Chapter XLIII: Appendix: I (4)

Though it be true, therefore, that neither Ens nor Unum is a true genus, nor separable, but both of them aggregates of analogical derivatives, yet since all these derivatives have their root in one and the same fundamentum, the study of all of them belongs to one and the same science (p. 1005, a. 6-11). It is not the province of the geometer to examine what is The Opposite, The Perfect, Ens, Unum, Idem, Diversum, except in their application to his own problems. The general enquiry devolves upon the First Philosopher; who will investigate Ens _quatenus_ Ens, together with the belongings or appendages ([Greek: ta\ u(pa/rchonta]) of Ens _quatenus_ Ens, including Prius, Posterius, Genus, Species, Totum, Pars, and such like (a. 11-18).

It falls to the First Philosopher also to investigate and explain what mathematicians call their Axioms: the mathematician ought not to do this himself, but to leave it to the First Philosopher. These Axioms are, in their highest generality, affirmations respecting Ens _quatenus_ Ens, all of which belong to the First Philosopher; from whom the mathematician accepts them, and applies them as far as his own department requires (p. 1005, a. 20, seq.).

In First Philosophy, the firmest, best known, and most unquestionable of all principles is this: It is impossible for the same predicate at the same time and in the same sense to belong and not to belong to the same subject (p. 1005, b. 20). No one can at the same time believe that the same thing both is and is not; though Herakleitus professed to believe this, we must not suppose that he really did believe it (b. 25). No man can hold two contrary opinions at the same time (b. 31). This is by nature the first principle of all other axioms; to which principle all demonstrations are in the last resort brought back (b. 33: [Greek: phu/sei ga\r a)rchê\ kai\ tô=n a)/llôn a)xiôma/tôn au(/tê pa/ntôn]).

Aristotle then proceeds to explain and vindicate at length this [Greek: a)rchê/]--the Principle of Contradiction, which many at that time denied. This principle is at once the most knowable, and noway assumed as hypothesis ([Greek: gnôrimôta/tên kai\ a)nupo/theton]--p. 1005, b. 13). You cannot indeed demonstrate it to be true; the very attempt to demonstrate it would be unphilosophical: demonstration of every thing, is an impossibility. You cannot march upwards in an infinite progression of demonstrations; you must arrive ultimately at some first truth which is not demonstrable; and, if any such first truth is to be recognized, no one can point out any truth better entitled to such privilege than the Principle of Contradiction (p. 1006, a. 11). But you can convict an opponent of self-contradiction ([Greek: a)podei=xai e)legktikô=s], a. 12, 15), if he will only consent to affirm any proposition in significant terms--that is, in terms which he admits to be significant to himself and which he intends as such to others; in other words, if he will enter into dialogue with you, for without significant speech there can be no dialogue with him at all (a. 21).

When the opponent has shown his willingness to comply with the conditions of dialogue, by advancing a proposition in terms each having one definite signification, it is plain, by his own admission, that the proposition does not both signify and not signify the same. First, the copula of the proposition (_est_) does not signify what would be signified if the copula were _non est_; so that here is one case wherein the affirmative and the negative cannot be both of them true (p. 1006, a. 30; see Alex. Schol. and Bonitz's note). Next, let the subject of the proposition be _homo_; a term having only one single definite signification, or perhaps having two or three (or any definite number of) distinct significations, each definite. If the number of distinct significations be indefinite, the term is unfit for the purpose of dialogue (a. 30-b. 10). The term _homo_ will signify one thing only; it will have one determinate essence and definition--say _animal bipes_: that is, if any thing be a man, the same will be _animal bipes_. But this last cannot be the essence and definition of _non-homo_ also: _non-homo_, as a different name, must have different definition; _homo_ and _non-homo_ cannot be like [Greek: lô/pion] and [Greek: i(ma/tion], two terms having the same signification, essence and definition; for _homo_ signifies one subject of constant and defined nature, not simply one among many predicates applicable by accident to this same constant subject; it signifies [Greek: mi/an phu/sin] and not [Greek: a)/llên tina\ phu/sin] (Scholia, p. 656, b. 21). Since each name indeed is applied by convention to what it denominates, the name _non-homo_ may be applied elsewhere to that which we term _homo_; but this is a mere difference of naming; what bears the name _homo_, and what bears the name _non-homo_, must always be different, if _homo_ is defined to signify one determinate nature (b. 22). The one single nature and essence defined as belonging to _homo_, cannot be the same as that belonging to _non-homo_. If any thing be _homo_, the same cannot be _non-homo_: if any thing be _non-homo_, the same cannot be _homo_ (b. 25-34). Whoever says that _homo_ and _non-homo_ have the same meaning, must say _à fortiori_ that _homo_, _fortis_, _musicus_, _simus_, _pulcher_, &c., have the same meaning; for not one of these terms is so directly and emphatically opposite to _homo_, as _non-homo_ is. He must therefore admit that the meaning, not merely of all these words but also, of a host besides is the same; in other words, that not merely Opposites are one, but all other things besides, under different names ([Greek: o(/ti e(\n pa/nta e)/stai kai\ ou) mo/non ta\ a)ntikei/mena]--p. 1007, a. 6).

