We thus see plainly that Peirastic and Eristic are not to be ranked as two distinct species of discourse, co-ordinate with Didactic and Dialectic; but that peirastic is in fact an epithet applicable generally to Dialectic, bringing to view one of its useful and appropriate functions; while eristic designates only a peculiar mode of conducting the process, the essential feature of which is that it is abusive or that it transgresses the rules and regulations. Still less ought Sophistic to be ranked as a distinct species; since it involves no intrinsic or intellectual differentia, but connotes only ethical and personal peculiarities ascribed to the Sophist, who is treated as an impostor practising dishonest tricks for the sake of pecuniary profit.10

While, however, we recognize as main logical distinctions only the two heads Didactic and Dialectic, we note another way that Aristotle has of bringing in what he calls Sophistic as a variety of the latter. Both in Didactic and Dialectic (he tells us) the speakers enunciate and prove their propositions by Syllogism; the didactic syllogism is derived from the principia belonging specially to one particular science, and proceeds from premisses that are true to conclusions that are true; while the dialectic syllogism starts from probable premisses (i.e., accredited by the ordinary public or by a few wise men), and marches in correct form to conclusions that are probable. Now, corresponding to each of these two, Aristotle recognizes farther a sort of degenerate counterpart. To the didactic syllogism there corresponds the pseudographic syllogism or the paralogism: which draws its premisses (as the didactic syllogism does) from the special matters of some given science,11 yet which nevertheless has only the appearance of truth without the reality; either because it is incorrect in syllogistic form, or because the matter of the premisses (the major, the minor, or both) is untrue. To the dialectic syllogism in like manner, there corresponds the eristic or sophistic syllogism: which is a good syllogism in appearance, but not in reality; either because it is incorrect in form, or because its premisses, in respect of their matter, appear to be probable without being really probable.12

One would suppose that the relation between the pseudo-didactic and the didactic syllogism, was the same as that between the pseudo-dialectic and the dialectic; so that, if the pseudo-dialectic deserved to be called sophistic or eristic, the pseudo-didactic would deserve these appellations also; especially, since the formal conditions of the syllogism are alike for both. This Aristotle does not admit, but draws instead a remarkable distinction. The Sophist (he says) is a dishonest man, making it his professional purpose to deceive; the pseudo-graphic man of science is honest always, though sometimes mistaken. So long as the pseudo-graphic syllogism keeps within the limits belonging to its own special science, it may be false, since the geometer may be deceived even in his own science geometry,13 but it cannot be sophistic or eristic; yet, whenever it transgresses those limits, even though it be true and though it solves the problem proposed, it deserves to be called by those two epithets. Thus, there were two distinct methods proposed for the quadrature of the circle — one by Hippokrates, on geometrical principles, the other by Bryson, upon principles extra-geometrical. Both demonstrations were false and unsuccessful; yet that of Hippokrates was not sophistic or eristic, because he kept within the sphere of geometry; while that of Bryson was so, because it travelled out of geometry. Nay more, this last would have been equally sophistic and eristic, and on the same ground, even if it had succeeded in solving the problem.14 If indeed the pseudo-graphic syllogism be invalid in form, it must be considered as sophistic, even though within the proper scientific limits as to matter; but, if it be correct in form and within these same limits, then, however untrue its premisses may be, it is to be regarded as not sophistic or eristic.15

Such is the test whereby Aristotle distinguishes the sophistication of the didactic process from the legitimate working of that process. Now this same test cannot be applied to Dialectic, which has no appropriate or exclusive specialty of matters, but deals with Omne Scibile, universally and indiscriminately. Aristotle therefore puts the analogy in another way. Both in Didactic and in Dialectic the Sophist is one who sins against the fundamental conditions of the task which he undertakes; these conditions being, that in Didactic he shall confine himself to the matters and premisses of a given science, — in Dialectic, to matters probable of whatever kind they may be. Transgression of these conditions constitutes unfair and dishonest manœuvre, whether of teacher or questioner; like breach of the regulations on the part of competitors, bent on victory at all price, in the Olympic games. Aristotle ranks this dishonesty as a species, under the name of Sophistic or Eristic, admitting of being analysed and defined;16 and his treatise on Sophistical Refutations is intended to describe and illustrate the Loci belonging to it, and contributing to its purpose.17

