Reading Aristotle: Physics 1.4: Being is Not Infinite

Since it has been almost a month since my last post in this series reading through Aristotle, I’ll give a brief summary of what has come so far: In Physics 1.1, Aristotle laid out that for any branch of knowledge, we are concerned with carrying out our analysis to the underlying, foundational principles, causes, and elements. To do this, we start with what is obvious and evident to the senses and work our way down. In 1.2, we apply this method to the branch of knowledge of “physics”, which is in general a study of physical reality. The main question he asks here is whether the underlying principles are one or many, whether it/they are in motion, and whether they are finite or infinite. In the rest of 1.2 and continuing through 1.3, he responds to specific views of other philosophers who held that being is one, and, by examining and deconstructing their arguments, he arrives at the conclusion that being cannot be one, in the sense those philosophers held.

We continue with Physics 1.4:

“The physicists on the other hand have two modes of explanation. The first set make the underlying body one–either one of the three [elements] or something else which is denser than fire and rarer than air–then generate everything else from this, and obtain multiplicity by condensation and rarefaction. Now these are contraries, which may be generalized into ‘excess and defect’. (Compare Plato’s ‘Great and Small’–except that he makes these his matter, the one his form, while the others treat the one which underlies as matter and the contraries as differentiae, i. e. forms.)” (Physics 1.4, 187a11-15) [1].

If you remember from the beginning of 1.2, Aristotle stated that the underlying principles in question must be either one or more than one, and if one, it must be either motionless, as Parmenides and Melissus hold, or in motion, as “the physicists” hold. In 1.2 and 1.3 he dealt with the positions of Parmenides and Melissus; now he turns back to the physicists.

A quick note of reminder about physics here. Physics is the study of nature, so it is necessary that the physicists would hold that the principle is in motion. As Aquinas commentates:

“And natural science, which is called physics, deals with those things which depend upon matter not only for their existence, but also for their definition.

And because everything which has matter is mobile, it follows that mobile being is the subject of natural philosophy. For natural philosophy is about natural things, and natural things are those whose principle is nature. But nature is a principle of motion and rest in that in which it is. Therefore natural science deals with those things which have in them a principle of motion” [2].

So Aristotle begins 1.4 by presenting the different branches of thought which the physicists have held. The first view is that everything is generated from one “underlying body.” This underlying body would be one of the three famous Greek fundamental elements: water, air, and fire (most often four are given, with earth being the fourth. But Aristotle is just discussing these three here as possibilities given for the one underlying body). Or it might be something in between these three elements. Of course now we know, from modern physics, that water, air, and fire aren’t really fundamental elements at all, but that’s irrelevant. This underlying body is one, but everything else in existence is generated from it, and this creates multiplicity (the existence of which Melissus and Parmenides denied). This, says Aristotle, could be done by either “condensation” or “rarefaction”, the former being an increase in density, the latter a lessening of density. As generalizations, condensation and rarefaction are “contraries”equivalent to “excess and defect.” In other, simpler words, as St. Thomas puts it:

“The dense is what has much matter, whereas the rare has little” [3].

So, say the physicists, everything is made out of the same basic underlying stuff, but we perceive different types of beings because this underlying stuff is collected in different variations of compression; an object is just the underlying stuff with a specific level of density. He then compares this view to Plato’s. Plato, explains Aristotle, held a dualistic view of nature, in which matter is not the entirety of reality. Plato did hold that there was a “great and small” amongst material objects, akin to the “excess and defect”, but Plato held that this division persists only amongst material reality. But there is also for Plato the immaterial reality of the forms, which is one underlying principle that determines and causes the multiplicity and differentiations in material objects. St. Thomas again:

“Plato held that the great and the small are on the side of matter, because he posited one formal principle which is a certain idea participated in by different things according to a diversity of matter” [4].

For the physicists, the contraries are in form, not in matter. Matter is one principle, one underlying body, but is differentiated by different “forms” which are just that matter compressed in a variety of densities. So for Plato, the unity of the formal principle causes multiplicity in nature. For the physicists, a unity in nature (the underlying body) causes a multiplicity of forms. It’s also important to note that for Plato form is more fundamental while for the physicists matter is more fundamental and forms are only emergent from that matter.


“The second set assert that the contrarieties are contained in the one and emerge from it by segregation, for example Anaximander and also all those who assert that ‘what is’ is one and many, like Empedocles and Anaxagoras; for they too produce other things from their mixture by segregation. These differ, however, from each other in that the former imagines a cycle of such changes, the latter a single series. Anaxagoras again made both his ‘homoeomerous’ substances and his contraries infinite in multitude, whereas Empedocles posits only the so-called elements” (Physics 1.4, 187a20-26) [5].

