2011 | Philosophical Logic: Intro to Advanced Topics |
Intro | p.2 | 13849 | Classical logic rests on truth and models, where constructivist logic rests on defence and refutation |
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. |
7 | p.132 | 13852 | Axioms are ω-incomplete if the instances are all derivable, but the universal quantification isn't |
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) |
8 | p.142 | 13913 | The four 'perfect syllogisms' are called Barbara, Celarent, Darii and Ferio |
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. |
8 | p.143 | 13914 | Syllogistic logic has one rule: what is affirmed/denied of wholes is affirmed/denied of their parts |
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. |
8 | p.144 | 13915 | Syllogistic can't handle sentences with singular terms, or relational terms, or compound sentences |
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) |
8 | p.146 | 13916 | Term logic uses expression letters and brackets, and '-' for negative terms, and '+' for compound terms |
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] |
Ch.2 | p.50 | 13850 | In modern logic all formal validity can be characterised syntactically |
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) |
Ch.3 | p.70 | 13851 | Unlike most other signs, = cannot be eliminated |
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) |