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CHAPTER XXIII: Of Some Minor Peculiarities of Doctrine in Sir William Hamilton’s View of Formal Logic - John Stuart Mill, The Collected Works of John Stuart Mill, Volume IX - An Examination of William Hamilton’s Philosophy 
The Collected Works of John Stuart Mill, Volume IX - An Examination of William Hamilton’s Philosophy and of The Principal Philosophical Questions Discussed in his Writings, ed. John M. Robson, Introduction by Alan Ryan (Toronto: University of Toronto Press, London: Routledge and Kegan Paul, 1979).
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Of Some Minor Peculiarities of Doctrine in Sir William Hamilton’s View of Formal Logic
the two theories examined in the preceding chapter are the only important novelties which Sir W. Hamilton has introduced into the Science or Art of Logic. But he has here and there departed from the common doctrine of logicians on subordinate points. Some of these deviations deserve notice from their connexion with some principal part of our author’s doctrine, others chiefly as throwing light on the character of his mind. The one to which I shall first advert is of the former class.
I. Almost all writers on the Syllogistic Logic have directed attention to the fact, that though we cannot, while observing the forms of Logic, draw a false conclusion from true premises, we may draw a true one from false premises: in other words, the falsity of the premises does not prove the falsity of the conclusion; nor does the truth of the conclusion prove the truth of the premises. The warning is needed; for it is by no means unusual to mistake a refutation of the reasons from which a doctrine has been deduced for a disproof of the doctrine itself; and there is no error of thought more common than the acceptance of premises because they lead to a conclusion already assented to as true. Not only is this caution useful, but it is relevant to Logic, even in the restricted point of view of Formal Logic. When it is affirmed that Formal Logic has nothing to do with Material Truth, all that ought to be meant, is that in Logic we are not to consider whether the conclusion supposed to be proved is true in fact. But we are to consider whether it is true conditionally, true if the premises are true: that question is the specific business of Formal Logic: if Formal Logic does not teach us that, there is nothing for it to teach. The theorem, that in a valid Syllogism the falsity of the premises does not prove the falsity of the conclusion, is as germane to Logic as that the truth of the premises proves the truth of the conclusion. We have therefore reason to be surprised at finding Sir W. Hamilton delivering himself as follows:
Logic does not warrant the truth of its premises, except in so far as these may be the formal conclusions of anterior reasonings; it only warrants (on the hypothesis that the premises are truly assumed) the truth of the inference. In this view the conclusion may, as a separate proposition, be true; but if this truth be not a necessary consequence from the premises, it is a false conclusion, that is, in fact, no conclusion at all. Now on this point there is a doctrine prevalent among logicians, which is not only erroneous, but if admitted, is subversive of the distinction of Logic as a purely formal science. The doctrine in question is in its result this,—that if the conclusion of a syllogism be true, the premises may be either true or false, but that if the conclusion be false, one or both of its premises must be false: in other words, that it is possible to infer true from false, but not false from true. As an example of this I have given the following syllogism:
The inference, in so far as expressed, is true; but I would remark, that the whole inference which the premises necessitate, and which the conclusion, therefore, virtually contains, is not true,—is false. For the premises of the preceding syllogism gave not only the conclusion, Aristotle is a European, but also the conclusion, Aristotle is not a Greek; for it not merely follows from the premises, that Aristotle is conceived under the universal notion of which the concept Roman forms a particular sphere, but likewise that he is conceived as excluded from all the other particular spheres which are contained under that universal notion. The consideration of the truth of the premise, Aristotle is a Roman, is, however, more properly to be regarded as extralogical; but if so, then the consideration of the conclusion, Aristotle is a European, on any other view than as a mere formal inference from certain hypothetical antecedents, is likewise extralogical. Logic is only concerned with the formal truth,—the technical validity,—of its syllogisms, and anything beyond the legitimacy of the consequence it draws from certain hypothetical antecedents, it does not profess to vindicate. Logical truth and falsehood are thus contained in the correctness and incorrectness of logical inference; and it was, therefore, with no impropriety that we made a true or correct, and a false or incorrect, syllogism convertible expressions.*