The second branch of thought which the physicists hold is that the “contrarieties”, that is, differences and distinctions of substances, actually exist within the one underlying body itself as a “mixture”. In other words, the one underlying body consists of a “mixed and confused” aggregation of all the different substances of things; almost like a muddy primordial soup. Then, these things are “segregated” from the underlying body in which they already exist into the distinct beings we perceive now. Thus these philosophers assert that “what is” is both one and many. Anaximander is known for his theory of “the Boundless” as the origin and principle of all things, which is without beginning or end. It is from the Boundless that all things emerge. It is a kind of indefinite, limitless, infinite primordial mass that never ages nor decays, which contains within its indeterminate nature all opposites, such that distinct substances could arise from it [6]. This Boundless is one principle that we might think of as having the potential for producing all substances.

He also references Empedocles and Anaxagoras. St. Thomas helps explain the difference between Anaximander and these latter physicists. Anaximander held that the principle itself is the “one confused state” which is the Boundless, while these latter thinkers

“held rather that the principles are the very things which are mixed together in that one confused state. And so they held many principles, although they also held that this one confused state is in some way a principle” [7].

Which is all very abstract and confusing, but is not entirely crucial to understand here. Next Aristotle distinguishes the views of Empedocles and Anaxagoras. Empedocles thought “that there is a certain cycle of mixing and separating. For he held that the world has been made and corrupted many times” [8]. In other words, the confused state which is a mixture of all substances is continually being separated and then mixed back together again, over and over. When it is separated, everything mixed within it becomes distinct, and that is why we perceive many different beings. But then it coalesces again into its confused state, and this happens in a continuous cycle. Anaxagoras, however, although he did believe in mixture and segregation, did not think this happens in a cycle, but rather in a series. Originally, Anaxagoras thought, all things were mixed together in the primordial confused state. But then, something which he calls the nous or the mind or intellect, began to draw out the mixed substances so that they became distinguished from each other, and he did this through a process of rotation:

“Anaxagoras maintained that the original state of the cosmos was a mixture of all its ingredients (the basic realities of his system). The ingredients are thoroughly mixed, so that no individual ingredient as such is evident, but the mixture is not entirely uniform or homogeneous. Although every ingredient is ubiquitous, some ingredients are present in higher concentrations than others, and these proportions may also vary from place to place (even if they do not do so in the original state of the cosmos). The mixture is unlimited in extent, and at some point in time it is set into motion by the action of nous (intellect). The mixture begins to rotate around some small point within it, and as the whirling motion proceeds and expands through the mass, the ingredients in the mixture are shifted and separated out (in terms of relative density) and remixed with each other, ultimately producing the cosmos of apparently separate material masses and material objects, with differential properties, that we perceive     . . . The continouous ever-expanding rotation produces more and more separation. The Everything-in-Everything principle [the original confused state held all substances mixed together] continues to hold, so there are all ingredients at all places at all times, but the different densities of ingredients allow for local variations, and so the rotating mass becomes qualitatively differentiated” [9].

This rotation which causes separation continues forever, so more and more ingredients are generated.

Another difference between Empedocles and Anaxagoras is that the latter thought the confused state contained within it substances “infinite in multitude”, while the former just thought the confused state contained a mixture of the basic elements, which, when separated, are the building blocks of different physical objects. (Much more could be said about Anaxagoras’s substances which Aristotle labels as ‘homoeomerous’, but this will have to suffice for now).

The Philosopher continues:

“The theory of Anaxagoras that the principles are infinite in multitude was probably due to his acceptance of the common opinion of the physicists that nothing comes into being from not-being. For this is the reason why they use the phrase ‘all things were together’ and the coming into being of such and such a kind of thing is reduced to change of quality, while some spoke of combination and separation. Moreover, the fact that the contraries proceed from each other led them to the conclusion. The one, they reasoned, must have already existed in the other; for since everything that comes into being must arise either from what is or from what is not, and it is impossible for it to arise from what is not (on this point all the physicists agree), they thought that the truth of the alternative necessarily followed, namely that things come into being out of existent things, i. e. out of things already present, but imperceptible to our senses because of the smallness of their bulk” (Physics 1.4, 187a27-187b1) [10].

Here Aristotle discusses the famous principle that “nothing comes into being from not-being” or more simply “nothing comes from nothing.” The reason, says Aristotle, that these physicists held that all things were once contained in a primordial mixture, is because they cannot see how otherwise everything could have come into existence. If it exists, and if it cannot have come into existence out of nothing, then it must have come from something. As we’ve seen, the physicists held that there are two ways in which this is possible:

“Lest they would be forced to hold that something new comes to be which previously was in no way at all, some held that all things from the beginning existed together, either in some one confused state, as Anaxagoras and Empedocles held, or in some natural principle, such as water, fire, and air, or some intermediate between these.

