+177. Deductive Reasoning.+--When once a general principle has been
established, we may demonstrate the truth of a specific proposition by
showing that the general principle applies to it. We see a gold ring and
say, "This ring is valuable," because we believe the general proposition,
"All articles made of gold are valuable." Expressed in full, the process
of reasoning would be--
_A._ All articles made of gold are valuable.
_B._ This ring is made of gold.
_C._ Therefore this ring is valuable.
A series of statements such as the above is called a syllogism. It
consists of a major premise (_A_), a minor premise (_B_), and a conclusion
(_C_).
Of course we shall not be called upon to prove so simple a proposition as
the one given, but with more difficult ones the method of reasoning is the
same. The process which applies a general proposition (_A_) to a specific
instance (_C_), is called deductive reasoning.
+178. Relation between Inductive and Deductive Reasoning.+--Deductive
reasoning is shorter and seems more convincing than inductive reasoning,
for if the premises are true and the statement is made in correct form,
the conclusions are irresistible. Each conclusion carries with it,
however, the weakness of the premises on which it is based, and as these
premises are general principles that have been themselves established by
inductive reasoning, the conclusions of deductive reasoning can be no more
_sure_ than those of inductive reasoning.
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