18We have here discussed these two maxims chiefly in reference to Aristotle’s manner of presenting them, and to the conceptions of his predecessors and contemporaries. An excellent view of the Maxims themselves, in their true meaning and value, will be found in Mr. John Stuart Mill’s Examination of the Philosophy of Sir W. Hamilton, ch. xxi. pp. 406-421.
18We have here discussed these two maxims chiefly in reference to Aristotle’s manner of presenting them, and to the conceptions of his predecessors and contemporaries. An excellent view of the Maxims themselves, in their true meaning and value, will be found in Mr. John Stuart Mill’s Examination of the Philosophy of Sir W. Hamilton, ch. xxi. pp. 406-421.
Now, Herakleitus, in his theory (a theory propounded much before the time of Protagoras and the persons called Sophists), denied all permanence or durability in nature, and recognized nothing except perpetual movement and change. He denied both durable substances and durable attributes; he considered nothing to be lasting except the universal law or principle of change — the ever-renewed junction or co-existence of contraries and the perpetual transition of one contrary into the other. This view of the facts of nature was adopted by several other physical philosophers besides.19Indeed it lay at the bottom of Plato’s new coinage — Rational Types or Forms, at once universal and real. The Maxim of Contradiction is intended by Aristotle to controvert Herakleitus, and to uphold durable substances with definite attributes.
19See ‘Plato and other Comp. of Sokr.’ I. i.pp. 28-38.
19See ‘Plato and other Comp. of Sokr.’ I. i.pp. 28-38.
Again, the theory of Anaxagoras denied all simple bodies (excepting Noûs) and all definite attributes. He held that everything was mingled witheverything else, though there might be some one or other predominant constituent. In all the changes visible throughout nature, there was no generation of anything new, but only the coming into prominence of some constituent that had before been comparatively latent. According to this theory, you could neither wholly affirm, nor wholly deny, any attribute of its subject. Both affirmation and denial were untrue: the real relation between the two was something half-way between affirmation and denial. The Maxim of Excluded Middle is maintained by Aristotle as a doctrine in opposition to this theory of Anaxagoras.20
20Ibid.pp. 49-57.
20Ibid.pp. 49-57.
Both the two above-mentioned theories are objective. A third, that of Protagoras — “Homo Mensura� — brings forward prominently the subjective, and is quite distinct from either. Aristotle does indeed treat the Protagorean theory as substantially identical with that of Herakleitus, and as standing or falling therewith. This seems a mistake: the theory of Protagoras is as much opposed to Herakleitus as to Aristotle.
We have now to see how Aristotle sustains these two Axioms (which he calls “the firmest of all truths and the most assuredly knownâ€�) against theories opposed to them. In the first place, he repeats here what he had declared in the Analytica Posteriora — that they cannot be directly demonstrated, though they are themselves theprincipiaof all demonstration. Some persons indeed thought that these Axioms were demonstrable; but this is an error, proceeding (he says) from complete ignorance of analytical theory. How, then, are these Axioms to be proved against Herakleitus? Aristotle had told us in the Analytica that axioms were derived from particulars of sense by Induction, and apprehended or approved by the Νοῦς. He does not repeat that observation here; but he intimates that there is only one process available for defending them, and that process amounts to an appeal to Induction. You can give no ontological reason in support of the Axioms, except what will be condemned as apetitio principii; you must take them in their logical aspect, as enunciated in significant propositions. You must require the Herakleitean adversary to answer some question affirmatively, in terms significant both to himself and to others, and in a proposition declaring his belief on the point. If he will not do this, you can hold no discussion with him: he might as well be deaf and dumb: he is no better than a plant (to use Aristotle’s own comparison). If he does it, he has bound himself to something determinate: first, the signification of the terms is a fact, excluding what is contrary or contradictory; next, in declaring his belief, he at the same time declares that he does not believe in the contrary or contradictory, and is so understood by the hearers. We may grant what his theory affirms — that the subject of a proposition is continually under some change or movement; yet the identity designated by its name is still maintained,21and many true predications respecting it remain true in spite of its partial change. The argument in defence of the Maxim of Contradiction is, that it is a postulate implied in all the particular statements as to matters of daily experience, that a man understands and acts upon when heard from his neighbours; a postulate such that, if you deny it, no speech is either significant or trustworthy to inform and guide those who hear it. If the speaker both affirms and denies the same fact at once, no information is conveyed, nor can the hearer act upon the words. Thus, in the Acharnenses of Aristophanes, Dikæopolis knocks at the door of Euripides, and inquires whether the poet is within; Kephisophon, the attendant, answers — “Euripides is within and not within.