A clever man has said that the use of language is to conceal thought. Its primary use is certainly not to reveal thought, but to enable one person to produce an effect on the mind of another or of others, either for their or his own advantage. In the course of using speech as an instrument of command, entreaty, persuasion, menace, or fustigation, it may happen that the movements of the speaker's mind are revealed to some extent, but this is a mere incident, not the main purpose of the speech.

Grammar is the system of rules which govern the use of language in its primary and ordinary capacity.

It follows from this that language is in no sense a revelation of the reasoning processes, nor do the rules of grammar coincide with the laws of intellect. It is just as reasonable to expect to find the metaphysic of thought revealed in any of the industrial and fine arts, as to look for it in the structure of speech. Aristotle drew his logic from the composition of the Greek sentence—he might as well have sought for logic in the constitution of the Greek buskin.¹⁶

Even when men begin to reason aloud and seek to render their logical movements as evident as possible, they are so hampered by the ordinary habits and rules of speech that their meaning is often difficult or impossible of comprehension. Whence arises the necessity, if we would reason aloud to any purpose, of redacting or translating language from the vernacular into a dialect more indicative of the logical processes that take place when we reason.

This redaction consists mainly in distinguishing clearly the four parts composing an argument, namely, the Subject of the Precedent; the Case which is brought under it for judgment; the Applicate or part of the precedent bearing on the case; the Conclusion, which is the ideal judgment concerning the case. When these four parts are expressed and clearly understood we have a perfect argument, so far as argumentation depends on language. But probably we have spoiled the language from the grammatical and rhetorical point of view. We may have had to supply much that would be redundant and unsightly in ordinary conversation or writing, and to take away much that is appropriate to colloquial discourse. We are diverting language to a use for which it was not designed, and we need not be surprised if the result is ungraceful. This cannot be helped since there exists no other means than language by which to express our concrete reasoning.

I have already shown practically how an argument can be arranged so as to indicate the logical relations subsisting between its parts. A Greek cross is drawn, and in the four angles thus made the four parts of the argument are written, or the principal words of each. Begin with the conclusion, for that is generally the most explicitly given; then find or supply the part of the precedent that agrees or logically rhymes with it; next place the subject in the first compartment, and the case under it. These relative positions should not be varied. When this has been practiced for a while it enables one to dismember the most intricate argument with ease and exactness.

The redaction or re-writing of the language can be abbreviated by regarding the horizontal line as equivalent to a declaration of resemblance between case and precedent-subject, and (by application) between the illustrative abstraction and conclusion. If there is an argument at all there must be this resemblance, and the right-hand parts must have one of the six categorical relations to the left-hand parts. The contents of the angles may be cut down to a word or two, as—

If the category be further indicated by a numeral over the upright line, we have the essential parts of the argument in a very compact form. The cross and categorical numeral may be regarded as a sufficient substitute for grammatical syntax and punctuation.

The negative word that generally occurs in stigmatic arguments requires special attention. It should always be put in the second angle, and when it may read so as to negative the subject it should be hyphened to the predicate, thus giving it the value of non, un, im, or other negative prefix. To say colloquially that 'all Russians are not angels' leaves room to believe that some Russians are angels, the 'not' applying to 'all' instead of to 'angels.' By linking 'not' to 'angels' we get a term equivalent to non-angelic, which expresses the meaning intended—that no Russians are angels.

Caution should be observed with partitive words like 'some,' 'many,' 'a few,' &c. There is little danger of ambiguity when they occur in the case, for that means that we bring only a portion of a group of things to judgment, which we are manifestly entitled to do. The conclusion however applies only to the portion in question, not to the rest of the group. 'Honest men deserve respect; some Negroes are honest men; these particular Negroes deserve respect.'

In the precedent, partitive words imply that only some of the subject have the applicate. If that portion is a dialectical 'all'—that is, if there has been no exception in the course of our experience—we may, though that experience has been limited, venture to treat the applicate as universal and ground a conclusion upon it. If the subject is really partitive—if we know for certain that some subjects have the applicate and others have it not—the conclusion must follow the greater probability. If the number and character of the observed cases is known we can express the probability arithmetically; it is the number of occurrences of a given character divided by the total number.

Redaction must not be used to correct original errors of observation; its purpose is to render explicit in language what is implicit in thought, not what might have been thought supposing the thinker had been more intelligent or industrious than he was.

'Conversion' is a process admitted or required in the artificial methods of syllogistic dialectic. It consists mainly in transposing the subject and predicate of a proposition, as 'some Europeans are Mohammedans'—'some Mohammedans are Europeans,' This operation never takes place in real argument, or is merely the emendation of a proposition at first awkwardly expressed. Conversion can take place only when the predicate is a class, hence the categorical propositions cannot be converted.

16: Though evidently suggested by language, the form which the syllogistic logic finally assumed is so unlike anything grammatical, that it is easily convertible into symbols having no resemblance to language. It has been put into literal symbols with algebraic values, and into geometrical diagrams. A logical machine has even been invented by Professor Jevons, 'worked by keys like a pianoforte,' which returns 'infallible answers'—of the Aristotelian sort—to every kind of question. That is sufficiently unlike both reason and language.