The statement that a true proposition may be correctly inferred from false premises, or in other words, that a true opinion may be supported by false reasons, is one of which we could hardly have expected to find the truth disputed, whatever might be said of the connexion of Logic with it. So unlooked-for a paradox required to be defended by the strongest arguments: who, then, would expect such shabby, not arguments, but hints of arguments, as the author presents us with? He stops short in the middle of the first, as if afraid that it would break down if relied upon, and hurries to the second, which is still more incapable of bearing weight. “The consideration of the conclusion, Aristotle is a European, on any other view than as a mere formal inference from certain hypothetical antecedents, is extralogical.” Nobody proposes to consider it as anything but a formal inference from certain hypothetical antecedents. The gist of the whole question is that it is such an inference, and consequently that a proposition really true, may be a formal inference from premises wholly or partially false: in other words, the falsity of the conclusion does not follow from the falsity of the premises. It is as much the business of the theory of “formal inference” to show what conclusions are not formally legitimate, as what are. It is not the business of Formal Logic to determine what is actually true, but it is, to tell what does or does not follow from what. In the first unfinished part of his argument, Sir W. Hamilton makes a faint attempt to show that the conclusion, Aristotle is a European, is not true. He admits it to be true as far as expressed, but says that it virtually contains something which is false, namely, that Aristotle is not a Greek. By what analysis can he find this in the proposition, Aristotle is a European? He does not pretend that it is in the proposition considered in itself, but only in the proposition as inferred from “Aristotle is a Roman.” But it is a strange doctrine that a proposition is true or false not according to what it asserts, but according to the mode in which the belief of it has been arrived at. It is a very irrational mode of speaking to say that a proposition, besides its obvious meaning, contains a meaning which the words do not convey, which in the mouths of other people it does not bear, but which is so essential a part of it as by its falsity to make the proposition false which otherwise would be true. Suppose that the register of a man’s birth having been destroyed, some one to whom the date is of importance, proves it by a false entry in the parish books: would that make the man not to have been born on the day he was born on? But let us concede this point, however unreasonable, and admit that the proposition Aristotle is a European, when inferred from the premise that he is a Roman, includes that premise as part of its own meaning. Does it therefore contain an implication that he is not a Greek? Suppose that I have never heard of Greeks; or that, having heard of them, I suppose a Greek to be a kind of Roman, or a Roman a kind of Greek. Will this ignorance or misapprehension on my part, prevent me from concluding, that if a Roman is a European and Aristotle a Roman, Aristotle must be a European; or will it make the inference illegitimate, or the conclusion false? One sentence in our quotation from Sir W. Hamilton is a singular illustration of the length he will go to support a favourite thesis. “The premises,” he says, “of the syllogism gave not only the conclusion, Aristotle is a European, but also the conclusion, Aristotle is not a Greek.” Let us try:
This is Formal Logic. This is the philosopher who is so rigidly bent upon excluding from Logic all consideration of what is true or false vi materiæ. What shadow of connexion is there, unless it be vi materiæ, between this conclusion, and those premises? Nothing can explain this aberration in a thinker of Sir W. Hamilton’s acuteness, except his dogged determination in no shape to recognise belief as an element of judgment, or truth as in any way concerned in Pure Logic.
Sir W. Hamilton has a salvo for all this, though it is one which would not occur to everybody. According to him there are two kinds of truth, or rather the word truth has two meanings, so that it is possible for a proposition to be true although it is false. There is Formal Truth, and Real Truth.* Real Truth is “the harmony between a thought and its matter.”[*] Formal Truth is of two kinds, Logical, and Mathematical. Logical Truth is “the harmony or agreement of our thoughts with themselves as thoughts, in other words the correspondence of thought with the universal laws of thinking.”[†] And Mathematical Truth is some other harmony of thought, in which truth of fact is equally dispensed with. In another place, he says that if the consequent is correctly “evolved out of” the antecedent, the conclusion out of the premises, this is “Logical or Formal or Subjective truth: and an inference may be subjectively or formally true, which is objectively or really false.”† To support his denial of the common doctrine, he has to alter the meaning of words, and make false in the new meaning what cannot be denied to be true in the old. But I object in toto to such an abuse of terms as affirming a false proposition to be true, because it is in such a relation to another false proposition, that if that false proposition had been true it would have been true likewise. There is no fitness in the word truth, to express this mere relation of consecution between false propositions. No qualification by adjectives, whether “logical,” or “formal,” or “subjective,” will make this assertion anything but a solecism in language, claiming to be the correction of a philosophical doctrine.
