George Grote

In regard to Aristotle, there are two points to be examined —

I. What position does he take up in respect to the authority of Common Sense?

II. What doctrine does he lay down about the first principia or beginnings of scientific reasoning — the ???a? s??????st??a??

I. — That Aristotle did not regard Cause, Substance, Time, &c., as Intuitions, is shown by the subtle and elaborate reasonings that he employs to explain them, and by the censure that he bestows on the erroneous explanations and shortcomings of others. Indeed, in regard to Causality, when we read the great and perplexing diversity of meaning which Aristotle (and Plato before him in the PhÆdon) recognizes as belonging to this term, we cannot but be surprised to find modern philosophers treating it as enunciating a simple and intuitive idea. But as to Common Sense — taking the term as above explained, and as it is usually understood by those that have no particular theory to support — Aristotle takes up a position at once distinct and instructive; a position (to use the phraseology of Kant) not dogmatical, but critical. He constantly notices and reports the affirmations of Common Sense; he speaks of it with respect, and assigns to it a qualified value, partly as helping us to survey the subject on all sides, partly as a happy confirmation, where it coincides with what has been proved otherwise; but he does not appeal to it as an authority in itself trustworthy or imperative.

Common Sense belongs to the region of Opinion. Now the distinction between matters of Opinion on the one hand, and matters of Science or Cognition on the other, is a marked and characteristic feature of Aristotle’s philosophy. He sets, in pointed antithesis, Demonstration, or the method of Science — which divides itself into special subjects, each having some special principia of its own, then proceeds by legitimate steps of deductive reasoning from such principia, and arrives at conclusions sometimes universally true, always true for the most part — against Rhetoric and Dialectic, which deal with and discuss opinions upon all subjects, comparing opposite arguments, and landing in results more or less probable. Contrasting them as separate lines of intellectual procedure, Aristotle lays down a theory of both. He recognizes the procedure of Rhetoric and Dialectic as being to a great degree the common and spontaneous growth of society; while Demonstration is from the beginning special, not merely as to subject, but as to persons, implying teacher and learner.

Rhetoric and Dialectic are treated by Aristotle as analogous processes. Of the matter of opinion and belief, with which both of them deal, he distinguishes three varieties: (1) Opinions or beliefs entertained by all; (2) By the majority; (3) By a minority of superior men, or by one man in respect to a science wherein he has acquired renown. It is these opinions or beliefs that the rhetorician and the dialectician attack and defend; bringing out all the arguments available for or against each.

The Aristotelian treatise on Rhetoric opens with the following words:— “Rhetoric is the counterpart of Dialectic; for both of them deal with such matters as do not fall within any special science, but belong in a certain way to the common knowledge of all. Hence every individual has his share of both, greater or less; for every one can, up to a certain point, both examine others and stand examination from others; every one tries to defend himself and to accuse others.”13 To the same purpose Aristotle speaks about Dialectic, in the beginning of the Topica:— “The dialectical syllogism takes its premisses from matters of opinion, that is, from matters that seem good to (or are believed by) all, or the majority, or the wise — either all the wise, or most of them, or the most celebrated.” Aristotle distinguishes these matters of common opinion or belief from three distinct other matters:— (1) From matters that are not really such, but only in appearance; in which the smallest attention suffices to detect the false pretence of probability, while no one except a contentious Sophist ever thinks of advancing them; on the contrary, the real matters of common belief are never thus palpably false, but have always something deeper than a superficial show; (2) From the first truths or principia, upon which scientific demonstration proceeds; (3) From the paralogisms, or fallacious assumptions (?e?d???af?ata), liable to occur in each particular science.

Now what Aristotle here designates and defines as “matters of common opinion and belief” (t? ??d??a) includes all that is usually meant, and properly meant, by Common Sense — what is believed by all men or by most men. But Aristotle does not claim any warrant or authority for the truth of these beliefs, on the ground of their being deliverances of Common Sense, and accepted (by all or by the majority) always as indisputable, often as self-evident. On the contrary, he ranks them as mere probabilities, some in a greater, some in a less degree; as matters whereon something may be said both pro and con, and whereon the full force of argument on both sides ought to be brought out, notwithstanding the supposed self-evidence in the minds of unscientific believers. Though, however, he encourages this dialectical discussion on both sides as useful and instructive, he never affirms that it can by itself lead to certain scientific conclusions, or to anything more than strong probability on a balance of the countervailing considerations. The language that he uses in speaking of these deliverances of Common Sense is measured and just. After distinguishing the real Common Opinion from the fallacious simulations of Common Opinion set up (according to him) by some pretenders, he declares that in all cases of Common Opinion there is always something more than a mere superficial appearance of truth. In other words, wherever any opinion is really held by a large public, it always deserves the scrutiny of the philosopher to ascertain how far it is erroneous, and, if it be erroneous, by what appearances of reason it has been enabled so far to prevail.

