Under this head come all fallacies which arise, not so much from a false estimate of the probative force of known evidence, as from an indistinct conception what the evidence is.

1. Thus, where there is an ambiguous middle, or a term used in different senses in the premisses and in the conclusion, the argument proceeds as though there were evidence to the point, when, in fact, there is none. This error does not occur much in direct inductions, since the things themselves are there present to the senses or memory; but chiefly, in Ratiocination, where we are deciphering our own or others' notes. The ambiguity arises very often from assuming that a word corresponds precisely in meaning with the root itself (e.g. representative), or with cognate words from the same root, called paronymous words (as, artful, with art). Other examples of ambiguities are; 'Money,' which, meaning both the currency and also capital seeking investment, is often thought to be scarce in the former sense, because scarce in the latter; 'Influence of Property,' which, signifying equally the influence of respect for the power for good, and of fear of the power for evil, which is possessed by the rich, is represented as being assailed under its former form when attacked really only under the latter; 'Theory,' which, because applied popularly to the accounting for an effect apart from facts, is ridiculed, even when expressing, as it properly does, the result of philosophical induction from experience; 'The Church,' which refers (as in the question of the inviolability of Church property) sometimes to the clergy alone, sometimes to all its members; 'Good,' in the Stoic argument that virtue, as alone good (in the Stoic sense), must therefore include freedom and beauty, because these are good (in the popular sense). So, the meaning of 'I' shifts from the laws of my nature to my will, in Descartes' À priori argument for the being of a God, viz. that there must be an external archetype whence I got the conception, for if I (i.e. the laws of my nature) made it, I (i.e. my will, and not, as it should consistently be, the laws of my nature) could unmake it; but I (i.e. my will) cannot. In the Free-Will controversy, 'I' is used ambiguously for volitions, actions, and mental dispositions, and 'Necessity' both for Certainty and for Compulsion. From the application of 'same,' 'one,' 'identical,' which primarily refer to a single object, to several objects because similar, grew up (for the purpose of accounting for the supposed oneness in things said to have the same nature or qualities) both the Platonic Ideas, and also the Substantial Forms and Second Substances of the Aristotelians, even though the latter did see the distinction between things differing both specie and numero, and those differing numero only. And thence, too, sprang Berkeley's proof of the existence of a Universal Mind from the supposed need of such a Being to harbour, in the interval, the idea, which, one and the same (really, only two similar ideas), a man's mind has entertained at two distinct times. The difficulty in Achilles and the Tortoise arises from the use of infinity, or, for ever, in the premisses, to signify a finite time which is infinitely divisible, and, in the conclusion, to signify an infinite time. Thus, again, 'right' is used to express, both what others have no right to stop a man from doing, and also what it is not against his own duty to do; both what people are entitled to expect from, and also what they may enforce from others. The Fallacy of Composition and Division, i.e. the use of the same term in a syllogism, at one time in a collective, at another in a distributive sense, is one of the Fallacies of Ambiguous Terms. Examples of it are the arguments, that great men (collectively) could be dispensed with, because the place of any particular great man might have been supplied (i.e., in fact, by some other great man); and, that a high prize in a lottery may be reasonably expected (by a certain individual, viz. oneself), because a high prize is commonly gained (by some one or other).

2. In Petitio Principii, the premisses are not even verbally sufficient for the conclusion, since one premiss is either clearly the same as the conclusion, or actually proved from it, or not susceptible of any other proof. Men commonly fall into it, through believing that the premiss was verified, though they have forgotten how. But the variety, termed Reasoning in a Circle, implies a conscious attempt to prove two propositions reciprocally from each other. This formal proof is not often attempted, except under the pressure of controversy; but, from mistaking mutual coherency for truth, propositions, which cannot be proved except from each other, are often admitted, when expressed in different language, without other proof. Frequently a proposition is presented in abstract terms as a proof of the same in concrete, as, in MoliÈre's parody, 'L'opium endormit parcequ'il a une vertu soporifique.' So, some qualities of a thing selected arbitrarily are termed its nature or essence, and then reasoned from as though not able to be counteracted by any of the rest. 'Question-begging appellatives,' particularly, are cases of Petitio Principii, e.g. the styling any reform an innovation, which it really is, only that innovation conveys, besides its dictionary meaning, a covert sense of something extreme. Thus, in Cicero's De Finibus, 'Cupiditas,' which usually implies vice, is used to express certain desires the moral character of which is the point in question. Again, the infinite divisibility of matter was assumed by the argument which was used to prove it, viz. that the least portion of matter must have both an upper and an under surface (which, as every other Fallacy of Confusion, when cleared up, appears as a fallacy of a different sort, under shelter of which, as indeed in ratiocinative fallacies generally, the mere verbal juggle at first escapes detection). Such, again, was Euler's argument, that minus multiplied by minus gives plus, because it could not give the same as minus multiplied by plus, which gives minus. So, some ethical writers begin by assuming, that certain general sentiments are the natural sentiments of mankind, and thence argue that any which differ are morbid and unnatural. Thus, lastly, Hobbes and Rousseau rested the existence of government and law on a supposed social compact, and not on men's perception of the interests of society, which, however, could be the only ground for their abiding by such compact if a fact.

3. In Ignoratio Elenchi, or, the Fallacy of Irrelevant Conclusion, the error lies not either in mistaking the import of the premisses, or in forgetting what they are, but in mistaking what is the conclusion to be proved. Sometimes, a particular is substituted for the universal as the proposition needing proof, and sometimes, a proposition with different terms. Under this fallacy come the cases, not only of proving what was not denied, but of disproving what was not asserted; e.g. the argument used against Malthus (whose own position was, that population increases only in so far as not kept down by prudence, or by poverty and disease), that, at times, population has been nearly stationary; or again, that, in some country or other, population and comfort are increasing together, Malthus himself having asserted that this might be so, if capital has increased. Similarly, even Reid, Stewart, and Brown (not merely Dr. Johnson) urged that Berkeley ought, if consistent, to have run his head against a post, as though the non-recognition of an occult cause of sensations implies disbelief in any fixed order among them.