Syllogistic


Also found in: Dictionary, Thesaurus, Legal, Wikipedia.
Related to Syllogistic: Syllogistic reasoning

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 ?
The premises apparently force the conclusion: they create an expectation for the conclusion, and the conclusion fits the premises, so the syllogistic form has propriety.
A temptation to rely on intellectual intuitions is the greatest temptation of all: it gives us confidence in areas where we should have none, it makes us forget the limitations of our minds (dependent as they are on our physical bodies) and the fact that without empirical or syllogistic proof, the validity of our thoughts is not vouchsafed by anyone or anything.
Johnson-Laird & Steedman, 1978) and more recent computer programs for syllogistic reasoning (Johnson-Laird, 1992).
By submitting aphorism to false syllogistic reasoning and fact to delightful narrative uncertainty, she exposes the mechanics of self-deception: whereby we use logical language systems in order to relieve our doubts and excuse our mistakes.
I would like to suggest that other factors contributed to this general tendency to sever poetry from Nature and treat it as an artifact that can be manipulated in syllogistic terms.
7) He understands "syllogistic necessity" as a universal quantifier: "the Aristotelian sign of syllogistic necessity represents a universal quantifier and may be omitted, since a universal quantifier may be omitted when it stands at the head of a true formula.
The present volume is the second of two and contains Valla's Books II and III in which he refutes Aristotle's works on propositions, topics, and the syllogistic.
When professors go beyond their immediate consideration of reasoning for their cognitive altruistic deliberations, they are in the state of reason's territory within boundaries of syllogistic logical rules.
While Kalin is absolutely right in arguing that Sadra tries to negotiate a synthetic middle course between the syllogistic and the intuition-based conceptions of knowledge, the fruitfulness of his emphasis on the mystical connotations of intuition can be debated.
De Strigimagis derives a grammatological theory of demonic semiology from Augustinian premises, particularly the account of speech as an act of remembrance expressive of desire, and from Aristotelian syllogistic logic.
1) Aristotle admits that the laws of a natural science may hold only "for the most part," yet he insists that standard syllogistic reasoning still applies to them.
Thus, it breaches the gap between those who see religion merely as a syllogistic system or merely as a matter of personal preference (xi).