| 639 | Socrates developed definitions as the basis of syllogisms, and also inductive arguments [Socrates, by Aristotle] |
| Full Idea: Socrates aimed to establish formal logic, of whose syllogisms essences are the foundations. He developed inductive arguments and also general definitions. | |
| From: report of Socrates (reports of career [c.420 BCE]) by Aristotle - Metaphysics 1078b |
| 22272 | Aristotle's later logic had to treat 'Socrates' as 'everything that is Socrates' [Potter on Aristotle] |
| Full Idea: When Aristotle moved from basic name+verb (in 'De Interpretatione') to noun+noun logic...names had to be treated as special cases, so that 'Socrates' is treated as short for 'everything that is Socrates'. | |
| From: comment on Aristotle (On Interpretation [c.330 BCE]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 02 'Supp' | |
| A reaction: Just the sort of rewriting that Russell introduced for definite descriptions. 'Twas ever the logicians' fate to shoehorn ordinary speech into awkward containers. |
| 9405 | Square of Opposition: not both true, or not both false; one-way implication; opposite truth-values [Aristotle] |
| Full Idea: Square of Opposition: horizontals - 'contraries' can't both be true, and 'subcontraries' can't both be false; verticals - 'subalternatives' have downwards-only implication; diagonals - 'contradictories' have opposite truth values. | |
| From: Aristotle (On Interpretation [c.330 BCE], Ch.12-13) | |
| A reaction: This is still used in modern discussion (e.g. by Stalnaker against Kripke), and there is a modal version of it (Fitting and Mendelsohn p.7). Corners read: 'All F are G', 'No F are G', 'Some F are G' and 'Some F are not G'. |
| 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. |
| 18953 | Modern notation frees us from Aristotle's restriction of only using two class-names in premises [Putnam] |
| Full Idea: In modern notation we can consider potential logical principles that Aristotle never considered because of his general practice of looking at inferences each of whose premises involved exactly two class-names. | |
| From: Hilary Putnam (Philosophy of Logic [1971], Ch.3) | |
| A reaction: Presumably you can build up complex inferences from a pair of terms, just as you do with pairs in set theory. |
| 13643 | Aristotelian logic is complete [Shapiro] |
| Full Idea: Aristotelian logic is complete. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 2.5) | |
| A reaction: [He cites Corcoran 1972] |
| 23505 | Aristotelian logic cannot express 'Everyone loves someone' [White,RM] |
| Full Idea: There is no way within Aristotelian logic that you can give a proper expression for the logical form of such a proposition as 'Everyone loves someone'. | |
| From: Roger M. White (Wittgenstein's 'Tractatus Logico-Philosophicus' [2006], 1 'Frege') | |
| A reaction: This needs a combination of two different quantifiers. |
| 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. |
| 18913 | Traditional term logic struggled to express relations [Engelbretsen] |
| Full Idea: The greatest challenge for traditional term logicians was the proper formulation and treatment of relational expressions. | |
| From: George Engelbretsen (Trees, Terms and Truth [2005]) | |
| A reaction: The modern term logic of Fred Sommers claims to have solved this problem. |