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Ideas for 'fragments/reports', 'Prior Analytics' and 'Are Freedom and Equality Compatible?'

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7 ideas

4. Formal Logic / A. Syllogistic Logic / 1. Aristotelian Logic
22271 Aristotle was the first to use schematic letters in logic [Aristotle, by Potter]
     Full Idea: It was Aristotle who initiated the use of the letter of the (Greek) alphabet 'schematically', to stand for an unspecified piece of language of some appropriate grammatical type.
     From: report of Aristotle (Prior Analytics [c.328 BCE]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 02 'Aris'
     A reaction: Did he invent it from scratch, or borrow it from the mathematicians? Euclid labels diagrams with letters.
11060 Aristotelian syllogisms are three-part, subject-predicate, existentially committed, with laws of thought [Aristotle, by Hanna]
     Full Idea: Aristotle's logic is based on the triadic syllogism, the distinction between subject and one-place predicates, that universal claims have existential commitment, and bivalence, excluded middle and noncontradiction.
     From: report of Aristotle (Prior Analytics [c.328 BCE]) by Robert Hanna - Rationality and Logic 2.2
18909 Aristotelian sentences are made up by one of four 'formative' connectors [Aristotle, by Engelbretsen]
     Full Idea: For Aristotle there are four formatives for sentences: 'belongs to some', 'belongs to every', 'belongs to no', and 'does not belong to every'. These are 'copulae'. Aristotle would have written 'wise belongs to some man'.
     From: report of Aristotle (Prior Analytics [c.328 BCE]) by George Engelbretsen - Trees, Terms and Truth 3
     A reaction: A rather set-theoretic reading. This invites a Quinean scepticism about whether wisdom is some entity which can 'belong' to a person. It makes trope theory sound attractive, offering a unique wisdom that is integrated into that particular person.
8080 Aristotelian identified 256 possible syllogisms, saying that 19 are valid [Aristotle, by Devlin]
     Full Idea: Aristotle identified four 'figures' of argument, based on combinations of Subject (S) and Predicate (P) and Middle term (M). The addition of 'all' and 'some', and 'has' and 'has not' got the property, resulted in 256 possible syllogisms, 19 of them valid.
     From: report of Aristotle (Prior Analytics [c.328 BCE]) by Keith Devlin - Goodbye Descartes Ch.2
     A reaction: [Compressed version of Devlin] What Aristotle did was astonishing, and must be one of the key ideas of western civilization, even though a lot of his assumptions have been revised or rejected.
13912 Aristotle replaced Plato's noun-verb form with unions of pairs of terms by one of four 'copulae' [Aristotle, by Engelbretsen/Sayward]
     Full Idea: Aristotle replaced the Platonic noun-verb account of logical syntax with a 'copular' account. A sentence is a pair of terms bound together logically (not necessarily grammatically) by one of four 'logical copulae' (every, none, some, not some).
     From: report of Aristotle (Prior Analytics [c.328 BCE]) by Engelbretsen,G/Sayward,C - Philosophical Logic: Intro to Advanced Topics 8
     A reaction: So the four copulas are are-all, are-never, are-sometimes, and are-sometime-not. Consider 'men' and 'mortal'. Alternatively, Idea 18909.
8071 Aristotle listed nineteen valid syllogisms (though a few of them were wrong) [Aristotle, by Devlin]
     Full Idea: Aristotle listed a total of nineteen syllogisms involved in logical reasoning, though some of the ones on his list were subsequently shown to be invalid.
     From: report of Aristotle (Prior Analytics [c.328 BCE], Ch.1) by Keith Devlin - Goodbye Descartes
     A reaction: It is quite upsetting to think that the founding genius got some of it wrong, but that just shows how subtle and complex the analysis of rational thought can be.
4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
13819 Aristotle's said some Fs are G or some Fs are not G, forgetting that there might be no Fs [Bostock on Aristotle]
     Full Idea: Aristotle's system accepted as correct some laws which nowadays we reject, for example |= (Some Fs are G) or (some Fs are not G). He failed to take into account the possibility of there being no Fs at all.
     From: comment on Aristotle (Prior Analytics [c.328 BCE]) by David Bostock - Intermediate Logic 8.4