There remain, therefore, as the only class of fallacies having properly their seat in deduction, those in which the premises of the ratiocination do not bear out its conclusion; the various cases, in short, of vicious argumentation, provided against by the rules of the syllogism. We shall call these, Fallacies of Ratiocination.
We have thus five distinguishable classes of fallacy, which may be expressed in the following synoptic table:--
of Simple Inspection 1. Fallacies _à priori_.
Inductive Fallacies 2. Fallacies of Observation. 3. Fallacies of Generalization.
Deductive Fallacies 4. Fallacies of Ratiocination.
from evidence indistinctly conceived 5. Fallacies of Confusion.
§ 3. We must not, however, expect to find that men's actual errors always, or even commonly, fall so unmistakeably under some one of these classes, as to be incapable of being referred to any other. Erroneous arguments do not admit of such a sharply cut division as valid arguments do. An argument fully stated, with all its steps distinctly set out, in language not susceptible of misunderstanding, must, if it be erroneous, be so in some one of these five modes unequivocally: or indeed of the first four, since the fifth, on such a supposition, would vanish. But it is not in the nature of bad reasoning to express itself thus unambiguously. When a sophist, whether he is imposing on himself or attempting to impose on others, can be constrained to throw his sophistry into so distinct a form, it needs, in a large proportion of cases, no further exposure.
In all arguments, everywhere but in the schools, some of the links are suppressed; _à fortiori_ when the arguer either intends to deceive, or is a lame and inexpert thinker, little accustomed to bring his reasoning processes to any test: and it is in those steps of the reasoning which are made in this tacit and half-conscious, or even wholly unconscious manner, that the error oftenest lurks. In order to detect the fallacy, the proposition thus silently assumed must be supplied; but the reasoner, most likely, has never really asked himself what he was assuming: his confuter, unless permitted to extort it from him by the Socratic mode of interrogation, must himself judge what the suppressed premise ought to be in order to support the conclusion. And hence, in the words of Archbishop Whately, "it must be often a matter of doubt, or rather, of arbitrary choice, not only to which genus each _kind_ of fallacy should be referred, but even to which kind to refer any one _individual_ fallacy; for since, in any course of argument, _one_ premise is usually suppressed, it frequently happens in the case of a fallacy, that the hearers are left to the alternative of supplying _either_ a premise which is _not true_, or _else_, one which _does not prove_ the conclusion: _e. g._ if a man expatiates on the distress of the country, and thence argues that the government is tyrannical, we must suppose him to assume _either_ that 'every distressed country is under a tyranny,' which is a manifest falsehood, _or_ merely that 'every country under a tyranny is distressed,' which, however true, proves nothing, the middle term being undistributed." The former would be ranked, in our distribution, among fallacies of generalization, the latter among those of ratiocination. "Which are we to suppose the speaker meant us to understand? Surely" (if he understood himself) "just whichever each of his hearers might happen to prefer: some might assent to the false premise; others allow the unsound syllogism."