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A syllogism takes the form (note: M – Middle, S – subject, P – predicate.): Major premise: All M are P. Minor premise: All S are M. Conclusion/Consequent: All S are P. The premises and conclusion of a syllogism can be any of four types, which are labeled by letters [14] as follows. The meaning of the letters is given by the table:
The word "propositio" is from the Latin, meaning the first premise of a syllogism. Aristotle uses the word premise (protasis) as a sentence affirming or denying one thing or another (Posterior Analytics 1. 1 24a 16), so a premise is also a form of words. However, as in modern philosophical logic, it means that which is asserted by the sentence.
[1] [2] abduction A form of reasoning characterized by drawing a conclusion based on the best available explanation for a set of premises. Often used in hypothesis formation. Abelian logic A type of relevance logic that rejects contraction and accepts that ((A → B) → B) → A. [3] [4] [5] absorption
At present, syllogism is used exclusively as the method used to reach a conclusion closely resembling the "syllogisms" of traditional logic texts: two premises followed by a conclusion each of which is a categorical sentence containing all together three terms, two extremes which appear in the conclusion and one middle term which appears in ...
The study of arguments using categorical statements (i.e., syllogisms) forms an important branch of deductive reasoning that began with the Ancient Greeks. The Ancient Greeks such as Aristotle identified four primary distinct types of categorical proposition and gave them standard forms (now often called A , E , I , and O ).
The first type of enthymeme is a truncated syllogism, or a syllogism with an unstated premise. [6] Here is an example of an enthymeme derived from a syllogism through truncation (shortening) of the syllogism: "Socrates is mortal because he's human." The complete formal syllogism would be the classic: All humans are mortal. (major premise ...
In some contexts, it means model, axiom, plan, legal proceeding, judicial sentence, or judgment. Nyaya could also mean, "that which shows the way" tracing its Sanskrit etymology. In the theory of logic, and Indian texts discussing it, the term also refers to an argument consisting of an enthymeme or sometimes for any syllogism. [1]
A polysyllogism is a complex argument (also known as chain arguments of which there are four kinds: polysyllogisms, sorites, epicheirema, and dilemmas) [1] that strings together any number of propositions forming together a sequence of syllogisms such that the conclusion of each syllogism, together with the next proposition, is a premise for the next, and so on.