23 ideas
| 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. |
| 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 |
| 9403 | There are three different deductions for actual terms, necessary terms and possible terms [Aristotle] |
| Full Idea: Since to belong, to belong of necessity, and to be possible to belong are different, ..there will be different deductions for each; one deduction will be from necessary terms, one from terms which belong, and one from possible terms. | |
| From: Aristotle (Prior Analytics [c.328 BCE], 29b29-35) | |
| A reaction: Fitting and Mendelsohn cite this as the earliest thoughts on modal logic. but Kneale and Kneale say that Aristotle got into a muddle, and so was unable to create a workable system. |
| 11148 | Deduction is when we suppose one thing, and another necessarily follows [Aristotle] |
| Full Idea: A deduction is a discourse in which, certain things having been supposed, something different from the things supposed results of necessity because these things are so. | |
| From: Aristotle (Prior Analytics [c.328 BCE], 24b18) | |
| A reaction: Notice that it is modal ('suppose', rather than 'know'), that necessity is involved, which is presumably metaphysical necessity, and that there are assumptions about what would be true, and not just what follows from what. |
| 18896 | Aristotle places terms at opposite ends, joined by a quantified copula [Aristotle, by Sommers] |
| Full Idea: Aristotle often preferred to formulate predications by placing the terms at opposite ends of the sentence and joining them by predicating expressions like 'belongs-to-some' or 'belongs-to-every'. | |
| From: report of Aristotle (Prior Analytics [c.328 BCE]) by Fred Sommers - Intellectual Autobiography 'Conceptions' | |
| A reaction: This is Sommers's picture of Aristotle, which led Sommers to develop his modern Term Logic. |
| 3300 | Aristotle's logic is based on the subject/predicate distinction, which leads him to substances and properties [Aristotle, by Benardete,JA] |
| Full Idea: Basic to Aristotle's logic is the grammatical distinction between subject and predicate, which he glosses in terms of the contrast between a substance and its properties. | |
| From: report of Aristotle (Prior Analytics [c.328 BCE]) by José A. Benardete - Metaphysics: the logical approach Intro | |
| A reaction: The introduction of quantifiers and 'logical form' can't disguise the fact that we still talk about (and with) objects and predicates, because no one can think of any other way to talk. |
| 11149 | Affirming/denying sentences are universal, particular, or indeterminate [Aristotle] |
| Full Idea: Affirming/denying sentences are universal, particular, or indeterminate. Belonging 'to every/to none' is universal; belonging 'to some/not to some/not to every' is particular; belonging or not belonging (without universal/particular) is indeterminate. | |
| From: Aristotle (Prior Analytics [c.328 BCE], 24a16) |
| 8079 | Aristotelian logic has two quantifiers of the subject ('all' and 'some') [Aristotle, by Devlin] |
| Full Idea: Aristotelian logic has two quantifiers of the subject ('all' and 'some'), and two ways to combine the subject with the predicate ('have', and 'have not'), giving four propositions: all-s-have-p, all-s-have-not-p, some-s-have-p, and some-s-have-not-p. | |
| From: report of Aristotle (Prior Analytics [c.328 BCE]) by Keith Devlin - Goodbye Descartes Ch.2 | |
| A reaction: Frege seems to have switched from 'some' to 'at-least-one'. Since then other quantifiers have been proposed. See, for example, Ideas 7806 and 6068. |
| 8628 | I hold that algebra and number are developments of logic [Jevons] |
| Full Idea: I hold that algebra is a highly developed logic, and number but logical discrimination. | |
| From: William S. Jevons (The Principles of Science [1879], p.156), quoted by Gottlob Frege - Grundlagen der Arithmetik (Foundations) §15 | |
| A reaction: Thus Frege shows that logicism was an idea that was in the air before he started writing. Riemann's geometry and Boole's logic presumably had some influence here. |
| 7720 | Two things can only resemble one another in some respect, and that may reintroduce a universal [Lowe] |
| Full Idea: A problem for resemblance nominalism is that in saying that two particulars 'resemble' one another, it is necessary to specify in what respect they do so (e.g. colour, shape, size), and this threatens to reintroduce what appears to be talk of universals. | |
| From: E.J. Lowe (Locke on Human Understanding [1995], Ch.7) | |
| A reaction: We see resemblance between faces instantly, long before we can specify the 'respects' of the resemblance. This supports the Humean hard-wired view of resemblance, rather than some appeal to Platonic universals. |
| 7712 | On substances, Leibniz emphasises unity, Spinoza independence, Locke relations to qualities [Lowe] |
