Chapter IX: Topica (5)

The canon being, That what is _posterius_ must be defined by its _prius_,--the definer may sin against this in defining the _prius_ by its _posterius_; _e.g._, if he defines the stationary and the determinate by means of the moveable and the variable.[281] Also, when his definition is neither _prius_, nor _posterius_, but of equal position with the definiend, he is at fault. This may happen (1) when he defines by an Opposite (for, according to some, the science of Opposites is one and the same, and it is impossible that either one of a pair can be absolutely more knowable than the other; though it is true that no relative can be understood or explained without the knowledge of its correlative, _e.g._, double and half); or (2) when he includes the definiend itself in his definition, either under its proper name or any other name;[282] or (3) when he defines by means of a contra-specific to the definiend--by something of equal specific rank or position, which is therefore _simul naturâ_ therewith (_e.g._, Odd is that which is greater than even by unity); or (4) when he defines by something specifically subordinate (_e.g._, An even number is that which may be bisected, where bisected means divisible by two, itself one among the even numbers[283]).

[Footnote 281: Ibid. a. 20: [Greek: pro/teron ga\r to\ me/non kai\ to\ ô(risme/non tou= a)ori/stou kai\ e)n kinê/sei o)/ntos.]]

[Footnote 282: Topic. VI. iv. p. 142, a. 22-b. 6.]

[Footnote 283: Ibid. b. 7-19: [Greek: pa/lin, ei) tô=| a)ntidiê|rême/nô| to\ a)ntidiê|rême/non ô(/ristai--o(moi/ôs de\ kai\ ei) dia\ tô=n u(poka/tô to\ e)pa/nô ô(/ristai.]]

2. The second _locus_ (after that bearing on the _Prius et Notius_) of argument for **impugning a definition is, where it does not enunciate the genus in which the definiend is really included. The mention of the genus, as enunciating the fundamental essence of the definiend, ought to stand first in the definition. If your opponent defines body--that which has three dimensions, or man--that which knows how to count, you attack him by asking, What is it that has three dimensions? What is it that knows how to count? No genus has been assigned.[284]

[Footnote 284: Ibid. v. p. 142, b. 22-29.]

3. A third _locus_ is, where the definiend is a complex whole having reference to several distinct facts or phenomena, while the definition indicates only one of them. Thus, if grammar be defined--the knowing how to write from dictation, you will object that it is just as much--the knowing how to read. The definition is incomplete unless it includes both.[285]

[Footnote 285: Ibid. b. 30.]

4. A fourth _locus_ is, where the definiend admits both of a better and a worse construction, and where the definition enunciates only the worse. You may impugn it, on the ground that every cognition and every power must be understood as tending to its best results.[286]

[Footnote 286: Ibid. p. 143, a. 9.]

6. A fifth _locus_ is, where the definiend is enunciated as ranking, not in the lowest and nearest species to which it belongs but, in some higher and more distinct genus. Here the real essence will not be declared, and the definition will thus be incomplete; unless indeed it includes, along with the highest genus, the superadded mention of all the differentiæ descending down to the lowest species. It will then be complete, because it will include, in circumlocutory phrase, all that would be declared by enunciating the specific name.[287]

[Footnote 287: Ibid. a. 15-28.]

6. Assuming the genus to be truly declared in the definition you will examine whether the differentiæ enunciated are differentiæ at all? whether they really belong to the definiend? what is it which they serve to contrast with and exclude,--since, if there be nothing such, they cannot be truly differentiæ? whether the differential term and its counter-differential apply to and cover the whole genus? whether, granting the differentia to be real, it be such, when taken along with the genus, as to constitute a true species, and whether its counter-differentia be such also? This is a _locus_ furnishing many possibilities of impugning the definition.[288]

[Footnote 288: Topic. VI. vi. p. 143, a. 29-b. 10.]

7. Perhaps the definition may enunciate a differentia which is merely negative; _e.g._, A line is length without breadth. If you are debating with a respondent who holds the (Platonic) doctrine of Ideas, and who considers each Idea or genus to be something numerically one, distinct from all its participants, you will find here a _locus_ for attacking them.[289] He asserts the existence of a Self-long or generical long, a Self-animal or generic animal, each numerically one. Now, upon this hypothesis, since of all long you may predicate either in the affirmative or the negative (_i.e._, either it is broad or it is not broad), so this alternative may be predicated of the Self-long or generical long; and thus the genus will coincide with, or fall under the definition of, one among its own species. Or, if this be denied, it will follow that the generic long must be both broad and not broad; which is a contradiction still more inadmissible. Accordingly, against one who holds the doctrine of Ideas, declaring the genus to be _unum numero_, the negative differentia will furnish grounds for attack; but not against any other respondent.[290] For there are various cases in which the negative must be employed as a part of the differentia: _e.g._, in privative terms, blind is one whose nature it is to see but who does not see. And, even when the differentia enunciated is affirmative, it may have for its condivident member only a negative term, _e.g._, length having-breadth has for its condivident member only the negative, length not-having-breadth.[291]

[Footnote 289: Ibid. b. 11-30.]

[Footnote 290: Ibid. b. 29: [Greek: ô(/ste _pro\s e)kei/nous mo/nous_ chrê/simos o( to/pos, o(/soi to\ ge/nos e(\n a)rithmô=| phasi\n ei)=nai. tou=to de\ poiou=sin oi( ta\s i)de/as tithe/menoi; au)to\ ga\r mê=kos kai\ au)to\ zô=|on ge/nos phasi\n ei)=nai.]]

[Footnote 291: Ibid. b. 33.]

8. Perhaps the definition may enunciate as a differentia what is really a subordinate species; or what is really the genus itself under another name; or what is not _Quale_, but _Quid_; or what belongs to the definiend as an accident only. Each of these is a _locus_ for arguments against the definition.[292]

[Footnote 292: Topica, VI. vi. p. 144, a. 5-27.]

9. Perhaps also, in the definition given, the differentia or the species may be found predicable of the entire genus; or the genus may be found predicable of the differentia itself, and not of objects under it; or the species (sometimes even one of its sub-species) may be found predicable of the differentia; or perhaps the differentia may not be a _prius_ as regards the species (which it ought to be, while it is a _posterius_ as regards the genus). Arguments against the definition may be drawn from any one of these loci.[293]

[Footnote 293: Ibid. a. 28-b. 11.]