â€� This answer is unintelligible; Dikæopolis cannot act upon it; until Kephisophon explains that “not withinâ€� is intended metaphorically. Then, again, all the actions in detail of a man’s life are founded upon his own belief of some facts and disbelief of other facts: he goes to Megara, believing that the person whom he desires to see is at Megara, and at the same time disbelieving the contrary: he acts upon his belief both as to what is good and what is not good, in the way of pursuit and avoidance. You may cite innumerable examples both of speech and action in the detail of life, which the Herakleitean must go through like other persons; and when, if he proceeded upon his own theory, he could neither give nor receive information by speech, nor ground any action upon the beliefs which he declares to co-exist in his own mind. Accordingly, the Herakleitean Kratylus (so Aristotle says) renounced the use of affirmative speech, and simply pointed with his finger.22
21This argument is given by Aristotle, Metaph.Γ.v. p. 1010, a. 7-25, contrasting change κατὰ τὸ ποσόν and change κατὰ τὸ ποιόν.
21This argument is given by Aristotle, Metaph.Γ.v. p. 1010, a. 7-25, contrasting change κατὰ τὸ ποσόν and change κατὰ τὸ ποιόν.
22Aristot. Metaph.Γ.v. p. 1010, a. 12. Compare Plato, Theætêt. pp. 179-180, about the aversion of the Herakleiteans for clear issues and propositions.
22Aristot. Metaph.Γ.v. p. 1010, a. 12. Compare Plato, Theætêt. pp. 179-180, about the aversion of the Herakleiteans for clear issues and propositions.
The Maxim of Contradiction is thus seen to be only the general expression of a postulate implied in all such particular speeches as communicate real information. It is proved by a very copious and diversified Induction, from matters of experience familiar to every individual person. It is not less true in regard to propositions affirming changes, motions, or events, than in regard to those declaring durable states or attributes.
In the long pleading of Aristotle on behalf of the Maxim of Contradiction against the Herakleiteans, the portion of it that appeals to Induction is the really forcible portion; conforming as it does to what he had laid down in the Analytica Posteriora about the inductive origin of theprincipiaof demonstration. He employs, however, besides, several other dialectical arguments built more or less upon theories of his own, and therefore not likely to weigh much with an Herakleitean theorist; who — arguing, as he did argue, that (because neither subject nor predicate was ever unchanged or stable for two moments together) no true proposition could be framed but was at the same time false, and that contraries were in perpetual co-existence — could not by any general reasoning be involved in greater contradiction and inconsistency than he at once openly proclaimed.23It can only be shown that such a doctrine cannot be reconciled with the necessities of daily speech, as practised by himself, as well as by others. We read, indeed, one ingenious argument whereby Aristotle adopts this belief in the co-existence of contraries, but explains it in a manner of his own, through his much employed distinction between potential and actual existence. Two contraries cannot co-exist (he says) in actuality; but they both may and do co-exist in different senses — one or both of them being potential. This, however, is a theory totally different from that of Herakleitus; coincident only in words and in seeming. It does indeed eliminate the contradiction; but that very contradiction formed the characteristic feature and keystone of the Herakleitean theory. The case against this last theory is, that it is at variance with psychological facts, by incorrectly assuming the co-existence of contradictory beliefs in the mind; and that it conflicts both with postulates implied in the daily colloquy of detail between man and man, and with the volitional preferences that determine individual action. All of these are founded on a belief in the regular sequence of our sensations, and in the at least temporary durability of combined potential aggregates of sensations, which we enunciate in the language of definite attributes belonging to definite substances. This language, the common medium of communication among non-theorizing men, is accepted as a basis, and is generalized and regularized, in the logical theories of Aristotle.
