Mathematical Things and Forms

We’ve reached the end of Aristotle’s Metaphysics, though there are in fact two more books, Mu (XIII) and Nu (XIV).

Aristotle’s main point of contention with his former colleagues of the Platonic Academy is whether or not mathematical objects and forms understood as universals are independent things in their own right. Both books Mu and Nu (XIV) are concerned with this, and have a somewhat polemical character. I think Aristotle’s own distinctive views on form are better expressed in what has been said already, so I will mostly focus on the other remarks he makes in book Mu, and will skip book Nu entirely.

Book Mu does not clearly refer to the preceding book Lambda (XII), but does refer to previous discussion of “the thinghood that has being as being-at-work” (Sachs tr., ch. 1, p. 253) as well as to discussion on aporias.

“Now it is necessary, if mathematical things are, that they be either in the perceptible things, as some people say, or separate from the perceptible things (and some people also speak of them that way); or if they are not present in either way, then they do not have being or they have it in some other manner. So for us the dispute will not be about whether they have being, but about the manner of their being” (pp. 253-254).

I take especial note of the last sentence above. This could also serve as a comment on what is at stake in the Metaphysics in general — questions not really about being as if it were one thing, but about what things are, and the ways they are.

He goes on to argue that mathematical things are neither “in” perceptible things, nor are they separate things in their own right. “In” for Aristotle suggests a material constituent.

“It has been said sufficiently, then, that mathematical things are not independent things more than bodies are, nor are they prior in being to perceptible things, but only in articulation, nor are they capable of being somewhere as separate; but since they are not capable of being in perceptible things either, it is clear that either they have no being at all, or that they have being in a certain manner and for this reason do not have being simply, for we speak of being in a number of ways” (ch. 2, p. 257).

For those who insist that the whole Metaphysics is a single linear development and not just generally coherent with itself, and also that being finally acquires an unequivocal sense, it seems inconvenient that now, after book Lambda, he continues to emphasize that being is said in many ways.

I think the Metaphysics is very much coherent with itself, but is not a single linear development pointing toward Being, and that he never wavers on the emphasis that being is said in many ways, although he does sometimes use the word equivocally himself. If the whole thing points toward something, that something is the good and the beautiful, and not Being.

He goes on to make some positive remarks about mathematics.

“Now just as the things that are universal within mathematics are not about things that are separate from magnitudes and numbers, but are about these, but not insofar as they are of such a sort as to have magnitude or to be discrete, it is clear that it is also possible for there to be both articulations and demonstrations about perceptible magnitudes, not insofar as they are perceptible but insofar as they are of certain sorts” (ch. 3, p. 257).

He is saying that insofar as there is mathematical knowledge, it is not about magnitude or number as such, but about more specific things such as right triangles or even numbers. Similarly, the meaning of articulations and demonstrations about perceptible magnitudes does not depend on their perceptibility as such.

“[S]ince it is true to say simply that there are not only separate things but also things that are not separate…, it is also true to say simply that there are mathematical things and that they are of such a sort as people say….If it is about things which incidentally are perceptible, but is not concerned with them insofar as they are perceptible, mathematical knowledge will not be about perceptible things; however, it will not be about other separate beings besides these either” (p. 258).

Mathematical things are bona fide things in the broad sense, but not all things are separate or independent. Some are attributed to others.

“[I]f someone examines anything concerning these attributes, insofar as they are such, positing them to be separate, he will not on this account cause anything to be false, any more than when one draws a line on the ground that is not a foot long, and says it is a foot long, for the false assumption is not in the proposition…. [F]or this reason the geometers speak rightly” (pp. 258-259).

Mistaken belief about the independence of mathematical things is incidental to the doing of mathematics. It is irrelevant to the results of constructions or calculations.

“And since the good and the beautiful are different (for the former is always involved in action but the beautiful is also present in motionless things), those who claim that the mathematical kinds of knowledge say nothing about what is beautiful and good are wrong…. The greatest forms of the beautiful are order and symmetry and determinateness, which the mathematical kinds of knowledge most of all display. And since these make their appearance as causes of many things…, it is clear that these kinds of knowledge would also speak about what has responsibility in the manner of the beautiful as a cause in some manner” (p. 259).

Here he not only recognizes mathematical beauty, but relates it to the beauty associated with that-for-the-sake-of-which as a cause.

“The opinion about the forms came to those who spoke about them as a result of being persuaded by the Heraclitean writings that it is true that all perceptible things are always in flux, so that, if knowledge and thought are to be about anything, there must be, besides the perceptible things, some other enduring natures, since there can be no knowledge of things in flux. And then Socrates made it his business to be concerned with the moral virtues, and on account of them first sought to define things in a universal way. For among those who studied nature, only to a small extent did Democritus attain to this… and before that the Pythagoreans did about some few things…. But it is reasonable that Socrates sought after what something is…. But Socrates did not make the universals or the definitions separate, while those who came next did, and called beings of this sort forms” (ch. 4, p. 260).

Aristotle rejects the Heraclitean doctrine of radical flux that influenced Plato. He says Plato was driven to assert separate forms because he wanted to assert that there is knowledge, in spite of his Heracliteanism about perceptible things. Aristotle says that driven by a concern for ethics, Socrates — and not any of those we know as the pre-Socratics — was the first to seriously inquire about what things are. Aristotle has been inquiring about the what-it-is of things and its causes and sources, and we have seen in abundance his concern for the good and the beautiful. Aristotle is claiming a Socratic heritage, and claiming to be truer to it than the Platonists: “Socrates did not make the universals or the definitions separate”.

There follows a long argument against Platonic views about the forms, at the end of which he observes:

“[K]nowledge, like knowing, has two senses, the one as in potency, the other as at-work. The potency, being, like material, universal and indeterminate, is of what is universal and indeterminate, but the being-at-work is determinate and of something determinate; being a this it is of a this, but incidentally sight sees a universal color because this color that it sees is a color, and this A that the grammarian contemplates is an A” (ch. 10, p. 279).

If I am reading this right, he is saying here that being as universal and indeterminate is to being-at-work as potentiality is to being-at-work. If that is so, then the priority of actuality over potentiality would also seem to be a priority of actuality over being. Once again, it just doesn’t seem that being is the principal term.

In any case, he returns to the ultimately ethical theme of the priority of actuality or being-at-work or fulfillment over potentiality, and of particular concrete things over universals in the ordinary logical sense. This still has to be carefully balanced with his other view that there is no knowledge of particulars; knowledge is of universals only.

Positive concern for the priority of actuality is in my opinion the primary thing that underlies his sharp critique of the Platonists. The second — evidenced in the part I skipped over — was the popularity within the Academy of a kind of Pythagorean mystique of numbers that also identified the forms with numbers, in sometimes baffling ways. Plato himself was apparently not immune to this.

Many think Aristotle claims to have knowledge of non-perceptible particular independent everlasting things. I think this interpretation relies on ambiguous use of Aristotle’s saying of “knowledge” in different ways in different contexts. Sometimes he means it very strictly, other times much more loosely. Some translations add confusion by using the same English “knowledge” for other Greek words like gnosis, which I think for Aristotle means personal acquaintance with things nearer to us, whereas episteme is supposed to be about things in their own right.

I do not think that Aristotle means to claim knowledge in the strong sense about ultimate things, but rather that his attitude was in a way closer to that of Kant, who held them to have the highest importance but not to be knowable in the strict sense. This means we do not have to equivocate about what knowledge is.

The wisdom that is called sophia in book capital Alpha initially seems to be concerned with universals in the ordinary sense, as true episteme or knowledge genuinely is. It turns out in book Lambda that sophia‘s primary concern is not with universals in the ordinary sense at all, but with analogous relations that a uniquely positioned particular or particulars has or have to all other things.

In any case, my own view is that the wisdom or sophia concerning these highest things ought to be understood as aligned not so much with knowledge or episteme, as with the ethical or “practical” wisdom (phronesis) that is explicitly said to be a wisdom about particulars. A wisdom about particulars is not prevented from making — and indeed presumably would make — use of knowledge of any universals that genuinely apply. Nonetheless it is the wisdom about particulars that judges which universals should apply in a particular case.

Pure Entelechy

Book Lambda (XII) of the Metaphysics sketches Aristotle’s brilliant and beautiful solution to the problems that have been under investigation in this work. The text of book Lambda itself, however, seems more like a series of fragments than the kind of tight, continuous development that characterizes the so-called “central books” Zeta (VII), Eta (VIII), and Theta (IX), or the books of Aristotle’s Physics.

He now clearly affirms that there is a first cause of all things — not only of their being what they are, but also of their motion. As a result, book Lambda presents a mix of philosophical theology and Aristotelian physics.

Aristotle has a very distinctive notion of what the first cause is. I would call this pure entelechy. I’m not aware that he literally uses that phrase, but he definitely says that the first cause is pure energeia (actuality, being-at-work, or fulfillment), and he very strongly identifies energeia with entelecheia (a new Greek word coined by Aristotle, meaning literally “in [it] end having”, or “being-at-work-staying-itself” in Sachs’ translation), for which I am using the English “entelechy”.

Entelechy is the theme that unifies Aristotle’s account of motion with the inquiry about why things are what they are. Motion is a kind of incomplete entelechy. The first cause, both of motion and of things being what they are — which he identifies with the good, that-for-the-sake-of-which, thought thinking itself, and what I would call a kind of pure delight — is a complete and pure entelechy. The concept of entelechy thus binds Aristotle’s physics together with his theology.

Apart from considerations related to the first cause, Aristotle normally distinguishes that-for-the-sake-of-which from the potentiality that is an internal source of motion in things. But he also says that every motion is for the sake of that toward which the potentiality inclines. And the first cause of all motion affects things purely as that-for-the-sake-of-which.

The kind of motion that best exemplifies entelechy is circular motion. Circularity is also a kind of figurative image or metaphor for entelechy. Continuous motion in a circle is in a sense always complete in the sense of unchangingly accomplishing its goal, and yet it is always ongoing. But not even the first motion is itself unconditionally complete as an entelechy, since it is still moving. Only the first cause is that.

For Aristotle, there is one thing that is directly moved by the first cause, and that is the sphere of the fixed stars, which also demarcates the most comprehensive whole of things that occupy space. Other motions are indirect consequences of this, which follow only in a conditional way.

The first cause is not just pure entelechy in the generic sense of a logical universal. It is a particular independent thing that turns out to be the unique exemplar of its kind.

In virtue of its unique relation to all other things, it plays the role of what Hegel would later call a concrete universal. Further, the unique character of that relation of “firstness” makes it an unconditioned concrete universal. This is the kind of unconditioned thing that Kant says reason is always reaching for, but that cannot be strictly known. It is also the kind of unconditioned thing that Hegel treats as the ultimate ground of intelligibility and value.

He begins by recalling that the path of the inquiry has approached “all things” by focusing on those sources and causes that make concrete independent things be what they are. Independent things turn out to be those that have some entelechy of their own, which exhibits greater self-determination than the minimal kind that applies to all motions. These include plants, animals, and the stars.

“Our study concerns thinghood, for it is the sources and causes of independent things that are being sought” (ch. 1, Sachs tr., p. 231).

“[E]verything changes from something that has being in potency to something that has being at-work” (ch. 2, p. 232).

All change for Aristotle is from something being potentially something to its being that same something in actuality or being-at-work or fulfillment. This is narrower than common English usage. In Physics book VII he says that “states, whether of the body or of the soul, are not alterations” (Collected Works, Barnes ed., vol. 1, p. 412).

“Now if something has being in potency, still this is not a potency to be any random thing, but a different thing comes to be from a different potency” (ibid).

Although one thing may have many potentialities, each of which may or may not be realized, each of these is a specific potentiality to be actual or at-work or fulfilled in some definite way.

“The kinds of thinghood are three, since the material is a this by coming forth into appearance (for whatever has being by way of contact, and not by having grown together, is material and underlies something else), while the nature of a thing is a this and an active condition into which it comes; and then the third kind is the particular thing that consists of these, such as Socrates or Callias” (ch. 3, p. 233).

He reminds us that when we speak of particular things, to avoid confusion we need to attend to whether we mean their matter, their form, or the composite consisting of both.

“Now things that cause motion are causes as being previously present, but things that are causes in the sense of rational patterns are simultaneous with what they produce” (p. 234).

Causes that are not of motion as such, but rather simply of being in a certain way, like form and that-for-the-sake-of-which, are not like more direct causes of motion in their mode of operation with respect to time. Their operation as causes does not involve a distinct externality related to a before and after, but rather unfolds immanently in their effects.

“Now there is a sense in which the causes and sources of different things are different, but there is a sense in which, if one speaks universally by way of analogy, they are the same for all things…. [B]ut the elements are different in different things, and the first cause that sets them in motion is also different in different things…. [B]ut still, over and above these, is the cause which, as the first of all things, sets all things in motion” (ch. 4, p. 234-236).

For Aristotle, everything has both a particular cause or causes, and a dependency on the first cause of all. The first cause of all operates through particular causes. This is the first time he has unambiguously implied that there is a first cause of all things. (In the middle above, when he speaks of “the first cause that sets them in motion”, this is not the first cause of all, but the first more specific cause of the motion in question.)

“Now since some things are separate while others are not separate, the former are independent things. And it is on account of this that all things have the same causes, because without independent things, attributes and motions are not possible. So then these causes will be, presumably, soul and body, or intellect, desire, and body. And in yet another way the sources of things are the same by analogy, namely being-at-work and potency, though these are both different and present in different ways in different things” (ch. 5, p. 236).