10. Recollect that the same differentia cannot belong to two distinct genera neither of which comprehends the other, unless both are comprehended under some higher genus. Examine whether this is observed in the definition tendered to you.[294]

[Footnote 294: Ibid. b. 12.]

11. No genuine differentia can be derived either from the Category _Ubi_ or from the Category _Passio_; for neither of them furnishes characteristics essential to the subject. All _Passio_ when intensified to a certain degree destroys the essence of the subject and removes it from its own appropriate species; but the differentia is inseparable from its subject; accordingly, nothing by virtue of which the subject is called [Greek: a)lloi=on] can be a true differentia. If the definition sins against this rule, it will be open to question.[295]

[Footnote 295: Ibid. b. 31-p. 145, a. 12: [Greek: o(ra=n de\ kai\ ei) to\ e)/n tini diaphora\n a)pode/dôken ou)si/as; ou) dokei= ga\r diaphe/rein ou)si/a ousi/as tô=| _pou_ ei)=nai.--pa/lin ei) to\ pa/thos diaphora\n a)pode/dôken.--a(plô=s d' ei)pei=n, kath' o(/sa a)lloiou=tai to\ e)/chon, ou)de\n tou/tôn diaphora\ e)kei/nou;--a(plô=s ga\r ou)k a)lloiou/metha kata\ ta\s diaphora/s.]]

12. If the subject be relative, its true differentia ought to be relative also; thus, science or cognition is a _relatum_, and accordingly its three differentiæ--theoretical, practical, constructive--are all _relata_ also.[296] The definition must conform to this; and it must also, in cases where the relative subject has more than one correlate, declare that correlate which is the ordinary and natural one, not any other which is rare and realized only on occasion.[297] You must watch to see whether this condition is observed; and also whether the correlative enunciated in the definition is the one strictly proximate. Thus, if the definition given of prudence be, It is an excellence of man or an excellence of the soul, this will not be a good definition. It ought to be--an excellence of the rational department of the soul; for it is through and by reason of this department that both man and soul are denominated prudent.[298]

[Footnote 296: Ibid. a. 13.]

[Footnote 297: Ibid. a. 19-26.]

[Footnote 298: Topic. VI. vi. p. 145, a. 28-32. [Greek: prô/ton ga\r tou= logistikou= a)retê\ ê( phro/nêsis; kata\ ga\r tou=to kai\ ê( psuchê\ kai\ o( a)/nthrôpos phronei=n le/getai.]]

13. When the definiend is given as an affection or lasting condition of some subject, you must examine whether it really resides or can reside (as by nature it ought to do) in the subject to which it is referred in the definition. If it cannot, the **definition is untenable; and this mistake is sometimes made, the producing conditions of a phenomenon being confounded with the phenomenon itself, or _vice versâ_.[299] Thus, some persons have defined sleep--incapacity of sensible perception; doubt--equality of contrary reasonings; pain--breach of continuity violently made in parts of the organism which naturally grow together. Now sleep does not reside in perception, nor doubt in reasonings. Sleep is that which produces or occasions incapacity of sensible perception; doubt is a state of mind produced by equality of contrary reasonings.[300] This will be a _locus_ for arguing against the definition.

[Footnote 299: Ibid. b. 11: [Greek: to\ poiou/menon ei)s to\ poiêtiko\n ê)\ a)na/palin sumbai/nei tithe/nai toi=s ou(/tôs o(rizome/nois.]]

[Footnote 300: Ibid. a. 33-b. 20.]

14. Another _locus_ is, when the definiend has direct bearing and reference to something different from what is enunciated in the definition. Thus, if the respondent defines justice--a power tending to make equal distribution, you may remark hereupon, that the just man is he who is deliberately resolved to make equal distribution, not he who has the power to do so. If this definition were allowed, the justest man would be he who has the greatest power of so distributing.[301]

[Footnote 301: Ibid. vii. p. 145, b. 34-p. 146, a. 2.]

15. Again, the definition will be assailable, if the definiend admits graduation of More or Less, while that which is enunciated in the definition does not admit it, or _vice versâ_; also, if both of them admit graduation, but the variations of the two are not corresponding and concomitant. The defining phrase ought to be identical in signification with the term defined.[302] If both of them agree in reference to some common correlate, but one is to this in the relation of more while the other is in the relation of less, the definition is faulty.[303]

[Footnote 302: Ibid. p. 146, a. 3-12. [Greek: ei)/per dê\ tau)to/n e)sti to\ kata\ to\n lo/gon a)podothe\n tô=| pra/gmati.]

Here we have a principle of Concomitant Variations analogous to that which is so well unfolded, as one of the Four Inductive Methods, in Mr. J. S. Mill's 'System of Logic.' See Book III. ch. viii. sect. 6.]

[Footnote 303: Topic. VI. vii. p. 146, a. 6-20: [Greek: e)/dei d' a)mpho/tera ma=llon tô=| au)tô=| u(pa/rchein, ei)/per tau)ta\ ê)=n], &c.]

16. Again, you will be able to object, if the definition enunciate references to two distinct correlates, severally or alternately: _e.g._, The beautiful is that which affords pleasure either through the eye or through the ear; _Ens_ is that which is capable either of suffering or acting. You may show that, according to this definition, beautiful and not beautiful, or that _Ens_ and Non-Ens, will coincide and be predicable of the same subjects.[304]

[Footnote 304: Topic. VI. vii. p. 146, a. 21-32.

The definition here given of _Ens_ appears in the Sophistes of Plato, p. 247, E. The definition of the beautiful ([Greek: to\ kalo/n]) appears in the Hippias Major of Plato (p. 298, E, seq.), where it is criticized by Sokrates.]

17. When the definition is tendered, you ought to examine and define its own terms, which, of course, profess to enunciate genus and differentia of the definiend.[305] You will see whether the definitions of those defining terms are in any way inapplicable to the definiend.

[Footnote 305: Ibid. a. 33-35.]

18. If the definiend be a _Relatum_, the definition ought to enunciate its true correlate, or the true correlate of the genus to which it belongs. You must examine whether this is done, and whether the correlate enunciated be an ultimate end, as it ought to be (_i.e._ not merely a means towards something ulterior). If the correlate enunciated is a generation or a process, this will afford you an argument against the definition; for all generation or process is a means towards some ulterior end.[306]

[Footnote 306: Ibid. viii. p. 146, a. 36-b. 19. This is a subtle distinction. He says that desire must be defined (not desire of _the pleasurable_, but) desire of _pleasure_: we desire _the pleasurable_ for the sake of _pleasure_. He admits, however, that there are cases in which the argument will not hold: [Greek: schedo\n ga\r oi( plei=stoi ê(/desthai ma=llon bou/lontai ê)\ pepau=sthai ê(do/menoi; ô(/ste to\ e)nergei=n ma=llon te/los a)\n poioi=nto tou= e)nêrgêke/nai.]]

