Reading Aristotle: Physics 1.6: The Number of Principles

In chapter 5 of his Physics, Aristotle established that the fundamental, underlying principles of natures must be “contraries”. In 1.6, he asks how many are the underlying principles.

“The next question is whether the principles are two or three or more in number. One they cannot be, for there cannot be one contrary. Nor can they be innumerable, because, if so, Being will not be knowable: and in any one genus there is only one contrariety, and substance is one genus: also a finite number is sufficient, and a finite number, such as the principles of Empedocles, is better than an infinite multitude; for Empedocles professes to obtain from his principles all that Anaxagoras obtains from his innumerable principles. Lastly, some contraries are more primary than others, and some arise from others–for example sweet and bitter, white and black–whereas the principles must always remain principles. This will suffice to show that the principles are neither one nor innumerable” (Physics 1.6, 189a11-21) [1].

So the Philosopher rules out from the start the possibility of the principles of nature being only one in number. This is because he has already shown that the principles must be contraries, but “there cannot be one contrary”. Obviously, a “contrary” must be of something. Hot and cold are contraries, but if just cold existed, then it could not be called a “contrary”, since it would not be contrary to anything. As Aquinas succinctly puts it in his commentary, “nothing is the contrary of itself” (Lectio 11.83) [2]. Aristotle also rules out the possibility of the principles being “innumerable” or infinite in number, giving four brief reasons for this conclusion: First “Because, if so, Being will not be knowable.” If the principles are innumerable, then by definition they cannot be known, and this would render being intelligible. Aquinas explains:

“The infinite as such is unknown. If, therefore, the principles are infinite, they must be unknown. But if the principles are unknown, then those things which are from the principles are unknown. It follows, therefore, that nothing in the world could be known” (Lectio 11.84) [3].

To summarize: if the principles were infinite, they would be unknowable. If the principles themselves were unknowable, then that which is derived from them (the nature and reality of our perceptual experience) would also be unknowable. But as was argued in 1.5, the very first assumption of any natural science or philosophy must be that being is in some sense intelligible and coherent. And so it cannot be that the principles are innumerable.

The second reason has to do with substance and genus. The only thing Aristotle says of this is that “in any one genus there is only one contrariety, and substance is one genus.” Aquinas extrapolates:

“The principles must be primary contraries, as was shown above. But the primary contraries belong to the primary genus, which is substance. But substance, since it is one genus, has one primary contrariety. For the first contrariety of any genus is that of the primary differentiae by which the genus is divided. Therefore, the principles are not infinite” (Lectio 11.85) [4].

This passage relies heavily on concepts introduced in another of Aristotle’s works, the Categories. In 1.5, Aristotle established that the principles must in fact be primary contraries. But, says Aquinas, primary contraries must belong to the “primary genus.” Substance is the primary genus, by its very definition. In Categories, Aristotle writes:

“Primary substances are most properly called substances in virtue of the fact that they are the entities which underlie everything else, and that everything else is either predicated of them or present in them” (Categories Chapter 5, 2b15-18) [5].

Examples of substances would be: man, horse, tree, etc. Substances are independent, unitary existing things. All other categories (quality, quantity, etc.) cannot exist on their own, but rather depend on, and inhere in, and are predicated of, substances. Thus “tall” or “tallness” cannot exist on its own; it does not have its own independent being. But “tallness” can exist in a man; we can say “that man is tall.” The “man”, however, can exist independently of the tallness. Substance is what underlies all the other categories. Since substance is the primary genus, it has one primary contrariety (set of contraries). The primary contrariety of a genus consists of the differentiae (the attributes which distinguish the different species of a genus). Obviously the species of a genus will in a sense be contraries to each other, and so the differentiae which define/separate the species constitute the “primary contrariety”. So, based on what seems to be an assumption that the species of a genus cannot be infinite, then it would be the case that the contraries which separate those species likewise could not be infinite. (I’m not entirely sure I’m getting the right gist of this part of the argument. Nevertheless, it’s only one of four total arguments given for the impossibility of infinite principles, so the others should make up for it).

