Syllogistic

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Syllogistic

 

a theory of logical deduction that studies inferences consisting of categorical statements (judgments): the universal affirmative (every S is P), universal negative (no S is P), particular affirmative (some S are P), and particular negative (some S are not P). Syllogistic examines the deduction of a conclusion from one premise (direct inferences) and complex and compound syllogisms, or polysyllogisms, which have at least three premises. However, syllogistic emphasizes primarily the theory of the categorical syllogism, which has only two premises and one conclusion of an abovementioned type.

Aristotle, the founder of logic as a science, devised a system of classifying and validating the forms (moods) of syllogisms. Subsequently, syllogistic was refined by various schools of classical and medieval logicians, including the Peripatetics and the Stoics. Although F. Bacon, R. Descartes, J. S. Mill, and other scholars noted that syllogistic was of limited applicability, it was long an integral, traditional element of classical education in the humanities. Thus, it is often called traditional logic. With the establishment of the calculi of mathematical logic, the role of syllogistic became very modest. It was proved that by using the one-place predicate calculus, a fragment of the predicate calculus, it is possible to obtain almost the entire content of syllogistic—all deductions not dependent on the typical syllogistic assumption of an empty object field. A number of axiomatic statements of syllogistic have also been obtained in the terms of modern mathematical logic (J.Łukasiewicz, 1939).

REFERENCES

Aristotle. Analiliki, pervaia i vtoraia. Leningrad, 1952. (Translated from Greek.)
Bacon, F. Novyi organon. Leningrad, 1935. (Translated from English.)
Descartes, R. Izbrannyeproizvedeniia. Moscow, 1950. (Translated from French.)
Hilbert, D., and W. Ackermann. Osnovy teoreticheskoi logiki. Moscow, 1947. Chapter II, sect. 3. (Translated from German.)
Łukasiewicz, J. Aristotelevskaia sillogistika s tochki zreniia sovremennoi formal’noi logiki. Moscow, 1959. (Translated from English.)
Bourbaki, N. Ocherki po istorii matematiki. Moscow, 1963. (Translated from French.)
Culbertson. J. T. Matematika i logika tsifrovykh ustroistv. Moscow, 1965. Chapter 5. (Translated from English.)
Subbotin, A. L. Teoriia sillogistiki v sovremennoi formal’noi logike. Moscow, 1965.
Subbotin, A. L. Traditsionnaia i sovremennaia formal’naia logika. Moscow, 1969.
References in periodicals archive ?
It's hard to encapsulate the argument without alleging chicanery, so we'll do it syllogistically with a series of facts:
The five narratives are explored through the theme of excess: Lee's starting point is Proust's countess's remark, 'Moi, je n'aime pas Balzac, je trouve qu'il est exagere', from which he moves, somewhat syllogistically, but rather more interestingly than had he kept to the tired theme of Balzac's 'exaggeration', to explore the excessive behaviours of Balzac's protagonists and narrators in these stories, each via a determinant theme--in Un Drame 'le nom', in Adieu and L'Auberge rouge 'le temoignage', in Melmoth reconcilie 'le don', and performatively in Le Chef-d'oeuvre inconnu.
Syllogistically speaking, just as man invents a god for his salvation and spiritual good and conceives that the salvation and the good rest upon acts of faith and belief in the deity, so the world (for Hardy's "philosophers") must needs turn upon the desires and prepossessions of mankind.
The official theory is that each new decision follows syllogistically from existing precedents....
Functioning both syllogistically and symbolically, a midrasbic composition charts a sage's intellectual path leading from a theological or cultural crisis at hand to the timeless truths found in the scriptural paradigms.
If we start with the categorical propositions `Every pair of rational numbers is a pair of rational numbers with a rational number between them' and `<A, B> is a pair of rational numbers', then we can infer syllogistically `<A, B> is a pair of rational numbers with a rational number between them'.
Both Communism and anti-Communism derive tests of faith syllogistically from shaky first principles.
Moral philosophers promised to deliver doctors from the self-contradictions into which the Hippocratic code led them: they would find the indubitable Cartesian proposition from which all ethical decisions would follow syllogistically. Let the moral philosophers into the intensive care unit and all would be, if not light exactly, at least intellectually consistent.
It is a mirror of Genesis' creation command, "Let there be light." It argues syllogistically about the word in the fashion of the Greek sophists.
If Aquinas reasons syllogistically at all, he does so not speculatively, but in the way Yangazoglou regards as legitimate and in the spirit of Palamas--from the data of revelation.
Recent studies on the effects of pretending on reasoning have indicated that a task setting that includes pretending enhances young children's ability to reason syllogistically (Dias & Harris, 1988).
Syllogistically, if bringing about death makes a medicine