19. The definition ought not to omit any of the differentiæ of the definiend; if any be omitted, the real essence is not declared. Here then is a defect in the definition, which it is your business always to assail on its defective side.[307] Thus, if the definiend be a _relatum_ corresponding, not to some correlate absolutely but, to some correlate specially quantified or qualified, the definition ought to enunciate such quantification or qualification; if it does not, it is open to attack.

[Footnote 307: Ibid. b. 20: [Greek: pa/lin e)p' e)ni/ôn ei) mê\ diô/rike tou= po/sou, ê)\ poi/ou, ê)\ pou=, ê)\ kata\ ta\s a)/llas diaphora/s,--a)polei/pôn ga\r diaphora\n ê(ntinou=n ou) le/gei to\ ti ê)=n ei)=nai; _dei= d' a)ei\ pro\s to\ e)ndee\s e)picheirei=n_.]]

20. Suppose that the definiend is one of the appetites, relative to an _appetitum_ as correlate, a mode of the good or agreeable. You will take notice whether the definition given thereof enunciates the correlate as only an apparent mode of good: if it does not, you have a _locus_ for attacking it. But if it does, and if the definer be one who believes in the Platonic Ideas, you may attack him by showing that his definition will not square with that doctrine. For the definition as so given will not suit for the ideal or generic appetite--the Self-appetite; which correlates with the ideal or generic good--the Self-good. In this no distinction is admissible of real and apparent: a Self-apparent-good is an absurdity.[308]

[Footnote 308: Topic. VI. viii. p. 146, b. 36-p. 147, a. 11. [Greek: e)a\n de\ kai\ a)podô=| to\ ei)rême/non, e)pi\ ta\ ei)/dê a)kte/on to\n tithe/menon i)de/as ei)=nai; ou) ga/r e)stin i)de/a phainome/nou ou)deno/s, to\ d' ei)=dos pro\s to\ ei)=dos dokei= le/gesthai, oi(=on au)tê\ e)pithumi/a au)tou= ê(de/os kai\ au)tê\ bou/lêsis au)tou= a)gathou=. ou)k e)/stai ou)=n phainome/nou a)gathou= ou)de\ phainome/nou ê(de/os; a)/topon ga\r to\ ei)=nai au)to\ phaino/menon a)gatho\n ê)\ ê(du/.]

Compare Plato, Parmenides, pp. 133-134, where this doctrine that if the _relatum_ be an Idea (_sensu Platonico_), the _correlatum_ must also be an Idea, is enunciated and pushed to its consequences: [Greek: o(/sai tô=n i)deô=n pro\s a)llê/las ei)si\n ai(/ ei)sin, au)tai\ pro\s au(ta\s tê\n ou)si/an e)/chousin, a)ll' ou) pro\s ta\ par' ê(mi=n ei)/te o(moiô/mata ei)/te o(/pê| dê/ tis au)ta\ ti/thetai], &c.--[Greek: au)tê\ de\ despotei/a au)tê=s doulei/as e)sti\n o(/ e)sti], &c. (133, C-E.)]

21. Again, suppose that the definiend is a habit or disposition. You will examine how far the definition fits as applied to the individual person who has the habit; and how far it fits when taken in comparison with subjects contrary or congeneric. Every such definition, if good, implies in a certain way the definition of the contrary: he who defines cognition furnishes by implication the definition of ignorance.[309]

[Footnote 309: Topic. VI. ix. p. 147, a. 12-22.]

22. Or suppose the definiend to be a generic _relatum_, and the definition to enunciate its generic correlate. You must call to mind the specific terms comprehended under these two generic terms, and observe whether they fit on to each other respectively. If they do not, the definition is faulty.[310]

[Footnote 310: Ibid. a. 23-28.]

23. You will farther examine whether the Opposite of the definition will serve as definition to the Opposite of the definiend, as the definition of half is opposite to the definition of double; thus, if double is that which exceeds equality, half is that which is exceeded by equality. The like is true of Contraries: if the profitable be that which is productive of good, the hurtful will be that which is productive of evil or destructive of good. If, on trying the contraries, you find that this will not hold, the definition originally given will be found unsatisfactory.[311] In defining the privative contrary of any term, a man cannot avoid enunciating in the definition the term of which it is the privative: but he is not allowed to define the term itself by means of its privative. To define equality--that which is contrary to inequality, is improper. You will require him at once to define inequality; and his definition must be--the privation of equality. Substitute this definition of the term inequality, in place of that term itself, in the above-named definition of equality: and the last definition will then run as follows: Equality is that which is contrary to the privation of equality. Here the definiend is enunciated as a part of the definition of itself; a proof that the original definition--Equality is the contrary of inequality--is itself wrong.[312]

[Footnote 311: Topic. VI. ix. p. 147, a. 29-b. 4.

We most remember that Aristotle, classifying _Relata_ as one species under the genus _Opposita_, treats double and half as _Opposita_, _i.e._ _Relative-Opposita_. I have already said that I think this classification improper, and that _Opposita_ ought to be ranked as a species under the genus _Relata_.]

[Footnote 312: Topic. VI. ix. p. 147, b. 4-25.]

24. When the definiend is a Privative Term, the definition given ought to enunciate that which it is, and that of which it is the privation; also that subject in which it resides naturally and in the first instance. In defining ignorance, the definition must enunciate not privation only, but privation of knowledge; nor will this be sufficient unless it be added that the privation of knowledge is in the rational department of the soul ([Greek: e)n tô=| logistikô=|]). Privation of knowledge in the soul or in the man, will not suffice; because neither of these subjects is that in which the attribute resides in the first instance: the rational department of the soul must be named by itself, as being the primary subject of the attribute. If the definition be wanting in any of these conditions, you will have an argument for impeaching it.[313]

[Footnote 313: Ibid. b. 26-p. 148, a. 2.]