The whole theory of the difference between Formal and Real Truth is treated as it deserves, in a passage from one of Sir W. Hamilton’s favourite authorities, Esser, which he quotes, and, strange to say, quotes with approbation.
One party of philosophers, [says Esser,] defining truth in general, the absolute harmony of our thoughts and cognitions,—divide truth into a formal or logical, and into a material or metaphysical, according as that harmony is in consonance with the laws of formal thought, or over and above, with the laws of real knowledge. The criterion of formal truth they place in the principles of Contradiction and of Sufficient Reason, enouncing that what is non-contradictory and consequent is formally true. This criterion, which is positive and immediate of formal truth (inasmuch as what is non-contradictory and consequent can always be thought as possible), they style a negative and mediate criterion of material truth: as what is self-contradictory and logically inconsequent is in reality impossible; at the same time, what is not self-contradictory and not logically inconsequent, is not, however, to be regarded as having an actual existence. But here the foundation is treacherous: the notion of truth is false. When we speak of truth, we are not satisfied with knowing that a thought harmonizes with a certain system of thoughts and cognitions; but, over and above, we require to be assured that what we think is real, and is as we think it to be. Are we satisfied on this point, we then regard our thoughts as true; whereas if we are not satisfied of this, we deem them false, how well soever they may quadrate with any theory or system. It is not, therefore, in any absolute harmony of mere thought, that truth consists, but solely in the correspondence of our thoughts with their objects. The distinction of formal and material truth is thus not only unsound in itself, but opposed to the notion of truth universally held, and embodied in all languages. But if this distinction be inept, the title of Logic, as a positive standard of truth, must be denied; it can only be a negative criterion, being conversant with thoughts and not with things, with the possibility and not with the actuality of existence.*
After all the experience we have had of the facility with which Sir W. Hamilton forgets in one part of his speculations what he has thought in another, it remains scarcely credible that he endorses, in his third volume, this emphatic protest against the distinction which he draws, and the opinion which he maintains, in his second and fourth. “Two opposite doctrines,” he says, “have sprung up, which, on opposite sides, have overlooked the true relations of Logic;”† and one of these is the doctrine (the “inaccuracy” our author styles it)[*] which Esser, in this passage, protests against. And he thereupon quotes Esser’s condemnation[†] of his (Sir W. Hamilton’s) own doctrine. Truly, if arguments ad hominem were sufficient, a controversialist who undertakes to refute Sir W. Hamilton would have an easy task.
II. I have already noticed one unacknowledged departure by our author from the usage of Logicians as regards the sense of the word Disjunctive; confining Disjunctive judgments to those in which all the alternative propositions have the same subject: A is either B, or C, or D. This limitation excludes two other forms of the assertion of an alternative: that in which the propositions have different subjects but the same predicate, “Either A, or B, or C, is D;” and that in which they have different subjects and different predicates, “Either A is B, or C is D.” The former is exemplified in such judgments as these, Either Brown or Smith did this act; Either John or Thomas is dead. The latter in such as these: Either the witness has told a falsehood, or the prisoner has committed a murder; Either Macbeth has killed all Macduff’s children, or Macduff has children who were not there present.[*] While arbitrarily excluding both these kinds of assertion from the class and denomination in which they had always been placed, our author does not assign to them any other; so that the effect is not a mere innovation in language, but a hiatus in his logical system; these two kinds of judgment having no place, name, or recognition in it. I have now to point out a second deviation from the received doctrine of logicians in connexion with the same subject. In respect to the class of judgments to which he restricts the name of Disjunctive, those in which two or more predicates are disjunctively affirmed of the same subject, he takes for granted through the whole of his exposition,* that when we say, A is either B or C, we imply that it cannot be both: that we may as legitimately argue, A is either B or C, but it is B, therefore it is not C, as we may argue, A is either B or C, but it is not B, therefore it is C. This is what enables him to affirm, as he does, that the principle of Disjunctive Judgments is the Law of Excluded Middle. The predicates are supposed to be either explicitly or implicitly contradictory, so that one or other of them must be true of the subject, but both of them cannot. I conceive this to be both an incompleteness in his theory, and a positive error in fact. An incompleteness, because we may judge, and legitimately judge, that a thing is either this or that, though aware that it may possibly be both. Sir W. Hamilton is so severe on the ordinary Logic for omitting, as he thinks, some valid forms of thought, that it was peculiarly incumbent on him not to commit a similar oversight in his own exposition of the science. But Sir W. Hamilton does not merely leave unrecognised those disjunctive judgments in which the alternative predicates are mutually compatible; he assumes that the disjunctive form of assertion denies their compatibility, which it assuredly does not. If we assert that a man who has acted in some particular way, must be either a knave or a fool, we by no means assert, or intend to assert, that he cannot be both. Very important consequences may sometimes be drawn from our knowledge that one or other of two perfectly compatible suppositions must be true. Suppose such an argument as this. To make an entirely unselfish use of despotic power a man must be either a saint or a philosopher; but saints and philosophers are rare; therefore those are rare, who make an entirely unselfish use of despotic power. The conclusion follows from the premises, and is of great practical importance. But does the disjunctive premise necessarily imply, or must it be construed as supposing, that the same person cannot be both a saint and a philosopher? Such a construction would be ridiculous.†