This argument is directed against those who maintain that affirmative and negative are both true at once, but who still desire to keep up dialogue (Alex. Schol. p. 658, a. 26, Br.: [Greek: tô=| tê/n te a)nti/phasin sunalêtheu/ein le/gonti, kai\ sô/zein boulome/nô| to\ diale/gesthai]). No man who maintains this opinion, can keep his consistency in dialogue, if he will only give direct answers to the questions put to him, without annexing provisoes and gratuitous additions to his answers. If you ask him, Whether it is true that Sokrates is _homo_? he ought to answer plainly Yes, or No. He ought not to answer: "Yes, but Sokrates is also _non-homo_," meaning that Sokrates is also the subject of many other accidental predicates--fair, flat-nosed, brave, accomplished, &c. He ought to answer simply to the question, whether the one essence or definition signified by the word man, belongs to Sokrates or not; he ought not to introduce the mention of these accidental predicates, to which the question did not refer. These accidental predicates are infinite in number; he cannot enumerate them all, and therefore he ought not to introduce the mention of any of them. Sokrates is _homo_, by the essence and definition of the word; he is _non-homo_, ten thousand times over, by accidental predicates; that is, he is fair, brave, musical, flat-nosed, &c., all of which are varieties of the general word _non-homo_ (p. 1007, a. 7-19).

Those who contend that both members of the Antiphasis are at once true disallow Essentia altogether, and the distinction between it and Accidens (p. 1007, a. 21). When we say that the word _homo_ signifies a certain Essentia, we mean that its Essentia is nothing different from this, and that the being _homo_ cannot be the same as the being _non-homo_, or the not being _homo_. Those against whom we are reasoning discard Essentia as distinguished from Accidens, and consider all predicates as Accidentia. _Albus_ belongs to _homo_ as an accident; but the essence of _albus_ does not coincide with that of _homo_, and cannot be predicated of _homo_ (a. 32). Upon the theory of these opponents, there would be no Prima Essentia to which all accidents are attached; but this theory is untenable. Accidents cannot be attached one to another in an infinite ascending series (b. 1). You cannot proceed more than two steps upward: first one accident, then a second; the two being joined by belonging to one and the same subject. No accident can be the accident of another accident. [Greek: To\ leuko/n] may have the accident [Greek: mousiko/n], or [Greek: to\ mousiko/n] may have the accident [Greek: leuko/n]; each of these may be called indifferently the accident of the other; but the truth is, that [Greek: leuko/s] and [Greek: mousiko/s] are both of them accidents belonging to the common Essentia--_homo_. But, when we affirm _homo est musicus_, we implicate the accident with the Essentia to which it belongs; that Essentia is signified by the subject _homo_. There must thus be one word which has signification as Essentia; and, when such is the case, we have already shown that both members of the Antiphasis cannot be predicated at once (b. 5-18).

(Alexander, in Scholia, p. 658, b. 40-p. 659, b. 14, Br., remarks on this argument of Aristotle: Those who held the opinion here controverted by Aristotle--[Greek: tê\n a)nti/phasin sunalêtheu/ein]--had in their minds accidental propositions, in regard to which they were right, except that both members of the Antiphasis cannot be true at the same time. _Sokrates est musicus_--_Sokrates non est musicus_: these two propositions are both true, in the sense that one or other of them is true only potentially, and that both cannot be actually true at the same time. One of them is true, and the other false, at the present moment; but that which is now false has been true in the past, and may become true in the future. Aristotle does not controvert this theory so far as regards accidental propositions; but he maintains that it is untenable about essential propositions, and that the theorists overlooked this distinction.)

Moreover, if you say that both members of the Antiphasis are alike true respecting every predicate of a given subject, you must admit that all things are one (p. 1007, b. 20). The same thing will be at once a wall, a trireme, a man. Respecting every subject, you may always either affirm or deny any given predicate; but, according to this theory, whenever it is true to affirm, it is always equally true to deny. If you can say truly, _Homo non est triremis_, you may say with equal truth, according to the theory before us, _Homo est triremis_. And, of course, _Homo non est triremis_ may be said truly; since (still according to this theory) the much more special negative, _Homo non est homo_, may be said truly (b. 32).

Again, if this theory be admitted, the doctrine that every predicate may be either affirmed or denied of any given subject, will no longer hold true. For, if it be true to say of Sokrates both _Est homo_ and _Est non-homo_: it must also be true to say of him both _Non est homo_ and _Non est non-homo_. If both affirmative and negative may be alike affirmed, both may be alike denied (p. 1008, a. 2-7). If both members of the Antiphasis are alike true, both must be alike false (Alex. Schol. p. 663, a. 14-34).

Again, the theory that both members of the Antiphasis are alike true, is intended by its authors to apply universally or not universally. Every thing is both white and not white, Ens and Non-Ens; or this is true with some propositions, but not with regard to others. If the theorists take the latter ground and allow some exceptions, so far at least as those exceptions reach, firm truth is left ([Greek: au(=tai a)\n ei)=en o(mologou/menai]--p. 1008, a. 11). But, if they take the former ground and allow no exceptions, they may still perhaps say: Wherever you can affirm with truth, we can also deny with truth; but, wherever we can deny with truth, we cannot in every case affirm with truth (a. 15). Meeting them upon this last ground, we remark that at any rate some negative propositions are here admitted to be knowable, and we obtain thus much of settled opinion; besides, wherever the negative is knowable, the corresponding affirmative must be still more knowable (a. 18). If they take the former ground and say that, wherever the negative is true, the affirmative is true also, they must either mean that each of them is true separately, or that neither of them is true separately but that both are true when enunciated together in a couple (a. 19). If they mean the latter, they do not talk either of these things or of any thing else: there is neither speech nor speaker, nothing but non-entity; and how can non-entity either speak or walk (a. 22)? Every thing would be confounded in one. If they mean the former--that affirmative and negative are each alike true taken separately, we reply that, since this must be true as much respecting one subject as respecting another, so there can be no distinction or difference between one subject and another; all must be alike and the same; if there be any difference of any kind, this must constitute a special and exceptional matter, standing apart from the theory now under discussion. Upon this view of the theory in question, then, as well as upon the preceding, we are landed in the same result: all things would be confounded into one (a. 27). All men would speak truly and all men alike (including the theorist himself, by his own admission) would speak falsely. Indeed in discussing with this theorist we have nothing to talk about; for he says nothing. He does not say, It is thus; he does not say, It is not thus; he says, It is both thus and not thus: then, again, he negatives both, saying, It is neither thus nor not thus; so that there is nothing definite in what he says (a. 32).