Once again, he recalls both the strategy of deriving the saying of being in the other categories from the saying of what independent things are, and the analogy by which the meanings of actuality and potentiality were illustrated. Again he emphasizes actuality and potentiality as sources of all things.

In passing, he seems to suggest thinking about human being in more specific terms of intellect and desire, rather than an undifferentiated soul. In the Nicomachean Ethics, he specifies that choice is grounded in a fusion of intellect and desire.

“Further, it is necessary to see that some things are possible to state universally, but others not. Now the primary sources of all things are a this that is first at work and something else which is in potency. So these are not the universal causes, since the source of particular things is particular; for a human being is the source of a human being universally, but no one is this universal, but rather Peleus is the source of Achilles and your father of you, and this particular B is the source of this particular BA, but B in general is the source of BA simply. And then, if the causes and elements of independent things are the sources of all things (but different ones of different ones), then as was said, of things not in the same class (colors and sounds, or independent things and quantity) they are different except by analogy; of things that are in the same kind they are also different, but not in kind, but because they are different for particular things, your material and form and mover from mine, though they are the same in their universal statement” (p. 237).

Again he emphasizes that particulars have particular causes. The kind of universality and operation that will be attributed to the first cause of all will be of a sort that respects this. He also again emphasizes that the primary sources of all things are particular actualities and potentialities.

“So as for seeking out what are the sources or elements of independent things and of relations and the of-what-sorts of things, and whether they are the same or different, it is clear that, since they are meant in more than one way, they do belong to everything, but when they have been distinguished they are not the same but different, except in one sense. And the causes of all things are the same in this sense — by analogy — because they are material, form, deprivation, and a mover, and the causes of independent things are the causes of all things in this sense — because when they are taken away everything is taken away; and further, the primary thing that is completely at work is the cause of all things. But the causes are different in this sense — they are as many as the primary contraries, described neither generically nor ambiguously, and as there are kinds of material as well. So what the sources are of perceptible things, and how many there are, and in what way they are the same and in what way different, have been said” (pp. 237-238).

At long last, we come to the argument that there really is a first cause of all things. Again he emphasizes that everything also has particular sources and causes.

“Now since there are three kinds of thinghood, two of them natural and one motionless, about the latter one must explain that it is necessary for there to be some everlasting motionless independent thing” (ch. 6, p. 238).

“For independent things are primary among beings, and if they were all destructible, everything would be destructible; but it is impossible for motion either to come into being or to be destroyed (since it always is), and impossible too for time” (ibid).

For Aristotle there is no first motion, or first moment in time. Instead, there must be an everlasting cause of motion.

“For if there were no time, there could be no before and after; and motion is continuous in just the way that time is; since time is either the same as or some attribute of motion” (ibid).

He points out that to speak of anything “before” there was any time is incoherent, since before and after presuppose time.

“But there is no continuous motion other than in place, and among these, other than in a circle” (ibid).

Only motion in a circle could continue forever. Space is vast, but Aristotle does not believe in infinite distances, so for him there could not be motion continuing forever in a straight line.

He seems to imply that the most fundamental motion of all — that of the fixed stars — provides a uniform measure for time. In modern terms, this is the earth’s rotation on its axis, as observed from a point on the earth. In the absence of evidence refuting what we see to be the case, he assumes that the stars forever rotate around the earth, and that the apparent motion of what is apparently the outermost sphere of the fixed stars is therefore a primary motion that spatially surrounds all things. If we take earth as the point of reference for whatever relativistic motions we see in the sky, this fits all the observational facts.

“But surely if there is something capable of moving and producing things, but not at work in any way, there will not be motion; for what has a potency admits of not being at work” (ibid).

Here he returns to the Physics sense of potentiality and actuality, and to the priority of the actual. Every potentiality is a source of motion that requires something external that is already an actuality of the same sort, in order for the potentiality to be actualized. The child requires a parent, the artifact a Platonic model.

“Therefore, there is no benefit even if we adopt everlasting independent things, as do those who bring in the forms, unless there is in them some source capable of producing change; moreover, even this is not enough, not even if there is another independent thing besides the forms, since if it is not going to be at work, there will not be motion” (ibid).

A pure form or logical universal that is not “actual” cannot explain motion. Once again, motion as the actualization of a potential depends on a pre-existing actuality.

“What’s more, it is not enough even if it will be at work, if the thinghood of it is potency, for there would not be everlasting motion, since what has being in potency admits of not being” (ibid).

Further, any first cause of motion must be everlasting, continuous, and unchanging in its action. That is to say, it must itself be purely actual, with no admixture of potentiality. It would not be sufficient to explain everlasting, continuous motion if the first cause just happened to be actual for some period of time.

“Therefore it is necessary that there be a source of such a kind that the thinghood of it is being-at-work. On top of that, it is necessary that these independent things be without material, for they must be everlasting, if indeed anything else is everlasting. Therefore they are being-at-work” (ibid).

As he just suggested, any first cause of all must therefore be a pure actuality with no potentiality. What Aristotle calls matter is kind of potentiality, so the first cause must have no matter either.

“For how will things have been set in motion, if there were not some responsible thing at work? For material itself, at any rate, will not set itself in motion” (p. 239).

“And this is why some people, such as Leucippus and Plato, bring in an everlasting activity, for they say there is always motion. But why there is this motion, and what it is, they do not say, nor the cause of its being in a certain way or some other way. For nothing moves at random, but always something must be present to it, just as now something moves in a certain way by nature, but in some other way by force or by action of intelligence or something else” (ibid).

It is not enough to simply posit motion. This does not explain anything.

“And then, what sort of motion is primary? For this makes so much difference one can hardly conceive it. But surely it is not possible for Plato to say what he sometimes thinks the source of motion is, which sets itself in motion; for the soul is derivative, and on the same level as the heavens, as he says” (ibid).

The thought here seems to be that if there is a first cause of motion, there must be a primary sort of motion that it primarily causes. For Aristotle, this is the movement of the fixed stars.

“Anaxagoras testifies that being-at-work takes precedence (since intellect is a being-at-work), as does Empedocles with love and strife, and so do those who say there is always motion, such as Leucippus; therefore there was not chaos or night for an infinite time, but the same things have always been so, either in a cycle or in some other way, if being-at-work takes precedence over potency. So if the same thing is always so in a cycle, it is necessary for something to persist always at work in the same way” (pp. 239-240).

If all things did not come from something that is an actuality or being-at-work or fulfillment, then they could only come from what the poets called “chaos and night”. But if all things came from chaos and night, there would be no hope of understanding anything. Aristotle suggests that several of his predecessors ought to have recognized the priority of actuality, as an implicit presupposition of what they did say.

“But since it is possible for it to be this way, and if it is not this way things will come from night and from ‘all things together’ and from not-being, these questions could be resolved; and there is a certain ceaseless motion that is always moving, and it is in a circle (and this is evident not only to reason but in fact), so that the first heaven will be everlasting” (ch. 7, p. 240).

He does not claim to positively know that actuality is necessarily prior to potentiality. He claims that the account is plausible, and that any alternative must lead back to sheer chaos, which would make it impossible for anything to be truly intelligible at all.

“Accordingly, there is also something that moves it. And since what is in motion and causes motion is intermediate, there is also something that causes motion without being in motion, which is everlasting, an independent thing, and a being-at-work” (ibid).

Behind each independent celestial motion, there must be some actual everlasting independent thing. Behind these, there must be something that is completely unmoved, and that is a pure actuality or being-at-work or fulfillment.

“But what is desired and what is thought cause motion in that way: not being in motion, they cause motion” (ibid).

For Aristotle, desire and thought are unmoved movers.

“But the primary instances of these are the same things, for what is yearned for is what seems beautiful, while what is wished for primarily is what is beautiful; but we desire something because of the way it seems, rather than its seeming so because we desire it, for the act of thinking is the beginning” (pp. 240-241).

Desire and thought both aim at what is good or beautiful. The way things seem — and consequently, the act of thinking or judging — drives wishing and willing, not vice versa. Further below, he will again emphasize the active rather than merely receptive role of thought.

“But the power of thinking is set in motion by the action of the thing thought, and what is thought in its own right belongs to an array of affirmative objects of which thinghood is primary, and of this the primary kind is that which is simple and at work” (p. 241).

Thinking itself is driven by the actuality of what it thinks. This does not negate his emphasis on thinking as act.

“But what is one and what is simple are not the same, for oneness indicates a measure, but what is simple is itself a certain way” (ibid).

The simplicity he attributes to the first cause is a stronger criterion than being one.

“But surely the beautiful and what is chosen in virtue of itself are also in that same array, and what is primary is always best, or analogous to it” (ibid).

First things are good and beautiful, and the first thing of all can be identified with the good and the beautiful.

“And that-for-the-sake-of-which is possible among motionless things, as the [following] distinction makes evident; for that-for-the-sake-of-which is either for something or belonging to something, of which the former is and the latter is not present among motionless things” (ibid).

Here he explicitly says that that-for-the-sake-of-which has a broader scope than any source of motion. Alone among the four kinds of causes, it provides ultimate reasons why things are what they are. Form may be identified with what things are, but that-for-the-sake of which is the cause of form and the reason why it is what it is.

“And it causes motion in the manner of something loved, and by means of what is moved moves other things” (ibid).

The highest kind of cause, that-for-the-sake-of-which, involves no force or compulsion or unconditional necessity. Other things are moved because they love it or are attracted by it, but they could not be so moved if they did not have their own sources of motion. They are not moved by some active power emanating from the first cause.

“But since there is something that causes motion while being itself motionless, this does not admit of being otherwise than it is in any respect at all” (ibid).

“For among changes, the primary one is change of place, and of this the primary kind is a circle, but this is what this mover causes” (ibid).

“Therefore [the first cause] is something that has being necessarily…. On such a source, therefore, the cosmos and nature depend” (pp. 241-242).

“And the course of its life is of such a kind as the best we have for a short time. This is so because it is always the same way (which for us is impossible), and because its being-at-work is also pleasure (which is what makes being awake, perceiving, and thinking the most pleasant things, while hopes and memories are pleasant on account of these)” (p. 242).

If we speak in terms of pleasure here, it would be of the highest possible sort. I think “pure delight” captures the meaning more clearly.

“And the thinking that is just thinking by itself is a thinking of what is best just as itself, and especially so with what is so most of all” (ibid).”

“But by partaking in what it thinks, the intellect thinks itself, for it becomes what it thinks by touching and contemplating it, so that the intellect and what it thinks are the same thing” (ibid).

And this, I say, is pure delight.

“For what is receptive of the intelligible and of thinghood is the intellect, and it is at work when it has them; therefore it is the being-at-work rather than the receptivity the intellect has that seems godlike, and its contemplation is pleasantest and best” (ibid, emphasis added).

He is saying that it is by virtue of the more perfect entelechy of intellect, which goes beyond the limited entelechy associated with motion — rather than intellect’s incidental touching or contemplation of something else — that intellect seems godlike. Here again he emphasizes the primarily active rather than receptive character of thought.

“So if the divine being is in this good condition that we are sometimes in, that is to be wondered at; and if it is in it to a greater degree than we are, that is to be wondered at still more. And that is the way it is” (ibid).

For Aristotle, the divine is not incommensurable with the human. Albeit in a very partial manner, we also partake of it, and the more so the more that we are moved by our highest values.

“But life belongs to it too, for the being-at-work of intellect is life, and that being is being-at-work, and its being-at-work is in itself the best life and is everlasting. And we say it is a god who everlastingly lives the best life, so that life and continuous and everlasting duration belong to a god; for this being is god” (ibid).

“That, then, there is an independent thing that is everlasting, motionless, and separate from perceptible things, is clear from what has been said. And it has also been demonstrated that this independent thing can have no magnitude, but is without parts and indivisible (for it causes motion for an infinite time, while no finite thing has an infinite power, and since every magnitude must be either finite or infinite, it cannot have magnitude, either finite, for the reason given, or infinite, because there is no infinite magnitude at all). But surely it has also been demonstrated that it cannot be affected or altered” (p. 243).

Sachs says in a note that the reference to a demonstration that the first cause is not involved with magnitude effectively incorporates the entire argument of the Physics by reference. Book VIII of the Physics has a far more thorough argument that there must be a first unmoved mover corresponding to the primary observable motion of the circling of the fixed stars, but that account does not address the what-it-is of things.

“But since… we see in addition to the motion of the whole heaven, other everlasting motions which belong to the planets…, it is necessary that each of these motions also be caused by something that is itself motionless and an everlasting independent thing. For the nature of the stars is for each to be an everlasting independent thing, while the mover is everlasting and takes precedence over the thing moved, and what takes precedence over an independent thing must be an independent thing” (ch. 8, p. 244).

The terrestrial independent things are mainly plants and animals. These have the richest entelechies among terrestrial perceptible things.

Aristotle also acknowledges each star participating in the motion of the heaven as an entelechy of its own. At least in a way, it is superior to ours, in that to all appearances it lasts forever.

The stars he calls planets are those that stand out by having observable independent motions of their own, different from the primary motion that they share with all the stars that are called “fixed” by contrast.

“[B]ut the number of motions is already something one must examine from that kind of mathematical knowledge that is the nearest kin to philosophy, namely from astronomy. For this kind makes its study about perceptible, everlasting thinghood, while the others, such as those concerned with numbers and with geometry, are not about thinghood at all” (ibid).