23This is stated by Aristotle himself, Metaph.Γ.vi. p. 1011, a. 15: οἱ δ’ ἐν τῷ λόγῳ τὴν βίαν μόνον ζητοῦντες ἀδύνατον ζητοῦσιν· ἐναντία γὰρ εἰπεῖν ἀξιοῦσιν, εὐθὺς ἐναντία λέγοντες. He here, indeed, applies this observation immediately to the Protagoreans, against whom it does not tell, instead of the Herakleiteans, against whom it does tell. The whole of the reasoning in this part of the Metaphysica is directed indiscriminately, and in the same words, against Protagoreans and Herakleiteans.
23This is stated by Aristotle himself, Metaph.Γ.vi. p. 1011, a. 15: οἱ δ’ ἐν τῷ λόγῳ τὴν βίαν μόνον ζητοῦντες ἀδύνατον ζητοῦσιν· ἐναντία γὰρ εἰπεῖν ἀξιοῦσιν, εὐθὺς ἐναντία λέγοντες. He here, indeed, applies this observation immediately to the Protagoreans, against whom it does not tell, instead of the Herakleiteans, against whom it does tell. The whole of the reasoning in this part of the Metaphysica is directed indiscriminately, and in the same words, against Protagoreans and Herakleiteans.
The doctrine here mentioned is vindicated by Aristotle, not only against Herakleitus, by asserting the Maxim of Contradiction, but also against Anaxagoras, by asserting the Maxim of Excluded Middle. Here we have the secondprincipiumof Demonstration, which, if it required to be defended at all, can only be defended (like the first) by a process of Induction. Aristotle adduces several arguments in support of it, some of which involve an appeal to Induction, though not broadly or openly avowed; but others of them assume what adversaries, and Anaxagoras especially, were not likely to grant. We must remember that both Anaxagoras and Herakleitus propounded their theories as portions of Physical Philosophy or of Ontology; and that in their time no such logical principles and distinctions as those that Aristotle lays down in the Organon, had yet been made known or pressed upon their attention. Now, Aristotle, while professing to defend these Axioms as data of Ontology, forgets that they deal with the logical aspect of Ontology, as formulated in methodical propositions. His view of the Axioms cannot be properly appreciated without a classification of propositions, such as neither Herakleitus nor Anaxagoras found existing or originated for themselves. Aristotle has taught us what Herakleitus and Anaxagoras had not been taught — to distinguish separate propositions as universal, particular and singular; and to distinguish pairs of propositions as contrary, sub-contrary, and contradictory. To take the simplest case, that of a singular proposition, in regard to which the distinction between contrary and contradictory has no application, — such as the answer (cited above) of Kephisophon about Euripides. Here Aristotle would justly contend that the two propositions — Euripides is within, Euripides is not within — could not be either both of them true, or both of them false;that is, that we could neither believe both, nor disbelieve both. If Kephisophon had answered, Euripides is neither within nor not within, Dikæopolis would have found himself as much at a loss with the two negatives as he was with the two affirmatives. In regard to singular propositions, neither the doctrine of Herakleitus (to believe both affirmation and negation) nor that of Anaxagoras (to disbelieve both) is admissible. But, when in place of singular propositions we take either universal or particular propositions, the rule to follow is no longer so simple and peremptory. The universal affirmative and the universal negative arecontrary; the particular affirmative and the particular negative aresub-contrary; the universal affirmative and the particular negative, or the universal negative and the particular affirmative, arecontradictory. It is now noted in all manuals of Logic, that of two contrary propositions, both cannot be true, but both may be false; that of two sub-contraries, both may be true, but both cannot be false; and that of two contradictories, one must be true and the other false.