Again, let us ask, Does he who believes things to be so, believe falsely, and he who believes things not to be so and so, believe falsely also, while he who believes both at once, believes truly? If this last person believes truly, what is meant by the common saying that such and such is the constitution of nature? If you even say that the last person does not indeed believe truly, but believes more truly than he who believes the affirmative alone, or he who believes the negative alone, we still have something definite in the constitution of nature, something which is really true, and not true and false at the same time. But, if there be no more truly or less truly--if all persons alike and equally speak truly and speak falsely--speech is useless to such persons; what they say, they at the same time unsay. If the state of their minds really corresponds to this description--if they believe nothing, but at once think so and so and do not think so and so--how do such persons differ from plants (b. 3-12; see Alexander's Scholion, p. 665, b. 9-17 Br., about the explanation of [Greek: ma=llon], and the distinction between [Greek: le/gein] and [Greek: u(polamba/nein], p. 665, b. 31, seq.)?

It is certain, however, that these theorists are not like plants, and do not act as such in matters of ordinary life. They look for water, when thirsty; they keep clear of falling into a well or over a precipice. In regard to what is desirable or undesirable, at least, they do not really act upon their own theory--That both members of the Antiphasis are equally true and equally false. They act upon the contrary theory--That one of the members is true, and the other false. But, if these theorists, admitting that they act thus, say that they do not act thus with any profession of knowing the truth, but simply on the faith of appearance and greater probability, we reply that this ought to impose upon them a stronger sense of duty in regard to getting at the truth. The state of Opinion stands to that of Knowledge in the same relation as that of sickness to health (p. 1008, b. 12-31).

Finally, to follow up this last argument, even if we grant to these theorists that both members of the Antiphasis are true, still there are degrees of truth: the More and the Less pervades the constitution of nature (p. 1008, b. 32). We shall not surely affirm that two and three are equally even; nor shall we say, when any one affirms four to be five, that he commits an equal error with one who affirms four to be a thousand. Clearly one of these persons is more near to the truth, the other is less near to the truth. But, if there be such a thing as _being nearer to the truth_, there must surely be some truth to which you have come nearer; and, even if this be denied, yet at least what we have already obtained (the [Greek: e)ggu/teron tê=s a)lêthei/as]) is something firmer and of a more truth-like character. We shall thus have got rid of that unqualified theory which forbids all definite conceptions of the intellect ([Greek: ka)\n ei) mê/ e)stin, a)ll' ê)/dê ge/ ti e)sti\ bebaio/teron kai\ a)lêthinô/teron, kai\ tou= lo/gou a)pêllagme/noi a)\n ei)/êmen tou= a)kra/tou kai\ kôlu/onto/s ti tê=| dianoi/a| o(ri/sai]--p. 1009, a. 2).

Having thus completed his refutation of the "unqualified theory," which declares both members of the Antiphasis to be alike true, Aristotle passes to the examination of the Protagorean doctrine "Homo Mensura:" he affirms that it proceeds from the same mode of thinking, and that the two must stand or fall together. For, if all things which appear true are true, all things must be at once true and false; since the opposition of men's opinions is a notorious fact, each man thinking his own opinions true and his opponent's opinions false (p. 1009, a. 16).

Aristotle here distinguishes between two classes of reasoners, both of whom he combats, but who require to be dealt with in a very different manner: (1) Those who are sincerely convinced of what they affirm; (2) Those who have no sincere conviction, but merely take up the thesis as a matter for ingenious argument ([Greek: lo/gou cha/rin]), and will not relinquish it until they are compelled by a strong case made out against them. The first require persuasion, for their ignorance may be easily cured, and the difficulties whereby they are puzzled may be removed; the second require to be constrained by a forcible Elenchus or refutation, which may correct their misuse of dialectic and language (p. 1009, a. 22).

Aristotle begins with the first class. The difficulties which perplex them proceed from sensible things ([Greek: e)k tô=n ai)sthêtô=n]--p. 1009, a. 23). They perceive contrary things generated by the same; and this leads them to believe that contraries are both alike real, and that the two members of the Antiphasis are alike true. For, since Non-Ens cannot be generated, both the two contraries must have pre-existed together as Entia, prior to the generation in the thing as it then stood (a. 25). This is the opinion of Anaxagoras, who affirms that every thing is mixed in every thing; and of Demokritus, who affirms that Plenum and Inane--in other words. Ens and Non-Ens--exist alike and together in every part (a. 28). To these reasoners we reply, that in a certain sense they are right, in a certain sense wrong. The term Ens is used in two senses: the same thing may therefore be at once Ens and Non-Ens, but not in the same sense; moreover, from Non-Ens in one sense something may be generated, but not from Non-Ens in the other. The same thing may be at once two opposites _in power_, but not _in act_ ([Greek: duna/mei me\n ga\r e)nde/chetai a(/ma tau)to\ ei)=nai ta\ e)nanti/a, e)ntelechei/a| d' ou)/]--a. 35). We must farther remind these reasoners that the basis on which they proceed is not universally admissible; for there are various Entia of completely distinct and different essence, in which there is neither movement nor generation nor destruction of any sort (a. 38).