25. A term that is privative in form may sometimes be used in the sense of mere negation, not in that of privation. If this term be defined generally by privation, the definition will not include the merely negative sense, and will therefore be impeachable. The only general explanation attainable is that by pure negation, which is common both to the negative and the privative. Thus, if the respondent defines ignorance--privation of knowledge, such privation can be predicated only of subjects whose nature it is to have knowledge or who might be expected to have it: such privation cannot be predicated of infants, or of inanimate objects like stones. To include these, ignorance must be explained as the mere negation or non-existence of knowledge; the definition thereof by privation is inadequate.[314]

[Footnote 314: Ibid. p. 148, a. 3-9: [Greek: o(ra=n de\ kai\ ei) mê\ legome/nou kata\ ste/rêsin sterê/sei ô(ri/sato, oi(=on kai\ e)pi\ tê=s a)gnoi/as do/xeien a)\n u(pa/rchein ê( toiau/tê a(marti/a toi=s mê\ kat' a)po/phasin tê\n a)/gnoian le/gousin.]

Waitz says in note, p. 503:--"Sensus loci hic est. Peccant qui per privationem ignorantiam definientes non eam ignorantiam definire voluerunt quæ est [Greek: kat' a)po/phasin], sed eam quæ est [Greek: kata\ dia/thesin]." Compare Analyt. Poster. I. xvi. p. 79, b. 23.]

26. If you are debating with one who holds the Platonic doctrine of Ideas, you will note whether any definition that he may give fits not only the definiend itself but also the Idea of the definiend. Thus, Plato in defining animal introduces mortality as a part of his definition;[315] but mortality cannot be predicated of the Idea or generic animal--the Self-animal; therefore, you will have an argument against his definition. In like manner, if any active or passive attribute is brought into his definition, you will object that this cannot apply to the Ideas; which are avowedly impassive and unchangeable.[316]

[Footnote 315: Topic. VI. x. p. 148, a. 15: [Greek: oi(=on ô(s Pla/tôn o(ri/zetai to\ thnêto\n prosa/ptôn e)n toi=s tô=n zô/|ôn o(rismoi=s.]

This may perhaps allude to Plato's manner of speaking of [Greek: zô=|a] in Sophistes, p. 246, E., p. 265, C.; Timæus, p. 69, C.]

[Footnote 316: Topica, VI. x. p. 148, a. 14-22. [Greek: a)pathei=s ga\r kai\ a)ki/nêtoi dokou=sin ai( i)de/ai toi=s le/gousin i)de/as ei)=nai].]

27. Another _locus_ for counter-argument is, where the definiend is Equivocal or Analogous, while one and the same definition is made to apply to all its distinct meanings. Such a definition, pretending to fit all, will in reality fit none; nothing but an univocal term can come under one and the same definition. It is wrong to attempt to define an equivocal term.[317] When its equivocation is not obvious, the respondent will put it forward confidently as univocal; while you as assailant will expose the equivocation. Sometimes, indeed, a respondent may pretend that an univocal word is equivocal, or that an equivocal word is univocal, in the course of the debate. To obviate such misconception, you will do well to come to an agreement with him prior to the debate, or to determine by special antecedent reasonings what terms are univocal or equivocal; for at that early stage, when he does not foresee the consequence of your questions, he is more likely to concede what will facilitate your attack. In the absence of such preliminary agreement, if the respondent, when you have shown that his bad definition will not apply universally, resorts to the pretence that the definiend, though really univocal, is equivocal, you will press him with the true definition of the part not included under his definition, and you will show that this true definition suits also for the remaining parts of the definiend. You will thus confute him by showing that, upon his original hypothesis, it must follow that there are two distinct definitions for the same definiend--the bad one which he has given, and the true one which you have constrained him to admit.[318] Perhaps, however, the term which he has undertaken to define may be really equivocal, and therefore indefinable; nevertheless, when you have shown the insufficiency of his definition, he may refuse to admit that the term is equivocal, but will deny a portion of its real meaning. You will then remind him that, as to the meaning of names, we must recognize tradition and custom without presuming to disturb it; but that, when we combine these names in our own discourse, we must beware of those equivocations which mislead the multitude.[319]

[Footnote 317: Ibid. a. 23-37: [Greek: e)/ti ei) tô=n kath' o(mônumi/an legome/nôn e(/na lo/gon a(pa/ntôn koino\n a)pe/dôken.--a)ll' ou)de\n ê(=tton, ei) o(poterôsou=n pepoi/êken, ê(ma/rtêken.]

Aristotle here cites and censures the definition of life given by a philosopher named Dionysius; he remarks that life is an equivocal term, having one meaning in animals, another and a different one in plants. Dr. Whewell has remarked that even at the present day a good definition of life is matter of dispute, and still a desideratum with philosophers.

Mr. John S. Mill adverts, in more than one portion of his 'System of Logic' (Bk. IV. ch. iii. s. 5, p. 222, seq.; Bk. V. ch. v. s. 8, p. 371), to the mistake and confusion arising from attempts to define Equivocal Terms. "The inquiries of Plato into the definitions of some of the most general terms of moral speculation, are characterized by Bacon as a far nearer approach to a true inductive method than is elsewhere to be found among the ancients, and are, indeed, almost perfect examples of the preparatory process of comparison and abstraction; but, from being unaware of the law just mentioned, he often wasted the powers of this great logical instrument on inquiries in which it could realize no result, since the phenomena, whose common properties he so elaborately endeavoured to detect, had not really any common properties. Bacon himself fell into the same error in his speculations on the nature of heat, in which he evidently confounded, under the name hot, classes of phenomena which had no property in common."--"He occasionally proceeds like one who seeking for the cause of hardness, after examining that quality in iron, flint, and diamond, should expect to find that it is something that can be traced also in hard water, a hard knot, and a hard heart."]

[Footnote 318: Topic. VI. x. p. 148, a. 37, seq. [Greek: e)pei\ d' e)/nia lantha/nei tô=n o(mônu/môn, _e)rôtô=nti me\n ô(s sunônu/mois chrêste/on, au)tô=| d' a)pokrinome/nô| diairete/on_. e)pei\ d' e)/nioi tô=n a)pokrinome/nôn to\ me\n sunô/numon o(mô/numo/n phasin ei)=nai, o(/tan mê\ e)pharmo/ttê| e)pi\ pa=n o( a)podothei\s lo/gos,--prodiomologête/on u(pe\r tô=n toiou/tôn ê)\ prosullogiste/on o(/ti o(mô/numon ê)\ sunô/numon, o(po/teron a)\n ê)=|; _ma=llon ga\r sugchôrou=sin ou) proorô=ntes to\ sumbêso/menon_.]

These counsels of Aristotle are remarkable, as bearing on the details, and even the artifices, of dialectical debate.]

