Syllogism

A syllogism (, syllogismos, 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true.

An enthymeme (, enthýmēma) is an argument with a hidden premise. Enthymemes are usually developed from premises that accord with the audience's view of the world and what is taken to be common sense. However, where the general premise of a syllogism is supposed to be true, making the subsequent deduction necessary, the general premise of an enthymeme is merely probable, which leads only to a tentative conclusion. Originally theorized by Aristotle, there are four types of enthymeme, at least two of which are described in Aristotle's work.

type of logic diagram

work by Aristotle

A polysyllogism is a complex argument (also known as chain arguments of which there are four kinds: polysyllogisms, sorites, epicheirema, and dilemmas) 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. Each constituent syllogism is called a prosyllogism except the last, because the conclusion of the last syllogism is not a premise for another syllogism.

term

non-deductive syllogism

mathematical argument