The doctrine held by Protagoras--That what appears true is truth, comes from the same source as the other doctrine--That both members of the Antiphasis are true. Both doctrines proceed from the sensible world ([Greek: o(moi/ôs de\ kai\ ê( peri\ ta\ phaino/mena a)lê/theia e)ni/ois e)k tô=n ai)sthêtô=n e)lê/luthen]--p. 1009, b. 2; [Greek: o(moi/ôs] refers back to a. 23--[Greek: au(/tê ê( do/xa], the other doctrine). Demokritus, Protagoras, and others observe that sensible phenomena are differently appreciated by different men, by other animals, and even by the same animal or man at different times. They do not think that truth upon these points of difference can be determined by a majority of voices. Demokritus says that either there is nothing true, or that we cannot know what it is (b. 10). These reasoners identified intelligence with sensible perception, and considered that this latter implied a change in the subject (b. 13): they conceived that what appeared to sense was necessarily true. Empedokles, Demokritus, Parmenides, Anaxagoras, Homer, &c., all lay down the doctrine, that the intelligence of men is varied with and determined by their sensible perceptions. They thought that men of wrong intelligence were nevertheless intelligent men, though their intelligence did not carry them to the same conclusions (b. 30); that if, both in one case and in the other, there were acts of intelligence, there must be realities corresponding to both, justifying the affirmative as well as the negative (b. 33).

That sincere and diligent enquirers should fall into these errors is very discouraging; but we must remark that their errors originated from this--that, while investigating the truth respecting Entia, they supposed that Entia were only the Percepta or Percipibilia (p. 1010, a. 2). Now in these Entia Perceptionis there is a great deal of the Indefinite and of mere Potential Entity (a. 3). Hence the theories of these reasoners were plausible, though not true. They saw that all the Entia Perceptionis were in perpetual movement, and they thought it impossible to predicate any thing with truth respecting what was at all times and in every way changing (a. 9). Kratylus and the Herakleitizers pushed this to an extreme. Even against their reasoning, we have something to say in reply. We grant that they have some ground for imagining that what undergoes change does not exist at the moment when it changes (a. 16). Yet even here there is room for dispute; for that which is in the act of casting off, still retains something of that which is being cast off; and of that which is being generated, something must already be in existence. As a general doctrine, if something is in course of being destroyed, something must be in existence; and, if something is in course of being generated, there must exist something out of which it proceeds and by which it is being generated; nor can this go back _ad infinitum_ (a. 22). Dropping this argument, however, let us advance another. Change as to Quantity is not the same as change as to Quality or Form. Let us grant that, as to Quantity, there is change continuous and perpetual--growth or decay--no such thing as stationary condition. But all our knowledge relates to Quality or Form, in which there is no continuous change (a. 24: [Greek: kata\ me\n ou)=n to\ poso/n, e)/stô mê\ me/non; a)lla\ kata\ to\ ei)=dos a(/panta gignô/skomen.]--Compare Alex. Schol., p. 671, b. 5-22; p. 670, a. 36: Bonitz has good remarks in his note, pp. 202-204**.).

Again, we have a farther reproach to make to these reasoners. Their argument is based only on the Percepta or Percipienda; yet, even as to these it is true only as to the minority and untrue as to the majority. It is true merely as far as the sublunary Percepta; but as to the superlunary or celestial it is the reverse of truth. Our earth and its neighbourhood is indeed in continual generation and destruction; but this is an insignificant part of the whole. In affirming any thing respecting the whole, we ought to follow the majority rather than the minority (p. 1010, a. 28-31**).

Lastly, we must repeat against these reasoners the argument urged just now. We must explain to them, that there exists, apart from and besides all generation, destruction, change, motion, &c., a certain Immovable Nature ([Greek: a)ki/nêto/s tis phu/sis]--a. 34). Indeed their own doctrine--That all things both are and are not--would seem to imply an universal stationary condition rather than universal change (a. 38). There can be no change; for there is no prospective terminus which can be reached by change. Every thing is assumed as already existing.

We have now to remark upon the special doctrine of Protagoras--[Greek: pa=n to\ phaino/menon a)lêthe/s]. If we grant that perception is always true upon matters strictly belonging to it, still phantasy is not identical with perception and we cannot say that what appears to the phantasy is always true ([Greek: to\ phaino/menon]--which implies a reference to [Greek: phantasi/a]--p. 1010, b. 2), Besides, it is strange that thinkers should puzzle themselves about the questions: Whether the magnitude and colour of objects is that which appears to a spectator near or to a spectator far off? and to a spectator healthy or jaundiced? Whether the weight of an object is as it appears to a weak or to a strong man? Whether objects are truly what they appear to men awake or to men asleep? Their own actions show that they do not think there is any doubt; for if, being in Libya, they happen to dream that they are in Athens, none of them ever think of going to the Odeium (b. 5-11). Moreover, respecting the future, as Plato remarks, the anticipations of the ignorant man are not so trustworthy as those of the physician, whether a patient will recover or not (b. 14). Then, again, in respect of present sensations, the perception of sight is not equally trustworthy with the perception of smell about a question of odour (b. 17); and the perception of smell will never report at the same time and about the same thing, that it is at once fragrant and not fragrant; nor, indeed, at different times about the affection itself, but only about the subject to which the affection belonged (b. 20). The same wine which tasted sweet last month, may now taste not sweet; but the sweet taste itself is the same now and last month, and the reports of the sense are never contradictory on this point. The sweet taste which is to come in the future will be of necessity like the sweet taste in the past. Now such necessity is abrogated by all those reasonings which affirm at once the two members of the Antiphasis. These reasonings disallow all essence of every thing, and all necessity; for whatever is necessary, cannot be at once both thus and not thus (b. 21-30).