“[A]s for how many [independent motions] there happen to be, we now state what some of the mathematicians say, for the sake of a conception of it, … and as for what remains, it is necessary to inquire into some things ourselves, while listening to what other inquirers say about others. If something should seem to those who busy themselves with these matters to be contrary to what has just now been said, it is necessary to welcome both accounts, but trust the more precise one” (pp. 244-245).

“[F]or let the number that is necessary be left for more relentless people to say” (p. 246).

Apparently he made an arithmetic error counting the motions (“either 55 or 47”, where the 47 should have been 48, according the details I have not reproduced), then made a joke of it. I don’t believe Aristotle is very attached to specific enumerations of any sort. It is the principles upon which distinctions are based that matter.

“There has been handed down from people of ancient and earliest times a heritage, in the form of myth, to those of later times, that these original beings are gods, and that the divine embraces the whole of nature. The rest of it was presently introduced in mythical guise for the persuasion of the masses and into laws for use and benefit” (p. 247).

The divine embraces the whole of nature. We still name the planets by the Roman names for the Greek gods that were associated with them in antiquity.

Next he seems to respond to, or perhaps anticipate, doubts about what he said earlier about intellect.

“Now concerning the intellect there are certain impasses, for it seems to be the most divine of things that are manifest to us, but the way it is if it is to be of that sort contains some things that are hard to digest. For if it thinks nothing, what would be solemn about that? Rather, it would be just like someone sleeping. But if it does think, but something else has power over it, then, since it is not thinking but potency that is the thinghood of it, it could not be the best independent thing, for it is on account of its act of thinking that its place of honor belongs to it. And still, whether the thinghood of it is a power of thinking or an activity of thinking, what does it think?” (ch. 9, p. 247).

“For [what intellect thinks] is either itself or something else, and if it is something else, either always the same one or different ones. And then does it make any difference, or none, whether its thinking is of what is beautiful or of some random thing? Isn’t it even absurd for its thinking to be about some things? Surely it is obvious that it thinks the most divine and honorable things, and does not change, since its change would be for the worse, and such a thing would already be a motion” (p. 248).

Intellect will prefer the beautiful and the good over any random thing. Physics book VII much better explains why certain things that we are used to calling “changes” are not considered changes in his way of speaking.

“First, then, if it is not an activity of thinking but a potency, … it is clear that something else would be more honorable than the intellect, namely what it thinks…. Therefore what it thinks is itself, if it is the most excellent thing, and its thinking is a thinking of thinking” (ibid).

For a third time, he insists that intellect is primarily active, rather than receptive. Its main concern seems to be with whatever is most good and beautiful and honorable. It is a thinking of thinking — true higher-order thinking, rather than a first-order “thinking” of something external.

“But [the human soul’s] knowledge and perception and opinion and step-by-step thinking seem always to be about something else, and about themselves only as something secondary” (ibid).

The above seems to be in implicit contrast with the active thinking about which he was speaking just before. In this way, intellect in its own right is unlike the human soul.

“What’s more, if the thinking and the being thought are different, then in virtue of which of them does what is good belong to it? For to be an act of thinking and to be something thought are not the same” (ibid).

They are the same and yet not the same. Of course, this is in different respects. This is the model for many similar formulations in Hegel.

“Or is it rather that in some cases the knowledge is the thing it is concerned with, so that in the case of the kinds of knowing that make something, the thinghood without material and what it is for something to be, or in the case of the contemplative kinds of knowing, the articulation, is both the thing the knowledge is concerned with and the activity of thinking it? So since what is thought and what is thinking are not different with as many things as have no material, they will be the same, and the act of thinking will be one with what is thought” (ibid).

Here he suggests that we may after all be able to see instances of this identity by reflecting on our experiences of productive and contemplative knowing. Insofar as we actually know anything, we partially escape the inherent limitations of the human soul.

“But there is still an impasse left as to whether what is thought is composite, for then thinking would be changing among the parts of the whole. Or is it the case that everything that has no material is indivisible?” (pp. 248-249).

Implicitly, he seems to favor the latter alternative. Then twice more he speaks of intellect’s predilection for what is good and best.

“So the condition the human intellect, or that of any composite being, is in at some period of time (for it does not have hold of what is good at this or that time, but in some whole stretch of time it has hold of what is best, since that is something other than itself), is the condition the thinking that thinks itself is in over the whole of time” (p. 249).

Again, for Aristotle we have a little bit of the divine within us insofar as we have intellect, so there is no radical incommensurability between the divine and the human.

“One must also consider in which of two ways the nature of the whole contains what is good and best, whether as something separate, itself by itself, or as the order of the whole of things. Or is it present in both ways…?” (ch.10, p. 249).

Book Lambda’s final chapter ends with a quote from a speech by Odysseus in Homer’s Iliad. The whole chapter is oriented toward this literary image. At this point in the Iliad, the Greeks had been in complete disarray, a confused mass, but Odysseus’ words restore their morale and disciplined unity. (Notably, Odysseus was not the high king or commander-in-chief, though he was a leader. It was what he said that mattered.) Aristotle wants us to see this as a metaphorical answer to the question just posed. What is good and best must indeed be present in both ways — both as from the first cause, and as distributed and embodied throughout the whole — but he wants to emphasize that the “for the sake of which” of the first cause plays a real leading role, even though it does not govern by force.

“But beings do not present the aspect of being badly governed” (pp. 251-252).

As we have seen, this does not mean that all the facts of the world are as they ought to be. It does mean that life and the world are essentially good.

Next in this series: Reflections on Book Lambda

Toward a First Cause

Book Kappa (XI) of Aristotle’s Metaphysics briefly reviews material from books Beta (III), Gamma (IV), and Epsilon (VI) about the aims of the ultimate inquiry into first things that is still to be pursued. It also incorporates a brief review of his discussions in Physics books II, III, and V about what motion and change are. Both parts of the presentation here add more explicit hints that we will be looking for something that is both separate and unmoved. These hints are the book’s main interest.

Perhaps surprisingly given its review of content from the Physics, Metaphysics Kappa makes no reference to the detailed argument in Physics book VIII that there is a first unmoved mover of all things, or to the related background about unmoved things in Physics book VII. The beginning of Physics book VIII refers back to “our course on physics”, which is ambiguous, but could imply that it was written later, and possibly after Metaphysics Kappa, which would explain why book VIII’s argument about the first mover is not mentioned here.

“But neither ought one to set down the kind of knowledge being sought as concerning the causes spoken of in the writings about nature, since it is not about that for the sake of which (for this sort of cause is the good, and this belongs among actions and things that are in motion, and it moves things first — for that is the sort of thing an end is — but a thing that first moves them is not present among immovable things). And in general, there is an impasse whether the knowledge now being sought is about perceptible independent things at all, or not, but about other things. For if it is about others, it would be about either the forms or the mathematical things, but it is apparent that there are no forms…. But neither is the knowledge being sought about mathematical things, nor is it a knowledge of perceptible independent things, since they are destructible” (ch. 1, Sachs tr., pp. 205-206).

This passage is interesting in a couple of ways. The knowledge being sought in the inquiry to be conducted is now more definitely said to be not about perceptible independent things, not about mathematical things, and not about Platonic forms.

He also points out that what he calls physics is concerned primarily with what he calls sources of motion and change. It does not address questions about the good or that-for-the-sake-of which, except in an incidental way. But in Parts of Animals book I, he clearly says that in the overall scheme of things, the good and that-for-the-sake-of-which are more primary than sources of motion. The implication here in Metaphysics Kappa is that the inquiry being prepared for will address them in their own right.

“Also, ought one to set down anything besides the particular thing or not, and is the knowledge being sought about particulars?” (ch. 2, p. 207).

For Aristotle, no universal is an independent thing. The knowledge being sought does seem to be about particulars.

“And there is besides an impasse, that all knowledge is of universals and of the suchness of things, but thinghood does not belong to universal” (p. 208).

Knowledge, however, is concerned with universals. This was the major impasse remaining at the end of book Zeta (VII).

“Now since the knowledge that belongs to the philosopher concerns being as being universally and not in relation to a part, … if it is meant in accordance with something common, it would be subject to one knowledge. It seems to be meant in the way that has been spoken of, in just the way that medical and healthy are meant” (ch. 3, p. 209).

He refers back to the discussion of how the saying of being in the other categories points back to the saying of substance-essence-thinghood.

“Since all being is meant in accordance with something that is one and common, even though it is meant in a number of ways, … such things are capable of being subject to one knowledge” (p. 211).

This enables us to say that there is after all one knowledge that can be said to be of being as such. It will address the proper saying of substance-essence-thinghood directly, and the proper saying of being in the other categories in a derivative way.

“And since the mathematician uses common notions in a particular way, it would also belong to the primary sort of philosophy to study the things that govern these” (ch. 4, p. 211).

He seems to assert in passing that first philosophy includes what we would call the foundations of mathematics. Elsewhere he mentions that the first principles of mathematics are similarly supposed to be applicable to all things. But mathematics does not address what things in general are in their own right.

“And it is the same way also with the knowledge about nature as with mathematics, for physics studies the attributes and sources of beings insofar as they are in motion and not insofar as they are, (but we have said that the primary sort of knowledge is about these things to the extent that the things underlying them are beings, but not insofar as they are anything else). For this reason one must set down both this sort of knowledge and the mathematical sort as parts of wisdom” (pp. 211-212).

Neither mathematics nor what Aristotle calls physics addresses substance-essence-thinghood, or what things are in their own right. It is left to first philosophy to do this, as well as to inquire into the ultimate principles that underlie mathematics and physics.

Just as in book Gamma (IV), Aristotle’s claim that there is after all a knowledge that applies to all being as such, and that the philosopher is the one who has it, is immediately followed by a somewhat lengthy expression of outrage against those who claim a right to contradict themselves, or deny that there is any such thing as contradiction. Just as in book Gamma, the concerns he expresses are about dialogue, the understanding of meaning, and the possibility of sound reasoning.

This makes perfect sense when we recall that Aristotle has consistently treated being in a transitive way, as always being this or being that; and as intimately involved with saying, especially the saying of what things properly are in their own right. He has at the same time treated saying as meaningful saying, intimately involved with reasoning. So we should not be surprised when it turns out that the knowledge that applies to all being as such has to do with fundamental principles and presuppositions of reasoning and the understanding of meaning.

“Now those who are going to participate in a discussion with each other must in some way understand what they say…. It is necessary then for each of the words to be intelligible and to mean something, and not many things but only one, but if it does mean more than one thing, it is necessary to make clear to which of these one is applying the word. So the one who says ‘this is and is not’ denies that which he says, and so he denies that the word means what it means, which is impossible” (ch. 5, p. 212).

Then he again expresses outrage at what he takes to be Protagoras’ claim that truth is entirely subjective. If this were the case, there would be no being as Aristotle understands it. Being “in its own right” is discursively communicable intelligibility.

“Something closely resembling these things being discussed is what was said by Protagoras, for he said that a human being is the measure of all things, meaning nothing else than that what seems so to each person is solidly so” (ch. 6, p. 213).

“And since it is necessary for each sort of knowledge to know in some way what something is, … one must not let it go unnoticed in what way the one who studies nature needs to define it and how he needs to get hold of the articulation of the thinghood of things” (ch. 7, p. 217).

The inquiry to be pursued here is implicitly presupposed by physical inquiries. To the extent that one of these two, taken in itself, governs the other, taken in itself, the inquiry to be pursued here is more primary than physics (or mathematics).

“Now the study of nature is about things having a source of motion within themselves, while mathematics is contemplative and concerns something that remains the same, but is not separate. Therefore, about the sort of being that is separate and motionless, there is another sort of knowledge that is different from both of these, if there is any such independent thing — I mean something separate and motionless — which is just what we shall try to show. And if there is any such nature among beings, that would be where the divine also is, and this would be the primary and most governing source of things. It is clear, then, that there are three classes of contemplative knowledge: physics, mathematics, and theology” (ibid).

What he calls nature is a source of motion within something “as itself” (all other sources of motion he calls potentialities).

Now he explicitly mentions that he intends to show that there is a kind of being that is both separate and motionless, as he understands these two terms. He says that if there is such a thing, it will be “where the divine is”, and it will be “the primary and most governing source of things”. First philosophy will therefore be alternately characterized as theology.

He returns to the impasse about knowledge in first philosophy. “One might be at an impasse whether the knowledge of being as being ought to be set down as universal or not” (p. 218). Knowledge is supposed to be concerned with universals, but we are seeking an independent thing, and no logical universal is an independent thing.

In the earlier suggestion of a solution to this impasse, he re-interpreted the many ways in which being is said for the different categories, re-describing them as multiple derivative meanings pointing to one primary meaning. This seemed to eliminate the need to refer to a universal that abstracts over the ways being is said for the different categories.

Now he complements this by introducing a new way of speaking universally, which does not depend on abstraction. Instead, universality can be achieved by referring to a concrete thing or things that is or are concretely the cause or causes of all things, and that therefore is or are prior to all the rest.

“So if natural independent things are primary among beings, then also physics would be the primary sort of knowledge; but if there is another nature and independent thing that is separate and motionless, it is necessary that the knowledge of it be other than and prior to physics, and universal by being prior” (ibid).

Everything that Aristotle calls independent, he also calls separate. Also equivalent to these is calling something a this. As noted earlier, the challenge is to find something that is independent and separate and a this, but that is also unmoved in his sense. The impasse about universality will be conclusively resolved by finding something that is universal not in the sense of being abstract, but rather, as he says, universal in the sense of being “prior” to all other things, because it is a cause for all of them.