And in accordance with this they posited two modes of production.

Those who held that all things pre-existed together as in one material principle said that to come to be is nothing other than to be altered. For they said that all things come to be from that one material principle through its condensation and rarefaction.

Others, however, who held that all things pre-existed together in some one confused state and mixture of many, said that the coming to be of things is only a joining together and a separation” [11].

So the first group held that there is one underlying body, and that the “coming to be” of different beings is just a “change in quality” or alteration of that one body, not the actually coming into existence of any new being. The second held that the principles already existed in a mixture, and that they “coming to be” of different beings is just the process of segregation of that mixture.

Where Aristotle says “the fact that the contraries proceed from each other led them to the conclusion,” he is referring to an idea that seems to have been commonly acknowledged amongst ancient Greek philosophers that opposites come from each other (this point is actually used in Plato’s dialogue “Phaedo” to argue for the immortality of the soul). For example, if you turn up the temperature in a room, the temperature becomes “hotter” by virtue of the fact that it was before “colder”, and vice versa. If you grow older it is because you were before younger. And etc. Contraries, these physicists held, proceed from each other. But if this is so, then an opposite must have already existed in its contrary. Since it is impossible for being to arise from non-being, then it must be the case that “things come into being out of existent things, i. e. out of things already present”. So hotness must already have existed somehow in coldness, or else hotness never could have come into existence. As Aquinas puts it, “he wished to say that everything which comes to be from something pre-existed in that from which it comes to be” [12]. But when we actually perceive something, we do not perceive its opposite in it. We do not see “darkness” contained within light, or light in darkness. So, reasons Anaxagoras, it must be contained in its contrary in a way that is “imperceptible to our senses because of the smallness of [its] bulk”. In other words, when something is contained in its opposite, it is so small in quantity in that opposite that it cannot be perceived by the senses.

“So they assert that everything has been mixed in everything, because they saw everything arising out of everything. But things, as they say, appear different from one another and receive different names according to the nature of the particles which are numerically predominant among the innumerable constituents of the mixture. For nothing, they say, is purely and entirely white or black or sweet, bone or flesh, but the nature of a thing is held to be that of which it contains the most” (Physics 1.4, 187b1-6) [13].

So just as one particular thing which comes to be from something is already existent in it, so everything that exists now must have been already existent in that from which it came. Since “they saw everything arising out of everything”, they concluded that “everything has been mixed in everything”. What this means is that in every single substance there is contained, in some minute way, all other substances. So from each substance, literally every other possible substance can arise. But if each substance contains within it all substances, then how do we see it as one substance, distinct from other substances? The answer, says Anaxagoras, is that the thing we see contains an infinite number of parts. But  whichever substance has the most parts in that particular object, that is the substance we call identify it as. To use an extremely simplistic example, suppose we have a square. Within that square, parts of every other shape are contained. Let’s say we can assign percentages to the amount of substance of other shapes contained with in: suppose it is composed 20% of triangles, 30% circles, 10% hexagon, and 40% square (although, in real substances, there would be an infinite number of these). Well, since the squares make up the most dominant part, that is the substance we call and perceive it as, even though it has literally all other substances held within it. Thus nothing is a pure substance. Nothing is just “white”, rather it contains all colors, but is just more white than it is those other colors.

How does Aristotle answer Anaxagoras?

“Now (I) the infinite qua infinite is unknowable, so that what is infinite in multitude or size is unknowable in quantity, and what is infinite in variety of kind is unknowable in quality. But the principles in question are infinite both in multitude and in kind. Therefore it is impossible to know things which are composed of them; for it is when we know the nature and quantity of its components that we suppose we know a complex” (Physics 1.4, 187a7-13) [14].

A thing which is infinite, responds Aristotle, is unknowable in the sense that it is infinite. So a thing that is of infinite size we might say is “indefinite”, we cannot actually know its size. But if a thing, as Anaxagoras maintains, is “infinite in variety”, meaning that it contains within it an infinitude of substances, then we cannot know what it actually is. As Aquinas puts it:

“What is known by the intellect is grasped by the intellect with respect to all that belongs to that thing. But this cannot happen with regard to something infinite” [15].

But Anaxagoras’s principles, says Aristotle, are infinite in both multitude and in kind, so therefore we cannot know them either in quantity or quality. Nor can we know “things which are composed of them”, which are just the normal objects of our experience. For we only “know” something by knowing the nature and quantity of its principles: what it is, what its physical dimensions are, what its composed of, etc.