On the whole, if nothing exist except Percepta, nothing can exist without animated beings; since without these last there can be no perception. It is indeed true, perhaps, that under such a supposition there exist neither Percepta nor acts of Perception (which are affections of the Percipient); but that the Substrata which cause Perception should not exist even without Perception--is an impossibility (p. 1010, b. 33: [Greek: to\ de\ ta\ u(pokei/mena mê\ ei)=nai, a(\ poiei= tê\n ai)/sthêsin, kai\ a)/neu ai)sthê/seôs, a)du/naton]). Perception is not perception of itself; there exists besides, apart from perception, something else which must necessarily be prior to perception. For the Movens is by nature prior to the Motum; and this is not the less true, though each of these two is enunciated in relation to the other (b. 35).

A difficulty is often started, and enquiry made, Who is to be the judge of health and sickness? Whom are we to recognize as the person to judge rightly in each particular case? Persons might as well raise difficulty and make enquiry, Whether we are now awake or asleep? It is plain by men's actual conduct that they have no real doubt upon the point in any particular case; and both these enquiries arise from the same fundamental mistake--that men require to have every thing demonstrated, and will recognize nothing without demonstration. (Alex. says in Scholia, p. 675, b. 3: [Greek: e)/sti ga\r pro\s a(\ e)k phu/seôs be/ltion e)/chomen ê)\ ô(/ste dei=sthai tê=s peri\ au)tô=n a)podei/xeôs; e)/sti de\ tau=ta ai(/ te ai)sthê/seis, kai\ ta\ a)xiô/mata kai\ ai( phusikai/ te kai\ koinai\ e)/nnoiai.]) Those who sincerely and seriously feel this difficulty, may be expected to acquiesce in the explanation here given (p. 1011, a. 2-14). But those who put forward the difficulty merely for the sake of argument, must be informed that they require an impossibility. They require to have a refutative case made out against them (which can only be done by reducing them to a [Greek: sullogismo\s a)ntipha/seôs]); yet they themselves begin by refusing to acknowledge this refutation as sufficient, for they maintain the thesis--That both members of the Antiphasis are alike and equally true (a. 16; compare Alex. Schol., p. 675, b. 20-28).

Those who maintain this last-mentioned thesis say, in other words, That every thing which appears true, is true. But this thesis of theirs cannot be defended except by the admission that every thing is relative, and that nothing is absolute. Accordingly they must take care to announce their thesis, not in absolute terms as it now stands, but in terms strictly relative: Every thing which appears true, appears true to some individual--at a certain moment of time--under certain circumstances and conditions (p. 1011, a. 24). For, if they affirm, in absolute phrase, that all things are alike false and true, on the ground that what appears true is true, urging that the same things do not appear true either to different persons, or to the same person at different times--nay, sometimes even to the same person at the same time, as may be seen by handling a pebble between two crossed fingers ([Greek: e)n tê=| e)palla/xei tô=n daktu/lôn]--a. 33), so that it appears two to the touch, but only one to the sight;--we shall reply, that there is no such contradiction of judgment, if they confine themselves to the same person, the same time, and one and the same sense. In these cases, there is only one affirmation which appears to be true, and therefore, according to their theory, that affirmation is true. They are not, therefore, justified in concluding that every thing is alike true and false (b. 1).

They can only escape this refutation by avoiding to say, This is true, and by saying, This is true to such an individual, at such a time, &c.; that is, by making every affirmation relative to some person's opinion or perception. Hence the inference is, that nothing either ever has occurred or ever will occur, without the antecedent opinion of some person ([Greek: mêtheno\s prodoxa/santos]--p. 1011, b. 6): if any thing ever has so occurred, it cannot be true that all things are relative to opinion. Moreover, if the Relatum be one, it must be relative to some one, some definite, Correlate; and, even if the same Relatum be both half and equal, it will not be equal in reference to a double Correlate, but half in reference to a double, and equal in reference to an equal (b. 9). Moreover, if _homo_ and _conceptum_ have both of them no more than a relative existence--that is, if both of them exist only in correlation with a _concipiens_--then the _concipiens_ cannot be _homo_; it will be the _conceptum_ that is _homo_. And, if every individual thing have existence only in relation to a _concipiens_, this _concipiens_ must form the Correlate to an infinite number of Relata (b. 12). (All this is very briefly and obscurely stated in Aristotle. The commentary of Alexander is copious and valuable: one might suppose that he had before him a more ample text; for it is difficult to find in the present text all that his commentary states**.)

Let thus much be said to establish the opinion, That the two members of the Antiphasis (the Affirmative and the Negative) are not both true at the same time. We have shown whence it arises that some persons suppose both to be true; and what are the consequences in which those who hold this opinion entangle themselves. Accordingly, since both sides of the Antiphasis cannot be truly predicated of the same subject, it is impossible that opposite attributes can belong at the same time to the same subject (p. 1011, b. 17: [Greek: ou)de\ ta)nanti/a a(/ma u(pa/rchein e)nde/chetai tô=| au)tô=|]). For one of these opposites includes in itself privation, and privation of a certain real essence; now privation is the negation of a certain definite genus. And, since affirmation and negation cannot be truly applied at the same time, it follows that opposite attributes cannot belong at the same time to the same subject. At least it is only possible thus far: one may belong to it absolutely, the other _secundum quid_; or both of them _secundum quid_ only ([Greek: tô=n me\n ga\r e)nanti/ôn tha/teron ste/rêsi/s e)stin ou)ch ê(=tton, ou)si/as de\ ste/rêsis a)po/phasi/s e)stin a)po/ tinos ô(risme/nou ge/nous]--b. 20).