“And that, of what is so incidentally, there are not causes and sources of the same sort as there are of what is so in its own right, is clear, for then everything would be by necessity” (ch. 8, p. 219).

As he said in book Zeta (VII), the contingency of incidental being must have contingent, incidental causes. Now he relates this more specifically to a consideration of that-for-the-sake-of-which.

“That which is for the sake of something is present in things that happen by nature or as a result of thinking, but it is fortune when any of these happen incidentally, for just as being is in one way in its own right and in another way incidental, so also with cause. And fortune is an incidental cause in the things that are by choice, among those that happen for the sake of something, for which reason fortune and thinking concern the same things, since there is no choice apart from thinking…. And since nothing incidental takes precedence over things in their own right, neither then do incidental causes, so if fortune or chance is a cause of the heavens, intelligence and nature have a prior responsibility” (pp. 219-220).

There is such a thing as fortune or things happening by chance, but “intelligence and nature have a prior responsibility”, just as what things are in their own right takes precedence over things that are the case incidentally.

“Something is in one way only as at-work, in another way as in potency, and in another way both in potency and at-work, and again in one way as a being, in another as a so-much, in other ways in the rest of the categories; and there is no motion apart from things, since something changes always according to the categories of being, and there is nothing common to these which is not within a single category” (ch. 9, p. 220).

Every change is understood by Aristotle as a change with respect to one of the categories. What is common to these is not an abstraction, but the single concrete sense for one category (substance-essence-thinghood), from which the senses for the other categories are derived.

Here he mentions being in the sense of potentiality and actuality, before he mentions being in the senses of the categories. Next, he summarizes the Physics‘ account of motion. “Motion” is the (incomplete) actualization of a potentiality, where actuality or being-at-work or fulfillment would be its complete actualization.

“So the being-at-work-staying-itself [entelechy, identified by Aristotle with actuality or being-at-work or fulfillment] of what is in potency, whenever it is at-work as a being-at-work-staying-itself, not as itself but as movable, is motion” (p. 221).

“And the reason for motion’s seeming to be indefinite is that it is not possible to place it as a potency or as a being-at-work of beings, for neither is what is capable of being so-much necessarily in motion, nor what is actively so-much; and motion seems to be a certain sort of being-at-work, but incomplete, and the reason is that the potency of which it is the [complete] being-at-work is itself incomplete. And for this reason it is hard to grasp what it is, for it is necessary to place it either as a deprivation or as a potency or as an unqualified being-at-work, but none of these seems admissible; so what remains is what has been said, both that it is a being-at-work and that it is the sort of being-at-work that has been described, which is difficult to bring into focus but capable of being” (p. 222).

Motion is an incomplete actuality or being-at-work or fulfillment. This is a rather subtle thought, the grasping of which requires that we first understand that-for-the-sake-of-which, actuality, and potentiality. (Motion in the modern sense, on the other hand, has no teleological significance. It is entirely reducible to measurable quantities. It it not that one of these is “right” and the other “wrong” — they are two different concepts, grounded in different kinds of explanation.)

“And it is clear that motion is in the movable thing, for it is the being-at-work-staying-itself of this by the action of the thing capable of causing motion. And the being-at-work of the thing capable of causing motion is not different, since it is necessary that it be the being-at-work-staying-itself of both; for a thing is capable of causing motion by its potency and is in motion by being-at-work, but it is capable of being-at-work upon the thing moved, so that the being-at-work of both alike is one, just as the interval from one to two and from two to one is the same, and the uphill and downhill road, though the being of them is not one, and similarly also in the case of the thing causing motion and the thing moved” (ibid).

Motion for Aristotle is always said to be in the thing moved, not in the mover. The potentialities of mover and moved with respect to any motion are said to be one.

“Now it is not possible for the infinite to be something separate…. Also, how could the infinite admit of being something in its own right, if number and magnitude, of which the infinite is an attribute, do not?…. And it is clear that it is not possible for there to be an infinite actively…. [T]hat there is no infinite among perceptible things is clear…. [N]or could there be a number that is separate and infinite, since a number or that which has a number is countable…. In general it is impossible for there to be an infinite body and a place for bodies” (ch. 10, pp. 222-224).

As he argues in greater detail in the Physics, there is no “separate” or “actual” infinite.

“[T]here is something that is moved primarily on account of itself, and this is what is moved in its own right. And this is the same way also with the thing that causes motion, for it does so either incidentally, or on account of a part, or in its own right” (ch. 11, p. 225).

There is something that is a mover in its own right.

“But the forms and the attributes…, such as knowledge and heat, are motionless; it is not heat that is a motion but the process of heating. Change that is not incidental is not present in all things but in contraries and what is between the and in contradictories, and belief in this comes from considering examples” (ibid).

For Aristotle, it is only composite things (i.e., those he understands as formed from material) that are subject to motion and change. In his sense, for instance, a composite thing may undergo a process of becoming warmer, and that would be a kind of motion of the thing. But heat itself is not a composite thing. (That heat itself does not move would be true even under the modern interpretation of it as the amount of molecular motion within a material.)

“A thing that changes does so either from one underlying thing to another, or from what is not a subject to what is not another subject, or from what is not a subject to that subject (and by ‘subject’ I mean what is declared affirmatively), so that there must be three kinds of change, since that from what is not one subject to what is not another subject is not a change, for they are neither contraries nor is there a contradiction, because there is no opposition between them” (ibid).

“And since every motion is a change, and the kinds of change mentioned are three, but those that result from coming-into-being or destruction are not motions, and these are the changes between contradictories, it is necessary that change from one subject to another be the only sort of change that is motion” (p. 226).

A “subject” here is just some thing that underlies something else that has the character of an attribute. I would infer that the change from one subject to another that is spoken of here is a reference to the way that something that is potentially X becomes actually X by the action of something else that is already actually X, as the parent of a child and the Platonic “model” of an artifact were said to be.

“So if the ways of attributing being are divided into thinghood, quality, place, acting or being acted upon, relation, and quantity, there are necessarily three kinds of motion, with respect to the of-what-sort, the how-much, and the place. There is no motion with respect to thinghood, because nothing is contrary to an independent thing, nor of relation …, nor is there a motion of acting and being acted upon, nor of moving and being moved, because there is not a motion of a motion or a coming into being of coming into being, or generally a change of a change…. For every motion is a change from one thing to another, and this is also with coming into being and destruction, except that these are changes into one sort of opposites, while motion is a change into another sort” (ch. 12, pp. 226-227).

The modern concept of acceleration is not a “change of a change”, but a change in a rate of change. Surprisingly, he does not seem to mention change with respect to place, or locomotion, here.

“Also, it would go to infinity if there were to be a change of a change and a coming into being of coming into being…. And since of infinite things there is no first one, there would not be a first becoming, and therefore no next one either, and then nothing would either come into being or be moved or change” (pp. 227-228).

Here as elsewhere, Aristotle is anxious to avoid any form of infinite regress. Showing that there is a separate, unmoved, everlasting thing that moves others is what will enable him to do that. That will be the main task of book Lambda (XII).

Next in this series: Pure Entelechy

Potentiality and Actuality

Here I will treat what Aristotle says about potentiality and actuality in Metaphysics book Theta (IX). On this closer reading, I was initially disappointed that he did not say more about how potentiality and actuality provide the detailed basis for the “internal” teleology that is at the core of his thinking. But on further reflection, perhaps this is another case of what I have elsewhere appreciated as a kind of careful minimalism.

“[L]et us make distinctions also about potency [aka potentiality] and complete being-at-work [aka actuality], and first about potency in the sense in which it is meant most properly, although it is not the sense that is most useful for what we now want. For potency and being-at-work apply to more than just things spoken of in reference to motion. But when we have discussed them in this sense, we will make clear their other senses in the distinctions that concern being-at-work” (ch. 1, Sachs tr., p. 167).

This most elementary sense of what I prefer to guardedly call potentiality was originally developed in the Physics, in connection with the theory of what he broadly calls “motion”. Here, he will ultimately extend it to cases that do not involve motion in this sense. I tend to think of the latter cases as primary.

“[A]s many [senses of potency] as point to the same form are all certain kinds of sources… of change in some other thing or in the same thing as other. For one kind is a power of being acted upon, which is a source in the acted-upon thing itself of passive change by the action of something else or of itself as other; another is an active condition of being unaffected for the worse…. And these potencies are in turn spoken of as only acting or being acted upon, or as acting and being acted upon” (pp. 167-168).

This is a thin, elementary definition, like that of substance in the Categories, with no mention of potentiality’s important role in Aristotle’s teleology. Until recently, working mostly from memory, I had not been thinking about what he calls “sources” (something strictly broader than “causes”) at all, or about this Physics sense of potentiality that is specifically a “source” of motion.

In the Physics, motion is in fact defined in terms of elementary versions of potentiality and actuality. Aristotle says “thus the fulfillment [actuality, being-at-work] of what is potentially, as such, is motion — e.g., the fulfillment of what is alterable, as alterable, is alteration; of what is increasable and its opposite, decreasable… increase and decrease; of what can come to be and pass away, coming to be and passing away; of what can be carried along, locomotion” (book III ch. 1, Collected Works, Barnes ed., vol. 1, p. 343).

I rather like the Collected Works translators’ choice of “fulfillment” as an English alternative to “actuality” or “being-at-work”. Grounded more in what Aristotle says about energeia than in the etymology of the new Greek word he coined for it, it does nicely capture the teleological role of actuality. Translation is often not a simple affair.

The Physics definition of motion, though, is a tricky thought: the actuality of something that as such is a potentiality. This illustrates that there can be a kind of layering with respect to these terms.

“And it is clear that there is a sense in which the potency of acting and being acted upon is one (since something is potential both by means of its own potency to be acted upon and by something else’s potency to be acted upon by it), but there is a sense in which they are different” (p. 168).

The way in which these potentialities of acting and being acted upon are said to be “one” is structurally similar to what he says in On the Soul and Metaphysics book Lambda about thought and the thing thought being one. It seems like Aristotle might consider that to be one case of this.

“[A]ll the arts and productive kinds of knowledge are potencies” (ch. 2, p. 169).

This sort of case is very important to remember when considering the meanings of “potentiality” or “source of motion”. When he is speaking the most carefully, Aristotle says the art of building is the primary “source of motion” for the building of a house.

“And all potencies that include reason are capable of contrary effects, but with the irrational ones, one potency is for one effect, as something hot has a potency only for heating, while the medical art is capable of causing disease or health” (ibid).

He treats this thesis about rational potentialities producing “contrary” effects as important. The sense seems to be that because the actualization of rational potentialities involves practical judgment about what is appropriate in a given situation, the judgment can go wrong, leading to the production of the “opposite” of the intended effect. Heat and similar things can’t “go wrong” in this way,

“And it is clear that, with the potency of doing something well, the potency of merely doing or suffering it follows along, while the former does not always follow along with the latter, since the one doing something well necessarily also does it, but the one merely doing it does not necessarily also do it well” (ibid).

This is a nice incidental mention of the normative dimension involved in all practical doing, though the technical point is about what cases include what other cases.

“There are some people, such as the Megarians, who say that something is potential only when it is active, but when it is not active it is not potential…. The absurd consequences of this opinion are not difficult to see…. [T]hese assertions abolish both motion and becoming. For what is standing will always be standing and what is sitting always sitting, since it will not stand up if it is sitting” (ch. 3, p. 170).

The Megarian logicians claimed that potentiality has no reality of its own — that everything that is, is actual. This position results in paradoxes similar to those following from the claims of Parmenides about non-being and being.

“What is capable is that which would be in no way incapable if it so happened that the being-at-work of which it is said to have the potency were present” (p. 171).

This is another specification I had lost track of working mainly from memory. I’m not sure how it would apply to his example of arts and productive knowledge, which comes closest to the extensions of Aristotelian potentiality that I have suggested (to characterize recent notions of both the “space of reasons” and “structure” as belonging to potentiality).

“And the phrase being-at-work, which is designed to converge in meaning with being-at-work-staying-complete [entelechy], comes to apply to other things from belonging especially to motions” (ibid).

This seems to be an application of Aristotle’s frequent distinction between how things are “for us” and how they are “in themselves”. The appeal to motion as a basis for understanding being-at-work or actuality is an appeal to common experience. But further below, he will contrast motion with being-at-work in a fuller sense.

He goes on to make a number of logical distinctions.

“[I]t cannot be true to say that such-and-such is possible, but will not be the case” (ibid).

(When we say something will not be the case, we are also implicitly saying there is no possibility that it will be the case. Therefore, it cannot be possible, and the statement contradicts itself.)

Potentiality is a more specific notion than possibility, but it seems that whatever is potential must also be possible, and therefore the generalization about possibility applies to all cases of potentiality.

“For the false and the impossible are not the same thing; for that you are now standing is false, but not impossible” (ch. 4, p. 172).

Similarly, generalizations about impossibility also apply to the more specific notion of potentiality.

“[I]t is also clear that, if it is necessary for B to be the case when A is, it is also necessary for B to be capable of being the case when A is capable of being the case” (ibid).

If there is a relation of necessity between actual things, then logically there must be a corresponding relation of necessity between the corresponding potential things. Possibility and necessity are the two most basic modalities in modern modal logic.

“Of all potencies, since some are innate, such as the senses, while others come by habit, such as that of flute playing, and others by learning, such as the arts, some, those that are by habit and reasoning need to have previous activity, while others that are not of that kind, and apply to being acted upon, do not need it” (ch. 5, p. 172).