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[The following Abstract — when not translation — of six books (Γ,E,Z,Η,Θ,Λ) out of the fourteen included under the title ‘Metaphysica,’ may be said to cover the whole of Aristotle’s dogmatic exposition of First Philosophy. According to the view of Brandis, now in its main features generally accepted, the exposition continued through BooksΓ,E,Z,Η, reaches back to BooksAandB, and comes to an end with BookΘ. Still it is only with BookΓthat the properly didactic treatment begins, BookAbeing a historical review of previous opinion, and BookBa mere collection of ἀπορίαι subjected to a preliminary dialectical handling; while, at the other end, BookΛ, though it has no direct connection with BookΘ, is, especially in its latter part, of undeniable importance for Aristotle's metaphysical doctrine.
The remaining books are known asα,Δ,I,K,M,N. The short Bookαis entirely unconnected with any of the others, and most probably is not the work of Aristotle. BookΔ(περὶ τῶν ποσαχῶς λεγομένων) — a vocabulary of philosophical terms — is Aristotelian beyond question, being referred to occasionally in the chief books; but it lies quite apart from the exposition proper. BookI— dealing with Unity and Opposites — though it also has no place in the actual line of treatment, is truly ontological in character, and probably was intended to fall within some larger scheme of metaphysical doctrine; the like, as far as can be judged, being true of BooksMandN, containing together a criticism of Pythagorean and Platonic theories. Finally, BookK, consisting in part of an epitomized excerpt from the Physica — hardly from the hand of Aristotle, gives otherwise only a sketch in outline of the argument of BooksB,Γ,E, and thus, although Aristotelian, is to be discounted.
The author nowhere states the principle upon which he selected the six books for a preliminary Abstract; but the actual selection, joined to various indications in the Abstract and marginal notes in his copies of the Metaphysica, leaves no doubt that he accepted the view of Brandis, more especially as set forth by Bonitz. On the whole question of the Canon of the Metaphysica, Bonitz’s Introduction to his Commentary may with advantage be consulted.]
In this First Philosophy, Aristotle analyses and illustrates the meaning of thegeneralissimaof language — the most general and abstract words which language includes. All these are words in common and frequent use; in the process of framing or putting together language, they have become permanently stamped and circulated as the result of many previous comparisons, gone through but afterwards forgotten, or perhaps gone through at first without any distinct consciousness. Men employ these words familiarly in ordinary speech, and are understood by others when they do so. For the most part, they employ the words correctly and consistently, in the affirmation of particular propositions relating to topics of daily life and experience. But this is not always or uniformly the case. Sometimes, more or less often, men fall into error and inconsistency in the employment of these familiar general terms. The First Philosophy takes up the generalities and established phrases in this condition; following back analytically the synthetical process which the framers of language have pursued without knowing or at least without recording it, and bringing under conscious attention the different meanings, more or fewer, in which these general words are used.
Philosophia Prima devotes itself, specially and in the first instance, to EnsquatenusEns in all its bearings; being thus distinguished from mathematics and other particular sciences, each of which devotes itself to a separate branch of Ens (p. 1003, a. 25). It searches into the First Causes or Elements of Ensper se, notper accidens(a. 31). But Ens is a commune, not generically, but analogically; constituted by common relationship to one and the same terminus, as everything healthy is related to health. The Principle (ἀρχή) of all Entia is Essence (οὐσία); but some Entia are so called as being affections of Essence; others, as being a transition to Essence, or as destruction, privation, quality, efficient or generative cause, of Essence or itsanaloga; others, again, as being negations (ἀποφάσεις) thereof, whence, for example, we say that Non-EnsisNon-Ens (b. 6-10). There is one science of all these primary, secondary, tertiary, &c., Entia; just as there is one science of all things healthy, of the primary, the secondary, the tertiary, &c.,quatenushealthy. But, in all such matters, that science bears in the first instance and specially (κυρίως) on the Primum Aliquid, from which all the secondary and other derivatives take their departure, and upon which they depend (b. 16). Accordingly, in the present case, since Essence is the Primum Aliquid, the province of First Philosophy is to investigate the causes andprinciples of Essences in all their varieties (b. 18-22). Now whatever varieties there are of Ens, the like varieties there are of Unum; for the two are always implicated together, though the words are not absolutely the same in meaning (b. 24-35). Accordingly both Ens and Unum with all the varieties of each belong to Philosophia Prima; likewise Idem, Simile, &c., and the opposites thereof. All opposites may be traced in the last analysis to this foundation — the antithesis of Unum and Multa (p. 1004, a. 1). We must set forth and discriminate the different varieties — primary, secondary, tertiary, &c. — of Idem and Simile, and also of their opposites, Diversum and Dissimile; and we must show how they are derived from or related to Primum Idem, &c., just as we must do in the case of Ens and Unum. All this task belongs to First Philosophy (a. 20-30). Aristotle speaks of ὁ φιλόσοφος, as meaning the master of Philosophia Prima (b. 1;B.p. 997, a. 14).