But, also, there can be nothing intermediate between the two members of the Antiphasis; we must of necessity either affirm or deny any one thing of any other (p. 1011, b. 24). This will appear clearly, when we have first defined what is Truth and Falsehood. To say that Ens is not, or that Non-Ens is, is false: To say that Ens is, or that Non-Ens is not, is true. Accordingly, he who predicates _est_--or he who predicates _non est_--will speak truly or speak falsely, according as he applies his predicate to Ens or to Non-Ens. But he cannot, either in application to Ens or to Non-Ens, predicate _est aut non est_ (b. 29). Such a predication would be neither true nor false, but improper and unmeaning. (I follow at b. 27 the text of the Berlin edition: [Greek: ô(/ste kai\ o( le/gôn ei)=nai ê)\ mê\ a)lêtheu/sei ê)\ pseu/setai]--which seems to me here better than that of Bonitz, who puts [Greek: ô(/ste kai\ o( le/gôn tou=to ei)=nai ê)\ mê\ a)lêtheu/sei ê)\ pseu/setai]--following Alexander's explanation, Schol., p. 680, a. 33, which I cannot think to be correct, though Bonitz praises it much. Aristotle defines Truth and Falsehood: When you say _Ens est_, or _Non-Ens non est_, you speak truth; when you say _Ens non est_, or _Non-Ens est_, you speak falsehood. Accordingly, when you employ the predicate _est_, or when you employ the predicate _non est_, you will speak truly or falsehood, according as the subject with which you join it is Ens or is Non-Ens. But neither with respect to the subject Ens nor with respect to the subject Non-Ens, can you employ the disjunctive predicate--_est aut non est_.**)

Again, a medium between the two horns of the Antiphasis must be either a medium between opposites, like grey between white and black, or like the neither between man and horse. If it be the latter, it will never change; for all change is either from a negative to its affirmative (_non-bonum_ to _bonum_) or _vice versâ_: now that which is both _non-homo_ and _non-equus_ must change, if it change at all, into that which is both _homo_ and _equus_; but this is impossible. We see change always going on; but it is always change either into one of the two extremes or into the medium between them. But can we assume that there is such a medium (so that the case supposed will belong to the analogy of grey, halfway between white and black)? No, we cannot assume it; for, if we granted it, we should be forced to admit that there was change into white not proceeding from that which is not white: now nothing of the kind is ever perceived. There cannot therefore be any admissible medium halfway between the two members of the Antiphasis--something which is neither white nor not-white, neither black nor not-black (p. 1011, b. 35: [Greek: ei) d' e)/sti metaxu/]--if such medium be admitted--[Greek: kai\ ou(/tôs ei)/ê a)/n tis ei)s leuko\n ou)k e)k mê\ leukou= ge/nesis; nu=n d' ou)ch o(ra=tai]).

Furthermore, whatever our intelligence understands or reasons upon, it deals with as matter affirmed or denied. The very definition of truth and falsehood recognizes them as belonging only to affirmation or negation: when we affirm or deny in a certain way we speak truth; when in another way, we speak falsely. Nothing is concerned but affirmation and denial (_i.e._, there is no mental operation midway between the two--p. 1012, a. 2-5). If there be any such medium or midway process, it is not confined to this or that particular Antiphasis, but belongs alike to all, and must lie apart from all the different Antiphases--at least if it is to be talked of as a reality, and not as a mere possible combination of words; so that the speaker will neither speak truth, nor not speak truth; which is absurd (a. 7). It must also lie apart both from Ens and from Non-Ens; so that we should be compelled to admit a certain mode of change of Essence, which yet shall neither be generation nor destruction; which is impossible. **(According to Aristotle's definition, all change of [Greek: ou)si/a] must be either Generation, _i.e._, passage from [Greek: to\ mê\ o)/n] to [Greek: to\ o)/n], or Destruction, _i.e._, passage from [Greek: to\ o)/n] to [Greek: to\ mê\ o)/n].--See Alex. Schol. p. 681, b. 30-40**.)

Again, there are certain genera in which negation carries with it the affirmation of an opposite; such as odd and even, in numbers. In such genera, if we are to admit any medium apart from and between the two members of the Antiphasis, we should be forced to admit some number which is neither odd nor even (p. 1012, a. 11). This is impossible: the definition excludes it. (Alexander gives this as the definition of number: [Greek: pa=s ga\r a)rithmo\s ê)\ a)/rtio/s e)stin ê)\ peritto/s, kai\ _a)rithmo/s e)stin o(\s ê)\ a)/rtio/s e)stin ê)\ peritto/s_]--Schol. p. 682, a. 16.)

Again, if the Antiphasis could be divided, and a half or intermediate position found, as this theory contends, the division of it must be admissible farther and farther, _ad infinitum_. After bisecting the Antiphasis, you can proceed to bisect each of the sections; and so on. Each section will afford an intermediate term which may be denied with reference to each of the two members of the original Antiphasis. Two new Antiphases will thus be formed, each of which may be bisected in the same manner; and so bisection, with the formation of successive new Antiphases, may proceed without end (p. 1012, a. 13).

Again, suppose a questioner to ask you, Is this subject white? You answer, No. Now you have denied nothing else than the being-white: this is the [Greek: a)po/phasis], or negative member of the Antiphasis. But you have neither denied nor affirmed the intermediate stage between the affirmative and the negative; nor is there any answer possible by which you could do so. Therefore there is no real intermediate stage between them ([Greek: e)/ti o(/tan e)rome/nou ei) leuko/n e)stin ei)/pê| o(/ti ou)/, ou)the\n a)/llo a)pope/phêken ê)\ to\ ei)=nai; a)po/phasis de\ to\ mê\ ei)=nai]--p. 1012, a. 15; see Alex. Schol. p. 682, b. 15-38, and Bonitz's note. Bonitz suggests, though timidly, [Greek: a)pope/phêken] instead of the common reading [Greek: a)pope/phuken], which none of the commentators explain, and which seems unintelligible. I think Bonitz is right, though [Greek: a)pope/phêken] is an unknown tense from [Greek: a)po/phêmi]: it is quite as regular as [Greek: a)pophê/sô] or [Greek: a)pe/phêsa]**.).

