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Syllogism is a form of mediate inference. In an immediate inference, we draw a conclusion from a single premise. But in case of a mediate inference, we draw a conclusion from the joint assertion of more than one premise.

Syllogism is a form of argument in which we draw a conclusion form the joint assertion of two premises. For example,

All teen-agers are fond of cartoon pictures.

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Some school-going students are teen-agers.

Therefore, some school-going students are fond of cartoon pictures.

In the above argument, the conclusion follows from both the premises taken together. The conclusion is justified by the assertion of both the premises. In other words, the premises jointly support the conclusion and the conclusion is supported by both the premises.

Syllogisms have different forms. Syllogisms may be classified as pure and mixed. Pure- syllogisms are classified as categorical and Hypothetical. Mixed-syllogisms are classified as Hypothetical, Alternative, Disjunctive and Dilemma. In this chapter we will deal with pure categorical syllogisms. Hereafter in this chapter we will often use ‘syllogism’ to mean pure categorical syllogism. When we will talk of other forms of syllogism we will qualify them accordingly.

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**Definition:**

A categorical syllogism is a deductive argument consisting of three categorical propositions that together contain exactly three terms, each of which occurs exactly twice in the argument. We may elaborate the definition as follows.

1. A syllogism must have three propositions (out of which two supporting propositions are the premises and the one drawn from the premises is the conclusion.)

2. A syllogism should have three terms.

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3. The premises and the conclusion are categorical propositions (like A, E, I and O).

4. The conclusion necessarily follows from the premises. The relation between the premises and the conclusion is one of logical implication.