If these investigations do not belong to the First Philosopher, to which among the other investigators can they belong? Who is to enquire whether Sokrates, and Sokrates sitting, is the same person? Whether Unum is opposite to Unum? In how many senses Opposite can be said? (p. 1004, b. 3). All these are affectionsper seof UnumquatenusUnum, and of EnsquatenusEns, notquatenusnumbers, or lines, or fire; that is, they are propria (sensu logico) of Ens and Unum (not included in the notion or definition, but deducible therefrom — “notæ consecutione notionisâ€�), just as odd and even, proportionality, equality, excess and defect, are propria of numbers; and there are other propria of solids, whether moved or unmoved, heavy or light. It is these propria of Ens and Unum that Philosophia Prima undertakes to explain (b. 7-16), and which others fail to explain, because they take no account of οὐσία (b. 10), or of the fundamental Ens or Essentia to which these belong as propria.
These Propria of Ens are the οἰκεῖα — the special and peculiar matter or principles — of Philosophia Prima. That all of them belong in this special way to the First Philosopher, we may farther see by the fact that all of them are handled by the Dialectician and the Sophist, who assume an attitude counterfeiting the Philosopher. All three travel over the same ground, and deal with Ens, as a matter common to all (p. 1004, b. 20). But the Sophist differs from the Philosopher in his purpose, inasmuch as he aims only at giving the false appearance of wisdom without the reality, while the Dialectician differs from the Philosopher in his manner of handling (τῷ τρόπῳ τῆς δυνάμεως — b. 24). The Dialectician discusses the subject in a tentative way, from many different points of view, suggested by current opinions; the Philosopher marches by a straight and assured road from the appropriate principles of his science to certain conclusions and cognitions.
The same view of the scope and extent of Philosophia Prima may be made out in another way. Almost all philosophers affirm that Entia are composed of contraries, and may be traced back to opposite principles — odd and even, hot and cold, limit and the unlimited, friendship and enmity, &c. Now these and all other contraries may be traced back to Unum and Multa: this we may assume (p. 1005, a. 1; according to Alexander Aph., it had been shown in the treatise De Bono — Schol. p. 648, a. 38, Br.).
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 EnsquatenusEns, together with the belongings or appendages (τὰ ὑπάρχοντα) of EnsquatenusEns, 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 EnsquatenusEns, 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 thathe 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: φύσει γὰρ ἀρχὴ καὶ τῶν ἄλλων ἀξιωμάτων αὕτη πάντων).
