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. |
| 15375 | If terms change their designations in different states, they are functions from states to objects [Fitting] |
| Full Idea: The common feature of every designating term is that designation may change from state to state - thus it can be formalized by a function from states to objects. | |
| From: Melvin Fitting (Intensional Logic [2007], 3) | |
| A reaction: Specifying the objects sounds OK, but specifying states sounds rather tough. |
| 15376 | Intensional logic adds a second type of quantification, over intensional objects, or individual concepts [Fitting] |
| Full Idea: To first order modal logic (with quantification over objects) we can add a second kind of quantification, over intensions. An intensional object, or individual concept, will be modelled by a function from states to objects. | |
| From: Melvin Fitting (Intensional Logic [2007], 3.3) |
| 15378 | Awareness logic adds the restriction of an awareness function to epistemic logic [Fitting] |
| Full Idea: Awareness logic enriched Hintikka's epistemic models with an awareness function, mapping each state to the set of formulas we are aware of at that state. This reflects some bound on the resources we can bring to bear. | |
| From: Melvin Fitting (Intensional Logic [2007], 3.6.1) | |
| A reaction: [He cites Fagin and Halpern 1988 for this] |
| 15379 | Justication logics make explicit the reasons for mathematical truth in proofs [Fitting] |
| Full Idea: In justification logics, the logics of knowledge are extended by making reasons explicit. A logic of proof terms was created, with a semantics. In this, mathematical truths are known for explicit reasons, and these provide a measure of complexity. | |
| From: Melvin Fitting (Intensional Logic [2007], 3.6.1) |
| 11026 | Classical logic is deliberately extensional, in order to model mathematics [Fitting] |
| Full Idea: Mathematics is typically extensional throughout (we write 3+2=2+3 despite the two terms having different meanings). ..Classical first-order logic is extensional by design since it primarily evolved to model the reasoning of mathematics. | |
| From: Melvin Fitting (Intensional Logic [2007], §1) |
| 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. |
| 11028 | λ-abstraction disambiguates the scope of modal operators [Fitting] |
| Full Idea: λ-abstraction can be used to abstract and disambiguate a predicate. De re is [λx◊P(x)](f) - f has the possible-P property - and de dicto is ◊[λxP(x)](f) - possibly f has the P-property. Also applies to □. | |
| From: Melvin Fitting (Intensional Logic [2007], §3.3) | |
| A reaction: Compare the Barcan formula. Originated with Church in the 1930s, and Carnap 1947, but revived by Stalnaker and Thomason 1968. Because it refers to the predicate, it has a role in intensional versions of logic, especially modal logic. |
| 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. |
| 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. |
| 15377 | Definite descriptions pick out different objects in different possible worlds [Fitting] |
| Full Idea: Definite descriptions pick out different objects in different possible worlds quite naturally. | |
| From: Melvin Fitting (Intensional Logic [2007], 3.4) | |
| A reaction: A definite description can pick out the same object in another possible world, or a very similar one, or an object which has almost nothing in common with the others. |
| 5959 | Some philosophers say the soul is light [Plutarch] |
| Full Idea: Some philosophers hold that the soul is in its essence light. | |
| From: Plutarch (75: Is 'Live Unknown' a Wise Precept? [c.85], §6) | |
| A reaction: A nice idea, to rival the stoic view that the soul is fire. It is understandable to propose that the soul is some sort of lightweight and fast moving matter. How else could thought be achieved physically? Nowadays, parallel processing is our only model. |
| 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. |