About Deductive Reasoning
Deductive reasoning is the use of general ideas to reach a particular conclusion "a priori," before experience yields the conclusion. It is a matter of examining "causes" in order to determine "effects."
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Syllogism
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The syllogism is the basic construct in deductive reasoning. A syllogism consists of three propositions. The third is the conclusion, which is drawn from the first two propositions, called premises.
Proposition
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A proposition can take one of three different forms. A hypothetical proposition is an "if-then" statement, while a disjunctive proposition is an "either-or" statement. The most basic proposition is a categorical statement, which has the form of "this is that." "All men are created equal" is a categorical proposition.
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Quantity and Quality
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A proposition can be either affirmative or negative depending on the copula, or connecting verb. "This is that" is a positive proposition, while "This is not that" is negative. A proposition can also be either universal or particular depending in the quantifiers. "All this is that" is universal, while "Some of this is that" is particular.
Truth and Validity
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A syllogism can be valid in presentation and construction, but not be true. For example:
All two-legged animals are dancers.
All dogs are two-legged animals.
Therefore, all dogs are dancers.
The syllogism is constructed and presented properly, so it is valid, but the propositions are false.
Terms
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The major term is always in the first, or major, premise and is the predicate, or last term, of the conclusion. In the previous example, "dancers" is the major term.
The minor term is always in the second, or minor, premise and is the subject, or first term, of the conclusion. In the previous example, "dogs" is the minor term.
The middle term connects the major and minor premises. In the previous example, "two legged animals" is the middle term.
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