[Footnote 319: Topic. VI. x. p. 148, b. 16-22. [Greek: r(ête/on pro\s to\n toiou=ton o(/ti tê=| me\n o)nomasi/a| dei= chrê=sthai tê=| paradedome/nê| kai\ parepome/nê| kai\ mê\ kinei=n ta\ toiau=ta, e)/nia d' ou) lekte/on o(moi/ôs toi=s polloi=s.]]

28. If the definiend, of which a definition is tendered to you, is a compound, you may subtract from this definition the definition of one of the parts of the definiend, and then examine whether the remainder will suit as a definition of the remaining part of the definiend. If the remainder should not suit, this will show that the entire definition tendered is not tenable. Thus, if the definiend be a finite straight line, and if the definition tendered be, It is the boundary of a finite plane, of which (boundary) the middle covers or stands in the way of the extremities; you may subtract from this definition the definition of a finite line, viz., the boundary of a plane surface having boundaries, and the remainder of the definition ought then to suit for the remainder of the definiend. Now the remainder of the definiend is--straight; and the remainder of the definition is--that of which the middle covers or stands in the way of the extremities. But these two will _not_ suit; for a line may be straight, yet infinite, in which case it will have neither middle nor extremities. Accordingly, since the remainder of the definition will not suit for the remainder of the definiend, this will serve as an argument that the entire definition tendered is not a good one.[320]

[Footnote 320: Topic. VI. xi. p. 148, b. 23-32.]

If the definiend be a compound, and if the definition contain no greater number of words than the definiend, the definition must be faulty; it will be nothing better than a substitution of words. Still more faulty will it be, if it substitutes rare and strange words in place of others which are known and familiar; or if it introduces a new word which signifies something different from that which it replaces.[321]

[Footnote 321: Ibid. b. 32-p. 149, a. 13.]

The definiend, being compound, will contain both a generic and a differential term. In general, the generic term will be the better known of the two; yet sometimes the other is the better known. Whichever of the two is the better known, the definer ought to choose that, if all that he aims at is a mere substitution of one name in place of another. But, if he aims at something more or at the substitution of an explanatory proposition in place of a name (without which there can be no true definition), he ought then to choose the differentia in preference to the genus; for the definition is produced for the purpose of imparting knowledge, and the differentia, being usually less known than the genus, stands most in need of extraneous help to cognition.[322] When the definition of the differentia has thus been tendered, you will examine whether it will be equally suitable for any other definiend also. If it be, you have an argument against the goodness of the definition. For example, the definition of odd number tendered to you may be--number having a middle. Here, since number is common both to the definiend and to the definition, having-a-middle is evidently put forward as the equivalent of odd. But this cannot stand as equivalent to odd; since various other subjects which are not odd (such, for example, as a body or a line), nevertheless have a middle. Since, then, we see that having-a-middle would be suitable in defining definiends which are not odd, it cannot be admitted, without some qualifying adjunct, as a good definition of odd. The adjunct annexed must declare in what sense middle is intended, since it is an equivocal phrase.[323]

[Footnote 322: Ibid. p. 149, a. 14-28.]

[Footnote 323: Ibid. a. 29-37.]

29. If the definiend be a something really existent, the definition given of it ought not to be a proposition declaring an incompatible combination, such as neither does nor can exist. Some, for example, define white--colour mingled with fire; which is incompatible, since that which is incorporeal (colour) cannot be mingled with a body (fire).[324]

[Footnote 324: Topic. VI. xii. p. 149, a. 38-b. 3.]

30. Again, suppose the definiend to be a _Relatum_: the correlate thereof must of course be declared in the definition. Care, however, must be taken that it shall be declared, not in vague generality but, distinctly and with proper specialization; otherwise, the definition will be incorrect either entirely or partially. Thus, if the respondent defines medicine--the science of the really existent, he is incorrect either wholly or partially. The _relatum_ ought to reciprocate or to be co-extensive with its correlate.[325] When the correlate, however, is properly specialized in the definition, it may be declared under several different descriptions; for the same real thing may be at once _ens_, _album_, _bonum_. None of these descriptions will be incorrect. Yet, if the correlate is thus described in the definition of a _relatum_, the definition cannot be considered good or sufficient. For it applies to more things besides the definiend; and a good definition ought to reciprocate or to be co-extensive with its definiend.[326]

[Footnote 325: Ibid. b. 4, seq.: [Greek: e)/ti o(/soi mê\ diairou=sin e)n toi=s pro/s ti pro\s o(\ le/getai, a)ll' e)n plei/osi perilabo/ntes ei)=pan, ê)\ o(/lôs ê)\ e)pi/ ti pseu/dontai, oi(=on ei)/ tis tê\n i)atrikê\n e)pistê/mên o)/ntos ei)=pen--o(moi/ôs de\ kai\ e)pi\ tô=n a)/llôn, e)peidê\ a)ntistre/phei pa/nta ta\ pro/s ti.]]

[Footnote 326: Ibid. b. 12-23. [Greek: e)/ti d' a)du/naton to\n toiou=ton lo/gon i)/dion tou= a)podothe/ntos ei)=nai;--dê=lon ou)=n o(/ti o( toiou=tos ou)demia=s e)sti\n e)pistê/mês o(rismo/s; i)/dion ga\r kai\ ou) koino\n dei= to\n o(rismo\n ei)=nai.]]

31. Another mistake in defining is committed, when a man defines, not the subject purely and simply but, the subject in a high measure of excellence. Sometimes the rhetor (_e.g._) is defined--one who can perceive and produce without omission all that there is plausible in any cause; the thief is defined--one who takes away secretly what belongs to another. But these are the definitions, not of a rhetor and a thief generally but, of a skilful rhetor and skilful thief. The thief is one who is bent on taking away secretly, not one who _does_ take away secretly.[327]

[Footnote 327: Ibid. b. 24-30. [Greek: ou) ga\r o( la/thra| lamba/nôn, a)ll' o( boulo/menos la/thra| lamba/nein, kle/ptês e)sti/n.]]