There is a great quantity of intricate and obscure speculation, in our author’s Lectures and their Appendices, relating to Disjunctive and Hypothetical Propositions. But, much as he had thought on the subject, the simple idea never seems to have occurred to him a(though he might have found it in Archbishop Whately’s Logic)a , that every Disjunctive judgment is compounded of two or more Hypothetical ones. “Either A is B, or C is D,” means, If A is not B, C is D; and if C is not D, A is B.[*] This is obvious enough to most people; but if Sir W. Hamilton had thought of it, he probably would have denied it: its admission would not have been in keeping with the disposition he shows in so many places, to consider as one judgment all that it is possible to assert in one formula. Again, though he takes much pains to determine what is the real import of a Hypothetical Judgment, the thought never occurs to him that it is a judgment concerning judgments. If A is B, C is D, means, The judgment C is D follows as a consequence from the judgment A is B. Not seeing this, Sir W. Hamilton tacitly adopts the assertion of Krug, that the conversion of a hypothetical syllogism into a categorical “is not always possible.”*
III. The next of Sir W. Hamilton’s minor innovations in Logic has reference to the Sorites. It is scarcely necessary to say, that a Sorites is an argument in the form, A is B, B is C, C is D, D is E, therefore A is E: an abridged expression for a series of Syllogisms, but not requiring to be decomposed into them in order to make its conclusiveness visible. Sir W. Hamilton accuses all writers on Logic of having overlooked the possibility of a Sorites in the second or third Figure.† By this he does not mean, one in which the ultimate syllogism, which sums up the argument, is in the second or third figure, for this all logicians have admitted. For example, to the Sorites given above, there might be added the proposition, No F is E; in which case, the ultimate syllogism would be, A is E, but no F is E, therefore A is not an F: a syllogism in the second figure. Or there might be added, at the opposite end of the series, A is G; when the ultimate syllogism would be in the third figure; A is E, but A is G, therefore some G is an E. These are real Sorites, real chain arguments, and they conclude in the second and third figures: we may call them, if we please, Sorites in the second and in the third figure, the truth being that they are Sorites in which one of the steps is in the second or third figure, all the others being in the first. And every one who understands the laws of the second and third figures (or even the general laws of the Syllogism) can see that no more than one step in either of them is admissible in a Sorites, and that it must either be the first or the last. About this, however, Logicians have always been agreed. These are not the kinds of Sorites which Sir W. Hamilton contends for. By a Sorites in the second or third figure, he means one in which all the steps are in the second, or all in the third, figure (a thing impossible in a real Sorites) and in which, accordingly, instead of a succession of middle terms establishing a connexion between the two extremes, there is but one middle term altogether. His paradigm in the second figure would be, No B is A, No C is A, No D is A, No E is A, All F is A, therefore no B, or C, or D, or E, is F. In the third figure, it would be, A is B, A is C, A is D, A is E, A is F, therefore some B, and C, and D, and E, are F. One would have thought that anybody who had the smallest notion of the meaning of a Sorites, must have seen that either of these is not a Sorites at all. It is not a chain argument. It does not ascend to a conclusion by a series of steps, each introducing a new premise. It does not deduce one conclusion from a succession of premises, all necessary to its establishment. It draws as many different conclusions as there are syllogisms, each conclusion depending only on the two premises of one syllogism. That no B is F, follows from No B is A, and All F is A; not from those premises combined with No C is A, No D is A, No E is A. That some B is F, follows from A is B and A is F; and would be proved, though all the other premises of the pretended Sorites were rejected. If Sir W. Hamilton had found in any other writer such a misuse of logical language as he is here guilty of, he would have roundly accused him of total ignorance of logical writers. Since it cannot be imputed to any such cause in himself, I can only ascribe it to the passion which appears to have seized him, in the later years of his life, for finding more and more new discoveries to be made in Syllogistic Logic. If he had transported his ardour for originality into the other departments of the science, in which there was so great an unexhausted field for discovery, he might have enlarged the bounds of philosophy to a much greater extent, than I am afraid he will now be found to have done.