13 Aristot. Rhetor. I. i. p. 1354, a. 1. Compare Sophist. Elench. xi. p. 172, a. 30.

Again, at the beginning of the Topica (in which he gives both a theory and precepts of dialectical debate), Aristotle specifies four different ends to be served by that treatise. It will be useful (he says) —

1. For our own practice in the work of debate. If we acquire a method and system, we shall find it easier to conduct a debate on any new subject, whenever such debate may arise.

2. For our daily intercourse with the ordinary public. When we have made for ourselves a full collection of the opinions held by the many, we shall carry on our conversation with them out of their own doctrines, and not out of doctrines foreign to their minds; we shall thus be able to bring them round on any matter where we think them in error.

3. For the sciences belonging to philosophy. By discussing the difficulties on both sides, we shall more easily discriminate truth and falsehood in each separate scientific question.

4. For the first and highest among the principia of each particular science. These, since they are the first and highest of all, cannot be discussed out of principia special and peculiar to any separate science; but must be discussed through the opinions commonly received on the subject-matter of each. This is the main province of Dialectic; which, being essentially testing and critical, is connected by some threads with the principia of all the various scientific researches.

We see thus that Aristotle’s language about Common Opinion or Common Sense is very guarded; that, instead of citing it as an authority, he carefully discriminates it from Science, and places it decidedly on a level lower than Science, in respect of evidence; yet that he recognizes it as essential to be studied by the scientific man, with full confrontation of all the reasonings both for and against every opinion; not merely because such study will enable the scientific man to study and converse intelligibly and efficaciously with the vulgar, but also because it will sharpen his discernment for the truths of his own science, and because it furnishes the only materials for testing and limiting the first principia of that science.

II. We will next advert to the judgment of Aristotle respecting these principia of science: how he supposes them to be acquired and verified. He discriminates various special sciences (geometry, arithmetic, astronomy, &c.), each of which has its own appropriate matter, and special principia from which it takes its departure. But there are also certain principia common to them all; and these he considers to fall under the cognizance of one grand comprehensive science, which includes all the rest; First Philosophy or Ontology — the science of Ens in its most general sense, quatenus Ens; while each of the separate sciences confines itself to one exclusive department of Ens. The geometer does not debate nor prove the first principia of his own science; neither those that it has in common with other sciences, nor those peculiar to itself. He takes these for granted, and demonstrates the consequences that logically follow from them. It belongs to the First Philosopher to discuss the principia of all. Accordingly, the province of the First Philosopher is all-comprehensive, co-extensive with all the sciences. So also is the province of the Dialectician alike all-comprehensive. Thus far the two agree; but they differ as to method and purpose. The Dialectician seeks to enforce, confront, and value all the different reasons pro and con, consistent and inconsistent; the First Philosopher performs this too, or supposes it to be performed by others, but proceeds farther: namely, to determine certain Axioms that may be trusted as sure grounds (along with certain other principia) for demonstrative conclusions in science.

Aristotle describes in his Analytica the process of Demonstration, and the conditions required to render it valid. But what is the point of departure for this process? Aristotle declares that there cannot be a regress without end, demonstrating one conclusion from certain premisses, then demonstrating those premisses from others, and so on. You must arrive ultimately at some premisses that are themselves undemonstrable, but that may be trusted as ground from whence to start in demonstrating conclusions. All demonstration is carried on through a middle term, which links together the two terms of the conclusion, though itself does not appear in the conclusion. Those undemonstrable propositions, from which demonstration begins, must be known without a middle term, that is, immediately known; they must be known in themselves, that is, not through any other propositions; they must be better known than the conclusions derived from them; they must be propositions first and most knowable. But these two last epithets (Aristotle often repeats) have two meanings: first and most knowable by nature or absolutely, are the most universal propositions; first and most knowable to us, are those propositions declaring the particular facts of sense. These two meanings designate truths correlative to each other, but at opposite ends of the intellectual line of march.