32. Again, another error consists in defining what is desirable in itself and on its own account, as if it were desirable as a means towards some other end--as productive or preservative thereof. For example, if a man defines justice--that which is preservative of the laws; or wisdom--that which is productive of happiness, he presents them as if they were desirable, not for themselves but, with reference to something different from themselves. This is a mistake; and it is not less a mistake, though very possibly the same subject may be desirable both for itself and for the sake of something else. For the definition ought to enunciate what is best in the definiend; and the best of everything resides most in its essence, not in what it is relatively to something else. It is better to be desirable _per se_, than _alterius causâ_.[328]

[Footnote 328: Topic. VI. xii. p. 149, b. 31-39. [Greek: e(ka/stou ga\r to\ be/ltiston e)n tê=| ou)si/a| ma/lista, be/ltion de\ to\ di' au(to\ ai(reto\n ei)=nai tou= di' e(/teron, ô(/ste tou=to kai\ to\n o(rismo\n e)/dei ma=llon sêmai/nein.]]

33. Perhaps the definition tendered may be a complex proposition, enunciating two terms either jointly or severally, in one or other of three combinations. Either the definiend is A and B; or it is that which springs out of A and B; or it is A with B.[329] In each of these three cases you may find arguments for impugning the definition.

[Footnote 329: Ibid. xiii. p. 150, a. 1-4: [Greek: skopei=n de\ kai\ ei)/ tinos o(rismo\n a)podidou\s ta/de, ê)\ to\ e)k tou/tôn, ê)\ to/de meta\ tou=de ô(ri/sato.]]

_a._ Thus, take the first of the three. Suppose the respondent to define justice by saying, It is temperance and courage. You may urge against him, that two men, one of whom is temperate without being courageous, while the other is courageous without being temperate, will be just together, though neither of them separately is just; nay, that each of them separately (the one being temperate and cowardly, the other courageous and intemperate), will be both just and unjust; since, if justice is temperance and courage, injustice will be intemperance and cowardice.[330] The definer is open to the farther objection that he treats enumeration of parts as identical with the whole; as if he defined a house--bricks and mortar, forgetting the peculiar mode of putting them together. Bricks and mortar may exist, and yet there may be no house.[331]

[Footnote 330: Ibid. a. 4-14.]

[Footnote 331: Ibid. a. 15-21. [Greek: dê=lon ga\r o(/ti tô=n merô=n o)/ntôn ou)de\n kôlu/ei to\ o(/lon mê\ ei)=nai; ô(/ste ou) tau)to\n ta\ me/rê tô=| o(/lô|.]]

_b._ Next, suppose the definition to declare, that the definiend is that which springs from A and B--is a result or compound of A and B. You will then examine whether A and B are such as to yield any result; for some couples (as a line and a number) yield no result. Or, perhaps, the definiend may by its own nature inhere in some first subject, while A and B do not inhere in any one first subject, but one in the other; in which case the definition is assailable.[332] Or, even granting that it is the nature of A and B to inhere in the same first subject, you may find that that first subject is not the same as the one in which the definiend inheres. Now the whole cannot thus inhere in one, and the parts in another: you will here have a good objection. Or, perhaps, it may appear that, if the whole be destroyed, the parts will be destroyed also; which ought not to be, but the reverse; for, when the parts are destroyed, the whole must necessarily vanish. Or, perhaps, the definiend may be good or bad, while the parts of the definition (A and B) are neither one nor the other. (Yet this last is not a conclusive objection; for it will sometimes happen in compound medicines that each of the ingredients is good, while they are bad if given in conjunction.)[333] Or, perhaps, the whole may bear the same name as one of its parts: this, also, will render the definition impeachable. Still more will it be impeachable, if it enunciates simply a result or compound of A and B, without specifying the manner of composition; it ought to declare not merely the parts of the compound, but also the way in which they are put together to form the compound.[334]

[Footnote 332: Ibid. a. 22-30. [Greek: e)/ti ei) to\ me\n ô(risme/non e)n e(ni/ tini pe/phuke tô=| prô/tô| gi/nesthai, e)x ô(=n d' e)/phêsen au)to\ ei)=nai, mê\ e)n e(ni/ tini tô=| prô/tô|, all' e(ka/teron e)n e(kate/rô|.]]

[Footnote 333: Topic. VI. xiii. p. 150, a. 30-b. 13.]

[Footnote 334: Ibid. b. 14-26. [Greek: e)/ti ei) mê\ ei)/rêke to\n tro/pon tê=s sunthe/seôs;] &c.]

_c._ Lastly, suppose the definition to declare that the definiend is A along with B. You will note, first, that this third head must be identical either with the first or with the second (_e.g._, honey _with_ water means either honey and water, or the compound of honey with water); it will therefore be open to impeachment on one or other of the above-named grounds of objection, according as the respondent may admit.[335] You may also distinguish all the different senses in which one thing may be said to be _with_ another (_e.g._, when the two are in the same recipient, justice and courage together in the soul; or in the same place; or in the same time), and you may be able to show that in none of these senses can the two parts of the definition be truly said to be one along with the other.[336] Or, if it be true that these two parts are co-existent in time, you may enquire whether they are not affirmed with relation to different correlates. _E.g._, The definition of courage may be tendered thus: Courage is daring along with right intelligence; upon which you may remark that daring may have reference to an act of spoliation, and that right intelligence may have reference to the preservation of health. Now a man who has both daring and right intelligence in _these_ senses, cannot be termed courageous, and thus you will have an argument against the definition. And, even if they be affirmed with reference to the same correlate (_e.g._, the duties of a physician), a man who has both daring and right intelligence in reference to these duties will hardly be styled courageous; the term courage must be so defined as to have reference to its appropriate end; _e.g._, the dangers of war, or any still more public-spirited end.[337] Another mistake may, perhaps, be committed in this same sort of definition--A along with B; as when, for example, the definition tendered of anger is--pain along with the belief of being treated with contempt. What the definer really intends here is, that the pain arises from the belief of being treated with contempt. But this is not expressed by the terms of his definition, in any one of their admissible meanings.[338]

[Footnote 335: Ibid. b. 27-32. [Greek: ô(/st' e)a\n o(poterô|ou=n tô=n ei)rême/nôn tau)to\n _o(mologê/sê|_ ei)=nai to\ to/de meta\ tou=de, tau)ta\ a(rmo/sei le/gein a(/per pro\s e(ka/teron tou/tôn e)/mprosthen ei)/rêtai.]]

[Footnote 336: Ibid. b. 32-39. [Greek: ê)\ ô(s e)/n tini tau)tô=| dektikô=|], &c.]

[Footnote 337: Topic. VI. xiii. p. 151, a. 1-13. [Greek: ou)/te ga\r pro\s e(/teron au)tôn e(ka/teron dei= le/gesthai ou)/te pro\s tau)to\n to\ tucho/n, a)lla\ pro\s to\ tê=s a)ndrei/as te/los, oi(=on pro\s tou\s polemikou\s kindu/nous ê)\ ei)/ ti ma=llon tou/tou te/los.]]

