[Footnote 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 XXIX--OF EQUIVOCATION AND MAL-OBSERVATION Fallacies are counterfeit or sham arguments. They may fail to be arguments--(1) because their antecedents are false; (2) because the antecedents though true are not arranged dialectically, and do not suggest the right conclusion; (3) because the language is equivocal. To take the last first. So many things are called by the same name, and so many different names may be applied to the same thing, that if we attempt to argue from words alone, without any personal knowledge of the things or judgments that are in question, we shall certainly make mistakes. The only security against this sort of fallacy is much experience, and the self-denial necessary to relinquish argument and the criticism of arguments, when we have no sufficient knowledge of the data. The degree of imperfection in observation which should be considered to render the theorem fallacious, is no easy matter to determine. One class of logicians (the Formal) get over the difficulty by declaring that dialectic is not concerned with concrete knowledge at all,[17] but only with its general properties (as conceived by Aristotle), and they have set up as a standard of logical truth the capability of being imagined. A centaur is to them as true a fact as a horse, and they would accept as valid such a theorem as this: 'All centaurs object to be shod with iron; Gryneus is a centaur; therefore we may conclude that he would resist being shod with iron.' No amount of conceivability or formal coherence can make this other than nonsense.