| Full Idea: Later philosophers emphasised different strands of Aristotle's concept of substances: Leibniz (in his theory of monads) emphasised their unity; Spinoza emphasised their ontological independence; Locke emphasised their role in relation to qualities. | |
| From: E.J. Lowe (Locke on Human Understanding [1995], Ch.4) | |
| A reaction: Note that this Aristotelian idea had not been jettisoned in the late seventeenth century, unlike other Aristotelianisms. I think it is only with the success of atomism in chemistry that the idea of substance is forced to recede. |
| 14641 | A deduction is necessary if the major (but not the minor) premise is also necessary [Aristotle] |
| Full Idea: It sometimes results that the deduction becomes necessary when only one of the premises is necessary (not whatever premise it might be, however, but only the premise in relation to the major extreme [premise]). | |
| From: Aristotle (Prior Analytics [c.328 BCE], 30a15) | |
| A reaction: The qualification is brackets is said by Plantinga (1969) to be a recognition of the de re/ de dicto distinction (later taken up by Aquinas). Plantinga gives two examples to illustrate his reading. |
| 7710 | Perception is a mode of belief-acquisition, and does not involve sensation [Lowe] |
| Full Idea: According to one school of thought, perception is simply a mode of belief-acquisition,and there is no reason to suppose that any element of sensation is literally involved in perception. | |
| From: E.J. Lowe (Locke on Human Understanding [1995], Ch.3) | |
| A reaction: Blindsight would be an obvious supporting case for this view. I think this point is crucial in understanding what is wrong with Jackson's 'knowledge argument' (involving Mary, see Idea 7377). Sensation gives knowledge, so it can't be knowledge. |
| 7711 | Science requires a causal theory - perception of an object must be an experience caused by the object [Lowe] |
| Full Idea: Only a causal theory of perception will respect the facts of physiology and physics ...meaning a theory which maintains that for a subject to perceive a physical object the subject should enjoy some appropriate perceptual experience caused by the object. | |
| From: E.J. Lowe (Locke on Human Understanding [1995], Ch.3) | |
| A reaction: If I hallucinate an object, then presumably I am not allowed to say that I 'perceive' it, but that seems to make the causal theory an idle tautology. If we are in virtual reality then there aren't any objects. |
| 18911 | Linguistic terms form a hierarchy, with higher terms predicable of increasing numbers of things [Aristotle, by Engelbretsen] |
| Full Idea: According to Aristotle, the terms of a language form a finite hierarchy, where the higher terms are predicable of more things than are lower terms. | |
| From: report of Aristotle (Prior Analytics [c.328 BCE]) by George Engelbretsen - Trees, Terms and Truth 3 | |
| A reaction: I would be a bit cautious about placing something precisely in a hierarchy according to how many things it can be predicated of. It is a start, though, in trying to give a decent account of generality, which is a major concept in philosophy. |
| 7714 | Personal identity is a problem across time (diachronic) and at an instant (synchronic) [Lowe] |
| Full Idea: There is the question of the identity of a person over or across time ('diachronic' personal identity), and there is also the question of what makes for personal identity at a time ('synchronic' personal identity). | |
| From: E.J. Lowe (Locke on Human Understanding [1995], Ch.5) | |
| A reaction: This seems to me to be the first and most important distinction in the philosophy of personal identity, and they regularly get run together. Locke, for example, has an account of synchronic identity, which is often ignored. It applies to objects too. |
| 7715 | Mentalese isn't a language, because it isn't conventional, or a means of public communication [Lowe] |
| Full Idea: 'Mentalese' would be neither conventional nor a means of public communication so that even to call it a language is seriously misleading. | |
| From: E.J. Lowe (Locke on Human Understanding [1995], Ch.7) | |
| A reaction: It is, however, supposed to contain symbolic representations which are then used as tokens for computation, so it seems close to a language, if (for example) symbolic logic or mathematics were accepted as languages. But who understands it? |
| 7722 | If meaning is mental pictures, explain "the cat (or dog!) is NOT on the mat" [Lowe] |
| Full Idea: If meaning is a private mental picture, what does 'the cat is NOT on the mat' mean, and how does it differ from 'the dog is not on the mat?'. | |
| From: E.J. Lowe (Locke on Human Understanding [1995], Ch.7) | |
| A reaction: Not insurmountable. We picture an empty mat, combined with a cat (or whatever) located somewhere else. A mental 'picture' of something shouldn't be contrued as a single image in a neat black frame. |