s a logical term; but in the consideration of the ideas denoted by it, we are led, at several points, beyond the ground occupied by Logic Proper. Especially there is often involved, in the scrutiny of fallacies, examina- Fallacy.

tion of the matter of arguments, that is, of the nature of the objects argued about. The chapters on fallacies, therefore, which appear as appendices in the most elaborate logical treatises, really travel more or less out of the proper domain of the science; and the topic may here deserve a few paragraphs of separate illustration.

A Fallacy is an unsound or inconclusive argument; an argument supposed or alleged to prove a conclusion which it does not prove. The name is sometimes confined to sophisms, that is, unsound arguments used with the intention to deceive. But the intention is a point of secondary importance in the theory of fallacies; and, indeed, those fallacies in which the reasoner deceives himself are by far more dangerous than the others, because they are by far more common. The term Fallacy, it will thus be observed, is applicable to an argument taken as a whole, not to any of the propositions of which the argument is composed. The propositions severally must be true or false; the argument which they constitute must be correct or fallacious; that is, its conclusion must either follow or not follow from the premises.

In demonstrative reasoning, such as that whose matter is mathematical truth, there is but slight occasion for a systematic consideration of fallacies. The ideas which arguments of this sort deal with are both few and simple; and the words in which the ideas are expressed have precise and well-fixed meanings. But in probable reasoning, the matter of which comprehends all questions directly regarding human character, and conduct, and destiny, the ideas are many and complex, and the language is seldom either precise or exactly defined. In testing such an argument, therefore, we have to begin by subjecting it to something like an anatomical dissection. We aim at exhibiting the bare skeleton of the argument, that we may be able to perceive whether its parts are or are not firmly knit together.

The process by which we gain such a view of an argument is twofold. There is required, on the one hand, a stripping off of everything inessential. Into every argument in probable matter, much that is inessential finds its way even in thought; and still more that is inessential intrudes into the argument when it passes into words. It is required, on the other hand, to bring distinctly into view all the points of junction—all the points at which one part of the argument is related to another. In the form which argumentation naturally and usually assumes, all those points are not exposed. We have, and we continually indulge, a tendency to argue elliptically, to omit steps of our reasoning; and, omitting largely in thought, we omit still more largely in expression. The honest thinker passes over hastily in his own mind, and denotes but briefly, if at all, in words, those steps as to which he himself has no doubt; and which he believes to be equally clear to others; the sophistical debater slurs over, or keeps back altogether, if it be possible, those steps in which he knows the weakness of his argument to lie.

In a word, paradoxical though the assertion may appear, it is found, when we aim at testing our ordinary acts of reasoning in probable matter, that they are irregular both by excess and by defect. The testing of the arguments by the laws of the syllogism is very easy, as soon as those faults have been cured. The difficulty lies in the process of cure, that is, in the analysis of the argument, and the exhibition of it in its naked form. Further, the two parts of the cure are not equally difficult: the least so far by far is the weeding out of the superfluities. The filling up of the gaps is often a very troublesome task. Indeed, when a chain of argumentation is very long and complex, it very frequently—whether through looseness of thinking, or through the design to mislead—deviates so widely from regularity of form, as to admit, and often at more points than one, of being filled up in any of several alternative ways. In such an instance, we are almost certainly safe in believing that the reasoning is fallacious; and it will almost always be possible to indicate two or more specific fallacies, one or another of which must have been committed. Such a position—satisfactory where a man wishes sincerely to estimate the accuracy of his own reasonings—is not so strong as might be wished when we endeavour either to convince a candid but confused disputant of error, or to expose sophisms committed by disputants who are not candid. Another case, which is often still more annoying, while it is also more common, is that in which one and the same argument is found to involve more fallacies than one; a case which is made particularly frequent by this, that almost every fallacious argument which is really troublesome owes its force, in a greater or less degree, to its introduction of ambiguous terms.