[Footnote 338: Ibid. a. 14-19.]

34. Perhaps the definition, while including two or more distinct parts, may be tendered in this form: The definiend is the composition of A and B; _e.g._, animal is the composition of soul and body. You will first note that the definer has not declared what sort of composition. There is a great difference between one mode of composition and another; the mode must be specialized. Both flesh and bone may be defined--a composition of fire, earth, and water; but one mode of composition makes flesh, another makes bone, out of these same elements. You may also take the farther objection that to define a compound as composition is erroneous; the two are essentially disparate, one of them being abstract, the other concrete.[339]

[Footnote 339: Ibid. a. 20-31.]

35. If the definiend be in its nature capable of receiving two contrary attributes, and if the respondent define it by one or other of them, you have an argument against him. If one of them is admissible, the other must be equally so; and upon this supposition there would be two distinct definitions of the same subject; which has been already declared impossible. Thus, it is wrong to define the soul as a substance which is recipient of knowledge; the soul is also recipient of ignorance.[340]

[Footnote 340: Ibid. a. 32-b. 2.]

36. Perhaps the definiend is not sufficiently well known to enable you to attack the definition as a whole, but you may find arguments against one or other of its parts; this is sufficient to upset it. If it be obscure and unintelligible, you should help to correct and re-model it until it becomes clear; you will then see what are the really assailable points in it. When you indicate and expose the obscurity, the respondent must either substitute some clearer exposition of his own meaning, or else he must acquiesce in that which you propose as substitute.[341] If the improved definition which you propose is obviously clearer and better, his previous definition is of course put out of court; since there cannot be several definitions of the same subject.[342]

[Footnote 341: Topic. VI. xiv. p. 151, b. 3-11. [Greek: o(/soi t' a)saphei=s tô=n o(rismô=n, sundiorthô/santa kai\ suschêmati/santa pro\s to\ dêlou=n ti kai\ e)/chein e)pichei/rêma, ou(/tôs e)piskopei=n; a)nagkai=on ga\r tô=| a)pokrinome/nô| ê)\ de/chesthai to\ e)klambano/menon u(po\ tou= e)rôtô=ntos, ê)\ au)to\n diasaphê=sai ti/ pote tugcha/nei to\ dêlou/menon u(po\ tou= lo/gou.]]

[Footnote 342: Ibid. b. 12-17.]

To conclude, one suggestion may be given bearing upon all the arguments that you have to carry on against definitions tendered by respondents:--Reflect on the definiend, and frame a definition of it for yourself, as cleverly as you can at the moment; or call to mind any good definition of it which you may have heard before. This will serve you as a standard with which to compare the definition tendered, so that you will see at once what there is in it either defective or redundant, and where you can find arguments against it.[343]

[Footnote 343: Ibid. b. 18-23. [Greek: a)na/gkê ga\r, ô(/sper pro\s para/deigma theô/menon, to/ t' e)llei=pon ô(=n prosê=ken e)/chein to\n o(rismo\n kai\ to\ proskei/menon perie/rgôs kathora=n, ô(/ste ma=llon e)picheirêma/tôn eu)porei=n.]]

VII.

In the Seventh Book of the Topica Aristotle continues his review of the manner of debating theses which profess to define, but enters also on a collateral question connected with that discussion: viz., By what arguments are we to determine whether two Subjects or Predicates are the same _Numero_ (_modo maxime proprio_), as distinguished from being the same merely _Specie_ or _Genere_? To measure the extent of identity between any two subjects, is important towards the attack and defence of a definition.[344]

[Footnote 344: Ibid. VII. i. p. 151, b. 28: [Greek: po/teron de\ tau)to\n ê)\ e(/teron kata\ to\n kuriô/taton tô=n r(êthe/ntôn peri\ tau)tou= tro/pôn (e)le/geto de\ kuriô/tata tau)to\n to\ tô=| a)rithmô=| e(/n)] &c.]

Two subjects (A and B) being affirmed as the same _numero_, you may test this by examining the Derivatives, the Co-ordinates, and the Opposites, of each. Thus, if courage is identical with justice, the courageous man will be identical with the just man; courageously will be identical with justly. Likewise, the opposite of courage (in all the four modes of Opposition) will be identical with the opposite of justice. Then, again, the generators and destroyers, the generations and destructions, of courage, will be identical with those of justice.[345] If there be any predicate applied to courage in the superlative degree, the same predicate will also be applied to justice in the superlative degree.[346] If there be a third subject C with which A is identical, B also will be identical therewith. The same attributes predicable of A will also be predicable of B; and, if the two be attributes, each will be predicable of the same subjects of which the other is predicable. Both will be comprised in the same Category, and will have the same genus and differentia. Both will increase or diminish under the same circumstances. Each, when added to or subtracted from any third subject, will yield the same result.[347]

[Footnote 345: Ibid. p. 152, a. 2.]

[Footnote 346: Topic. VII. p. 152, a. 5-30: [Greek: skopei=n de\ kai\ ô(=n tha/teron ma/lista le/getai o(tiou=n, ei) kai\ tha/teron tô=n au)tôn tou/tôn kata\ to\ au)to\ ma/lista le/getai, katha/per Xenokra/tês to\n eu)dai/mona bi/on kai\ to\n spoudai=on a)podei/knusi to\n au)to/n, e)peidê\ pa/ntôn tô=n bi/ôn ai(retô/tatos o( spoudai=os kai\ o( eu)dai/môn; e(\n ga\r to\ ai(retô/taton kai\ to\ me/giston;] &c.

Aristotle remarks that Xenokrates here carried his inference too far: that the application of the same superlative predicate to A and B affords indeed a presumption that they are _Idem numero_, but not a conclusive proof thereof; that the predicate might be applied in like manner, if B were a species comprised in A as genus.

Xenokrates made the mistake of drawing an affirmative conclusion from syllogistic premisses in the Second figure.]

[Footnote 347: Topic. VII. i. p. 152, a. 31-b. 16.]

