# IAS: Philosophy: Logic

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## Logic

The art of thinking and reasoning in strict accordance with the limitations and incapacities of the human misunderstanding. The basic of logic is the syllogism, consisting of a major and a minor premise and a conclusion

Major Premise: Thirty men can do a piece of work thirty times as quickly as one man.

Minor Premise: One man can dig a posthole in thirty seconds.

therefore-Conclusion: Thirty men can dig a posthole in one second.

Syllogisms are arguments that take several parts, typically with two statements which are assumed to be true (or premises) that lead to a conclusion. There are three major types of syllogism:

- Conditional syllogism: If A is true then B is true (If A then B) .
- Categorical syllogism: If A is in C then B is in C.
- Disjunctive syllogism: If A is true, then B is false (A or B) .

## The Structure of Syllogism

A categorical syllogism is an argument consisting of exactly three categorical propositions (two premises and a conclusion) in which there appear a total of exactly three categorical terms, each of which is used exactly twice. One of those terms must be used as the subject term of the conclusion of the syllogism, and we call it the minor term of the syllogism as a whole. The major term of the syllogism is whatever is employed as the predicate term of its conclusion. The third term in the syllogism doesn՚t occur in the conclusion at all, but must be employed in somewhere in each of its premises; hence, we call it the middle term.

Since one of the premises of the syllogism must be a categorical proposition that affirms some relation between its middle and major terms, we call that the major premise of the syllogism. The other premise, which links the middle and minor terms, we call the minor premise.

Consider, for example, the categorical syllogism:

- No geese are felines.
- Some birds are geese.
- Therefore, Some birds are not felines.

Clearly, “Some birds are not felines” is the conclusion of this syllogism. The major term of the syllogism is “felines” (the predicate term of its conclusion) , so “No geese are felines” (the premise in which “felines” appears) is its major premise. Simlarly, the minor term of the syllogism is “birds,” and “Some birds are geese” is its minor premise. “geese” is the middle term of the syllogism.

## Standard Form of a Syllogism

A categorical syllogism in standard form always begins with the premises, major first and then minor, and then finishes with the conclusion.

The mood of a syllogism is simply a statement of which categorical propositions (A, E, I, or O) it comprises, listed in the order in which they appear in standard form. Thus, a syllogism with a mood of OAO has an O proposition as its major premise, an A proposition as its minor premise, and another O proposition as its conclusion; and EIO syllogism has an E major premise, and I minor premise, and an O conclusion; etc.

In addtion to mood, a syllogism is characterized by its figure which is solely determined by the position in which its middle term appears in the two premises: In a first-figure syllogism, the middle term is the subject term of the major premise and the predicate term of the minor premise; in second figure, the middle term is the predicate term of both premises; in third, the subject term of both premises; and in fourth figure, the middle term appears as the predicate term of the major premise and the subject term of the minor premise.

There are exactly 256 distinct forms of syllogisms, out of which only 24 are valid.