Aristotle continues:

“Further (2) if the parts of a whole may be of any size in the direction either of greatness or of smallness (by ‘parts’ I mean components into which a whole can be divided and which are actually present in it), it is necessary that the whole thing itself may be of any size. Clearly, therefore, since it is impossible for an animal or plant to be indefinitely big or small, neither can its parts be such, or the whole will be the same. But flesh, bone, and the like are the parts of animals, and the fruits are the parts of plants. Hence it is obvious that neither flesh, bone, nor any such things can be of indefinite size in the direction either of the greater or of the lesser” (Physics 1.4, 187b14-21) [16].

In order for Anaxagoras’s theory to be right, it is necessary to hold that the parts in each substance are indefinitely small, because they are infinite in number and yet are so minuscule as to be imperceptible. But if the actual parts of an object are indefinitely small or large, then the object itself will also be indefinite in size (if, for example, my arm were infinitely long, and my arm is an actual part of my body, then my body as a whole would be infinitely long). But the objects in our experience aren’t indefinite in size; they have actual, quantifiable dimensions as part of their very nature of being finite bodies, so their parts cannot be indefinite in size either.

A quick point on this in reference to modern science. Today we know, of course, that the objects of our experience are in fact constructed from extremely minuscule parts, such as atoms and subatomic particles. But this is not quite what Aristotle means here in saying that something cannot have parts of “indefinite” smallness. Remember that he is responding to Anaxagoras’s assertion that everything that exists contains with in it parts of everything else that exists, but these parts are just so infinitely small that they are imperceptible. Now suppose we take a tree and measure its most basic composition. We’ll be able to detect (maybe not with our senses, but at least mathematically) that it consists of cells, atoms, and subatomic particles. But all these things, those particular cells, atoms, and subatomic particles, are all part of the tree itself. Anaxagoras’s claim would be that even beyond those fundamental subatomic particles in the substance of that tree there are even more minuscule parts that are not part of the tree at all, but rather of all other substances, and yet somehow they are contained within the tree, by being so indefinitely small that they are not detectable even along the lines of subatomic particles. It is this that Aristotle is refuting.

Going on:

“Again (3) according to the theory all such things are already present in one another and do not come into being but are constituents which are separated out, and a thing receives its designation from its chief constituent. Further, anything may come out of anything–water by segregation from flesh and flesh from water. Hence, since every finite body is exhausted by the repeated abstraction of a finite body, it seems obviously to follow that everything cannot subsist in everything else. For let flesh be extracted from water and again more flesh be produced from the remainder by repeating the process of separation: then, even though the quantity separated out will continually decrease, still it will not fall below a certain magnitude. If, therefore, the process comes to an end, everything will not be in everything else (for there will be no flesh in the remaining water); if on the other hand it does not, and further extraction is always possible, there will be an infinite multitude of finite equal particles in a finite quantity–which is impossible. Another proof may be added: Since every body must diminish in size when something is taken from it, and flesh is quantitatively definite in respect both of greatness and smallness, it is clear that from the minimum quantity of flesh no body can be separated out; for the flesh left would be less than the minimum of flesh” (Physics 1.4, 187b22-188a2) [17].

Basically, Aristotle here shows the pure mathematical absurdity of Anaxagoras’s position. For Anaxagoras, as we’ve seen, holds that everything that comes to be, comes to be from something which it pre-existed in. But since physical objects are finite, then when something “comes to be” from what it pre-existed in, it is subtracted from that thing. But if we subtract a finite thing from a finite thing, we reduce the latter, until eventually it is nothing. If, for example, we take our tree again, and begin plucking off its leaves one by one, we reduce the overall quantity of the tree. If we pluck off all the leaves, and then take off all the branches, and finally saw away the trunk, and dig up the roots, etc., etc., if we take away every single physical part to the tree, eventually we will be left with nothing, since the tree is finite. But then “it seems obviously to follow that everything cannot subsist in everything else.” Everything cannot come from everything. If we have a pool filled with water, and take one cup of water away again and again, eventually we will empty the pool. If we do so, we know that the pool is not actually infinite. No matter how big a finite number of some objects you have, repeated, continuous subtraction of finite numbers will always eventually reach zero (you could perhaps proceed to infinity in division of a finite thing with respect to fractions, but Aristotle specifies that he is talking about “equal” particles).

