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All the ideas for 'talk', 'Philosophical Logic: Intro to Advanced Topics' and 'What is innate and why'

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11 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]
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)
13. Knowledge Criteria / E. Relativism / 2. Knowledge as Convention
1556 By nature people are close to one another, but culture drives them apart [Hippias]
     Full Idea: I regard you all as relatives - by nature, not by convention. By nature like is akin to like, but convention is a tyrant over humankind and often constrains people to act contrary to nature.
     From: Hippias (fragments/reports [c.430 BCE]), quoted by Plato - Protagoras 337c8
18. Thought / B. Mechanics of Thought / 4. Language of Thought
2605 If everything uses mentalese, ALL concepts must be innate! [Putnam]
     Full Idea: Fodor concludes that every predicate that a brain could learn to use must have a translation into the computer language of that brain. So no "new" concepts can be acquired: all concepts are innate!
     From: Hilary Putnam (What is innate and why [1980], p.407)
     A reaction: Some misunderstanding, surely? No one could be so daft as to think that everyone has an innate idea of an iPod. More basic innate building blocks for thought are quite plausible.
2606 No machine language can express generalisations [Putnam]
     Full Idea: Computers have a built-in language, but not a language that contains quantifiers (that is, the words "all" and "some"). …So generalizations (containing "all") cannot ever be stated in machine language.
     From: Hilary Putnam (What is innate and why [1980], p.408)
     A reaction: Computers are too sophisticated to need quantification (which is crude). Computers can work with very precise and complex specifications of the domain of a given variable.