Aristotle then proceeds to explain and vindicate at length this ἀρχή â€” the Principle of Contradiction, which many at that time denied. This principle is at once the most knowable, and noway assumed as hypothesis (γνωριμωτάτην καὶ ἀνυπόθετον — 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 (ἀποδεῖξαι ἐλεγκτικῶς, 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 werenon 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 behomo; 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 termhomowill signify one thing only; it will have one determinate essence and definition — sayanimal bipes: that is, if any thing be a man, the same will beanimal bipes. But this last cannot be the essence and definition ofnon-homoalso:non-homo, as a different name, must have different definition;homoandnon-homocannot be like λώπιον and ἱμάτιον, two terms having the same signification, essence and definition; forhomosignifies one subject of constant and defined nature, not simply one among many predicates applicable by accident to this same constant subject; it signifies μίαν φύσιν and not ἄλλην τινὰ φύσιν (Scholia, p. 656, b. 21). Since each name indeed is applied by convention to what it denominates, the namenon-homomay be applied elsewhere to that which we termhomo; but this is a mere difference of naming; what bears the namehomo, and what bears the namenon-homo, must always be different, ifhomois defined to signify one determinate nature (b. 22). The one single nature and essence defined as belonging tohomo, cannot be the same as that belonging tonon-homo. If any thing behomo, the same cannot benon-homo: if any thing benon-homo, the same cannot behomo(b. 25-34). Whoever says thathomoandnon-homohave the same meaning, must sayà fortiorithathomo,fortis,musicus,simus,pulcher, &c., have the same meaning; for not one of these terms is so directly and emphatically opposite tohomo, asnon-homois. 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 (ὅτι ἓν πάντα ἔσται καὶ οὐ μόνον τὰ ἀντικείμενα — 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.: τῷ τήν τε ἀντίφασιν συναληθεύειν λέγοντι, καὶ σώζειν βουλομένῳ τὸ διαλέγεσθαι). 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 ishomo? he ought to answer plainly Yes, or No. He ought not to answer: “Yes, but Sokrates is alsonon-homo,â€� 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 ofany of them. Sokrates ishomo, by the essence and definition of the word; he isnon-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 wordnon-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 wordhomosignifies a certain Essentia, we mean that its Essentia is nothing different from this, and that the beinghomocannot be the same as the beingnon-homo, or the not beinghomo. Those against whom we are reasoning discard Essentia as distinguished from Accidens, and consider all predicates as Accidentia.Albusbelongs tohomoas an accident; but the essence ofalbusdoes not coincide with that ofhomo, and cannot be predicated ofhomo(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. Τὸ λευκόν may have the accident μουσικόν, or τὸ μουσικόν may have the accident λευκόν; each of these may be called indifferently the accident of the other; but the truth is, that λευκός and μουσικός are both of them accidents belonging to the common Essentia —homo. But, when we affirmhomo est musicus, we implicate the accident with the Essentia to which it belongs; that Essentia is signified by the subjecthomo. 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 — τὴν ἀντίφασιν συναληθεύειν — 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 triremismay 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 bothEst homoandEst non-homo: it must also be true to say of him bothNon est homoandNon 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 (αὗται ἂν εἶεν ὁμολογούμεναι — 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 groundand 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 μᾶλλον, and the distinction between λέγειν and ὑπολαμβάνειν, 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 asbeing 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 ἐγγύτερον τῆς ἀληθείας) 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 (κἂν εἰ μή ἐστιν, ἀλλ’ ἤδη γέ τι ἐστὶ βεβαιότερον καὶ ἀληθινώτερον, καὶ τοῦ λόγου ἀπηλλαγμένοι ἂν εἴημεν τοῦ ἀκράτου καὶ κωλύοντός τι τῇ διανοίᾳ ὁρίσαι — 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, eachman 