Of these undemonstrable principia, indispensable as the grounds of all Demonstration, some are peculiar to each separate science, others are common to several or to all sciences. These common principles were called Axioms, in mathematics, even in the time of Aristotle. Sometimes, indeed, he designates them as Axioms, without any special reference to mathematics; though he also uses the same name to denote other propositions, not of the like fundamental character. Now, how do we come to know these undemonstrable Axioms and other immediate propositions or principia, since we do not knew them by demonstration? This is the second question to be answered, in appreciating Aristotle’s views about the Philosophy of Common Sense.

He is very explicit in his way of answering this question. He pronounces it absurd to suppose that these immediate principia are innate or congenital, — in other words, that we possess them from the beginning, and yet that we remain for a long time without any consciousness of possessing them; seeing that they are the most accurate of all our cognitions. What we possess at the beginning (Aristotle says) is only a mental power of inferior accuracy and dignity. We, as well as all other animals, begin with a congenital discriminative power called sensible perception. With many animals, the data of perception are transient, and soon disappear altogether, so that the cognition of such animals consists in nothing but successive acts of sensible perception. With us, on the contrary, as with some other animals, the data of perception are preserved by memory; accordingly our cognitions include both perceptions and remembrances. Farthermore, we are distinguished even from the better animals by this difference — that with us, but not with them, a rational order of thought grows out of such data of perception, when multiplied and long preserved. And thus out of perception grows memory; out of memory of the same matter often repeated grows experience, since many remembrances of the same thing constitute one numerical experience. Out of such experience, a farther consequence arises, that what is one and the same in all the particulars, (the Universal or the One alongside of the Many), becomes fixed or rests steadily within the mind. Herein lies the principium of Art, in reference to Agenda or Facienda — of Science, in reference to Entia.

Thus these cognitive principia are not original and determinate possessions of the mind, nor do they spring from any other mental possessions of a higher cognitive order, but simply from data of sensible perception; which data are like runaway soldiers in a panic, first one stops his flight and halts, then a second follows the example, afterwards a third and fourth, until at length an orderly array is obtained. Our minds are so constituted as to render this possible. If a single individual impression is thus detained, it will presently acquire the character of a Universal in the mind; for, though we perceive the particular, our perception is of the Universal (i.e., when we perceive Kallias, our perception is of man generally, not of the man Kallias). Again the fixture of these lowest Universals in the mind will bring in those of the next highest order; until at length the Summa Genera and the absolute Universals acquire a steady establishment therein. Thus, from this or that particular animal, we shall rise as high as Animal universally; and so on from Animal upwards.

We thus see clearly (Aristotle says) that only by Induction can we come to know the first principia of Demonstration; for it is by this process that sensible perception engraves the Universal on our minds.14 We begin by the notiora nobis (Particulars), and ascend to the notiora natur or simpliciter (Universals). Some among our mental habits that are conversant with truth, are also capable of falsehood (such as Opinion and Reasoning): others are not so capable, but embrace uniformly truth and nothing but truth; such are Science and Intellect (????). Intellect is the only source more accurate than Science. Now the principia of Demonstration are more accurate than the demonstrations themselves, yet they cannot (as we have already observed) be the objects of Science. They must therefore be the object of what is more accurate than Science, namely, of Intellect. Intellect and the objects of Intellect will thus be the principia of Science and of the objects of Science. But these principles are not intuitive data or revelations. They are acquisitions gradually made; and there is a regular road whereby we travel up to them, quite distinct from the road whereby we travel down from them to scientific conclusions.