For the last part of the argument, I’ll let St. Thomas explain:

“Every body becomes a smaller one when something is taken from it, because every whole is greater than its parts. Since then the quantity of flesh is determinately great or small, as is clear from what was said above, there must be some smallest bit of flesh. Therefore from this nothing can be separated, because the remainingfiesh would be smaller than this smallest piece of flesh. Therefore it is impossible that everything comes to be from everything by separation” [18].

Aristotle continues his response:

“Lastly (4) in each of his infinite bodies there would be already present infinite flesh and blood and brain–having a distinct existence, however, from one another, and no less real than the infinite bodies, and each infinite: which is contrary to reason” (Physics 1.4, 188a3-4) [19].

In other words, if everything exists in everything, then parts that exist in an object contain with themselves everything, and the parts which exist within that part contain everything within them, and so on. To go back to our earlier example of a shapes: If you have a square, the square contains an infinite number of all shapes within it. But suppose you take out of the square a triangle. That triangle also has within it an infinite number of all shapes. So you are taking everything from everything. And yet, to go back to the tree, if you take just one branch from the tree, the rest of the tree is still there, and still contains everything within it. So you are taking everything away from everything, and you are left with everything. Which is, to put it mildly, “contrary to reason”.

Having refuted his argument, Aristotle shows that Anaxagoras’s position is untenable in itself:

“The statement that complete separation never will take place is correct enough, though Anaxagoras is not fully aware of what it means. For affections are indeed inseparable. If then colours and states had entered into the mixture, and if separation took place, there would be a ‘white’ or a ‘healthy’ which was nothing but white or healthy, i. e. was not the predicate of a subject. So his ‘Mind’ is an absurd person aiming at the impossible, if he is supposed to wish to separate them, and it is impossible to do so, both in respect of quantity and of quality–of quantity, because there is no minimum magnitude, and of quality, because affections are inseparable” (Physics 1.4, 188a5-13) [20].

Remember that Anaxagoras believed that nothing is a pure substance on its own, it is always a mixture, and that the Nous/Mind/Intellect will always be undergoing the process of separating the mixtures. Aristotle agrees with Anaxagoras that, in a sense, “complete separation never will take place”, but not because there is an infinite multitude of parts within each substance. It is rather because everything has both substance and accident (quality, attributes), and the accidents cannot exist on their own, apart from a substance. You cannot separate “white” from that which is white, and have it as a color on its own. As we’ve said before, “whiteness” does not exist on its own, but rather only in the objects which possess it as an attribute (a white horse, a white house, etc). Presumably, when Anaxagoras refers to a mixture of all things, this includes both substance and accident, such that the Mind is trying to separate one from the other, which is impossible.

Finally, we reach the conclusion of 1.4:

“Nor is Anaxagoras right about the coming to be of homogeneous bodies. It is true there is a sense in which clay is divided into pieces of clay, but there is another in which it is not. Water and air are, and are generated, ‘from’ each other, but not in the way in which bricks come ‘from’ a house and again a house ‘from’ bricks; and it is better to assume a smaller and finite number of principles, as Empedocles does (Physics 1.4, 188a14-18) [21].

Anaxagoras thought that since being cannot come from non-being, then that what is must come from what is similar; what it comes from must somehow contain it within itself. So if we take material from a house and form it into a brick, those materials were contained in that from which it came. But Aristotle says it is false to assume this has to be so for everything. Not everything comes to be from what is similar to it. This is a point he develops more fully later on. And in conclusion, he states that “it is better to make the principles smaller in number and finite, as Empedocles does, than to make them many and infinite, as does Anaxagoras” [22].




[1]. McKeon, Richard, editor. The Basic Works of Aristotle. New York: Random House, Inc, 1941. Print, 224.

[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. <>.

[3]. Ibid.

[4]. Ibid.

[5]. McKeon. The Basic Works of Aristotle. 224.

[6]. See Couprie, Dirk L. “Anaximander (c. 610—546 B.C.E.).” Internet Encyclopedia of Philosophy. Web. 11 Nov. 2016. <;.

[7]. 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. <>.

[8]. Ibid.

[9]. Curd, Patricia, “Anaxagoras”, The Stanford Encyclopedia of Philosophy (Winter 2015 Edition), Edward N. Zalta (ed.), URL = <;.

[10]. McKeon. The Basic Works of Aristotle. 224-225.

[11]. 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. <>.

[12]. Ibid.

[13]. McKeon. The Basic Works of Aristotle. 225.

[14]. Ibid.

[15]. 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. <>.

[16].  McKeon. The Basic Works of Aristotle. 225.

[17]. Ibid. 225-226.

[18]. 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. <>.

[19]. McKeon. The Basic Works of Aristotle. 226.

[20]. Ibid.

[21]. Ibid.

[22]. 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. <>.

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






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