For dealing efficiently with serious difficulties of the kind, we require two qualifications. The first is exact knowledge of the syllogistic laws, with readiness and correctness in the use of them. The second is familiar acquaintance, and aptness in the use of our acquaintance, with the various forms of fallacy, or methods of incorrect reasoning. Towards the attainment of the latter of the two, the fuller and more accurate of the treatises on logic aim at giving assistance in their supplementary consideration of fallacies. A complete enumeration and classification of fallacies has not been achieved by any of the logicians, and is indeed impossible; but those which are most common and most dangerous may be and have been identified and described, and arranged according to several different principles, each of which has its uses in particular applications.

There has been a general agreement in accepting, as the first step in the classification of fallacies, the Aristotelian division of all of them into two classes: Fallacies in Dictione (τροπα την λεξιν); Fallacies extra Dictionem (εκ της λεξιν). The former are otherwise describable as Formal or Logical Fallacies, as errors in the process of reasoning itself; the latter as Material or Non-Logical Fallacies, as errors arising beyond the reasoning process. The distinction thus indicated is perfectly sound; but the application of it is difficult, and the distinction itself sometimes evaporates in the attempt to apply it. Fallacies referred to the second class by some logicians are placed in the first by others; and by some of the schoolmen (Occam for one) it has been maintained, that the Aristotelian classes are not separated by a distinction really identical at all points with the distinction between fallacies formal and fallacies material (a parte rei et a parte rei). The details, accordingly, have been worked out variously by different writers; none of the elaborations perhaps being so useful as that of Archbishop Whately, which exhibits the author's usual success in dealing with questions having a close practical bearing. Whately's distribution and description of fallacies will, with other authorities, furnish much to the hasty outline here to be given. There may advantageously be compared with it Mr Mill's classification, which is specially designed for bringing out the forms which error is most likely to assume when reasoning is used in the process of scientific discovery. Some other recent treatises on fallacies aim at exemplifying the application of fallacious reasoning in other special departments of thought. Thus Bentham's Book of Fallacies may be described as showing, how certain wrong rules of judgment in political questions may be referred to the several kinds of fallacy, and most easily detected. Comte's discussion of fallacies embraces only an incidental denunciation of certain prevalent opinions, which stand in the way of his Positive Philosophy.

I. Perhaps our path may most readily be cleared, if, first of all, we regard Fallacies as distributable into Three Classes. They are either Fallacies of Assumption, Fallacies of Exposition, or Fallacies of Inference.

II. For the detection of Fallacies of Assumption, logic cannot afford any direct assistance. It can aid us only through the training it gives us in clearness of thought, and in sub- Fallacy.

The error of Assumption consists in our reasoning from premises which are either untrue in themselves, or not admitted by those whom we wish to convince. The unwarranted assumption may take place in either of two ways. (1.) The more common of the two was comprehended by the Aristotelians in their second class of fallacies; it was called petitio principii or quæsitio, and is familiarly known to us as the "Begging of the Question." It consists in taking for granted the thing to be proved. We assume a premise, which either is identical with our conclusion, or (more frequently because more available) is so far dependent on our conclusion that it cannot be held as established till the conclusion is admitted. That which is strictly denoted by "Reasoning in a Circle" is the use of two arguments of this kind, in the second of which, assuming the conclusion of the first, we thus try to prove the premise which in the first we had wrongly assumed. A genuine and complete instance of reasoning in a circle is a rare incident. (2.) The second kind of the fallacy of assumption, embraces all cases of wrong assumption not resolvable into the begging of the question. Evidently its possible varieties are innumerable. In our own reasonings, we may be tempted to assume an untrue premise by any circumstance which makes our knowledge imperfect or erroneous; in attempting honestly to convince others, we may use a premise unadmitted by them, whenever it happens that we are incompletely informed as to the state of their belief in regard to the question argued about. For the sophistical use of the fallacy, occasion may be furnished by circumstances of either kind.