Fallacious dialectical refutation being thus referred altogether to dishonesty of purpose (either contentious or profit-seeking) and being assumed as unknown in fair dialectical debate, we have to see by what characteristic Aristotle discriminates fallacious premisses from fair and admissible premisses. Dialectic (he tells us) has for its appropriate matter probable premisses — beliefs accredited either by the multitude or by a wise few. But (he goes on to say) not everything which appears probable is really probable. Nothing that is really probable is a mere superficial fancy; wherever this last is the case, the probabilia are apparent only and not real; they have the character of falsehood stamped upon them, so as to be immediately manifest and obvious, even to persons of very narrow intelligence. It is such apparent probabilia as these, which make up the premisses of eristic or sophistic discourse, and upon which the sophistical or fallacious refutations turn.18

Aristotle thus draws a broad and marked line between Dialectic on the one hand, and Eristic or Sophistic on the other; and he treats the whole important doctrine of Logical Fallacies as coming under this latter department. The distinction that he draws between them is two-fold: first as to purpose, next as to subject-matter. On the part of the litigious or sophistical debater there is the illicit purpose of victory at all cost, or for profit; and probabilities merely apparent — such as any one may see not to be real probabilities — constitute the matter of his syllogisms.

Now, as to the distinction of purpose, we may put aside the idea of profit as having no essential connection with the question. It is quite possible to suppose the fair Dialectician, not less than the Sophist, as exhibiting his skill for pecuniary reward; while the eagerness for victory on both sides is absolutely indispensable even in well-conducted debate, in order that the appropriate stimulus and benefit of dialectical exercise may be realized. But, if the distinction of purpose and procedure, between the Dialectician and the Sophist, is thus undefined and unsatisfactory, still more unsatisfactory is the distinction of subject-matter. To discriminate between what is really probable (i.e., accredited either by the multitude or by a wise few), and what is only probable in appearance and not in reality — is a task of extreme difficulty. The explanation given by Aristotle himself19 — when he describes the apparently probable as that which has only superficial show, and which the most ordinary intelligence discerns at once to be false — includes only the more gross and obvious fallacies, but leaves out all the rest. Nothing can be more incorrect than the assumption, in regard to fallacies generally, that the appearance of probability is too faint to impose upon any ordinary man. If all fallacies could be supposed to come under this definition, the theory of Fallacies would undoubtedly be worthless (as Mr. Poste suggests that it is, in the Preface to his translation of the Sophistici Elenchi); and the most dishonest Sophist would at any rate be harmless. But, in fact, Aristotle himself departs from this definition even in the beginning of the Sophistici Elenchi; for he there treats the sophistic syllogism and refutation as having a semblance of validity plausible enough to impose upon many persons, and to be difficult of detection; like base metals having the exterior appearance of gold and silver, and like men got up for the purpose of looking finer and stronger than they really are.20 Here we have the eristic or sophistic syllogism presented as fallacious, yet as very likely to be mistaken for truth, by unprepared auditors, unless warning and precaution be applied; not (as it was set forth in the definition above cited) as bearing the plain and obvious stamp of falsehood, recognizable even by the vulgar. At the time when Aristotle constructed that definition, he probably had present to his mind such caricatures of dialectical questions as Plato (in the dialogue Euthydêmus) puts into the mouth of the Sophists Euthydêmus and Dionysodorus. And, since Aristotle chose to connect fallacious reasoning with dishonest purposes, and to announce it as employed exclusively by dishonest debaters, he seems to have found satisfaction in describing it as something which no honest man of ordinary understanding could accept as true: the Sophist being thus presented not merely as a knave but as a fool.

I think it a mistake on the part of Aristotle to treat the fallacies incidental to the human intellect as if they were mere traps laid by Sophists and litigants; and as if they would never show themselves, assuming dialectical debate to be conducted entirely with a view to its legitimate purposes of testing a thesis and following out argumentative consequences. It is true that, if there are infirmities incident to the human intellect, a dishonest disputant will be likely to take advantage of them. So far it may be well to note his presence. But the dishonest disputant does not originate these infirmities: he finds them already existing, and manifested undesignedly not merely in dialectical debate, but even in ordinary discourse. It is the business of those who theorize on the intellectual processes to specify and discriminate the Fallacies as liabilities to intellectual error among mankind in general, honest or dishonest, with a view to precaution against their occurrence, or correction if they do occur; not to present them as inventions of a class of professional cheats,21 or as tares sown by the enemy in a field where the natural growth would be nothing but pure wheat.