IV. I next turn to a singular misapplication of logical language, in which Sir W. Hamilton departs from all good authorities, and misses one of the most important distinctions drawn by the Aristotelian logic. I refer to his use of the word Contrary. He confounds contrariety with simple incompatibility. “Opposition of Notions,” he says,
is twofold: 1°. Immediate or Contradictory Opposition, called likewise Repugnance (τὸ ἀντιφατικῶς ἀντικεῖσϑαι, ἀντίφασις, oppositio immediata sive contradictoria, repugnantia); and 2°. Mediate or Contrary Opposition (τὸ ἐναντίως ἀντικεῖσϑαι, ἐναντιότης, oppositio media vel contraria). The former emerges, when one concept abolishes (tollit) directly or by simple negation, what another establishes, ponit; the latter, when one concept does this not directly or by simple negation, but through the affirmation of something else.*
The exemplification and illustration of this is not of our author’s devising, but is a citation from Krug, who had preceded him in the error.
To speak now of the distinction of Contradictory and Contrary Opposition, or of Contradiction and Contrariety; of these the former, Contradiction, is exemplified in the opposites,—yellow, not yellow; walking, not walking. Here each notion is directly, immediately, and absolutely, repugnant to the other,—they are reciprocal negatives. This opposition is, therefore, properly called that of Contradiction or of Repugnance; and the opposing notions themselves are contradictory or repugnant notions, in a single word, contradictories. The latter, or Contrary Opposition, is exemplified in the opposites, yellow, blue, red, &c., walking, standing, lying, &c.†
It can hardly have been imagined by Krug or Sir W. Hamilton, that this is the meaning of Contrariety in common discourse, or that any one ever speaks of yellow or blue as the contrary of red, or even as the opposite of it. The very phrase, “the contrary,” testifies that a thing cannot have more contraries than one. Black is regarded as the contrary of white, but no other contrariety is recognised among colours at all. Sir W. Hamilton, versed as he was in the literature of logic, can hardly have fancied that the world of logicians, any more than the common world, was on his side. In the language of logicians, as in that of life, a thing has only one contrary—its extreme opposite; the thing farthest removed from it in the same class. Black is the contrary of white, but neither of them is the contrary of red. Infinitely great is the contrary of infinitely small, but is not the contrary of finite. It is the more strange that Krug and Sir W. Hamilton should have misunderstood or rejected this, as the definition they ignore is the foundation of the distinction between Contradictory and Contrary Propositions, in the famous Parallelogram of Opposition. The contrary proposition to All A is B, is No A is B, its extreme opposite; the assertion most widely differing from it that can be made; denying, not it merely, but bevery part of itb . Its contradictory is merely, Some A is not B. Sir W. Hamilton could not have imagined the distinction between these negative propositions to be, that the one denies by simple negation, the other through the affirmation of something else.