III. When a fallacy of assumption has occurred, the argument is of course unconvincing, even though no error has been committed in the process of inference. So is it likewise when the fallacy is a Fallacy of Exposition. The word "relevant" and its cognates have been branded as Scotticisms; but they are extremely convenient; and in this application they are adopted by Whately. Placing this kind of paradoxism among the fallacies of matter, he apply translates its scholastic name "ignoratio elenchi" by the phrase "Irrelevant Conclusion." The Latin name bears reference to the case of disputation: the disputant who uses the fallacy is said not to know, or to profess not to know, the "elenchus," that is, the proposition which, as being the contradictory of his opponent's conclusion, it was his duty to prove. The fallacy is committed when the conclusion which we infer, although it may be legitimately deduced from premises true or admitted, is not the conclusion we were bound to prove. We denounce such a fallacy when we say, "that is not the point," or "that is not the question."

When the error is described as a Fallacy of Exposition, the feature intended to be brought into view is this; that it consists essentially in a mis-statement or wrong exposition of the question argued. Its varieties are indefinitely various: it has correctly been said that no fallacy has so wide a range as this. It is always, in one shape or another, referable to the case which is usually set down as one of its specific kinds, namely, that which is spoken of as a "shifting of the ground." Under such names as this, it is especially familiar to lawyers, and not very rare in controversies ecclesiastical and theological. Several kinds of it, which shift the ground of argument in certain specific directions, have received specific names. One such is the "Argumentum ad Hominem," when it is used fallaciously (sometimes this argument is quite legitimate); all such arguments as those which seek to challenge a conclusion, not on its own merits, but on the score of inconsistency on the part of the person maintaining it. Another is the "Argumentum ad Verecundiam," the appeal to authority; which evidently may in some kinds of questions be really an impregnable argument, while still oftener it may fairly avail for securing a suspension of judgment; but which still oftener is used illegitimately, and must always be so when the matter is of a kind in which independent thinking ought to rule. To this kind belong also all attempts (in the popular phrase) to Move the Passions; all attempts to bias the judgment through emotion, desire, or aversion, when the question is one which should be decided on grounds purely intellectual. Under this head also may most conveniently be placed all such errors as we commit, when we hold a conclusion as disproved when it has merely been unproved; or when we treat the use of any of the last-named kinds of argument as fallacious and inapplicable to the case, the case being one in which they are legitimately applicable.

It may appear to some, that Fallacies of Exposition ought to be considered as being nothing else than a particular kind of fallacies of assumption. It is, in fact, a point carefully to be observed, that they come into play only through the unwarranted assumption of a premise or premises in the last step of the reasoning, the step which leads directly to that which is represented as the conclusion. But they are peculiar in this: that, whereas in proper fallacies of assumption there may be, and often is, a shifting of premises, there is not there, and is here, a shifting of conclusion. Altogether, the fallacies of exposition seem entitled to the middle place here given them; a place which intimates their alliance on the one side to the fallacies of assumption, and on the other to the fallacies of inferences, while it denotes also that they are essentially distinguishable from both. Here, as in fallacies of assumption, logic does not directly help us; but here, as in fallacies of inferences, the conclusion wanted is not proved.

IV. All fallacies rightly referable to the two classes hitherto described would fall, in the scholastic scheme, within the class of Fallacies extra dictioinem. Fallacies of the Third Class above named, those of Inference, are all of them Fallacies in dictioinem.

