Syllogism

A syllogism (Greek: συλλογισμός syllogismos, 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two or more propositions that are asserted or assumed to be true. All men are mortal.Socrates is a man.Therefore, Socrates is mortal.Calemes is like Celarent with S and P exchanged.Similar: Camestres (AEE-2)Dimatis is like Darii with S and P exchanged.Similar: Disamis (IAI-3)Bamalip is like Barbari with S and P exchanged: A syllogism (Greek: συλλογισμός syllogismos, 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two or more propositions that are asserted or assumed to be true. Some of the earliest syllogisms are defined in the Nyaya school of thought. In a form, defined by Aristotle, from the combination of a general statement (the major premise) and a specific statement (the minor premise), a conclusion is deduced. For example, knowing that all men are mortal (major premise) and that Socrates is a man (minor premise), we may validly conclude that Socrates is mortal. Syllogistic arguments are usually represented in a three-line form: In antiquity, two rival theories of the syllogism existed: Aristotelian syllogistic and Stoic syllogistic. Aristotle defines the syllogism as 'a discourse in which certain (specific) things having been supposed, something different from the things supposed results of necessity because these things are so'. Despite this very general definition, in Prior Analytics Aristotle limits himself to categorical syllogisms that consist of three categorical propositions. These include categorical modal syllogisms. From the Middle Ages onwards, categorical syllogism and syllogism were usually used interchangeably. This article is concerned only with this traditional use. The syllogism was at the core of traditional deductive reasoning, where facts are determined by combining existing statements, in contrast to inductive reasoning where facts are determined by repeated observations. Within academic contexts, the syllogism was superseded by first-order predicate logic following the work of Gottlob Frege, in particular his Begriffsschrift (Concept Script) (1879), but syllogisms remain useful in some circumstances, and for general-audience introductions to logic. The use of syllogisms as a tool for understanding can be dated back to the logical reasoning discussions of Aristotle. Prior to the mid-twelfth century, medieval logicians were only familiar with a portion of Aristotle's works, including titles such as Categories and On Interpretation, works that contributed heavily to the prevailing Old Logic, or 'logica vetus'. The onset of a New Logic, or 'logica nova', arose alongside the reappearance of Prior Analytics, the work in which Aristotle develops his theory of the syllogism. Prior Analytics, upon re-discovery, was instantly regarded by logicians as 'a closed and complete body of doctrine', leaving very little for thinkers of the day to debate and re-organize. Aristotle's theory on the syllogism for assertoric sentences was considered especially remarkable, with only small systematic changes occurring to the concept over time. This theory of the syllogism would not enter the context of the more comprehensive logic of consequence until logic began to be reworked in general in the mid-fourteenth century by the likes of John Buridan. Aristotle's Prior Analytics did not, however, incorporate such a comprehensive theory on the 'modal syllogism'—a syllogism that has at least one modalized premise (that is, a premise containing the modal words 'necessarily', 'possibly', or 'contingently'). Aristotle's terminology in this aspect of his theory was deemed vague and in many cases unclear, even contradicting some of his statements from On Interpretation. His original assertions on this specific component of the theory were left up to a considerable amount of conversation, resulting in a wide array of solutions put forth by commentators of the day. The system for modal syllogisms laid forth by Aristotle would ultimately be deemed unfit for practical use, and would be replaced by new distinctions and new theories altogether. Boethius (c. 475 – 526) contributed an effort to make the ancient Aristotelian logic more accessible. While his Latin translation of Prior Analytics went primarily unused before the twelfth century, his textbooks on the categorical syllogism were central to expanding the syllogistic discussion. Boethius' logical legacy lay not in any addition he personally made to the field, but rather in his effective transmission of prior theories to later logicians, as well as his clear and primarily accurate presentations of Aristotle's contributions.