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- Main article: Inductive deductive reasoning
A syllogism is a kind of logical argument in which one proposition (the conclusion) is inferred from two others (the premises) of a certain form. In Aristotle's Prior Analytics, he defines syllogism as "a discourse in which, certain things having been supposed, something different from the things supposed results of necessity because these things are so." (24b18–20) Despite this very general definition, he limits himself first to categorical syllogisms (and later to modal syllogisms). The syllogism is at the core of deductive reasoning, where facts are determined by combining existing statements, in contrast to inductive reasoning where facts are determined by repeated observations.
A syllogism (henceforth categorical unless otherwise specified) consists of three parts: the major premise, the minor premise, and the conclusion. In Aristotle, each of the premises is in the form "Some/all A belong to B," where "Some/All A' is one term and "belong to B" is another, but more modern logicians allow some variation. Each of the premises has one term in common with the conclusion: in a major premise, this is the major term (i.e., the predicate) of the conclusion; in a minor premise, it is the minor term (the subject) of the conclusion. For example:
- Major premise: All humans are mortal.
- Minor premise: Socrates is human.
- Conclusion: Socrates is mortal.
Each of the three distinct terms represents a category, in this example, "human," "mortal," and "Socrates." "Mortal" is the major term; "Socrates," the minor term. The premises also have one term in common with each other, which is known as the middle term -- in this example, "human." Here the major premise is universal and the minor particular, but this need not be so. For example:
- Major premise: All mortal things die.
- Minor premise: All men are mortal things.
- Conclusion: All men die.
Here, the major term is "die", the minor term is "men," and the middle term is "[being] mortal things." Both of the premises are universal.
A sorites is a form of argument in which a series of incomplete syllogisms is so arranged that the predicate of each premise forms the subject of the next until the subject of the first is joined with the predicate of the last in the conclusion. For example, if one argues that a given number of grains of sand does not make a heap and that an additional grain does not either, then to conclude that no additional amount of sand will make a heap is to construct a sorites argument.
Types of syllogismEdit
Although there are infinitely many possible syllogisms, there are only a finite number of logically distinct types. We shall classify and enumerate them below. Note that the syllogisms above share the same abstract form:
- Major premise: All M are P.
- Minor premise: All S are M.
- Conclusion: All S are P.
The premises and conclusion of a syllogism can be any of four types, which are labelled by letters as follows.
|1):||A||All||S||are||P||universal affirmatives||All humans are mortal.|
|2):||E||All||S||are not||P||universal negatives||All humans are not perfect / No humans are perfect.|
|3):||I||Some||S||are||P||particular affirmatives||Some humans are healthy.|
|4):||O||Some||S||are not||P||particular negatives||Some humans are not clever.|
(See Square of opposition for a discussion of the logical relationships between these types of propositions.)
By definition, S is the subject of the conclusion, P is the predicate of the conclusion, M is the middle term, the major premise links M with P and the minor premise links M with S. However, the middle term can be either the subject or the predicate of each premise that it appears in. This gives rise to another classification of sy