In these logical error has place. The conclusion which the argument is supposed or alleged to prove, does not follow from the premises. Therefore, such a fallacy is effectually exposed, as soon as the argument containing it has been resolved into the form of a syllogism. A pretended argument, doubtless, may have in it so little even of the resemblance of reasoning, that its resolution into the syllogistic form is impossible; and in such a case the varieties of possible error are indefinitely numerous: but no such case is worth considering, since none such could for a moment mislead any rational being. Again, where the argument is so like a genuine act of reasoning as to be resolvable into the syllogistic form, there are some of the syllogistic rules (such as those for negatives) which cannot have been violated. Accordingly, all the Fallacies of Inference that require enumeration are four: Illicit Process, either of the Major Term or of the Minor; Non-Distribution of the Middle Term; and the occurrence of More Terms than Three. The last of these fallacies is found, on a strict analysis, to comprehend the other three: all of these are just specific instances of it. In a legitimate act of reasoning, we use three terms and three only, comparing each of these once with each of the other two. Every logical error consists really in the introduction of a fourth term, which carries with it the want of one of our three comparisons. The fallacy may be, our having either two major terms, two minors, or two middles. This doctrine is worth remembering, because of its bearing on that kind of logical fallacy which is practically most important.

A distinction now presents itself, separating Fallacies of Inference into Two well-marked Genera. First, the fallacy may appear on the face of the argument; it may be evident before we have considered the meaning of the terms, or when (as in the use of the symbolic terms so common in logical examples and essential in algebra) none of the terms has any appropriated meaning. Secondly, the fallacy may not appear until we have ascertained, by interpretation, the meaning of the term in which it occurs. Fallacies of the first kind have been called Purely Logical Fallacies, those of the second kind Semi-Logical. The names are justly applied; for interpretation of terms is not a function of logic, and fallacies of the second kind are not cognisable by logical tests until the process of interpretation has been performed.

(1.) The Fallacies Purely Logical are not named by Aristotle among the thirteen kinds into which he distributes all fallacies; and they receive little attention, oftenest none at all, in the special discussions on fallacies by the schoolmen. The reason is plain. The systematic doctrines of the syllogism, taught in preceding parts of the logical treatises, were supposed to have furnished, for the detection of these fallacies, all the aid that is either attainable or needful. They should be at least named, however, in any scheme professing to enumerate the possible kinds of fallacies; and it is questionable whether they do not deserve, in modern times, a larger share of attention than that which may once have sufficed for them. "We live," says Mr De Morgan, "in an age in which formal logic has long been nearly banished from education—entirely, we may say, from the education of the habits. . . . Offences against the laws of syllogism (which are all laws of common sense) are as common as any species of fallacy; not that they are always offences in the speaker's or writer's mind, but that they frequently originate in his attempt to speak his mind. And the excuse is, that he meant differently from what he said; which is received because no one can throw the first stone at it; but which in the middle ages would have been regarded as a plea of guilty." Even for the applicabilities of the syllogistic tests to the argumentative section of our common affairs, notice is merited by the hint here involved, of the intimate relation between the fallacies purely logical, and those others (avowedly very frequent) which we speak of as semi-logical. Of the close hearing of the theory of the syllogism on the theory of scientific discovery, proof will be found by any one who glances at Mr Mill's treatise on Fallacies, in his great logical work.

(2.) All the Semi-Logical fallacies of inference are referable to one cause, Ambiguity of Terms. Two remarks are here necessary. In the first place, we must understand distinctly what the logicians mean, when they say that a syllogism is fallacious because one of its terms is ambiguous. Every term we can use, every single word, and, far more clearly, every combination of words, is ambiguous in this sense, that it is susceptible of more meanings than one; but when the use of an ambiguous term is said to be the source of a fallacy, what is signified is, that, each of the three terms of an argument occurring twice in it, the term in question is actually used in one of its meanings on its first appearance, and in another on its second. That every phrase or word is capable of being so used, is a fact which shows how extensive is the risk we run of committing the Fallacy of Ambiguity. In the ordinary and familiar uses of argumentation, where we employ words whose significations are fixed only by custom and tacit convention, our liability to the error is proportional to the closeness of relation between two meanings of any given word or phrase, plus the probability that both of the meanings will suggest themselves to us or to others in the course of a given argument. In philosophical and scientific discussions, there is no effectual protection against mistakes thus arising, unless by the precedent definition of every term that is to be used; a precaution which, notoriously, is not fully attainable anywhere except in the pure mathematics. Secondly, the books on logic are nearly unanimous in describing the ambiguity that causes fallacy, as occurring in the middle term only; the fallacy is called that of "ambiguous middle," even by writers who explicitly allow that this is not the only possible instance. It is true that the middle term is much oftener used in two meanings than is either of the other terms; chiefly because, not emerging in the conclusion of an argument, it is by much the least prominent of the three. But undoubtedly the fallacious double meaning is to be found sometimes in the major term or in the minor.