That the teachers of the Syllogistic Logic have taken this view, and not Sir W. Hamilton’s, of the meaning of Contrariety, might be shown by any number of quotations. I have only looked up the authorities nearest at hand. I begin with Aristotle: Τὰ γὰρ πλεῖστον ἀλλήλων διεστηκότα τῶν ἐν τῷ αὐτῷ γένει, ἐναντία ὁρίζονται.*
Aristotle again: Τὰ γὰρ ἐναντία τῶν πλεῖστον διαφερόντων περὶ τὸ αὐτό.†
Aristotle ἐν τῷ δεκάτῳ τῆς θεολογικῆς πραγματείας, as cited by Ammonius Hermiæ: Ἐπεὶ δὲ διαφέρειν ἐνδέχεται ἀλλήλων τὰ διαφέροντα πλεῖον καὶ ἔλαττον, ἔστι τις, καὶ μεγίστη διαφορά, καὶ ταύτην λέγω ἐναντίωσιν.[*]
Ammonius himself thereon: Ἡ τῶν ἐναντίων διαφορὰ μεγίστη τῶν ἄλλων, καὶ οὐδὲν ἔχουσα ἐξωτέρω αὐτὴς δυνάμενον πεσεῖν.‡
My next extract shall be from a well-known treatise, which Sir W. Hamilton particularly recommended to his pupils: Burgersdyk’s Institutiones Logicæ.
Oppositorum species sunt quinque: Disparata, contraria, relative opposita, privative opposita, et contradictoria.
Disparata sunt, quorum unum pluribus opponitur, eodem modo. Sic homo et equus, album et cæruleum, sunt disparata: quia homo non equo solum, sed etiam cani, leoni, cæterisque bestiarum speciebus, et album, non solum cæruleo, sed etiam rubro, viridi, cæterisque coloribus mediis, opponitur eodem modo, hoc est, eodem oppositorum genere. . . .
Contraria sunt duo absolute, quæ sub eodem genere plurimum distant.§
This passage informs us, not only that what Sir W. Hamilton terms Contraries were not so called by the Aristotelian logicians, but also what they were called. They were called Disparates: a term employed by Sir W. Hamilton, but in a totally different meaning.¶
The next is from one of the ablest, and, though in a comparatively small compass, one of the completest in essentials, of all the expositions I have seen of Logic from the purely Aristotelian point of view: Manuductio ad Logicam, by the Père Du Trieu, of Douai.
Contraria sunt, quæ posita sub eodem genere maxime a se invicem distant, eidem subjecto susceptivo vicissim insunt, a quo se mutuo expellunt, nisi alterum insit a natura; ut, album, et nigrum.
In hac definitione continentur quatuor conditiones, sive leges contrariorum.
Prima, ut sint sub eodem genere. . . .
Secunda conditio contrariorum est ut sub illo eodem genere maxime distent, id est precise repugnent. . . . Hinc excluduntur disparata.*
The next is from Saunderson’s Logicæ Artis Compendium, one of the best-known elementary treatises on Logic by British authors.
Oppositio Contraria est inter terminos contrarios. Sunt autem ea contraria quæ posita sub eodem genere maxime inter se distant, et vim habent expellendi se vicissim ex eodem subjecto susceptibili.†
Contraria sunt Opposita quorum unum alteri sic opponitur ut nulli alteri aut æque aut magis opponatur. Sic Albedo Nigredini, Homini Brutum, Rationale Irrationali contrarium est. Nam nihil est quod æque Albedini opponitur atque Nigredo, et sic in reliquis.
On the other hand,
Disparata sunt Opposita quorum unum uni sic opponitur, ut alteri vel æque vel magis opponatur. Sic Liberalitas et Avaritia disparata sunt. Nam Avaritia magis opponitur Prodigalitati quam Liberalitati. Sic Albedo et Rubedo disparata sunt, quia Albedo æque opponitur Viriditati atque Rubedini, et magis Nigredini quam ambobus. Nam plus inter se semper distant extrema, quam vel media inter se, vel medium ab alterutro extremo.‡
Contraria a Dialecticis ita definiri solent: Sunt Opposita quæ sub eodem genere posita maxime a se invicem distant, et eodem subjecto susceptibili vicissim insunt, a quo se mutuo expellunt, nisi alterum insit a natura. . . . Sed quoniam hæc definitio (quamvis sit præcipue in Dialecticorum scholis authoritans) laborat et tædio, et summa difficultate, placet ex Aristotele faciliorem adducere, et breviorem: Contraria sunt quæ sub eodem genere posita, maxime distant.§
Contraria sunt quæ sub eodem genere posita, maxime a se invicem distant, et eidem susceptibili vicissim insunt, a quo se mutuo expellunt, nisi alterum eorum insit a natura. Ad Contraria igitur tria requiruntur: primo ut sint sub eodem genere, scilicet Qualitatis: nam solarum qualitatum est contrarietas; secundo, ut maxime a se invicem distent in natural positiva, id est, ut ambo extrema sint positiva.¶
Contraria definiri solent, quæ sub eodem genere maxime distant. Ut calidum et frigidum, album et nigrum: quæ contrariæ qualitatis dici solent.*
Even Aldrich, right for once, may be added to the list of Oxford authorities.