The doctrines which we have been just controverting (Aristotle says) arise, like other paradoxes, either from the embarrassment in which men find themselves when they cannot solve a sophistical difficulty; or from their fancying that an explanation may be demanded of every thing. In replying to them, you must take your start from the definition, which assigns to each word one fixed and constant signification. The doctrine of Herakleitus--That all things are and all things are not--makes all propositions true; that of Anaxagoras--That every thing is intermingled with every thing--makes all propositions false: such mixture is neither good, nor not good; neither of the members of the Antiphasis is true (a. 17-28). Our preceding reasonings have refuted both these doctrines, and have shown that neither of the two one-sided extremes can be universally true: neither the doctrine--Every proposition is true; nor that--Every proposition is false; still less that which comprehends them both--Every proposition is both true and false. Among these three doctrines, the second might seem the most plausible, yet it is inadmissible, like the other two (b. 4).

In debating with all these reasoners, you must require them (as we have already laid down), not to admit either existence or non-existence but, to admit a constant signification for each word. You must begin by defining truth and falsehood; each of them belongs only to affirmation in a certain way. Where the affirmation is true the denial is false; all propositions cannot be false; one member of each Antiphasis must be true, and the other member must be false. Each of these doctrines labours under the often-exposed defect--that it destroys itself (p. 1012, b. 14, [Greek: to\ thrullou/menon]--allusion to the Theætetus, according to Alexander). For whoever declares all propositions to be true, declares the contradictory of this declaration to be true as well as the rest, and therefore his own declaration not to be true. Whoever declares all propositions to be false, declares his own declaration to be false as well as all other propositions (b. 17). And, even if we suppose each of these persons to make a special exception in regard to the particular propositions here respectively indicated, still this will not serve. The man who declares all propositions to be false, will be compelled to admit an infinite number of true propositions; because the proposition declaring the true proposition to be true, must itself be true; a second proposition declaring this last to be true, will itself be true; and so on to a third, a fourth, &c., in endless scale of ascent. The like may be said about the man who declares all propositions to be true: he too will be obliged to admit an infinite number of false propositions; for that which declares a true proposition to be false, must itself be false; and so on through a second, a third, &c., in endless scale of ascent as in the former case (b. 22).

It follows from what has been just proved, that those who affirm every thing to be at rest, and those who affirm every thing to be in motion, are both alike wrong. For, if every thing were at rest, the same propositions would be always true and always false. But this is plainly contrary to evidence; for the very reasoner who affirms it was once non-existent, and will again be non-existent. On the other hand, if every thing were in motion, no proposition would be true, and all would be false: but we have proved above that this is not so. Nor is it true that all things are alternately in motion or at rest; for there must be something ever-moving and other things ever-moved--and this prime movent must be itself immovable (p. 1012, b. 22-30).

. . . . . .

Book E.

The First Philosophy investigates the causes and principles of Entia _quatenus_ Entia (p. 1025, b. 3). It is distinguished from other sciences, by applying to all Entia, and in so far as they are Entia; for each of the other sciences applies itself to some separate branch of Entia, and investigates the causes and principles of that branch exclusively. Each assumes either from data of perception, or avowedly by way of hypothesis, the portion or genus of Entia to which it applies; not investigating the entity thereof, but pre-supposing this process to have been already performed by Ontology: each then investigates the properties belonging _per se_ to that genus (b. 13). It is plain that by such an induction not one of these sciences can demonstrate either the essence of its own separate genus, nor whether that genus has any real existence. Both these questions--both [Greek: ei) e)/stin] and [Greek: ti/ e)stin]--belong to Ontology (b. 18). (The belief derived from perception and induction never amounts to demonstration, as has been shown in the Analytica; you may always contest the universality of the conclusion--Alex. p. 734, b. 16, Br.)

Apart from Ontology, each of these separate sciences is either theoretical, or practical, or constructive (p. 1025, b. 21). Two of the separate sciences are theoretical--Physics and Mathematics; and, as Ontology (or Theology) is also theoretical, there are three varieties of theoretical science (p. 1026, a. 18).

Physical Science applies to subjects having in themselves the principle of mobility or change, and investigates, principally and for the most part, the Essence or Form thereof; yet not exclusively the Form, for the Form must always be joined with Matter. The subject of Physics includes Matter in its definition, like hollow-nosed, not like hollow (p. 1025, b. 33). All the animal and vegetable world is comprised therein; and even some soul, as far as soul is inseparable from Matter ([Greek: peri\ psuchê=s **e)ni/as theôrê=sai tou= phusikou=, o(/sê mê\ a)/neu tê=s u(/lês e)sti/n]--p. 1026, a. 5).

Mathematics is another branch of theoretical science; applying to subjects immovable and in part inseparable from Matter; that is, separable from Matter only in logical conception (p. 1026, a. 7-15).

Theology, or First Philosophy, or Ontology, is conversant with subjects self-existent, immovable, and separable from Matter (p. 1026, a. 16).

Now all causes are necessarily eternal; but these more than any other, because they are the causes active among the visible divine bodies; for, clearly, if the Divinity has any place, it must be found among subjects of that nature; and the most venerable science must deal with the most venerable subjects (p. 1026, a. 19). The theoretical sciences are more worthy than the rest ([Greek: ai(retô/terai]), and First Philosophy is the most worthy among the theoretical sciences (a. 22). A man may indeed doubt whether First Philosophy is distinguished from the other theoretical sciences by being more universal, and by comprehending them all as branches; or whether it has a separate department of its own, but more venerable than the others; as we see that Mathematics, as a whole, comprehends Geometry and Astronomy (a. 27). If there exist no other distinct Essence beyond the compounds of Nature ([Greek: para\ ta\s phu/sei sunestêkui/as]--a. 28), Physics would be the first of all sciences. But if there be a distinct immovable Essence, that is first; accordingly the science which deals with it is first, and, as being first, is for that reason universal ([Greek: kai\ katho/lou ou(/tôs o(/ti prô/tê]--a. 30). It is the province of this First Philosophy to theorize respecting Ens _quâ_ Ens--what it is and what are its properties _quâ_ Ens (a. 32). (Alexander says the First Philosophy is more universal than the rest, but does not comprehend the rest: [Greek: prô/tê pa/ntôn kai\ katho/lou ô(s pro\s ta\s a)/llas, ou) perie/chousa e)kei/nas, a)ll' ô(s prô/tê]--Schol. p. 736, a. 27.)

