Deduction

(Lat. de ducere, to lead, draw out, derive from; especially, the 
function of deriving truth from truth). The topic will be treated 
in two sections: 

I. As an argument or reasoning process: that kind of mediate 
inference by which from truths already known we advance to a 
knowledge of other truths necessarily implied in the former; the 
mental product or result of that process. 

II. As a method: the deductive method, by which we increase our 
knowledge through a series of such inferences. 

I. AS AN ARGUMENT OR REASONING PROCESS

The typical expression of deductive inference is the syllogism. 
The essential feature of deduction is the necessary character of 
the connexion between the antecedent or premises and the 
consequent or conclusion. Granted the truth of the antecedent 
judgments, the consequent must follow; and the firmness of our 
assent to the latter is conditioned by that of our assent to the 
former. The antecedent contains the ground or reason which is the 
motive of our assent to the consequent; the latter, therefore, 
cannot have greater firmness or certainty than the former. This 
relation of necessary sequence constitutes the formal aspect of 
deduction. It can be realized most clearly when the argument is 
expressed symbolically, either in the hypothetical form: 

1."If anything (S) is M it is P; 

2.but this S is M; 

3.therefore this S is P", 

or in the categorial form, 

1."Whatever (S) is M is P; 

2.but this S is M; 

3.therefore this S is P". 

The material aspect of the deductive argument is the truth or 
falsity of the judgments which constitute it. If these be certain 
and evident the deduction is called demonstration, the 
Aristotelian apodeixis. Since the conclusion is necessarily 
implied in the premises, these must contain some abstract, general 
principle, of which the conclusion is a special application; 
otherwise the conclusion could not be necessarily derived from 
them; and all mediate inferences must be deductive, at least in 
this sense, that they involve the recognition of some universal 
truth and do not proceed directly from particular to particular 
without the intervention of the universal. 

AS A METHOD

When, starting from general principles, we advance by a series of 
deductive steps to the discovery and proof of new truths, we 
employ the deductive or synthetic method. But how do we become 
certain of those principles which form our starting-points?