14 Aristot. Anal. Post. II. p. 100, b. 3: d???? d? ?t? ??? t? p??ta ?pa???? ??????e?? ??a??a???· ?a? ??? ?a? a?s??s?? ??t? t? ?a????? ?p??e?; also ibid. I. xviii., p. 81, b. 3, upon which passage Waitz, in his note, explains as follows (p. 347):— “Sententia nostri loci hÆc est. Universales propositiones omnes inductione comparantur, quum etiam in iis, quÆ a sensibus maxime aliena videntur, et quÆ, ut mathematica (t? ?? ?fa???se??), cogitatione separantur a materia quacum conjuncta sunt, inductione probentur ea quÆ de genere (e.g., de linea vel de corpore mathematico), ad quod demonstratio pertineat, prÆdicentur ?a?’ a?t? et cum ejus natura conjuncta sint. Inductio autem iis nititur quÆ sensibus percipiuntur: nam res singulares sentiuntur, scientia vero rerum singularium non datur sine inductione, non datur inductio sine sensu.”

The chapter just indicated in the Analytica Posteriora, attesting the growth of those universals that form the principia of demonstration out of the particulars of sense, may be illustrated by a similar statement in the First Book of the Metaphysica. Here, after stating that sensible perception is common to all animals, Aristotle distinguishes the lowest among animals, who have this alone; then, a class next above them, who have it along with phantasy and memory, and some of whom are intelligent (like bees), yet still cannot learn, from being destitute of hearing; farther another class, one stage higher, who hear, and therefore can be taught something, yet arrive only at a scanty sum of experience; lastly, still higher, the class men, who possess a large stock of phantasy, memory, and experience, fructifying into science and art.15 Experience (Aristotle says) is of particular facts; Art and Science are of Universals. Art is attained, when out of many conceptions of experience there arises one universal persuasion respecting phenomena similar to each other. We may know that Kallias, sick of a certain disease — that Sokrates, likewise sick of it — that A, B, C, and other individuals besides, have been cured by a given remedy; but this persuasion respecting ever so many individual cases, is mere matter of experience. When, however, we proceed to generalize these cases, and then affirm that the remedy cures all persons suffering under the same disease, circumscribed by specific marks — fever or biliousness — this is Art or Science. One man may know the particular cases empirically, without having generalized them into a doctrine; another may have learnt the general doctrine, with little or no knowledge of the particular cases. Of these two, the last is the wiser and more philosophical man; but the first may be the more effective and successful as a practitioner.

In the passage above noticed, Aristotle draws the line of intellectual distinction between man and the lower animals. If he had considered that it was the prerogative of man to possess a stock of intuitive general truths, ready-made, and independent of experience, this was the occasion for saying so. He says the exact contrary. No modern psychologist could proclaim more fully than Aristotle here does the derivation of all general concepts and general propositions from the phenomena of sense, through the successive stages of memory, association, comparison, abstraction. No one could give a more explicit acknowledgment of Induction from particulars of sense, as the process whereby we reach ultimately those propositions of the highest universality, as well as of the highest certainty; from whence, by legitimate deductive syllogism, we descend to demonstrate various conclusions. There is nothing in Aristotle about generalities originally inherent in the mind, connate although dormant at first and unknown, until they are evoked or elicited by the senses; nothing to countenance that nice distinction eulogized so emphatically by Hamilton (p. 772, a. note): “Cognitio nostra omnis À mente primam originem, À sensibus exordium habet primum.” In Aristotle’s view, the senses furnish both originem and exordium: the successive stages of mental procedure, whereby we rise from sense to universal propositions, are multiplied and gradual, without any break. He even goes so far as to say that we have sensible perception of the Universal. His language undoubtedly calls for much criticism here. We shall only say that it discountenances altogether the doctrine that represents the Mind or Intellect as an original source of First or Universal Truths peculiar to itself. That opinion is mentioned by Aristotle, but mentioned only to be rejected. He denies that the mind possesses any such ready-made stores, latent until elicited into consciousness. Moreover, it is remarkable that the ground whereon he denies it is much the same as that whereon the advocates of intuitions affirm it, viz., the supreme accuracy of these axioms. Aristotle cannot believe that the mind includes cognitions of such value, without being conscious thereof. Nor will he grant that the mind possesses any native and inherent power of originating these inestimable principia.16 He declares that they are generated in the mind only by the slow process of induction, as above described; beginning from the perceptive power (common to man with animals), together with that first stage of the intelligence (judging or discriminative) which he combines or identifies with perception, considering it to be alike congenital. From this humble basis men can rise to the highest grades of cognition, though animals cannot. We even become competent (Aristotle says) to have sensible perception of the Universal; in the man Kallias, we see Man; in the ox feeding near us, we see Animal.