The third reason is based on the sufficiency or adequacy of positing a finite number of principles as opposed to infinite. Basically, Aristotle seems to be suggesting that if it is possible to explain nature using only finite principles, then it is better to do so (perhaps a kind of of Occam’s Razor appeal?). “A finite number,” he says, “. . . is better than an infinite multitude.” This could also be building off of the first reason he gave about the unintelligibility of having innumerable principles. In that sense it is quite clear that a finite number is better than an infinite number of principles. So if an explanation in terms of a finite number of principles is possible, it is better to hold to such. And is it possible? In answering the affirmative Aristotle makes reference to Empedocles (see 1.4), who held that everything comes from a confused, mixed state of all the substances, which in an endless cycle are separated into distinct objects and then reassumed into the mixture. Empedocles’s theory accounted for how things come to be, and it did so using only a finite number of principles. Aristotle has already shown why the Empedocles’s specific view is wrong, but the theory itself shows that at least such an explanation is possible, and therefore that such an explanation is superior to one, such as Anaxagoras’s (also in 1.4), which posited “innumerable principles”.

The final reason concerns the very nature of what principles must be. Aquinas explains:

“Principles are contraries. If, therefore, the principles are infinite, it is necessary that all the contraries be principles. But all of the contraries are not principles. This is clear for two reasons. First, the principles must be primary contraries, but not all contraries are primary, since some are prior to others. Secondly, the principles ought not to be from each other, as was said above. But some contraries are from each other, as the sweet and the bitter, and the white and the black. Therefore, the principles are not infinite” (Lectio 11.87) [6].

Since principles are contraries, then if there are an infinite number of principles, there must be an infinite number of contraries, and this will (apparently) include all contraries. But the principles cannot include all contraries, for while principles are contraries, not all contraries are first principles. In 1.5 the distinction between primary contraries and contraries in general was made, and it was shown that the first principles must be primary contraries. Also in 1.5 was the discussion of why principles cannot be derived from each other, for then they would not truly be principles. But some contraries are derived from other contraries. So not all contraries can be principles, and thus the principles cannot be infinite.

And so, “This will suffice to show that the principles are neither one nor innumerable.” These are ruled out from the start, but how then can we discover how many there actually are?

“Granted, then, that they are a limited number, it is plausible to suppose them more than two. For it is difficult to see how either density should be of such a nature as to act in any way on rarity or rarity on density. The same is true of any other pair of contraries; for Love does not gather strife together and make things out of it, nor does Strife make anything out of Love, but both act on a third thing different from both. Some indeed assume more than one such thing from which they construct the world of nature” (Physics 1.6, 189a22-28) [7].

So since there cannot be one or unlimited principles, it must either be two, or more than two (but less than infinity). Here he argues against there being only two by pointing out that “it is difficult to see” how two things which are contrary can act upon each other. Remember that one condition for something being a first principle is that everything else must derive from it. But “If, however, there are only two contrary principles, it is not apparent how all things can come to be from these two. For it cannot be said that one of them makes something from the other one” (Lectio 11.90) [8]. Contraries by their nature are opposed to each other; and when we say that contraries arise or come to be from each other, we do not mean that one contrary in itself comes to be the other (an excellent explanation of this would look at Plato’s Phaedo, in which Socrates argues this very point, but that will have to be left to some other time). In other words, “heat” in itself never becomes “cold”, because if heat were to become cold it would no longer be heat, it would no longer be what it is. Rather there is some subject in which heat inheres, and in which that heat passes from heat to cold. “Both act on a third thing different from both”. Or as Aquinas puts it:

“For heat does not make coldness itself to be hot, but makes the subject of coldness to be hot. And conversely, coldness does not make heat itself to be cold, but makes the subject of heat to be cold. Therefore, in order that other things can come to be from the contraries, it seems that it is necessary to posit some third thing which will be the subject of the contraries” (Lectio 11.90) [9].