Contraria sub eodem genere maxime distant. Non maxime distant omnium; magis enim distant quæ nec idem genus summum habent, magis Contradictoria: sed maxime eorum quæ in genere conveniunt.†
Keckermann does not employ this, but another definition of Contraries; not, however, Sir W. Hamilton’s: and all his examples of Contraries are taken from Extreme Opposites.‡
Contraria sunt, quæ sub eodem genere maxime distant, eidemque subjecto susceptibili a quo se mutuo expellunt, vicissim insunt, nisi alterum insit a natura.§
Oppositio contraria est inter duo extrema positiva, quæ sub eodem genere posita maxime distant, et ab eodem subjecto sese expellunt.¶
Grammatica Rationis, sive Institutiones Logicæ:
Contraria adversa sunt accidentia, posita sub eodem genere, quæ maxime distant, et se mutuo pellunt ab eodem subjecto in quo vicissim insunt.∥
Familiar as Sir W. Hamilton was with the whole series of writers on Logic, he cannot have overlooked, and can hardly have forgotten, such passages as these. I have not had the fortune to meet with a single passage, from a single Aristotelian writer, cwhichc can be cited in his support. I presume, therefore, that he intentionally made (or adopted from Krug) a change in the meaning of a scientific term, the inverse of that which it is the proper office and common tendency of science to make. Instead of giving a more determinate signification to a name vaguely used, by binding it down to express a precise specific distinction, he laid hold of a name which already denoted a definite species, and applied it to the entire genus, which stood in no need of a name; leaving the particular species unnamed. But if he knowingly took this very unscientific liberty with a scientific term, diverting it from both its scientific and its popular meaning,—leaving the scientific vocabulary, never too rich, with one expression the fewer, and an important scientific distinction without a name,—he at least should not have done so without informing the reader. He should not have led the unsuspecting learner to believe that this was the received use of the term. Remark, too, that he embezzles not only the English word, but its Greek and Latin equivalents, exactly as if he agreed with the writers of the Greek and Latin treatises, and was only explaining their meaning.
V. One of the charges brought by Sir W. Hamilton against the common mode of stating the doctrine of the Syllogism, is that it does not obviate the objection often made to the syllogism of being a petitio principii, grounded on the admitted truth, that it can assert nothing in the conclusion which has not already been asserted in the premises. This objection, our author says, “stands hitherto unrefuted, if not unrefutable.”* But he entertains the odd idea, that it can be got rid of by merely writing the propositions in a different order, putting the conclusion first. One might almost imagine that a little irony had been intended here. Putting the conclusion first, certainly makes it impossible any longer to say that the syllogism asserts in the conclusion what has already been asserted in the premises; and if any one is of opinion that the logical relation between premises and a conclusion depends on the order in which they are pronounced, such an objector, I must allow, is from this time silenced. But our author can have meditated very little on the meaning of the objection of petitio principii against the Syllogism, when he thought that such a device as this would remove it. The difficulty, which that objection expresses, lies in a region far below the depth to which such logic reaches; and he was quite right in regarding the objection as unrefuted. Nor is its refutation, I conceive, possible, on any theory but that which considers the Syllogism not as a process of Inference, but as the mere interpretation of the record of a previous process; the major premise as simply a formula for making particular inferences; and the conclusions of ratiocination as not inferences from the formula, but inferences drawn according to the formula. This theory, and the grounds of it, having been very fully stated in another work, need not be further noticed here.[*]
[* ]Lectures, Vol. III, pp. 450-1.
[* ]Ibid., Vol. IV, pp. 64-8.
[[*] ]Ibid., p. 66.
[[†] ]Ibid., p. 65.
[† ]Ibid., Vol. II, p. 343.
[* ]Ibid., Vol. III, pp. 106-7. [Cf. Esser, Logik, pp. 65-6.]