It is plain that, when the Fallacy of Ambiguity is committed, the argument has really more terms than three. It is only in appearance that a term used in two meanings is one term: it is really two terms; it is one term in the one of its meanings, and a different term in the other. It is equally plain that, in one or another of its forms, this is the most common, and also the most dangerous, of all instruments that effect either mistake or deception. It is, as was asserted a little ago, the most frequent ally of fallacies of the other kinds; which, when the case does not lay open a firm enough foundation for them to occupy alone, gain support by their union with a convenient ambiguity. But the fallacy is so tempting, through the manifold imperfections of language as the vehicle of thought, that, even without foreign aid, it is continually productive of error. It is the curse of all those sciences which have human nature as their object-matter, especially of those higher and more analytic ones which, in the incorrect phraseology of common use, are often slumped together by the name of metaphysics. Its effects are not less injurious, when the communication of belief is aimed at through that which we speak of as eloquence, whether oral or written. The loose and inconclusive declamation, both of sophistry and of imperfect knowledge, gains a hearing through its adoption of one name to denote two things substantially different; and, in applications less extensive, but not less serious, truth is obscured, or positive error substituted for it, by the eagerness of cultivated writers to attain what they regard as elegance of style, for which, in our day, one of the favourite prescriptions is a needless variation of phrase.

The shapings assumed by the Fallacy of Ambiguity must clearly be so diverse, as to baffle all attempts at classification, or even enumeration. The ambiguity which is caused by the construction of clauses (the ampliboly or ampliphily of the old writers) is probably less frequent than that (the homonymy of Aristotle) which is caused by the double meaning of a single word or term. The Homonymy, or ambiguity strictly so called, arises out of something in the term itself; and the sources of it might be shown to embrace all those relations of things which, when used in an opposite direction, give rise to tropes and figures of speech. Several varieties of ambiguity spring from the particular way in which the term is applied on the particular occasion. Of these, the most nearly akin to the homonymy (and rightly transferred by Whately from the class of material fallacies) are the "Fallacia a dicto simpliciter ad dictum secundum quid;" and the counter-fallacy, called also the "Fallacia accidentis." In each of these, a term is used absolutely in the one of its appearances, and with a qualification in the other. If, from assuming as to the term taken absolutely, we infer in regard to it as qualified, the fallacy is of the first kind; if we infer the other way, it belongs to the second. Like to this pair in several respects are the counter-fallacies of Composition and Division. In the fallacy to which the former of these names is strictly applicable, we assume that something is true of a common term taken distributively, or, in other words, that something is true of each of the individuals comprehended under the term; and we thence infer to the term taken collectively, that is, to the aggregate of those individuals. In the counter-fallacy the process is reversed. The principle of the two fallacies last described affords also the easiest means of exposing many fallacies, in which the form of the argument does not directly present the antithesis of collection and distribution, and which, accordingly, might be placed under other heads, and analysed by a different method. The heads thus named are very far indeed from presenting an exhaustive list even of the principal Fallacies of Ambiguity. It is the fact, indeed, that a vast proportion of the errors in reasoning by which we are perplexed or seduced, are referable, in the first instance, to that wide class which Mr Mill calls Fallacies of Confusion; the main reason of the fact lies in the frequency with which double meanings insinuate themselves into acts of ratiocination; and, when we are at a loss to determine the class to which an argument evidently fallacious may most properly be referred, and are consequently doubtful as to the best method of exposing it, a rigorous analysis will probably show that the difficulty is caused by some deeply lurking fallacy of ambiguity. (w.s.)