For Aristotle, a sense like vision is to be understood first of all as a potentiality for the complete act of actually seeing. All other details — of optics, of physiology, of the operations of imagination, of what modern people might call the consciousness of seeing — that are conditions of the complete act, are subordinate to the complete act itself as a realized end. This is a good example of how Aristotle uses teleology to organize and coordinate other sorts of explanation.

The distinction between by “habit” (hexis, or acquired disposition) and by learning does not seem to be strict. Further below, he mentions practicing in order to play the harp as a form of learning, rather than habit. I think he is speaking casually both times. One might even say that all habits are learned; at the very least, they are acquired. (This broader term related to “second nature” seems to have been particularly important for al-Farabi, who uses it in his classic neoplatonizing elaboration of the Aristotelian theory of intellect.)

“[With irrational potencies] it is necessary, whenever a thing that is active and a thing that is passive in the sense that they are potential come near each other, that the one act and the other be acted upon” (pp. 172-173).

This formulation is surprising. I don’t understand why the qualification he applies immediately below for the case of rational potentialities (“not in every situation but when things are in certain conditions”) would not also apply to irrational potentialities. The distinction between the “rational” and “irrational” cases is based on presence or absence of a dimension of desire or choice, which seems not to affect the relevance of situations and conditions.

“[B]ut with [rational potencies] this is not necessary…. It is necessary, therefore, that there be something else that is governing; by this I mean desire or choice. For whatever something chiefly desires is what it will do whenever what it is capable of is present and it approaches its passive object…. not in every situation but when things are in certain conditions” (p. 173).

“Since what concerns the kind of potency that corresponds to motion has been discussed, let us make distinctions about being-at-work, to mark out both what it is and what sort of thing it is. For that which is potential will also be clear at the same time to those who make distinctions, since we speak of the potential not only as that which is of such a nature as to move some other thing or be moved by something else, … but also in another way, and it is because we are inquiring after that other meaning that we went through this one” (ch. 6, p. 173).

He explicitly says he will not define actuality or being-at-work, but instead suggests that we infer a pattern from a series of examples. Actually, it turns out that the more abstract pattern he is thinking of includes two distinct variants.

“The other way these things are present is in activity. And what we mean to say is clear by looking directly at particular examples, nor is it necessary to look for a definition of everything, but one can see at a glance, by means of analogy, that which is as the one building is to the one who can build, and the awake to the asleep, and the one seeing to the one whose eyes are shut but who has sight, and what has been formed out of material to the material, and what is perfected to what is incomplete…. But not all things that are said to be in activity are alike, except by analogy…. For some of them are related in the manner of a motion to a potency, others in the manner of thinghood to a material” (pp. 173-174).

At the end, he is now saying that motion and substance-essence-thinghood are the two alternate kinds of actuality or being-at-work. Motion is the “imperfect” kind that is still in process of realization, and substance-essence-thinghood is the “perfect” or “complete” kind that is an entelechy.

“And since, of the actions that do have limits, none of them is itself an end, but it is among things that approach an end, (such as losing weight, for the thing that is losing weight, when it is doing so, is in motion that way, although that for the sake of which the motion takes place is not present), this is not an action, or at any rate not a complete one; but that in which the end is present is an action. For instance, one sees and is at the same time in a state of having seen, understands and is at the same time in a state of having understood, or thinks contemplatively and is at the same time in a state of having thought contemplatively, but one does not learn while one is at the same time in a state of having learned, or get well while in a state of having gotten well. One does live well at the same time one is in a state of having lived well, and one is happy at the same time one is in a state of having been happy” (p. 174).

“And it is appropriate to call the one sort of action motion, and the other being-at-work. For every motion is incomplete: losing weight, learning, walking, house-building…; but one has seen and is at the same time seeing the same thing, and is contemplating and has contemplated the same thing. And I call this sort of action a being-at-work, and that sort a motion. So that which is by way of being-at-work, both what it is and of what sort, let it be evident to us from these examples” (pp. 174-175).

Motion and being-at-work are both said to be forms of “action”. Anything broad enough to comprehend both of these will not fit common connotations of the English word “action”, so we need to recognize that it is being used in a special sense closer to “activity”, which seems better suited to something that includes both.

“Now when each thing is in potency and when not must be distinguished, since it is not the case at just any time whatever…. Then it would be just as not everything can be healed, by either medical skill or chance, but there is something that is potential, and this is what is healthy in potency” (ch. 7, p. 175).

The reference to time does not seem to be essential. What seems decisive for these distinctions are the possibly blocking circumstances or “conditions” mentioned earlier.

“And since the various ways in which something is said to take precedence have been distinguished, it is clear that being-at-work takes precedence over potency. And I mean that it takes precedence not only over potency as defined, … but over every source of motion or rest in general. For nature too is in the same general class as potency, since it is a source of motion, though not in something else but in a thing itself as itself” (ch. 8, p. 177).

This is the first of several iterations on the precedence of actuality or being-at-work over potentiality. The way that he respectively defines potentiality and nature as sources of motion, they are strict logical complements of one another, so he is implying that all sources of motion are either natures or potentialities.

“And this is why it seems to be impossible to be a house-builder if one has not built any houses, or a harpist if one has not played the harp at all; for the one learning to play the harp learns to play the harp by playing the harp, and similarly with others who learn things…. But since something of what comes into being has always already come into being, and in general something of what is in motion has always already been moved…, presumably the one who is learning must also already have something of knowledge” (p. 178).

Aristotle’s account of the precedence of actuality over potentiality might be the origin of the “always already” theme. This is also the root of many interesting things that Hegel says about Wirklichkeit (commonly translated as “actuality”, with Aristotle in mind).

“But surely [being-at-work] takes precedence in thinghood too, first because things that are later in coming into being take precedence in form and in thinghood (as a man does over a boy, or a human being over the germinal fluid, since the one already has the form, and the other does not), and also because everything that comes into being goes up to a source and an end (since that for the sake of which something is is a source, and coming to be is for the sake of an end), but the being-at-work is an end, and it is for the enjoyment of this that the potency is taken on. For it is not in order to have the power of sight that animals see, but they have sight in order to see, and similarly too, people have the house-building power in order that they may build houses, and the contemplative power in order that they may contemplate; but they do not contemplate in order that they may have the contemplative power, unless they are practicing, and these people are not contemplating other than in a qualified sense, or else they would have no need to be practicing contemplating” (ibid).

Here he implicitly mentions the teleological aspect, referring to ends and that-for-the-sake-of-which.

Sachs aptly comments, “How does nature display that a squirrel has reached the completion for the sake of which it exists? In the spectacle of the squirrel at work being a squirrel…. Aristotle is arguing that the very thinghood of a thing is not what may be hidden inside of it, but a definite way of being unceasingly at-work, that makes it a thing at all and the kind of thing it is” (p. 179n).

(I would say “is what it is” instead of “exists” in the part about the squirrel.) The other part, that thinghood is not hidden inside things, but rather manifest in their ways of being at work, makes me think of what Hegel says about essence.

“[T]he putting to use of some things is ultimate (as seeing is in the case of sight…), but from some things something comes into being….[O]f those things from which there is something else apart from the putting-to-use that comes into being, the being-at-work is in the thing that is made…; but of those things which have no other work besides their being-at-work, the being-at-work of them is present in themselves (as seeing is in the one seeing and contemplation in the one contemplating, and life is in the soul, and hence happiness too, since it is a certain sort of life). And so it is clear that thinghood and form are being-at-work” (p. 179).

The last sentence is a principal new conclusion of book Theta: substance-essence-thinghood and form are both said to be cases of actuality or being-at-work.

Since actuality or being-at-work has already been identified with entelechy, this means that both independent things and (some) forms are now also being said to be entelechies. In the case of independent things, this is not surprising, given everything that was said about them in book Zeta. In the case of forms, I suspect he means that those forms that are souls are entelechies.

“But being-at-work takes precedence in an even more governing way; for everlasting things take precedence in thinghood over destructible ones, and nothing that is in potency is everlasting…. Therefore nothing that is simply indestructible is simply in potency (though nothing prevents it from being potentially in some particular respect, such as of a certain sort or at a certain place), and so all of them are at work. And none of the things that are by necessity is in potency (and yet these are primary, since if they were not, nothing would be), nor is motion, if there is any everlasting one; … and this is why the sun and moon and the whole heaven are always at work” (p. 180).

Aristotle generously calls everything “everlasting” that is apparently so, and for which he has no evidence to the contrary.

“And things that undergo change, such as earth and fire, mimic the indestructible things, since they too are always at work, for they have motion in virtue of themselves and in themselves” (p. 181).

What Aristotle calls matter is not itself alive, but nonetheless he says it has intrinsic motion. Motion, as we saw above, is defined in implicitly teleological terms in the Physics, using both potentiality and actuality. This is how the behavior of inanimate matter for Aristotle ends up having teleological characteristics.

“And that being-at-work is a better and more honorable thing than a potency for something worth choosing, is clear from these considerations. For whatever is spoken of as being potential is itself capable of opposite effects…. And in the case of bad things, it is necessary that the completion and being-at-work be worse than the potency…. Therefore it is clear that there is nothing bad apart from particular things, since the bad is by nature secondary to potency. Therefore among things that are from the beginning and are everlasting, there is nothing bad, erring, or corruptible” (ch. 9, pp. 181-182).

Things that don’t measure up to what they are supposed to be are “bad” examples of the kind of things that they are. I am surprised that he speaks of any “completion and being-at-work” of bad things at all.

“And geometrical constructions are discovered by means of activity, since it is by dividing up the figures that people discover them…. And so it is clear that the things that are in the figures in potency are discovered by being drawn into activity, … and for this reason it is only those who make a construction who know it” (p. 182).

Aristotle seems to anticipate the attitude of mathematical constructivism.

“[B]ut the most governing sense [of being and not being] is the true or the false…. For it is necessary to examine in what way we mean this. For you are not pale because we think truly that you are pale, but rather it is because you are pale that we who say so speak the truth” (ch. 10, p. 183).

I was a bit surprised when he earlier ruled out further discussion of being in the sense of the true and false attributed to the “is” or “is not” used to form propositions. But here, he goes on to speak of a different notion of truth, which seems to be more like metaphorically “grasping” an essence.

“But now for things that are not compound, what is being or not being, and the true and the false? For the thing is not a compound, so that it would be when it is combined and not be if it is separated, like the white on a block of wood or the incommensurability of the diagonal; and the true and false will not still be present in a way similar to those things. Rather, just as the true is not the same thing for these things, so too being is not the same for them, but the true or false is this: touching and affirming something uncompounded is the true (for affirming is not the same thing as asserting a predication), while not touching is being ignorant (for it is not possible to be deceived about what it is, except incidentally). And it is similar with independent things that are not compound, since it is not possible to be deceived about them; and they are all at work, not in potency, for otherwise they would be coming into being and passing away, but the very thing that is does not come to be or pass away, since it would have to come from something. So it is not possible to be deceived about anything the very being of which is being-at-work, but one either grasps it or does not grasp it in contemplative thinking; about them, inquiring after what they are is asking whether they are of certain kinds or not” (p. 184).

What is meant to be included under “independent things that are not compound” and “anything the very being of which is being-at-work” — about both of which it is said to be impossible to be deceived — has yet to be specified.

The “grasping” and “touching” metaphors here need not be taken as literally implying a kind of immediate experiencing. The next book will be explore at length the ways in which things are one, and thus form wholes. I think the implicit emphasis here is on a grasping of things as integral wholes. When we think of an essence as an integral whole, either we get it or we don’t, just as he says here. How we are able to do this is another question, not addressed here, but I think that for rational animals, the immediacy of grasping an essence can only be what Hegel would call a “mediated” immediacy.

“The true is the contemplative knowing of these things, and there is no falsity, nor deception, only ignorance, and not the same sort of thing as blindness; for blindness would be as if someone were not to have the contemplative power at all” (ibid).

Next in this series: One, Many, Same, Different

The Innovation of Potentiality-Actuality

The couple dynamis/energeia (for lack of better English terms, potentiality and actuality) has excited my imagination for nearly 50 years. There are at least three huge, unprecedented innovations in Aristotle’s concept, which I find still immensely and freshly relevant today.

From the pre-Socratics all the way to the present, the great majority of attempts at ultimate explanation have aimed at a monomorphic account of some sort or other — an account in a single shape, whether in the form of simple assertions about how things are, or of an elaborate system following a single order of development. Against this background, Aristotle’s thinking stands out as richly polymorphic and polyphonous. Things are analyzed as said in many ways; multiple kinds of causes are investigated for the same thing; necessity is hypothetical rather than categorical. The innovation of the potentiality/actuality pair gives a whole extra dimension to all of this. The concrete comes to be teeming with alternatives, but without falling into arbitrariness. Things aren’t just what they are, full stop, and they don’t just follow a single, predetermined trajectory, but at the same time there is supple coherence and meaning everywhere. Potentiality itself is polymorphic; we don’t have just one potential, but many. But it is also bound to concrete reality.

Second, Aristotle puts actuality before potentiality, reversing the logical order of precedence implicitly followed by nearly everyone else, before and since. This has all sorts of implications. It directs our attention toward the concrete. It gives positive ethical value to concrete manifestation and particular being. It supersedes the arbitrary or random aspect of mere logical possibility, while still leaving flexibility in things through the additional dimension of potentiality. Potentiality is not abstract possibility.