It must be remembered that, when Aristotle, in this analysis of cognition, speaks of Induction, he means induction completely and accurately performed; just as, when he talks of Demonstration, he intends a good and legitimate demonstration; and just as (to use his own illustration in the Nikomachean Ethica), when he reasons upon a harper, or other professional artist, he always tacitly implies a good and accomplished artist. Induction thus understood, and Demonstration, he considers to be the two processes for obtaining scientific faith or conviction; both of them being alike cogent and necessary, but Induction even more so than Demonstration; because, if the principia furnished by the former were not necessary, neither could the conclusions deduced from them by the latter be necessary. Induction may thus stand alone without Demonstration, but Demonstration pre-supposes and postulates Induction. Accordingly, when Aristotle proceeds to specify those functions of mind wherewith the inductive principia and the demonstrated conclusions correlate, he refers both of them to functions wherein (according to him) the mind is unerring and infallible — Intellect (????) and Science. But, between these two he ranks Intellect as the higher, and he refers the inductive principia to Intellect. He does not mean that Intellect (????) generates or produces these principles. On the contrary, he distinctly negatives such a supposition, and declares that no generative force of this high order resides in the Intellect; while he tells us, with equal distinctness, that they are generated from a lower source — sensible perception, and through the gradual upward march of the inductive process. To say that they originate from Sense through Induction, and nevertheless to refer them to Intellect (????) as their subjective correlate, — are not positions inconsistent with each other, in the view of Aristotle. He expressly distinguishes the two points, as requiring to be separately dealt with. By referring the principia to Intellect (????), he does not intend to indicate their generating source, but their evidentiary value and dignity when generated and matured. They possess, in his view, the maximum of dignity, certainty, cogency, and necessity, because it is from them that even Demonstration derives the necessity of its conclusions; accordingly (pursuant to the inclination of the ancient philosophers for presuming affinity and commensurate dignity between the cognitum and the cognoscens), they belong as objective correlates to the most unerring cognitive function — the Intellect (????). It is the Intellect that grasps these principles, and applies them to their legitimate purpose of scientific demonstration; hence Aristotle calls Intellect not only the principium of Science, but the principium principii.

In the Analytica, from which we have hitherto cited, Aristotle explains the structure of the Syllogism and the process of Demonstration. He has in view mainly (though not exclusively) the more exact sciences, arithmetic, geometry, astronomy, &c. But he expressly tells us that all departments of inquiry are not capable of this exactness; that some come nearer to it than others; that we must be careful to require no more exactness from each than the subject admits; and that the method adopted by us must be such as will attain the admissible maximum of exactness. Now each subject has some principia, and among them definitions, peculiar to itself; though there are also some principia common to all, and essential to the march of each. In some departments of study (Aristotle says) we get our view of principia or first principles by induction; in others, by sensible perception; in others again, by habitual action in a certain way; and by various other processes also. In each, it is important to look for first principles in the way naturally appropriate to the matter before us; for this is more than half of the whole work; upon right first principles will mainly depend the value of our conclusions. For what concerns Ethics, Aristotle tells us that the first principles are acquired through a course of well-directed habitual action; and that they will be acquired easily, as well as certainly, if such a course be enforced on youth from the beginning. In the beginning of the Physica, he starts from that antithesis, so often found in his writings, between what is more knowable to us and what is more knowable absolutely or by nature. The natural march of knowledge is to ascend from the first of these two termini (particulars of sense) upward to the second or opposite,17 and then to descend downward by demonstration or deduction. The fact of motion he proves (against Melissus and Parmenides) by an express appeal to induction, as sufficient and conclusive evidence. In physical science (he says) the final appeal must be to the things and facts perceived by sense. In the treatise De Coelo he lays it down that the principia must be homogeneous with the matters they belong to: the principia of perceivable matters must be themselves perceivable; those of eternal matters must be eternal; those of perishable matters, perishable.

