Syllogistic


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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 ?
He advanced syllogistic by fully incorporating the Scholastic introduction of negative terms with the Port-Royal innovations.
In this case, the demonstranda "AaD" and "AaE" would not fall into our MC-scenario, since a syllogistic proof of greater explanatory power would be available:
(98) He must have found inspiration in one of his direct sources, Fenner's Artes of Logike and Rethorike, which used syllogistic proof to enforce major articles of Presbyterian faith.
Our main objective in this experiment was to study the influence of the presentation format in a syllogistic reasoning task.
Discussed below are the rhetorical lessons of contemporary rational choice theory in three areas: (1) rhetoric-1 framing of legal issues to respond to biases and heuristics and to situational conditions on rational choice as a mode of invention and arrangement; (2) rhetoric-2 topics of arrangement and invention (synthesis and syllogistic structure) to appeal to the rational audience; and (3) rhetoric-3 uses of pathos-centric modes of argument--metaphor, parable/mythical/fable forms, character archetypes, and other forms of narrative reasoning--as topics of invention and tropes of style to address anchoring, endowment effects, and other heuristics and biases of legal audiences based on the lessons of pathos from modern cognitive studies and brain science.
The legal reasoning is neither 'a simple syllogistic deduction', nor 'the mere search for an equitable solution'.
Following a simple line of deductive logic, the syllogistic conclusion shows that the development of new uranium mines will only be considered once the price exceeds US$75 per pound.
He scrutinizes the work of George Lindbeck, Robert Jenson, Stanley Hauerwas, John Howard Yoder, Daniel Hardy, David Ford, and John Milbank to argue, in rather stronger terms than may be warranted, that when these theologians are postliberal they are necessarily nonsupersessionist, and when they lapse into classic triumphalist Christian claims--as Yoder and Milbank do--they cease to be postliberal and become "non-nonsupersessionist." Ochs wants to make a tight syllogistic case, but it is likely that it is the deep ecumenical sensibilities of his high church Protestant friends that both attract them to him and make them sensitive to what Ochs idiosyncratically sees as postliberalism and less inclined to classic Christian triumphalism, which is, of course, bad for the Jews.
She suggests that a depiction of two couples, one Algonkin, the other Abenaki, in an inset panel of the map demonstrates the European attitude that "Native people could be 'boxed in.'" This type of syllogistic use of language to interpret an image recurs repeatedly in the text and thus detracts from the overall ambition of her project.
As above, let us point out that thesis 4 is syllogistic reasoning at its best (or worst), thus a form of rhetoric, a game, a purely arbitrary convention.
In general, these studies show that the central executive plays an important role in both syllogistic (e.g., Gilhooly, 1998; Gilhooly, Logie, & Wynn, 2003) and conditional reasoning (e.g., De Neys, Schaeken, & D'Ydewalle, 2005; Toms, Warris, & Ward, 1993).