So we must posit at least three principles: the two contraries and one subject in which the contraries come to be. This subject possibly could be more than one, however, as “some indeed assume more than one such thing from which they construct the world of nature”.

Aristotle continues:

“Other objections to the view that it is not necessary to assume a third principle as a substratum may be added. (1) We do not find that the contraries constitute the substance of any thing. But what is a first principle ought not to be the predicate of any subject. If it were, there would be a principle of the supposed principle: for the subject is a principle, and prior presumably to what is predicated of it. Again (2) we hold that a substance is not contrary to another substance. How then can substance be derived from what are not substances? Or how can non-substance be prior to substance?” (Physics 1.6, 189a28-33) [10].

A first principle cannot be an accident, since, if it were, it would be predicated of something, and that something would thus be more fundamental than it, such that there would be “a principle of the supposed principle”. But they also cannot be substances, since “we do not find that the contraries constitute the substance of any thing”. But, “if we hold that only the contraries are principles, it is necessary that the principles be an accident predicated of a subject” (Lectio 11.91) [11].  So if the only principles are contraries, and if substance cannot be a contrary, then the principles would have to be accidents. But, as was just said, the principles cannot be accidents, because they’d have to be predicated of something more fundamental. To resolve this contradiction, we must hold that contraries cannot be the only principles; there must be something else which acts as a principle.

Some might object to the assertion that substance cannot be a contrary. Is it not so that, when one constructs a house, the substance “house” comes to be from “non-house”? (Never-mind here that a house is an artifact, not a substance; we’re using it merely as an illustration of a substance). Wouldn’t this be an example of two contrary substances? No, because there is no substance that is “non-house”. Rather, as was discussed in 1.5, separated materials are brought together in composition, such that “composition” comes from “non-composition”, but this is only possible given the pre-existing subject of the materials. Being composite and non-composite are both accidents. And accidents are predicated of something, of some substance. But “composite” and “non-composite” are not primary contraries, since they arise from each other. Primary contraries are not accidents.

He gives another reason for holding a third principle, which also starts from the fact that substance is not a contrary. Since substance is not a contrary, then if the contraries were the only principles, “substance” would have to come from non-substance. For in that case, substance would not be a principle, and “everything which is not a principle must be from principles” (Lectio 11.92) [12] by definition, so substance would have to be from something more fundamental than itself. But, asks Aristotle, “how can non-substance be prior to substance?” It cannot, again by the very definition of what a substance is. Says Aquinas:

“But this is impossible. For substance which is being per se is the first genus of being. Therefore, it cannot be that only the contraries are principles; rather it is necessary to posit some other third thing” (Lectio 11.92) [13].

So in order to avoid these difficulties, we most hold that there are at least three principles, two of them contraries.

Now, a quick point must be mentioned. Some think that Aristotle has just contradicted himself and undermined his own argument. For principles must be that from which everything else is derived, and they cannot themselves be derived from anything. But now Aristotle insists that there must be something that “underlies” the contraries. Would this not mean that the contraries are not actually principles, but rather that what underlies them is the real principle? I do not think this necessarily has to be the case. As we’ll see further in 1.7, the underlying “substratum” post be posited to account for change. But that does not mean that the contraries themselves are “derived” from that underlying substratum, just that they must exist with the substratum. Indeed, the whole point of the Physics is to account for change in nature, and if we just had the substratum, with no principles of contraries, then there would be no change at all. So it seems that we must keep the contraries along with the underlying substratum altogether as three first principles.

Moving on:

“If then we accept both the former argument and this one, we must, to preserve both, assume a third somewhat as the substratum of the contraries, such as is spoken of by those who describe the All as one nature–water or fire or what is intermediate between them. What is intermediate seems preferable; for fire, earth, air, and water are already involved with pairs of contraries. There is, therefore, much to be said for those who make the underlying substance different from these four; of the rest, the next best choice is air, as presenting sensible differences in a less degree than the others; and after air, water. All however, agree in this, that they differentiate their One by means of the contraries, such as density and rarity and more and less, which may of course be generalized, as has already been said, into excess and defect. Indeed this doctrine too (that the One and excess and defect are the principles of things) would appear to be of old standing, though in different forms; for the early thinkers made the two the active and the one the passive principle, whereas some of the more recent maintain the reverse” (Physics 1.6, 189a34-189b15) [14].

