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.
FALLACIES