Farther, in examining the thesis (A is identical _numero_ with B) you must look not merely whether it involves actually any impossible consequences, but also whether any cases can be imagined in which it would involve such;[348] whether the identity is not merely _specie_ or _genere_; finally, whether the one can exist without the other.[349]

[Footnote 348: Ibid. b. 17-24. Aristotle illustrates this _locus_ as follows:--Some say that to be _void_, and to be _full of air_, are the same. But suppose the air to be drawn away; then the place will no longer be full of air, yet it will still be void, even more than it was before. One of the two terms declared to be identical is thus withdrawn, while the other remains. Accordingly, the two are not really identical. This illustration fits better to the principle laid down, b. 34: [Greek: ei) du/naton tha/teron a)/neu thate/rou ei)=nai; ou) ga\r a)\n ei)/ê tau)to/n.]]

[Footnote 349: Ibid. b. 25-35.]

Such are the various _loci_ available for argument against the thesis affirming the equivocal predicate _same_. All of them may be useful when you are impugning a definition; for the characteristic of this is to declare that the defining proposition is equivalent or identical with the defined name; and, if you can disprove such identity, you upset the definition. But these _loci_ will be of little avail, if your task is to defend or uphold a definition; for, even if you succeed in establishing the above-mentioned identity, the definition may still be open to attack for other weaknesses or defects.[350]

[Footnote 350: Ibid. ii. p. 152, b. 36-p. 158, a. 5. [Greek: a(/pantes oi( pro\s tau)to\n a)naskeuastikoi\ to/poi kai\ pro\s o(/ron chrê/simoi--tô=n de\ kataskeuastikô=n to/pôn ou)dei\s chrê/simos pro\s o(/ron;] &c.]

To uphold, or prove by way of syllogism, requires a different procedure. It is a task hard, but not impossible. Most disputants assume without proving their definition, in the same way as the teachers of Geometry and Arithmetic do in their respective sciences. Aristotle tells us that he does not here intend to give a didactic exposition of Definition, nor of the proper way of defining accurately or scientifically. To do this (he says) belongs to the province of Analytic; while in the present treatise he is dealing merely with Dialectic. For the purposes, then, of Dialectic, he declares that syllogistic proof of a definition is practicable, inasmuch as the definition is only a proposition declaring what is essential to the definiend; and nothing is essential except genus (or genera) and differentiæ.[351]

[Footnote 351: Topic. VII. iii. p. 153, a. 6-22. Compare Analyt. Post. II. iii.-x., where the theory of Scientific Definition is elaborately worked out; supra, Vol. I. ch. viii. pp. 346-353.]

Towards the establishment of the definition which you have to defend, you may find arguments by examining the Contraries and Opposites of the component terms, and of the defining proposition. If the opposite of the definition is allowed as defining properly the opposite of the definiend, you may argue from hence that your own definition is a good one.[352] If you can show that there is declared in your definition a partial correspondence of contraries either separately in the genus, or separately in the differentia, you have a certain force of argument in your favour; and, if you can make out both the two separately, this will suffice for your entire definition.[353] You may also draw arguments from the Derivatives, or Co-ordinates of your own terms; from Analogous Terms, or from Comparates (More or Less). If the definition of any one of these is granted to you, an argument is furnished for the defence of an analogous definition in the case of your own term. If it is conceded as a good definition that forgetfulness is--the casting away of knowledge, then the definition must also hold good that to forget is--to cast away knowledge. If destruction is admitted to be well defined--dissolution of essence, then to be destroyed is well defined--to be dissolved as to essence. If the wholesome may be defined--that which is productive of health, then also the profitable may be defined--that which is productive of good; that is, if the declaration of the special end makes a good definition in one case, so it will also in the other.[354]

[Footnote 352: Ibid. a. 28: [Greek: ei) ga\r o( a)ntikei/menos tou= a)ntikeime/nou, kai\ to\n ei)rême/nou tou= prokeime/nou a)na/gkê ei)=nai (o(/ron).]]

[Footnote 353: Ibid. b. 14: [Greek: katho/lou d' ei)pei=n, e)pei\ o( o(rismo/s e)stin e)k ge/nous kai\ diaphorô=n, a)\n o( tou= e)nanti/ou o(rismo\s phanero\s ê)=|, kai\ o( tou= prokeime/nou o(rismo\s phanero\s e)/stai.]]

[Footnote 354: Topic. VII. iii. p. 153, b. 25-p. 154, a. 11: [Greek: e)/ti e)k tô=n ptô/seôn kai\ tô=n sustoi/chôn; a)na/gkê a)kolouthei=n ta\ ge/nê toi=s ge/nesin kai\ tou\s o(/rous toi=s o(/rois.--e(no\s ou)=n o(poiouou=n tô=n ei)rême/nôn o(molêthe/ntos, a)na/gkê ki\ ta\ loipa\ o(mologei=sthai.--kai\ e)k tô=n o(moi/ôs e)cho/ntôn pro\s a)/llêla--o(moi/ôs ga\r e(/kaston tô=n ei)rême/nôn pro\s to\ oi)kei=on te/los e)/chei.]]

These _loci_, from _Analoga_, from Derivatives, from Conjugates, are of the most frequent avail in dialectical debates or definitions. The disputant must acquire promptitude in the employment of them. He must learn, moreover, to test a definition tendered to him by calling to mind particulars and sub-species, so as to determine whether the definition fits them all. Such a procedure will be found especially serviceable in debate with one who upholds the Platonic Ideas. Care must also be taken to see whether the definiend is distorted from its proper signification, or whether it is used in defining itself.[355]

[Footnote 355: Topic. VII. iv. p. 154, a. 12-22.]

These last observations are addressed to the questioner or assailant of the definition. We have already seen however that his task is comparatively easy; the grand difficulty is to defend a definition. The respondent cannot at once see what he ought to aim at; and, even when he does see it, he has farther difficulty in obtaining the requisite concessions from his opponent, who may decline to grant that the two parts of the definition tendered are really the genus and differentia of the definiend; while, if there be any thing besides these two parts contained in the essence of the definiend, there is an excuse for declining to grant it.[356] The opponent succeeds, if he can establish one single contradictory instance; accordingly, a syllogism with particular conclusion will serve his purpose. The respondent on the other hand, must meet each one of these instances, must establish an universal conclusion, and must show that his definition reciprocates with the definiend, so that, wherever the latter is predicable, the former is predicable likewise, and not in any other case whatever.[357]

[Footnote 356: Topic. VII. v. p. 154, a. 23, seq. [Greek: kai\ ga\r i)dei=n au)to\n kai\ labei=n para\ tô=n e)rôtôme/nôn ta\s toiau/tas prota/seis ou)k eu)pete/s], &c.]

[Footnote 357: Ibid. a. 32-b. 12.]