In point of fact the actual classification of Fallacies given by Aristotle is far sounder than his announcement would lead us to expect. Though he entitles them Sophistical Refutations, describing them as intentionally cultivated and exclusively practised by professional Sophists for gain, or by unprincipled litigants for victory, yet he recognises them as often very difficult of detection, and as an essential portion of the theory of Dialectic generally.22 The various general heads under which he distributes them are each characterized by intellectual or logical marks.

His first and most general observation is, that language is the usual medium and instrument through which fallacies are operated.23 Names and propositions are of necessity limited in number; but things named or nameable are innumerable; hence it happens inevitably that the same name or the same proposition must have several different meanings. Since we cannot talk of things except by means of their names, the equivocation inseparable from these names is a constant source of false conclusions.24

In dialectical procedure, the Sophist and the litigious debater aim at the accomplishment of five distinguishable ends:— (1) To refute, or obtain the false appearance of refuting, the thesis; (2) To catch, or appear to catch, the opponent in affirming something false or contradictory; (3) Or in affirming something paradoxical; (4) Or in uttering incorrect and ungrammatical speech; (5) Or in tautological repetition. The first of these five ends is what the Sophist most desires; where that cannot be had, then, as secondary purposes, the succeeding four, in the order in which they are enumerated.25

The syllogism whereby the Sophist appears to refute without really refuting, is either faulty in form, or untrue in matter, or irrelevant to the purpose. The Fallacies that he employs to bring about this deceitful appearance of refutation are various, and may be distributed first under two great divisions:—

I. Fallaciæ Dictionis.

II. Fallaciæ Extra Dictionem.

I. The first division — Fallaciæ Dictionis — includes all those cases wherein, under the same terms or propositions, more than one meaning is expressed. Six heads may be distinguished:—

1. Homonymy (Equivocation): where the double meaning resides in one single term — noun or verb.

2. Amphiboly: where the double meaning resides, not in a single word but, in a combination of words — proposition, phrase, or sentence.

3. Conjunction (hardly distinguishable from that immediately preceding — Amphiboly).

4. Disjunction: where what is affirmed conjunctively is not true disjunctively, or the reverse. (E.g., Five are two and three; but you cannot say, Five are even and odd. The greater is equal and something besides; but you cannot say, The greater is equal.)

5. Accentuation: where the same word differently accentuated has a different meaning.

6. Figura Dictionis: where two words, from being analogous in form, structure, or conjugation, are erroneously supposed to be analogous in meaning also.26

Such are the six heads of Fallaciæ Dictionis — Fallacies or Paralogisms arising from words as such, or something directly appertaining to them.

II. Under the second division — Fallacies or Paralogisms Extra Dictionem — there are seven heads:

1. Fallacia Accidentis.

2. Fallacia a dicto Secundum Quid ad dictum Simpliciter.

3. Ignoratio Elenchi.

4. Fallacia Consequentis

5. Petitio Principii.

6. Non Causa pro Causâ.

7. Fallacia Plurium Interrogationum.27

1. The first of these varieties, called Fallacia Accidentis, arises when a syllogism is made to conclude that, because a given predicate may be truly affirmed of a given subject, the same predicate may also be truly affirmed respecting all the accidents of that subject: as when Koriskus is denied to be a man, because he is not Sokrates, who is a man; or is denied to be Koriskus, because he is a man, while a man is not Koriskus.

In the title given to this general head of Fallacy,28 we must understand Accident, not in its special logical sense as opposed to Essence, but in a far larger sense, including both Genus when predicated separately from Differentia, and Differentia when predicated separately from Genus; including, in fact, every thing which is distinguishable from the subject in any way, and at the same time predicable of it — every thing except the Definition, which conjoins Genus and Differentia together, and is thus identical and convertible with the definitum.

