Logic

Discourse is connected thought, expressed in words. It moves this way and that, like the shuttle in the loom (as Plato said) weaving the fabric of reasoned argument. In discourse with others opinion is formed, knowledge is acquired, and truth attained. What is said by one speaker, combined with what is said by another speaker, may yield a truth, not previously known to either speaker. In that discourse with oneself which is called reflection or meditation, a truth learned today links up with a truth learned yesterday, and the two truths may point the way to some advance or even discovery of tomorrow. From what others have said or from what we ourselves have thought, conclusions and inferences are drawn and they are the special concern of Logic. It is all too easy to draw wrong conclusions and false inferences; and discourse without the discipline of Logic is a fruitful source of false opinion, ignorance and error.

Logic trains the mind to draw the right conclusion, and to avoid the wrong, to make the true inference and not the false. It has formulated rules of inference to govern and guide debate and to promote discovery. Logic has to deal as well with other important elements of discourse, but its main province has always been, and still is, inference.

Idle talk and trivial conversation do not rank as discourse for our purpose. Logic has little to do with the frivolous; its business is with the serious statement which admits truth or falsity. Logic promotes truth; yet we can go far in Logic without knowing or caring much whether a particular statement is true or false, in the ordinary acceptation of those words. By true in ordinary speech we mean true to fact, and by false we mean the opposite. Now a statement, true to fact, may in its context infringe a rule of Logic; and a statement, false in fact, may in its context conform to the rules of Logic. The logician, as such, is not directly concerned with fact, but is much more concerned with the observance of the rules of Logic, and therefore he uses a pair of technical terms, valid and invalid, to express, respectively, what conforms to the rules of logic and what does not conform thereto. By the aid of these terms he can set out the rules of reasoning without committing himself as to whether a particular statement is true to fact, or not. Valid comes from the Latin, validus, strong. A valid passport may make mistakes in fact, but if duly signed and not out of date, it may do its work and get you through the barrier. On the other hand, it may give the colour of the eyes and all the other facts correctly, but if it is out of date, it will not do its work; it is invalid. The distinction between truth and validity must be carefully observed. It is illogical and therefore incorrect to speak of a true syllogism, if you mean a valid syllogism, or of a valid conclusion, if you mean a true conclusion.

This distinction is of special importance here; for in the study of the syllogism, as such, Logic concentrates on the form of the reasoning, for the most part, and is not directly concerned with the truth of its contents. If the syllogism complies with the formal rules, it is valid, if not, not. If the conclusion follows from the premisses, the conclusion is valid, even though premiss and conclusion may not be true to fact. Example:

The first premiss is true; the second is false; the conclusion is false; but the conclusion is correctly drawn from the premisses, and therefore valid in its syllogism, even though it is not true to fact.

The reverse can happen too. A proposition, true to fact, may appear as the conclusion of an invalid syllogism. Example:

These examples are warnings against the habit of judging the validity or invalidity of a syllogism by the truth or falsity of the conclusion. As students of Logic our first duty is to look at the working of the syllogism, and to judge its validity, or otherwise, by the rules. No good comes of confusing the two sets of terms, as is sometimes done. Truth is truth, and validity is validity, and neither can do duty for the other. The lazy habit of styling a valid conclusion true, or a true conclusion valid, weakens both our sense of truth and our feeling for Logic.

(From Teach Yourself Logic, by A. A. Luce.)