Third, actuality is not factuality. It is through-and-through a normative concept of the realization of an end that may or may not be achieved. Since potentiality is defined by its relations to actuality, it acquires a normative aspect as well. Each potentiality is a capability for realizing a definite end, not just a general ability to do things. Thinking in terms of actuality and potentiality puts what Aristotle calls that-for-the sake-of-which and the good first in the order of explanation.

Reaching this point in my own modest textual commentary on the Metaphysics thus has a bit of the feeling of glimpsing the promised land. With such extraordinarily high expectations, the beginning of a more disciplined confrontation of the text of book Theta (IX) has been sobering. There are gaps between what I imagine it ought to say and what it does say, and I find the remainder of the text of the Metaphysics to be quite uneven. This may in part have to do with ancient editing of the manuscripts, and the loss of many more Aristotelian writings (see The Unity of Aristotle’s Metaphysics; Fortunes of Aristotle). But from internal references in the text, some of the issues seem to belong to the original.

I have several frustrations with the text of book Theta. In spite of the importance for Aristotle of conceptually putting actuality before potentiality, the account of potentiality is placed first in the text. Then for some reason he makes the choice to focus almost entirely on potentiality’s relation to the causing of motion as discussed in the Physics, even while acknowledging that this is “not the sense that is most useful for what we now want” (Sachs tr., p. 167). What we now want, in my opinion, is an account relating the original and distinctive aspects of potentiality and actuality to Aristotle’s original and distinctive view of that-for-the-sake-of-which and its ultimate relation to the good as first in the order of explanation. This ought to be the crown jewels of the whole Metaphysics. But the way it is presented, it falls short of what I would hope for. Later books partly make up for what is missing here, but on many points we are left to read between the lines. This leaves Aristotle’s overall message less clear than we might wish. However, I am extremely impressed with what Gwenaëlle Aubry has managed to pull out from it.

Next in this series: Potentiality and Actuality

Toward Potentiality and Actuality

With the discussion of independent things, the saying of what they are, and the provision for deriving sayings in the other categories from this, we have taken simple saying in the various senses of Aristotle’s Categories about as far as it can go. Although higher dialectical aspects will emerge in what is yet to come, I think the main results of Metaphysics book Zeta (VII) are qualified well enough to be counted by Aristotle as a permanent acquisition that will still be enhanced, but never rolled back.

Aristotelian saying is far from exhausted by saying in the syntactic senses of the Categories, however. We have yet to touch upon its all-important normative aspect, and the corresponding saying of things with an additional modal dimension of potentiality or actuality. This will be intimately involved with that-for-the-sake-of-which (see also Aristotle on Explanation). Book Eta (VIII), treated here, serves as a transition to the main discussion of potentiality and actuality that lies ahead in book Theta (IX).

For Aristotle (and Hegel as well), to say that something is actually X is to judge that it has achieved and is stably continuing to achieve a full expression of what it is to be X, which means it is actively fulfilling that for the sake of which X’s do what they characteristically do (see also Entelechy). In thinking about this, it is important not to set the bar too high — Aristotle thinks it is true of many things.

Then for something to be potentially X, at least within itself it has to be fully “ready” to undergo whatever is required by the process of becoming an actual X, though its becoming an actual X in fact will usually depend on conditions external to it, and in particular on the activity of some other actual X — parents in the case of offspring, and something like a Platonic “model” of the thing in the case of artificial things.

Book Eta begins with a summary of book Zeta, so here it is evident from the text itself that the two are intended to develop one continuous argument. Then book Theta will begin with a very short summary of both Zeta and Eta.

“Now one ought to reckon up the results of what has been said, and, putting them all together, to set out the final point to which they come. And it has been said that the causes, sources, and elements of independent things are being looked for” (ch. 1, Sachs tr., p. 155).

Here again we have a more refined statement of the goal of the inquiry. He then cheerfully points out what is in fact the big new impasse reached in the previous book, concerning the impossibility of defining independent things:

“But in one way it follows from the discussions that what it is for something to be, and what underlies something, are kinds of thinghood, and in another way that thinghood is the general class, more than the specific one, and the universal more than the particulars; and the forms are also connected with the universal and the general class (since it is by the same argument that they seem to be independent things). And since what it is for something to be is thinghood, and the articulation of that is a definition, for that reason distinctions were made about definition and about what something is in virtue of itself; and since a definition is a statement, and a statement has parts, it was also necessary to know about the parts — which sort are parts of an independent thing and which not, and if these are the same ones that are parts of the definition. And further, in the course of this, it turned out that neither the universal nor the general class is thinghood” (ibid).

He highlights the discussion of definition, saving till the end the major issue that the independent thing itself is a particular that cannot be the direct subject of a definition. The subtle cue that there will be something problematic in what is said is his “in one way it follows”.

It is typical of both Aristotle and Hegel to appear to endorse an argument for a while, only to eventually overturn it. This can be seen as preliminarily giving each current argument the benefit of the doubt, rather than attempting to anticipate its future refutation. Both Aristotle and Hegel consider it essential for learning to go through the process of an argument’s dialectical development, and not just anticipate ultimate conclusions, as if out of nowhere.

The last statement — that universals do not directly characterize substance-essence-thinghood, which is always particular — is one of the most important conclusions of the Metaphysics. It means that for Aristotle, knowledge (episteme) also will not apply to independent things, since independent things are particulars. This implies that for independent things, we have to rely on something like the practical judgment cultivated for ethical practice, which is directed at particulars.

Those who have wanted to treat “metaphysics” as a “science of being” are going in the opposite of Aristotle’s direction. First he characterizes “being” as having to do with what things are and what can properly be said about them. Then he says the inquiry is really about the causes of independent things. Then he eventually concludes that knowledge does not apply to independent things, because they are particulars. What he is after here is a kind of practical wisdom, not scholastic “science”.

“But now let us go over what concerns the acknowledged independent things. And these are the perceptible ones. And all perceptible independent things have material. And what underlies something is its thinghood, and in one sense this is the material (and by material I mean that which, while not being actively a this, is a this potentially), but in another sense what underlies something is its articulation and form, which, being a this, is separate in articulation; and a third sort of underlying thing is what is composed of these, of which alone there is coming into being and destruction, and which is separate simply. For of the independent things in the sense that corresponds to the articulation, some are separate simply, while others are not” (pp. 155-156).

Here he explicitly generalizes the notion of an “underlying thing”. In the previous book, he started with the accepted view that this must be some kind of material. Then he adopted a Platonic lesson that the form or articulation of things better characterizes what they are. Then he diverged from the Platonists and concluded that independent things are even more important than form.

He certainly discussed all three cases, but my reading of the previous book was that only the composite of both form and matter ended up fully and properly qualifying as an independent thing. In part, he is being extra generous here to his former colleagues in the Platonic Academy, as well as to common-sense views of material. But he is also setting the stage for a new conclusion we will see shortly.

At this point, I am a little mystified by the implication that both all composites and some forms (presumably, some forms of non-perceptible things, which have been mentioned in passing but not discussed yet) will turn out to be in the same way “separate simply”. His only developed argument about the applicability of “separateness” to forms so far has been against the separateness of the Platonic forms, at least in any context involving perceptible things.

However, it is also true that the previous book does in passing seem to defer discussion of the possibility that there are non-perceptible independent things. To anticipate, it does seem true that any first cause of all, analogous to the first cause of motion he argues for in the Physics, must also be independent, for by definition, “first” means having no dependencies.

“[I]t remains to say what the thinghood of perceptible things is in the sense of being-at-work. And Democritus seems to think there are three ways things differ (for he thinks that the underlying body, the material, is one and the same, while what differ are design, which is shape, twist, which is position, and grouping, which is order). But it is obvious that there are many differences; for instance, some things are spoken of by reference to the composition of their material, as are all those made by mixing, such as milk blended with honey; others by way of a binding-cord, such as a bundle, others by means of glue, such as a book, others by means of bolts, such as a box, others by more than one of these, others by position, such as a threshold and a capstone (since these differ by being placed in a certain way), others by time, such as dinner and breakfast, others by place, such as the winds, and others by the attributes of perceptible things such as hardness and softness, density and rarity, or dryness and fluidity, some things differing by some of these, some by all of them” (ch. 2, pp. 156-157).

As this passage makes clear for non-independent perceptible things, in no case does what he calls the “being-at-work” or “actuality” of things involve what we ordinarily think of as work (which is why I still guardedly use “actuality”). In the case of non-independent perceptible things, the “being-at-work” has to do with whatever makes a unified thing out of material components.

“So one must grasp the kinds of differences (since these will be the source of being)…. So it is clear from these considerations that if thinghood is the cause of each thing’s being, it is among these differences that one must look for what is responsible for the being of each of these things. None of these examples is an independent thing, but still there is an analogous structure in each of them” (p. 157).

As we saw in the previous book, Aristotle sees definitions not in the modern formalist sense of characterizations we simply posit in isolation, but as built up from an ordered series of essential differences that progressively distinguish something from other things. To define something for Aristotle is to clarify its relation to classifying distinctions from other things.

“Now it is clear from these examples that the being-at-work and the articulation are different for different materials” (p. 158).

Kinds of materials are a sort of universals, so we do expect their distinctions to be fully articulable. From his examples above, what is responsible for the unity of material things that are not independent living things is itself something material. What kind of thing this source of material unity will be varies according to the case.

“One must not ignore the fact that it sometimes escapes notice whether a name indicates a composite independent thing or its being-at-work and form” (ch.3, p. 158).

“[W]hat it is for something to be belongs to the form and the being-at-work” (p. 159).

Form establishes a what, though it is a universal what and not a particular what. So far we have only seen examples of the somewhat non-intuitive being-at-work of material, non-independent things, which I just called the “source” in Aristotle’s sense for their material unity.

“Now it is obvious to those who inquire about it that a syllable is not made of its letters plus combination, nor a house out of bricks plus combination…. Nor indeed is humanness animalness plus two-footedness, but there has to be something which is apart from these, since these are its material, and that something is neither an element nor derived from an element, but since people leave this out, they describe its material” (ibid).

Here he continues his dispute with Plato’s other students. Combination is not a material ingredient of anything, even in the sense of purely logical or “intelligible” material.

“But whether those things that are the thinghood of destructible things have being separately is not at all clear yet, except that it is clear for certain things at least that this is not possible, as many as are not capable of being apart from the particulars, such as a house or a piece of furniture. So presumably these things themselves are not independent things, nor is any of the other things that are not composed by nature, for one may posit that nature alone is the thinghood in destructible things” (ibid).

I find the above a bit perplexing. The previous book clearly seemed to assume that there are perceptible independent things, and that at least all earthly perceptible things are destructible, though he seems to assume the stars and planets are indestructible, since he sees no evidence to the contrary. But it seemed that animals and plants were implied to be independent things, and to have their own distinctive substance-essence-thinghood. He definitely said that “the soul of an animal… is its thinghood disclosed in speech”. Isn’t an animal a destructible thing?

“[I]t does not belong to an independent thing to be capable of a definition” (p. 160).

This again was a major conclusion of the previous book.

“[E]ach independent thing is a complete being-at-work-staying-itself [entelechy], and a particular nature” (pp. 160-161).

Here he explicitly associates the independence of independent things with the teleological notion of entelechy.

“[W]henever one is inquiring after what is responsible for something, one must state all the causes the thing admits of” (ch. 4, p. 162).

I silently passed over his discussion of his predecessors in book I, but his main argument there was that none of them took all the causes into account. In particular, even Plato resorted to treating the Good as a formal or efficient cause. Aristotle regards interpretation by that-for-the-sake-of-which as his own major innovation.

“And what is the cause in the sense of form? What it keeps on being in order to be. And what is the cause for the sake of which it is? Its end, though presumably both of the last two causes are the same. And one must state the nearest causes: What is the material? Not fire or earth but the material peculiar to the thing” (ibid).

I just pointed out that Aristotle regards the distinction of that-for-the-sake-of-which from a formal cause as of major importance. His identification of the two here therefore must be intended as less than fully general. Form has senses that do not primarily emphasize any normative component, such as the form of triangularity. But as we have seen, Aristotle also speaks of the souls of animals as forms.

One might say that the soul is the entelechy (literally, “in [it] end having”) of a living body. Entelechies may come in layers. More precisely, the soul would be a name for the “first entelechy” of the body, or its achieved and continuing organic functioning. For Aristotle, this is intrinsically a normative concept. To speak of the entelechy of a body implies that it is not only functioning, but functioning well in relation to its intrinsic ends. Higher ongoing functions — just insofar as they are well realized — involve higher entelechies.

He makes an important point about material. What is usually most relevant is “not fire or earth but the material peculiar to the thing“, such as an organic body or a particular mineral. The more specific a material is, the more form-like it is. We will see shortly that Aristotle takes this to the point of identity between the most specific material and the form of a material thing.

“[T]here will not be material in those things that are or are not without changing” (ch. 5, p. 163).

In the Physics, the material cause was originally developed as part of the explanation of change.

“[A]ll things that have more than one part, and of which the sum is not like a heap, but a whole that is something over and above the parts, have something responsible for them…. But a definition is one statement not by being bundled together like the Iliad, but by being of one thing” (ch. 6, pp. 163-164).

A form is normally treated as an integral whole. A definition implicitly refers to an integral whole.

“Now it is clear that, for those who approach defining and explaining in this way that they are accustomed to [crudely adding specifications together, as in “animal plus two-footed”], it is not possible to give an account of it and resolve the impasse. But if, as we say, there is one thing that is material and one that is form, and the former has being as potency and the latter as being-at-work, the thing sought after would no longer seem to be an impasse” (p. 164).

