As the supposed habitual connexion or repugnance of two facts may be admitted, either as a self-evident and axiomatic truth, or as itself an inference, the first great division is into Fallacies of Simple Inspection or à priori Fallacies, and Fallacies, of Inference. But there is also an intermediate class. For, sometimes an inference is erroneous through our not conceiving what our premisses precisely are, and from our therefore substituting new premisses for the old, or a new conclusion for the one we undertook to prove; and this is called the Fallacy of Confusion. Under this head, indeed, of Fallacies of Confusion, might strictly be brought almost any fallacy, though falling also under some other head: for, some of the links in an argument, especially if sophistical, are sure to be suppressed; and, it being left doubtful which is the proposition to be supplied, we can seldom tell with certainty under which class the fallacy absolutely comes. It is, however, convenient to reserve the name Fallacy of Confusion for cases where Confusion is the sole cause of the error.
Cases, then, where there is more or less ground for the error in the nature of the apparent evidence itself, the evidence being assumed to be of a certain sort, and a false conclusion being drawn from it, may be classed as Fallacies of Inference. According as the apparent evidence consists of particular facts, or of foregone generalisations, we call the errors Fallacies of Induction or of Deduction. Each of these classes, again, may be subdivided into two species, according as the apparent evidence is either false, or, though true, inconclusive. Such subdivisions of the Fallacy of Induction are respectively called, in the former case, Fallacies of Observation (including cases where the facts are not directly observed, but inferred), and, in the latter, Fallacies of Generalisation. Among Fallacies of Deduction, those which proceed on false premisses have no specific name, for they must fall under one of the other heads of Fallacies; but those, the premisses of which, though true, do not support the conclusion, compose a subdivision, which may be specified as Fallacies of Ratiocination.
CHAPTER III.
FALLACIES OF SIMPLE INSPECTION; OR, À PRIORI FALLACIES.
There must be some à priori knowledge, some propositions to be received without proof; for there cannot be a chain suspended from nothing. What these are is disputed, one school recognising as ultimate premisses only the facts of our subjective consciousness, e.g. Sensations, while Ontologists hold that the mind intuitively, and not through experience, recognises as realities other existences, e.g. Substances, which are suggested by, though not inferrible from, those facts of consciousness. But, as both schools, in fact, allow that the mind infers the reality from the idea of a thing, and that it may do this unduly, there results a class of Fallacies resting on the tacit assumption that the objects in nature have the same order as our ideas of them. Hence not only arose the vulgar belief that facts which make us think of an event are omens foreboding (e.g. lucky or unlucky names), or even causing its occurrence; but even men of science both did and do fall into this Fallacy. The following dogmas express the different forms of this error:—
1. α [Greek: a]. Things which we cannot help thinking of together must coexist; thus Descartes held that, because existence is involved (though really only by the thinker himself) in the idea of a geometrical figure, a thing like the idea must exist. β [Greek: b]. Whatever is inconceivable is false. The latter proposition has been defended by drawing a distinction between the principle, and its possibly wrong application to facts, e.g. to Antipodes; but how can we ever know that it has been rightly applied? Coleridge, again, has distinguished between the unimaginable, which he thinks may possibly be true, and the inconceivable, which he thinks cannot be; but Antipodes were imaginable at the same period when they were inconceivable. In fact, as even to Newton it seemed inconceivable, that a thing should act where it is not (e.g. that the sun should act upon the earth without the medium of an ether), simply because his mind was not familiar with the idea, so it may be with our incapability (if not, indeed, resulting merely from our limited faculties) of conceiving, e.g. that matter cannot think; that space is infinite; that ex nihilo nihil fit. Leibnitz's tenet that all natural phenomena must be explicable à priori, and the further assumption by some that Nature always acts by the simplest, i.e. by the most easily conceivable means (and that, therefore, e.g. the heavenly bodies have a circular movement), exhibit vividly this Fallacy of Simple Inspection.
2. Whatever can be thought of apart, or has a separate name, exists apart as a separate entity, e.g. Nature, Time, qualities, as e.g. Whiteness, and, worst of all, the Substantiæ Secundæ. Mysticism is this habit of ascribing objective existence to the subjective creations of the mind, and reasoning from them to the things themselves.
3. A fact must follow a certain law, because we see no reason for its deviating from it in one way rather than in another. This, which is the same as the Principle of the Sufficient Reason, has been used to prove the Law of Inertia (the very point to be proved, viz. that only external force can be a sufficient reason for motion in a particular direction, being assumed), and also the First Law of Motion, the argument being, in the latter case, that a moving body, if it do not continue of itself to move uniformly in a straight line, must deviate right or left, and that there is no reason for its going one way more than the other: to which the answer is, that, apart from experience, we could not know whether or not there were a reason. Geometers often fall into this Fallacy.