# Syllogism

## Syllogism

﻿Syllogism

A syllogism is an argument containing two premises and a conclusion. Aristotle’s syllogism is specific in the sense that all statements in the argument have to be categorical. That is, the terms of a statement have to belong to categories. Take the famous example: All men are mortal. Socrates is a man. Therefore, Socrates is mortal. In the first statement, ‘men’ are placed in the category of mortal beings. In the second statement ‘Socrates’ falls into the category of ‘men’. Therefore, in the third statement, which is the conclusion, Socrates falls into the category of mortal beings.

Each premise has two of three terms – the major term (P), middle term (M) and minor term (S). The premise that contains the major term is called the major premise, and the premise that contains the minor term is called the minor premise. For syllogisms to be applied, there has to be a link between one of the terms in the first premise and one of the terms in the second premise. This is the middle term. In a sense, this middle term cancels out, leaving the other two terms to form the conclusion. In the above example, ‘All men are mortal’ is the major premise, because mortality is the major term as it appears as the predicate in the conclusion. ‘Socrates is a man’ is the minor premise, as it contains ‘Socrates’, the minor term, as it is the subject in the conclusion. The category of ‘men’ is common to both the premises, and therefore is the middle term. It is by virtue of this that the conclusion is formed.

There are four logical variations that the premises are subject to, and these are denoted by a, e, i and o. They (arbitrarily) stand for the operations ‘all’, ‘none’, ‘some’ and ‘indefinite’. That is, aFG stands for ‘All F is G’ and eFG stands for ‘No F is G’.

Two concepts that are very important to understanding Aristotle’s syllogisms are ‘Moods’ and ‘Figures’. A mood is an order of possible logical variations. That is, an argument could be in the form...