I think what he is saying here is that the definition applies to the form only, not to the composite. That is probably why he earlier mentioned the ambiguity between a name’s referring to the form, and its referring to the composite. This does resolve some of the earlier puzzles about the applicability of definitions (a definition applies to a form). It is important to recall, though, that he just said again that there is still no direct applicability of definitions — which are expressed in universal terms — to independent things, which are particulars.

“But as many things as do not have either intelligible or perceptible material, are each of them some very thing that is one, just as also some very thing that is, a this, an of-this-sort, a so-much (and this is why neither being nor one is included in definitions), and what it is for something to be is immediately a particular one and a particular being. Hence there is no other thing responsible for the being-one of any of these, nor of the being-a-being of each, since each is immediately a certain being and a certain one, not in the sense of being in a class of beings or ones, nor of being among things that have being apart from particulars” (pp. 164-165).

Now he begins to speak in general about things that have no material. What this will apply to is as yet unspecified.

“But as was said, the highest level of material and the form are one and the same thing; the former potentially, the latter actively, so that looking for what is responsible for their being one is like looking for a cause of one thing; for each of them is a certain one, and what is in potency and what is in activity are in a certain way one thing. Therefore there is nothing else responsible, unless in the case of something that moves it from potency to being-at-work, but everything that does not have material is simply something that is itself one” (p. 165).

Back again to things that do have material, here he makes a point I alluded to earlier. One aspect of Aristotle’s hylomorphism is this identity of the most specific material with the form (for things that have material). Each independent thing has its own entelechy that is the primary cause of its being what it is.

Finally, he reiterates that things without material do not require anything external to give them unity.

Next in this series: The Innovation of Potentiality-Actuality

Entelechy

“Entelechy” — which I closely associate with what Kant called internal teleology — is probably the most important guiding concept of Aristotle’s Metaphysics (rather than the “Being” championed by many). There is a great deal to unpack from this single word. Here is a start.

The primary examples of entelechy are living beings. Aristotle also suggests that pure thought (nous) is an entelechy. I think the same could be said of ethos, or ethical culture.

Sachs’ invaluable glossary explains the Greek entelecheia as “A fusion of the idea of completeness with that of continuity or persistence. Aristotle invents the word by combining enteles (complete, full-grown) with echein (= hexis, to be a certain way by the continuing effort of holding on in that condition), while at the same time punning on endelecheia (persistence) by inserting telos (completion [what I have been calling “end”]). This is a three-ring circus of a word, at the heart of everything in Aristotle’s thinking, including the definition of motion. Its power to carry meaning depends on the working together of all the things Aristotle has packed into it. Some commentators explain it as meaning being-at-an-end, which misses the point entirely” (p. li).

He points out the etymological connection of echein (literally, “to have”) with hexis, or “Any condition that a thing has by its own effort of holding on in a certain way. Examples are knowledge and all virtues or excellences, including those of the body such as health” (p. xlix).

I previously suggested a very literal rendering of what Sachs calls the punned meaning of entelechy as something like “in [it] end having”, with the implication that it more directly means being subject to internal teleology with a certain stability, and I think something like this is the primary meaning. As Sachs says, this is very different from just being at an end. The latter would imply a completely static condition not subject to further development.

Entelechy is Aristotle’s more sophisticated, “higher order” notion of an active preservation of stability within change, which in the argument of the Metaphysics accompanies the eventual replacement of the initial definition of ousia (“substance”, which Sachs renders as “thinghood”) from the Categories as a kind of substrate or logical “subject” in which properties inhere. What he replaced that notion of substrate with was a series of more refined notions of ousia as form, “what it was to have been” a thing, and what I am still calling potentiality and actuality.

Whether we speak of active preservation of stability within change or simply of persistence (implicitly in contrast with its absence), time is involved. Reference to change makes that indisputable. Persistence is a bit more of a gray area, since in popular terms lasting forever is associated with eternity, but strictly speaking, “eternal” means outside of time (which is why the scholastics invented the different word “sempiternal” for things said to persist forever in time).

Sachs’ translation for what I will continue to simply anglicize as “entelechy” is “being-at-work-staying-itself”. This is closely related to energeia (“actuality”), which Sachs renders as being-at-work. I think it is important that there is nothing literally corresponding to “being” in the Greek for either of these, and want to avoid importing connotations of Avicennist, Thomist, Scotist, or Heideggerian views of the special status of being into Aristotle.

I also think “staying itself” tends to suggest a purely static notion of the identity of a “self” that is foreign to Aristotle. Sachs might respond that “at-work-staying” negates the connotation that “itself” is static, but I don’t think this necessarily follows. It might take significant effort to remain exactly the same, but this is not what Aristotle is getting at. To be substantially the same is not to be exactly the same.

Entelechy is intimately connected with actuality (energeia) and potentiality (dynamis). As Sachs points out, “actuality” in common contemporary usage has connotations of being a simple matter of fact that are at odds with the teleological, value-oriented significance of energeia in Aristotle.

“The primary sense of the word [entelecheia] belongs to activities that are not motions; examples of these are seeing, knowing, and happiness, each understood as an ongoing state that is complete at every instant, but the human being that can experience them is similarly a being-at-work, constituted by metabolism. Since the end and completion of any genuine being is its being-at-work, the meaning of the word [energeia] converges [with that of entelecheia]” (p. li).

If we take “being” purely as a transitive verb (as it is indeed properly meant here), my objection above to connotations of its use as a noun could be overcome. But in English, “being” remains ambiguous, and it is not there in the Greek.

Further, though it has the good connotation of something being in process, “at work” also introduces all the ambiguities of agency and efficient causation, in which overly strong modern notions tend to get inappropriately substituted for Aristotle’s carefully refined “weak” concepts. Aristotle very deliberately develops weak concepts for these because — unlike most of the scholastics and the moderns — he thinks of all agency and causing of motion as subordinate to value-oriented entelechy and teleology.

Sachs’ glossary explains dynamis (“potentiality”, which he calls “potency”) as “The innate tendency of anything to be at work in ways characteristic of the kind of thing it is…. A potency in its proper sense will always emerge into activity, when the proper conditions are present and nothing prevents it” (p. lvii).

He notes that it has a secondary sense of mere logical possibility, but says Aristotle never uses it that way.

I fully agree that potentiality in Aristotle never means mere logical possibility. Kant’s notion of “real” as distinct from logical possibility comes closer, but it still lacks any teleological dimension. I think Paul Ricoeur’s “capability” comes closer than Sachs’ “potency”, because it it seems more suggestive of a relation to an end.

However, I am very sympathetic to Gwenaëlle Aubry’s argument that Aristotelian dynamis should not be understood in terms of any kind of Platonic or scholastic power. “Power” once again suggests all the ambiguities of efficient causality. I think such a reading is incompatible with the primacy of final causality over efficient causality in Aristotle. (Historically, of course, the divergence of scholastic “power” from Aristotelian dynamis was accompanied by assertions of a very non-Aristotelian primacy of efficient causality.) To my ear, “potency” has the same effect. (See also Potentiality and Ends.)

Sachs had said that entelechy is also at the heart of Aristotle’s definition of motion. (Motion with respect to place is only one kind of motion for Aristotle; he also speaks of changes with respect to substance, quality, and quantity as “motions”. He also says there are activities that are not motions.)

Properly speaking, motion (kinesis) for Aristotle is only “in” the thing that is moved. That is how it becomes reasonable to speak of unmoved movers. A moved mover is indeed moved, but not insofar as it is itself a mover, only in some other way. He says there is no “motion” in being-at-work or actuality as such, but there is activity.

In book III chapter 1 of the Physics, Aristotle says that “the fulfillment [energeia] of what is potentially, as such, is motion — e.g. the fulfillment of what is alterable, as alterable, is alteration; … of what can come to be and pass away, coming to be and passing away; of what can be carried along, locomotion” (Collected Works, Barnes ed., vol. I, p. 343).

Sachs expresses this by saying that as long as “potency is at-work-staying-itself as a potency, there is motion” (p. lv). Otherwise said, motion is the entelechy and “actuality” of a potentiality as potentiality. As I’ve noted before, Aristotle doesn’t just divide things into actual and potential, as if they were mutually exclusive, but at times uses these notions in a layered way.

A mover (kinoun) is “Whatever causes motion in something else. The phrase ‘efficient cause’ is nowhere in Aristotle’s writings, and is highly misleading; it implies that the cause of every motion is a push or a pull…. That there should be incidental, intermediate links by which motions are passed along when things bump explains nothing. That motion should originate in something motionless is only puzzling if one assumes that what is motionless must be inert; the motionless sources of motion to which Aristotle refers are fully at-work, and in their activity there is no motion because their being-at-work is complete at every instant” (pp. lv-lvi).

It is worth noting that Aristotle has a relatively relaxed notion of completeness or perfection. We tend to define perfection in a kind of unconditional terms that are alien to him. For Aristotle in general, complete actualization or perfection is always “after a kind”, and it is supposed to be achievable. But also, it is only unmoved movers (and not organic beings) whose being-at-work is being said to be complete at every instant.

When he says “the phrase ‘efficient cause’ is nowhere in Aristotle’s writings”, he means that “efficient” is another Latin-derived term that diverges from the Greek. Aristotle in book II chapter 3 of the Physics speaks of “the primary source of the change or rest” (Collected Works, Barnes ed., vol. I, p. 332), but again we have to be careful to avoid importing assumptions about what this means.

As I’ve pointed out several times before, the primary source of the change in building a house according to Aristotle is the art of building, not the carpenter or the hammer or the hammer’s blow, and everything in this whole series is a means to an end. The end of building a house, which guides the form of the whole series, is something like protection from the elements. Neither the end nor the source of motion is itself an entelechy. But the house-building example is a case of external teleology. Correspondingly, it requires an external source of motion.

Internal teleology and the entelechy that implements it are more subtle; entelechy is an in itself “unmoving” and “unchanging” activity (which may nonetheless have new relational states, due to the narrow way in which Aristotle defines “change”). The things subject to motion and change in the proper sense are only indirectly moved by the activity-as-end of entelechy (by means of some source of motion).

We might say that Kantian transcendental subjectivity and Hegelian spirit are also entelechies.

Recently I suggested that what makes Hegel’s “subjective logic” to be “subjective” is its focus on the activity of interpretation and judgment, which in fact always aims to be “objective” in the sense of reaching toward deeper truth, and has nothing at all to do with what we call “merely subjective”. This is a sense of “subjective” appropriate to what Kant calls transcendental as opposed to empirical subjectivity. This higher kind of subjectivity, characteristic of what Hegel calls “self-consciousness” and of the activity of Kantian reflective judgment, would be very well characterized as an entelechy.

I strongly suspect that what Hegel metaphorically calls “logical motion” would be expressed by Aristotle in terms of the end-governed “unmoving activity” of entelechy. (See also Reflection, Apperception, Narrative Identity.)

Next in this series: Aristotle on Being

The Logic’s Ending

We’ve reached the very end of a walk-through of Robert Pippin’s Hegel’s Realm of Shadows, discussing Hegel’s Science of Logic. I have particularly valued the way Pippin brings to the fore Hegel’s close ongoing dialogue with Kant and Aristotle.

It now seems to me there is more hope of giving an ethical meaning to the specifically “logical” part of Hegel’s work than I had realized. My suspicion that Hegel ought to have something interesting to say about his removal of the qualifications in Kant’s recovery of Aristotelian teleology has certainly been confirmed. I also appreciated learning about Hegel’s specific use of the Kantian vocabulary of “reflection”, which plays a significant role in the admirable work of Paul Ricoeur.

I very much like Pippin’s idea that the Logic fundamentally develops a rich and multi-layered notion of judgment. His recognition of the normative character of Aristotelian and Hegelian actuality is salutary. Finally, I appreciate his foregrounding of the effectively hermeneutic rather than “given” notion of being that Hegel adopts from Aristotle.

He quotes Hegel’s ironic remark near the end of the Encyclopedia Logic, “When one speaks of the absolute idea, one can think that here finally the substantive must come to the fore, that here everything must become clear” (p. 317). I think Pippin also stole some of his own thunder for the climax by front-loading his detailed discussion of apperceptive judgment and related matters, rather than treating these in-line in his account of the Logic‘s major transitions.

Hegel’s fusion of the meta-level hermeneutics of Aristotle’s Metaphysics with Kantian “transcendental” logic — concerned with questions of the constitution of meaning — is a very different enterprise from scholastic and classical early modern “metaphysics”, which was supposed to give us “Being” and entities and general truths about the world.

Hegel nonetheless wants to insist that knowing can and does get at the real truth of things. But that truth is higher-order, not any kind of simple correspondence of statements and facts. Hegel insists that it is actually the lower-order, ordinary “truths” that should be called abstract, because they fail to make explicit what they depend on.

“[A] pure concept is not a class concept under which instances fall, but the ‘truth’ of any object” (p. 301).

In the final section of the logic of the concept, Hegel introduces “the idea”, which results from one more reflective turn beyond the preliminary identification of subject and object in the concept. In this final turn, we look back again at the things in experience and recognize how they fall short of what the concept tells us they ought to be. For Hegel, this means they fall short of Aristotelian actuality — as presented, they can’t be “really real” or true in a philosophical sense.

