The logical ideas developed within the system of Classical Philosophy are simply developments of Common Sense (in the ordinary usage of that phrase).

Logic provides certain rules for the right guidance of the operations of the Mind. Logicians tend to distinguish three kinds of operations:

1. Simple Apprehension consists in representing an object without affirming or denying anything about it. Thus by a simple apprehension of the mind I can conceive the idea ‘being’, or ‘tree’ or ‘man’.
2. Judgment — (and a proposition is merely the oral or written expression of a judgment) — is the act by which one object already known is brought into mental relation with another known object. This action may be affirmative or negative. That which is brought to the other is known as the predicate of the judgment, what it is referred to is known as the subject: e.g. "this tree is high" or "the whole is greater than one of its parts".
3. Reasoning or ratiocination — expressed in a syllogism — is the act by which the mind compares two notions (between which it does not immediately perceive the agreement or disagreement) with a third idea. That third idea is called the Middle Term and the two notions for which agreement or otherwise is sought are called the extreme terms — one of these is the major and the other the minor term.

The premisses of that reasoning compares the two extremes with the middle term, and the result of that twofold comparison is expressed in the conclusion of the syllogism.

When each of the extreme terms agrees with the middle term, the conclusion is affirmative; when one agrees and the other does not, the conclusion is negative.

A judgment, as opposed to the conclusion of an argument is said to be immediate; and the conclusion of a reasoning process mediate.

A conclusion is strictly deduced from two certain principles is itself certain; and a conclusion deduced from two uncertain premisses is itself uncertain, i.e doubtful or only more or less probable.

A reasoning process which leads to a certain conclusion is a proof or demonstration.

Demonstration in the strict sense, however, requires something more than mere certain reasoning: it requires that the premisses be based not on extrinsic considerations — which would be an extrinsic proof — nor upon the absurdity that would result from the conclusion being false, upon a reductio ad absurdum that is; but it requires that they be drawn from the analysis of the subject. This intrinsic, causal, a priori demonstration is the only one which is strictly speaking scientific (in the Aristotelian understanding of the term).

To attain to this is the constant aim of the of the true scientist and philosopher; by this alone is Science built up, if we use the word in its highest sense.

Deduction is the demonstration of a conclusion from an examination of the premisses.

Scientific induction is a different process; being that by which the scientist discovers the laws of nature (The law of a natural body is the manner in which it exercises its actions — e.g. it is the law of chlorine and hydrogen under certain conditions of temperature and pressure, to combine in the proportion of 35.5 and 1 to form by their union 36.5 of hydrochloric acid) A law is the natural outcome of the properties a body has, i.e. certain qualities necessarily inherent in the body.

The rational, exact sciences, are deductive in method; the sciences of observation, experimental or empirical, are inductive. Yet their logical validity rests on a deduction.

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