Here Aristotle compares the arguments just given to the positions of other philosophers. There is a certain tension that exists at this point in the development of the argument. For in 1.5 he showed that the principles must be contraries. But now in 1.6 he has shown that contraries are not sufficient on their own as principles. And to resolve this we must “assume a third somewhat as the substratum of the contraries”, and this was also assumed “by those who describe the All as one nature”, or “by those who held that the whole universe is some one nature, understanding nature to mean matter, such as water, or fire or air, or some intermediate state between these, such as vapour, or some other thing of this sort” (Lectio 11.93) [15]. He then discusses the various ways these other philosophers understood the material in terms of the “elements”. Different thinkers held different elements to be the one nature, water or fire or air or an intermediate between them. Aristotle suggests that the intermediate is the “preferable” choice, because the other elements “are already involved with pairs of contraries”, and the third principle is supposed to be distinct from the contraries. As Aquinas puts it:

“For fire and earth and air and water have contrariety attached to them, e.g., the hot and the cold, the wet and the dry. Hence, it is not unreasonable that they make the subject something other than these and something in which the contraries are less prominent” (Lectio 11.93) [16].

Of those who do not hold an intermediary, but rather some specific element, as matter, Aristotle thinks that “the next best choice is air”, because the contraries attached to the element of air are apparently less noticeable to the senses than those attached to other elements. And after air is water, presumably for similar reasons.

But despite their differences in identifying the material principle, all these other philosophers agreed, insists Aristotle, on including contraries as principles along with the material principle: “they differentiate their One by means of the contraries”. We’ve seen examples of this in 1.5. The contraries they chose to differentiate the One are reducible to “excess and defect”. Thus the three principles amongst these other philosophers would be: the One, excess, and defect, “though in different forms”. The older thinkers (such as some of those examined in 1.5) thought that excess and defect are “active” principles which act upon the “passive principle” of matter, while “some of the more recent” (such as Plato) reversed this, holding that the one active principle is Form, while there are two passive principles which make up matter. Says Aquinas:

“But the Platonists, thinking that many individuals in one species are distinguished by a division of matter, posited one principle on the part of the form, which is the active principle, and two on the part of the matter, which is the passive principle” (Lectio 11.94) [17].

Aristotle goes on:

“To suppose then that the elements are three in number would seem, from these and similar considerations, a plausible view, as I said before. On the other hand, the view that they are more than three in number would seem to be untenable” (Physics 1.6, 189b16-18) [18].

So we have established that the principles cannot be one or infinite, but that they must be at least three. And now the Philosopher will argue that they cannot be more than three either:

“For the one substratum is sufficient to be acted on; but if we have four contraries, there will be two contrarieties, and we shall have to suppose an intermediate nature for each pair separately. If, on the other hand, the contrarieties, being two, can generate from each other, the second contrariety will be superfluous. Moreover, it is impossible that there should be more than one primary contrariety. For substance is a single genus of being, so that the principles can differ only as prior and posterior, not in genus; in a single genus there is always a single contrariety, all the other contrarieties in it being held to be reducible to one” (Physics 1.6, 189b19-27) [19].

Again at the start he is insisting as before that if something is sufficient as explanation there is no need to appeal to something other than it. So if one material principle or substratum is sufficient to be acted upon by the contraries in change, then there is no reason to think that there is more than the one principle.

Next, where he says “if we have four contraries, there will be two contrarieties”, the contrarieties are just the set or pair of the contraries. In a change or becoming, one contrary comes from another, such that we must posit two contraries. But if, for whatever reason, we needed to account for four contrarieties, and thus two contrarieties, then we would need to posit two different underlying subjects, one for each contrariety. “An intermediate nature for each pair separately”. If, to continue the experiment, we for some reason thought there must be six contraries and thus three contrarieties, then we would have to conclude that there are three subjects or underlying material principles. And so on. But since, “on the other hand, the contrarieties, being two, can generate from each other, the second contrariety will be superfluous”. Or in other words, two contraries are sufficient to explain change, so we only need to posit one substratum.

