apart from the vague, the undecidable etc.

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)