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All the ideas for 'Aristotle and Descartes on Matter', 'Later Letters to Dedekind' and 'Philosophical Logic: Intro to Advanced Topics'

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10 ideas

4. Formal Logic / A. Syllogistic Logic / 1. Aristotelian Logic

13913	The four 'perfect syllogisms' are called Barbara, Celarent, Darii and Ferio [Engelbretsen/Sayward]
	Full Idea: There are four 'perfect syllogisms': Barbara (every M is P, every S is M, so every S is P); Celarent (no M is P, every S is M, so no S is P); Darii (every M is P, some S is M, so some S is P); Ferio (no M is P, some S is M, so some S is not P).
	From: Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], 8)
	A reaction: The four names are mnemonics from medieval universities.

13914	Syllogistic logic has one rule: what is affirmed/denied of wholes is affirmed/denied of their parts [Engelbretsen/Sayward]
	Full Idea: It has often been claimed (e.g. by Leibniz) that a single rule governs all syllogistic validity, called 'dictum de omni et null', which says that what is affirmed or denied of any whole is affirmed or denied of any part of that whole.
	From: Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], 8)
	A reaction: This seems to be the rule which is captured by Venn Diagrams.

4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic

13915	Syllogistic can't handle sentences with singular terms, or relational terms, or compound sentences [Engelbretsen/Sayward]
	Full Idea: Three common kinds of sentence cannot be put into syllogistic ('categorical') form: ones using singular terms ('Mars is red'), ones using relational terms ('every painter owns some brushes'), and compound sentences.
	From: Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], 8)

4. Formal Logic / A. Syllogistic Logic / 3. Term Logic

13916	Term logic uses expression letters and brackets, and '-' for negative terms, and '+' for compound terms [Engelbretsen/Sayward]
	Full Idea: Term logic begins with expressions and two 'term functors'. Any simple letter is a 'term', any term prefixed by a minus ('-') is a 'negative term', and any pair of terms flanking a plus ('+') is a 'compound term'. Parenthese are used for grouping.
	From: Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], 8)
	A reaction: [see Engelbretsen and Sayward for the full formal system]

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets

17831	Cantor gives informal versions of ZF axioms as ways of getting from one set to another [Cantor, by Lake]
	Full Idea: Cantor gives informal versions of the axioms of ZF as ways of getting from one set to another.
	From: report of George Cantor (Later Letters to Dedekind [1899]) by John Lake - Approaches to Set Theory 1.6
	A reaction: Lake suggests that it should therefore be called CZF.

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)

26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / b. Prime matter

19399	Prime matter is nothing when it is at rest [Leibniz]
	Full Idea: Primary matter is nothing if considered at rest.
	From: Gottfried Leibniz (Aristotle and Descartes on Matter [1671], p.90)
	A reaction: This goes with Leibniz's Idea 13393, that activity is the hallmark of existence. No one seems to have been able to make good sense of prime matter, and it plays little role in Aristotle's writings.