[† ]Ibid., p. 106.
[[*] ]Ibid., p. 107.
[[†] ]I.e., in the passage quoted above.
[[*] ]See William Shakespeare, Macbeth, IV, iii, 211-19.
[* ]Lectures, Vol. III, pp. 326ff.
[† ]Mr. Mansel does not fall into this mistake (Prolegomena Logica, p. 221).
[[*] ]See Whately, Elements of Logic, pp. 107-9, 112-13.
[* ]Lectures, Vol. III, p. 342. [See Krug, Logik, p. 258.]
[† ]Ibid., Vol. IV, App. ix, p. 395.
[* ]Lectures, Vol. III, pp. 213-14. [See Aristotle, On Interpretation, in The Categories, On Interpretation, Prior Analytics, pp. 124-8 (17b), and Metaphysics, pp. 24-8 (1055a-1056b).]
[† ]Lectures, Vol. III, pp. 214-15. [See Krug, Logik, pp. 118-20.]
[b-b]651, 652 a great deal more
[* ]Categoriæ, Cap. vi [6a17-18; in The Categories, On Interpretation, Prior Analytics, p. 44].
[† ]Περὶ Ἑρμηνείας, Cap. xiv [23b23-4; On Interpretation, p. 174].
[[*] ]Metaphysics, Vol. II, p. 20 (X, iii, 1055a4-6).
[‡ ][Ammonius Hermiæ,] Ammonii Hermiæ in Aristotelis de Interpretatione Librum Commentarius, ed. Aldi [i.e., Venice: Aldus, 1546], pp. 175-6.
[§ ][Franco Burgersdijck, Institutionum logicarum libri duo (Cambridge: Field, 1660), pp. 94-5,] Lib. I, Cap. 22; Theorema i.
[¶ ]Lectures, Vol. III, p. 224.
[* ][(London: printed McMillan, 1826), Tractatus Primus,] Pars Tertia, Cap. iii, Art. 1 [p. 74].
[† ][Robert Sanderson, Logicæ Artis Compendium, 2nd ed. (Oxford: Lichfield and Short, 1618), p. 52,] Pars Prima, Cap. xv [§4].
[‡ ][Richard Crakanthorp,] Logicæ [(London: Teage, 1622), Lib. II,] Cap. xx [p. 206].
[§ ][Edward Brerewood,] Tractatus Quidam Logici de Prædicabilibus et Prædicamentis. [Oxford: Turner, 1628.] Tractatus Decimus, “de Post-Prædicamentis,” §§8 and 9. [Pp. 404-5. (The concluding sentence, which appears in modified form in all the other Latin texts quoted, is a translation of the passage of Aristotle’s Categories cited above [VI, 6a17-18]).]
[¶ ]Aditus ad Logicam [7th ed.] (Oxford [: Hall], 1656), Lib. I, Cap. xiv [p. 56].
[* ][John Wallis,] Institutio Logicæ [3rd ed. (Oxford: West, Crosley, Clements, and Peisley, 1702), p. 63], Lib. I, Cap. xvi.
[† ][Henry Aldrich,] Artis Logicæ Compendium [Oxford: Sheldonian Theatre, 1704], “Quæstionum Logicarum Determinatio,” quæst. 19 [p. 118].
[‡ ][Bartholomæus Keckermannus,] Systema Logicæ [(Geneva: de la Rouière, 1611); see pp. 278ff. (Lib. I, Sectio Posterior, Cap. vi).]
[§ ]Enchiridion Logicum [ex Aristotele, 3rd ed.], (Leipzig [: Cober], 1618), Lib. I, Cap. xxiii [p. 186].
[¶ ][Jean Baptiste Du Hamel,] Philosophia vetus et nova ad usum scholæ accommodata, 5th ed. (Amsterdam [: Gallet], 1700), [Vol. I,] pp. 197-8.
[∥ ][John Fell, Grammatica Rationis,] (Oxford [: Sheldonian Theatre], 1673) [p. 111].
[c-c]651, 652 who
[* ]Lectures, Vol. IV, App. x, p. 401, and Appendix [II(A)] to Discussions, p. 652n.
[[*] ]See System of Logic, Bk. II, Chap. iii. §4, in Collected Works, Vol. VII, p. 193.