Furthermore, it is actually impossible “that there should be more than one primary contrariety”. For, Aquinas explains, “If there are more than three principles, it is necessary that there be many primary contrarieties” (Lectio 11.96) [20]. For as we’ve just seen, the three principles account for one contrariety and one underlying subject, so if there were more principles, there would be more than one contrariety. This is impossible, according to Aristotle, on the basis of the following: 1) “In a single genus there is always a single contrariety,all the other contrarieties in it being held to be reducible to one”. As we mentioned earlier, the contrariety in a genus is its differentiate, what distinguishes its species. And one genus will have just one primary contrariety, to which all others reduce. 2) But there is just one primary genus of being, which is substance. 3) Because there is just one primary genus, the primary principles cannot differ in genus, they can differ only “as prior and posterior” in relation to each other. 4) Since the principles are all contained in one genus, and since each genus has one contrariety, then the principles must have only one contrariety, and thus only two contraries. And, as explained above, two contraries only need one underlying subject. So we need in total only three principles, and we cannot have more than that.

Some may notice that we’ve said that substance cannot be contrary, and yet that substance has one primary contrariety. Aquinas explains how this can be the case:

“It must be noted . . . that there is no contrariety in substances, and that in substances there is only one primary contrariety. For if we take substance to mean ‘that which is’, it has no contrary. If, however, we take substance to mean formal differentiae in the genus of substance, then contrariety is found in them” (Lectio 11.96) [20].

Finally, in conclusion:

“It is clear then that the number of elements is neither one nor more than two or three; but whether two or three is, as I said, a question of considerable difficulty” (Physics 1.6, 189b28-29) [21].

So in chapter six he narrowed down the possible number of principles to two or three, but in the end established, albeit not without “considerable difficulty”, that it must be three.

A brief note in finish: 1.6 was perhaps the most difficult chapter in the Physics so far to adequately grasp and comprehend what exactly Aristotle was saying. Contemporary scholars themselves aren’t entirely sure how to interpret some points, and there is much debate about many of the issues therein. In addition, much of 1.6 requires a knowledge of the Categories in order to understand, and as I have not yet written about that work, much of what was said in this chapter had to go without complete explanation. However, pushing through these difficulties, 1.7, to which we will turn next, is an extremely significant chapter which sheds more light on what has already been said and brings us closer to the finish of Book 1.



[1]. McKeon, Richard, editor. The Basic Works of Aristotle. New York: Random House, Inc, 1941. Print, 228.

[2]. Thomas Aquinas. Commentary on Aristotle’s Physics. Books I-II translated by
Richard J. Blackwell, Richard J. Spath & W. Edmund Thirlkel
Yale U.P., 1963. Lectio 11.83 <>.

[3]. Ibid. Lectio 11.84.

[4]. Ibid. Lectio 11.85.

[5]. McKeon. The Basic Works of Aristotle. 10.

[6]. Aquinas. Commentary. Lectio 11.87.

[7]. McKeon. Aristotle. 229.

[8]. Aquinas. Commentary. Lectio 11.90.

[9]. Ibid.

[10]. McKeon. Aristotle. 229.

[11]. Aquinas. Commentary. Lectio 11.91.

[12]. Ibid. Lectio 11.92.

[13]. Ibid.

[14]. McKeon. Aristotle. 229.

[15]. Aquinas. Commentary. Lectio 11.93.

[16]. Ibid.

[17]. Ibid. 11.94.

[18]. McKeon. Aristotle. 229.

[19]. Ibid. 229-230.

[20]. Aquinas. Commentary. Lectio 11.94.

[21]. McKeon. Aristotle. 230.

Cover image in the Public Domain in the United States, taken from Wikimedia Commons:



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