2. The second general variety arises when a proposition is affirmed with qualification or limitation in the premisses, but is affirmed without qualification, simply and absolutely, in the conclusion. The Ethiopian is white in his teeth and black in his skin; therefore, he is both white and not white — both white and black. In this example the fallacy is obvious, and can hardly escape any one; but there are many other cases in which the distinction is not so conspicuous, and in which the respondent will hesitate whether he ought to grant or refuse a question simply and absolutely.29 One example given by Aristotle deserves notice on its own account: Non-Ens est opinabile, therefore Non-Ens est; or, again, Ens non est homo, therefore, Ens non est. This is one among Aristotle’s ways of bringing to view what modern logicians describe as the double function of the substantive verb — to serve as copula in predication, and to predicate existence.30 He regards the confusion between these two functions as an example of the Fallacy now before us — of passing a dicto Secundum Quid ad dictum Simpliciter.31

3. The third of these heads of Fallacy — Ignoratio Elenchi — is, when the speaker, professing to contradict the thesis, advances another proposition which contradicts it in appearance only but not in reality, because he does not know what are the true and sufficient conditions of a valid Elenchus. In order to be valid, it must be real, not merely verbal; it must be proved by good syllogistic premisses, without any Petitio Principii; and it must deny the same matter, in the same relations, and at the same time, as that which the thesis affirmed. Thus, it is no contradiction to affirm and deny doubleness of the same body; both affirmation and denial may be true, if you take the comparison against different numbers or different bodies, or at different times. Sometimes persons neglect some of these conditions, and fancy that they have contradicted the thesis, when they have not: this is Ignoratio Elenchi.32 (If the thesis be an affirmative universal, it is sufficient contradiction if you prove a negative particular against it.)

4. The fourth head includes what are called Fallaciæ Consequentis: when a man inverts the relation between predicate and subject in a categorical proposition affirmative and universal, thinking that it may be simply converted or that the subject may be truly affirmed of the predicate; or when, in an hypothetical proposition, he inverts the relation between antecedent and consequent, arguing that, because the consequent is true, the antecedent must for that reason be true also. Honey is of yellow colour; you see a yellow substance, and you infer for that reason that it must be honey. Thieves generally walk out by night; you find a man walking out by night, and you infer that he must be a thief. These are inferences from Signs, opinions founded on facts of sense, such as are usually employed in Rhetoric; often or usually true, but not necessarily or universally true, and therefore fallacious when used as premisses in a syllogism.33

5. The fifth head is that of Petitio Principii: a man sometimes assumes for his premiss what is identical with the conclusion to be proved, without being aware of the identity.34

6. The sixth head of Fallacy — Non Causa pro Causâ — is, when we mistake for a cause that which is not really a cause; or, to drop the misleading word cause, and to adopt the clearer terms in which this same fallacy is announced in the Analytica Priora35 — Non per Hoc — Non propter Hoc, it arises when we put forward, as an essential premiss of a given conclusion, something that is not really an essential premiss thereof. When you intend to refute a given thesis by showing, that, if admitted, it leads to impossible or absurd conclusions, you must enunciate that thesis itself among the premisses that lead to such absurdities.36 But, though enunciated in this place, it may often happen that the thesis may be an unnecessary adjunct — not among the premisses really pertinent and essential: and that the impossible conclusion may be sufficiently proved, even though the thesis were omitted. Still, since the thesis is declared along with the rest, it will appear falsely to be a part of the real proof. It will often appear so even to yourself the questioner; you not detecting the fallacy.37 Under such circumstances the respondent meets you by Non propter Hoc. He admits your conclusion to be impossible, and at the same time to be duly proved, but he shows you that it is proved by evidence independent of his thesis, and not by reason or means of his thesis. Accordingly you have advanced a syllogism good in itself, but not good for the purpose which you aimed at;38 viz., to refute the thesis by establishing that it led to impossible consequences. You will fail, even if the impossible consequence which you advance is a proposition conjoined with the thesis through a continuous series of intermediate propositions, each of them having one common term with the next. Much more will you fail, if your impossible consequence is quite foreign and unconnected with the thesis; as we sometimes find in Dialectic.