The treatises composing the Organon stand apart among Aristotle’s works. In them he undertakes (for the first time in the history of mankind) the systematic study of significant propositions enunciative of truth and falsehood. He analyses their constituent elements; he specifies the conditions determining the consistency or inconsistency of such propositions one with another; he teaches to arrange the propositions in such ways as to detect and dismiss the inconsistent, keeping our hold of the consistent. Here the signification of terms and propositions is never out of sight: the facts and realities of nature are regarded as so signified. Now all language becomes significant only through the convention of mankind, according to Aristotle’s express declaration: it is used by speakers to communicate what they mean to hearers that understand them. We see thus that in these treatises the subjective point of view is brought into the foreground — the enunciation of what we see, remember, believe, disbelieve, doubt, anticipate, &c. It is not meant that the objective point of view is eliminated, but that it is taken in implication with, and in dependence upon, the subjective. Neither the one nor the other is dropped or hidden. It is under this double and conjoint point of view that Aristotle, in the Organon, presents to us, not only the processes of demonstration and confutation, but also the fundamental principia or axioms thereof; which axioms in the Analytica Posteriora (as we have already seen) he expressly declares to originate from the data of sense, and to be raised and generalized by induction.

Such is the way that Aristotle represents the fundamental principles of syllogistic Demonstration, when he deals with them as portions of Logic. But we also find him dealing with them as portions of Ontology or First Philosophy (this being his manner of characterizing his own treatise, now commonly known as the Metaphysica). To that science he decides, after some preliminary debate, that the task of formulating and defending the axioms belongs, because the application of these axioms is quite universal, for all grades and varieties of Entia. Ontology treats of Ens in its largest sense, with all its properties quatenus Ens, including Unum, Multa, Idem, Diversum, Posterius, Prius, Genus, Species, Totum, Partes, &c. Now Ontology is with Aristotle a purely objective science; that is, a science wherein the subjective is dropt out of sight and no account taken of it, or wherein (to state the same fact in the language of relativity) the believing and reasoning subject is supposed constant. Ontology is the most comprehensive among all the objective sciences. Each of these sciences singles out a certain portion of it for special study. In treating the logical axioms as portions of Ontology, Aristotle undertakes to show their objective value; and this purpose, while it carries him away from the point of view that we remarked as prevailing in the Organon, at the same time brings him into conflict with various theories, all of them in his time more or less current. Several philosophers — Herakleitus, Anaxagoras, Demokritus, Protagoras — had propounded theories which Aristotle here impugns. We do not mean that these philosophers expressly denied his fundamental axioms (which they probably never distinctly stated to themselves, and which Aristotle was the first to formulate), but their theories were to a certain extent inconsistent with these axioms, and were regarded by Aristotle as wholly inconsistent.

The two Axioms announced in the Metaphysica, and vindicated by Aristotle, are —

1. The Maxim of Contradiction: It is impossible for the same thing to be and not to be; It is impossible for the same to belong and not to belong to the same, at the same time and in the same sense. This is the statement of the Maxim as a formula of Ontology. Announced as a formula of Logic, it would stand thus: The same proposition cannot be both true and false at the same time; You cannot both believe and disbelieve the same proposition at the same time; You cannot believe, at the same time, propositions contrary or contradictory. These last-mentioned formulae are the logical ways of stating the axiom. They present it in reference to the believing or disbelieving (affirming or denying) subject, distinctly brought to view along with the matter believed; not exclusively in reference to the matter believed, to the omission of the believer.

2. The Maxim of Excluded Middle: A given attribute either does belong, or does not belong to a subject (i.e., provided that it has any relation to the subject at all) — there is no medium, no real condition intermediate between the two. This is the ontological formula; and it will stand thus, when translated into Logic: Between a proposition and its contradictory opposite there is no tenable halting ground; If you disbelieve the one, you must pass at once to the belief of the other — you cannot at the same time disbelieve the other.

These two maxims thus teach — the first, that we cannot at the same time believe both a proposition and its contradictory opposite; the second, that we cannot at the same time disbelieve them both.18

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.19 Indeed 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.

Again, the theory of Anaxagoras denied all simple bodies (excepting NoÛs) and all definite attributes. He held that everything was mingled with everything 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

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 known”) 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 the principia of 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 ????. 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 a petitio 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,21 and 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.” This answer is unintelligible; DikÆopolis cannot act upon it; until Kephisophon explains that “not within” 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

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 the principia of 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.23 It 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.

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 second principium of 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 are contrary; the particular affirmative and the particular negative are sub-contrary; the universal affirmative and the particular negative, or the universal negative and the particular affirmative, are contradictory. 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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