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 (λόγου χάριν), 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 (ἐκ τῶν αἰσθητῶν — 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 oppositesin power, but notin act(δυνάμει μὲν γὰρ ἐνδέχεται ἅμα ταὐτὸ εἶναι τὰ ἐναντία, ἐντελεχείᾳ δ’ οὔ — 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 (ὁμοίως δὲ καὶ ἡ περὶ τὰ φαινόμενα ἀλήθεια ἐνίοις ἐκ τῶν αἰσθητῶν ἐλήλυθεν — p. 1009, b. 2; ὁμοίως refers back to a. 23 — αὕτη ἡ δόξα, 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 whichit proceeds and by which it is being generated; nor can this go backad 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: κατὰ μὲν οὖν τὸ ποσόν, ἔστω μὴ μένον· ἀλλὰ κατὰ τὸ εἶδος ἅπαντα γιγνώσκομεν. — 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 (ἀκίνητός τις φύσις — 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 — πᾶν τὸ φαινόμενον ἀληθές. 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 (τὸ φαινόμενον — which implies a reference to φαντασία — 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: τὸ δὲ τὰ ὑποκείμενα μὴ εἶναι, ἃ ποιεῖ τὴν αἴσθησιν, καὶ ἄνευ αἰσθήσεως, ἀδύνατον). 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 theseenquiries 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: ἔστι γὰρ πρὸς ἃ ἐκ φύσεως βέλτιον ἔχομεν ἢ ὥστε δεῖσθαι τῆς περὶ αὐτῶν ἀποδείξεως· ἔστι δὲ ταῦτα αἵ τε αἰσθήσεις, καὶ τὰ ἀξιώματα καὶ αἱ φυσικαί τε καὶ κοιναὶ ἔννοιαι.) 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 συλλογισμὸς ἀντιφάσεως); 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 (ἐν τῇ ἐπαλλάξει τῶν δακτύλων — 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 (μηθενὸς προδοξάσαντος — 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, ifhomoandconceptumhave both of them no more than a relative existence — that is, if both of them exist only in correlation with aconcipiens— then theconcipienscannot behomo; it will be theconceptumthat ishomo. And, if every individual thing have existence only in relation to aconcipiens, thisconcipiensmust 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: οὐδὲ τἀναντία ἅμα ὑπάρχειν ἐνδέχεται τῷ αὐτῷ). 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 othersecundum quid; or both of themsecundum quidonly (τῶν μὲν γὰρ ἐναντίων θάτερον στέρησίς ἐστιν οὐχ ἧττον, οὐσίας δὲ στέρησις ἀπόφασίς ἐστιν ἀπό τινος ὡρισμένου γένους — 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 predicatesest— or he who predicatesnon 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, predicateest 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: ὥστε καὶ ὁ λέγων εἶναι ἢ μὴ ἀληθεύσει ἢ ψεύσεται — which seems to me here better than that of Bonitz, who puts ὥστε καὶ ὁ λέγων τοῦτο εἶναι ἢ μὴ ἀληθεύσει ἢ ψεύσεται — 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 sayEns est, orNon-Ens non est, you speak truth; when you sayEns non est, orNon-Ens est, you speak falsehood. Accordingly, when you employ the predicateest, or when you employ the predicatenon 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-bonumtobonum) orvice versâ: now that which is bothnon-homoandnon-equusmust change, if it change at all, into that which is bothhomoandequus; 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: εἰ δ’ ἔστι μεταξύ — if such medium be admitted — καὶ οὕτως εἴη ἄν τις εἰς λευκὸν οὐκ ἐκ μὴ λευκοῦ γένεσις· νῦν δ’ οὐχ ὁρᾶται).
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 οὐσία must be either Generation,i.e., passage from τὸ μὴ ὄν to τὸ ὄν, or Destruction,i.e., passage from τὸ ὄν to τὸ μὴ ὄν. — 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: πᾶς γὰρ ἀριθμὸς ἢ ἄρτιός ἐστιν ἢ περιττός, καὶἀριθμός ἐστιν ὃς ἢ ἄρτιός ἐστιν ἢ περιττός— 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 ἀπόφασις, 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 (ἔτι ὅταν ἐρομένου εἰ λευκόν ἐστιν εἴπῃ ὅτι οὔ, οὐθὲν ἄλλο ἀποπέφηκεν ἢ τὸ εἶναι· ἀπόφασις δὲ τὸ μὴ εἶναι — p. 1012, a. 15; see Alex. Schol. p. 682, b. 15-38, and Bonitz’s note. Bonitz suggests, though timidly, ἀποπέφηκεν instead of the common reading ἀποπέφυκεν, which none of the commentators explain, and which seems unintelligible. I think Bonitz is right, though ἀποπέφηκεν is an unknown tense from ἀπόφημι: it is quite as regular as ἀποφήσω or ἀπέφησα.).
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, τὸ θρυλλούμενον — 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).