Now Ens has many different meanings:--

1. Ens [Greek: kata\ sumbebêko/s].

2. Ens [Greek: ô(s a)lêthe/s]--Non-Ens [Greek: ô(s pseu=dos].

3. Ens [Greek: kata\ ta\ schê/mata tê=s katêgori/as] (decuple).

4. Ens [Greek: duna/mei kai\ e)nergei/a|].

1. Respecting the first, there can be no philosophical speculation (p. 1026, b. 3). No science, either theoretical, or practical, or constructive, investigates Accidents. He who constructs a house, does not construct all the accidents or concomitants of the house; for these are endless and indeterminate. It may be agreeable to one man, hurtful to a second, profitable to a third, and something different in relation to every different Ens; but the constructive art called house-building is not constructive of any one among these concomitants (b. 7-10). Nor does the geometer investigate the analogous concomitants belonging to his figures; it is no part of his province to determine whether a triangle is different from a triangle having two right angles (b. 12). This is easy to understand: the Concomitant is little more than a name--as it were, a name and nothing beyond (b. 13). Plato came near the truth when he declared that Sophistic was busied about Non-Ens; for the debates of the Sophists turn principally upon Accidents or Concomitants, such as, Whether musical and literary be the same or different? Whether Koriskus or literary Koriskus, be the same or different? Whether everything which now is, but has not always been, has become; as in the case of a man who being musical has become literary or being literary has become musical? and such like debates (see Alexander, Schol. p. 736, b. 40). For the Concomitant or Accident appears something next door to Non-Ens ([Greek: e)ggu/s ti tou= mê\ o)/ntos], p. 1026, b. 21), as we may see by these debates. Of other Entia there is generation or destruction, but of Accidents there is none (b. 23).

Nevertheless, we shall state, as far as the case admits, what is the nature of the Accident, and through what cause it is ([Greek: ti/s ê( phu/sis au)tou=, kai\ dia/ tin' ai)ti/an e)sti/n;]--p. 1026, b. 25): we shall perhaps at the same time explain why there can be no science respecting it. Among Entia, some are always and necessarily the same, others are usually but not always the same. These which come to pass in neither of these two ways, are called Accidents or Concomitants. Of the first two, the Constant and the Usual, there is always some definite cause; of the third, or Accidents, there is none: the cause of these is an Accident (p. 1027, a. 8). In fact, Matter is the cause of Accidents, admitting as it does of being modified in a way different from the usual and ordinary way (a. 13). It is plain that there can be neither science nor teaching of Accidents: the teacher can teach only what is constant or usual, and nothing beyond (a. 20).

Now of these Accidents, there is a certain principle or cause which it is indispensable to admit--Chance ([Greek: ê( tou= o(po/ter' e)/tuchen]--p. 1027, b. 12). There must be principles and causes, generable and destructible, yet which never are either generated or destroyed; if this were not so, all events would occur by necessity (p. 1026, b. 29-31). (Thus the builder, considered as cause of the house which he builds, has been generated, _i.e._, he has acquired the art of building and the proper accessories; and he will be destroyed, _i.e._, he will lose his art, and its conditions of being exercised. But, considered as the cause of the accidents belonging to the house, of its being annoying or inconvenient to A or B, he has not been generated nor will he be destroyed; _i.e._, he has neither acquired, nor will he lose, any skill or conditions tending to the production of this effect. As the contact of two substances is not generated, but appears of itself along with the substances when they are generated; as the limits of periods of time appear without generation along with the periods of time themselves; so the builder, when he acquires the power of building the house, stands possessed thereby, without any additional time or special generation, of the power to produce the concomitant accidents of the house. The house is thus produced by necessity; its concomitant accidents not by necessity--Alex. Schol. p. 738, a. 19-33.)

But whether this [Greek: to\ o(po/ter' e)/tuchen] is to be considered as referable to Matter, End, or Movent, is a point important to be determined (p. 1027, b. 15). Aristotle shows elsewhere that it is referable to the last of the three--[Greek: to\ poiêtiko/n] (Asklepius, p. 738, b. 41).

Having now said enough upon Ens _per Accidens_, we proceed to touch upon the second variety of Ens--Ens as the True, Non-Ens as the False.

This variety of Ens depends upon conjunction and disjunction, and forms an aggregate of two portions separately exhibited and brought together in the Antiphasis. Such conjunction and disjunction is not in things themselves; but in the act of intelligence which thinks the two things together and not successively: in regard to simple matters and Essence, not even any special conjoining act of intelligence is required; such things must be conceived together, or not conceived at all (p. 1027, b. 27). The mental act of apprehension, in these cases, is one and indivisible: you either have it entire at once, or not at all.

The cause of this variety of Ens is to be found in a certain affection of the intelligence; that of the preceding variety of Ens is an undefined or indeterminate cause (b. 34). Both these two varieties of Ens are peculiar, standing apart from what is most properly and _par excellence_ Ens, _i.e._, from the Ens according to the ten Categories, on which we shall now say something.

. . . . . .

Book Z.