At the same time, Hegel resists the Fichtean idea of an infinite progress, which implies that the actual can never be fully achieved in knowledge. He seems to suggest that the fault is not with the inherent capabilities of philosophical knowledge, but rather with the world, and that it is up to us to do something about that.

Pippin quotes, “But since the result now is that the idea is the unity of the concept and objectivity, the true, we must not regard it as a goal which is to be approximated but itself remains a kind of beyond; we must rather regard everything as actual only to the extent that it has the idea in it and expresses it. It is not just that the subject matter, the objective and the subjective world, ought to be in principle congruent with the idea; the two are themselves rather the congruence of concept and reality; a reality that does not correspond to the concept is mere appearance, something subjective, accidental, arbitrary, something in which there is not the truth” (p. 300).

Pippin comments, “[T]his last non-correspondence of concept and reality takes in all of the finite world, the world we want to know and on which, in which, we act” (ibid).

“[W]hat specifies the realization of [a living being’s] life is always other than such an individual life — it must always work, strive to live — and in so being a manifestation of the idea at work becoming itself and already having become itself, being a living being, it introduces us to the structure of knowing, a striving self-realization that does not achieve what would be the end of such striving — complete wisdom — and that focuses self-conscious attention on this logical structure of knowing, and how one comes to know it by working through the opposition of the subject-object relation in its finitude. (This characteristic is what we know in knowing the Absolute Idea, not the completed knowledge of content. The ‘realm of shadows’ metaphor is relevant again.) Life is presented as the model for understanding the object-concept relationship at the heart of knowing” (p. 302).

He quotes Hegel, “The identity of the idea with itself is one with the process; the thought that liberates actuality from the seeming of purposeless mutability and transfigures it into idea must not represent this truth of actuality as dead repose, as a mere picture, numb, without impulse and movement, … or as an abstract thought; the idea, because of the freedom which the concept has attained in it, also has the most stubborn opposition within it” (ibid).

“Said in a more Aristotelian way, a living being’s form, its principle of intelligibility, is its norm, not just a means of classification. This norm can be realized poorly or well. This is the way we understand the relation between objects in general and the Concept. (This does not amount to any suggestion that Hegel thinks we should view everything as alive, because every being’s truth is its concept. The domain of relevance implied [is] the nonempirical attempt to say what is, for those objects about which we can nonempirically say what they are: Geist [spirit], the state, friendship, art, religion.) Or, said in a Kantian way, pure concepts are constitutive of objecthood itself, not empirical classifications. In knowing this constitutive relationship, we acknowledge both the identity of conceptuality with determinate being, and the speculative nature of this identity, that is, the difference or ‘opposition’ remaining within this identity. Any finite thing can be known to be what it is only by knowing its concept, even though as finite, it is not, never will be, fully its concept, and the full articulation of its concept is not possible. That is what it means to say it is finite. And in just this sense, knowing can genuinely be knowing” (p. 303).

“More properly, in the appropriate philosophical register, we should say that what we want is to understand, not to know in the modern scientific sense, that is, to explain. When we understand something, we understand its cause, but in the Aristotelian sense, we mean we know why it is what it is, its mode of being. And this knowledge does not then ground explanation; it is self-standing. (Hegel is not leading us to: ‘Why does it rain?’ ‘Because it is in the nature of rain to water the crops’.)” (ibid).

Here Pippin is using “explanation” in the limited sense of accounting for empirical events, and “understanding” for something broader and more hermeneutic, taking into account form and ends. I use “explanation” in a more Aristotelian way, as what promotes what Pippin here calls “understanding”.

“Thinking can either overcome any opposition of being to knowing, by transforming itself… or transform the world in order to overcome the one-sidedness of subjectivity. The semblance of objectivity — that some being is the ‘actuality’ it presents itself as — can be penetrated, understood not to be such an actuality, and transformed by ‘the drive of the good to bring itself about'” (p. 305, emphasis in original).

Thinking transforming the world means us as thinking beings transforming the world.

“[I]n practical knowing, the subject does not face the world as an alien element that must be transformed on the basis of a subjective demand descending wholly from pure practical reason. Practical knowing consists both in acknowledging the ‘reality of the good’ and in participating in the world’s own constant realization of its ‘purpose’ by acting” (ibid, emphasis in original).

Hegelian practical “knowing” or practical judgment has the attitude of what I have called being “at home in otherness”.

“Material assumptions… must be and are present, are usually hidden, and reflect a specific historical context. We need to know something material about human beings to make any progress, and human beings being historical, some sort of practical knowledge is necessary to determine any rightful relation to others, a knowledge of practical reality inseparable from an assessment of what is to be done” (p. 306).

The Logic aims among other things to help us find the reflectively grounded wisdom to be able to formulate this kind of practical judgment of what ought to be in concrete cases.

He quotes Hegel, “The unsatisfied striving disappears if we know that the final purpose of the world has been brought about and to the same degree eternally brings itself about” (p. 307).

“It is this last phrase, ‘eternally brings itself about’… that makes it impossible to ascribe to Hegel the claim that with the arrival of representative institutions, a market economy, the bourgeois family, romantic art, and Protestant Christianity, the ‘world’s purpose’ simply has been achieved and may now only be contemplated in full reconciliation, or even that there is an ‘end of history'” (ibid).

“It is at least clear that Hegel is making an implicit distinction between, on the one hand, distinctly practical reasoning, as it is understood in Aristotle — that is, reasoning that concludes in an action, not in a judgment about what is to be done — and practical knowledge of the situation in which action is called for. (Something close to what the practically wise person, the phronimos as Aristotle understands her, would understand.) The assumption is that any such reasoning always relies on some knowledge of what we would call ‘practical actuality’, the ability to rightly distinguish between the ‘surface’ actuality, ‘vacuous and vanishing’, and ‘the genuine essence of the world’. We know from our discussion of the logic of essence that this is not a strictly either/or picture; such an essence is manifest in, and has to be seen in, such a surface or Schein. And Hegel is insisting that any exercise of action-oriented practical rationality is inseparable from such an attempt at practical knowledge, a knowledge that will have the speculative form we have been investigating” (p. 309).

Again there is a terminological difference from Sachs’ translation of Aristotle that I have been using for these terms, but the inseparability of what Sachs calls deliberation and what he calls practical judgment (which for Aristotle results in action) is the same in Hegel and Aristotle.

“Hegel’s position on the historicity of reason is quite complicated, and can sometimes seem like a moving target, at times making conceptual, a priori claims about what it is to be spirit (i.e., free, in the sense of self-realizing), and at times linking any understanding of spirit to an account of concrete historical actuality” (pp. 313-314).

In a way, this is Hegel’s whole point. He is neither simply a “historicist” affirming the relativity of circumstances, nor a Kantian/Fichtean moralist aiming to make universal prescriptions of what ought to be, but rather commends an Aristotelian mean that avoids the one-sidedness of both.

“The absolute idea, or ‘the logical idea’, is also called, revealingly for our interests, ‘the idea of thinking itself’…. Pure thinking, in determining what could be the object of a true self-conscious judgment, has turned to itself as the object of speculative judgment, since it has discovered, in detail, that the ‘truth’ of objects is the relevant pure ‘concept’, that conceptual determination without which no empirical determination would be possible, that is: qualitative and quantitative predication, a determination based on an essence-appearance distinction, the right understanding of substance, causality, and now the right understanding of the ‘thoughts’ that have made up the account thus far. Pure thinking is now in a position to ‘recollect’ what it ‘was’ to have been thinking purely. (We don’t thereby know any qualities or essences or attributes of modes of substance. We know the logic of substance-attribute, essence-appearance, and so forth…)” (p. 316).

At this final stage of the Logic, we are recollectively turning back to survey the whole “long detour” that was necessary for Hegel to be able to say what intelligibility is, and consequently, according to Hegel, for us to be able to judge what is actually true and good and right in concrete situations.

Pippin quotes, “Each of the stages considered up to this point is an image of the absolute, albeit in a limited manner at first, and so it drives itself on to the whole, the unfolding of which is precisely what we have designated the method” (p. 317).

“[T]his last characterization of method as the culmination of the entire book, as the absolute idea, is crucial” (ibid).

He quotes, “[The absolute idea] has shown itself to amount to this, namely that determinateness does not have the shape of a content, but that it is simply as form…. What is left to be considered here, therefore, is thus not a content as such, but the universal character of its form — that is, method” (p. 318).

Hegel is here telling us that what he has been discussing has been intended to clarify the “method” he implicitly follows throughout his work. Conversely, a fuller justification of that method will come from the concrete results of its use.

For Hegel, “truth, … the absolute idea, just is self-conscious conceptuality, or the right understanding of the implications of the logical structure of apperception, or purely logical knowledge, and in this purity the manifestation of absolute freedom” (p. 319; see also The True and the Good).

Reflection and Dialectic

As with dialogue, reflection provides a kind of model for dialectic. Reflection can be understood as an either metaphorical or literal dialogue with ourselves. We “question ourselves”, which is to say we examine and potentially criticize or refine the basis of our own commitments. Further, actual dialogue is always implicitly dialogue among fellow rational beings, all of whom are engaged at least to some extent in their own reflective activity, just by virtue of being rational beings, so dialogue implicitly presupposes reflection.

Pippin quotes Hegel: “But at issue here is neither the reflection of consciousness, nor the more specific reflection of the understanding that has the particular and the universal for its determination, but reflection in general…. For the universal, the principle or the rule and law, to which reflection rises in its process of determination is taken to be the essence of the immediate from which the reflection began…. Therefore, what reflection does to the immediate, and the determinations that derive from it, is not anything external to it but is rather its true being” (Hegel’s Realm of Shadows, pp. 238-239).

And again: “In general, this means nothing but this: Anything which is, is to be considered to exist not as an immediate, but as a posited; there is no stopping at immediate determinate being [Dasein] but a return must rather be made from it back into its ground, and in this reflection it is a sublated being and is in and for itself. What is expressed by the principle of sufficient reason is, therefore, the essentiality of immanent reflection as against mere being” (p. 239).

In the first quote, Hegel is again emphasizing that what he means by reflection is not just looking in a figurative mirror, but rather something more like finding an orientation among (or building a synthesis of) the potentially infinite mutual reflections in a hall of mirrors. Reflection “in general” is a name Hegel gives to reflection with this kind of potentially infinite dimension. (That the infinity here should be called potential is my friendly Aristotelian interpolation.)

In the second quote, he is saying that this kind of reflection — lifted out from the distinction between reflective activity and what it reflects upon — is what he would call the “truth” of everything that appears to be immediately determinate.

The principle of sufficient reason as formulated by Leibniz effectively says that for everything that is in some definite way, there is a reason why it is that way. Hegel is saying more specifically that such “reasons why” emerge immanently from the reflective grounding of what he is in a nonstandard way calling essence. What Leibniz cannot show is how a particular essence or monadic point of view results in certain predicates and not others; despite great sophistication, he is still to some extent using essence and monads as unexplained explainers to avoid what Hegel calls the “problem of indifference”. Hegel on the other hand explicitly makes essence and explanation interdependent.

“[T]he ‘principles’ of identification and differentiation are deeply intertwined, not independent of each other” (p. 240).

“[A] thing’s determinate properties are not, cannot be, a mark of that thing’s unlikeness from other things, just by being those properties…. If one thing is red and another square, we do not thereby know one is unlike the other; they are just two different things. A locomotive has nothing to do with a melody; it is not unlike a melody. We are trying to account not for determinate otherness, as in the logic of being, but for how objects that share properties (are like) could be, even with an extraordinary degree of such likeness, still unlike” (p. 241).

“Some of this anticipates topics in the logic of the Concept. Two trees are alike in being trees but unlike in being two individual trees. The idea will be that just in their likeness, their way of being alike, that they are unlike (different trees), just in the way each distinctly instantiates ‘treeness’ that they are unlike. Such a different ‘way of being a tree’ is not another property but the way the tree-properties are ‘had’ by the individual” (p. 242).

“Hegel is thinking of the way in which the specifying work of ‘unlikeness’ cannot be a matter of individual properties, atomistically conceived, but unlikeness within likeness is best understood as some content, the unlikeness of which is strict, even within such likeness. Some charge can be both positive and negative; some number, 4, can be both +4 and -4; some quantity of money can be an asset and also a debt pending; some force can be attractive and repelling; some distance marched east is canceled by the same distance marched west, and all these are ‘opposed’ only within some common likeness” (ibid).

I find “either-or” language more appropriate to these cases than the “both-and” language above, but the intent is the same. The distinctions in each sub-case are concrete “opposites” applicable to some specific context, and each definable only in reference to the other. In each case, it is possible to abstract an indifferent thing being measured or assessed — “positive-or-negative-quantity” for the one, and “virtue-or-vice” for the other.

“The ‘world’s being contradictory’ means nothing more than that, as he says, virtue cannot be virtue just by being other than, different from, in comparison with, vice, but only by ‘the opposition and combat in it’ against vice” (p. 243, emphasis in original).

Pippin complicates the matter with this example, because “relative” seems to have a different significance in the context of virtue and vice than it does in, say, that of positive and negative numbers. But the intended point is a very abstract one about constitution of meanings that is common to both cases. Whatever the difference between the two “oppositions” (positive/negative, virtue/vice), in each case the two sub-terms are somehow measured or assessed “against” one another.

“Hegel is trying to specify how affirming contrary predicates (‘in opposition’) does not amount to a logical contradiction. That is the point of his discussion, to make this distinction, not to treat such oppositions as if they were logically contradictory and then to affirm them anyway. As [Michael] Wolff puts it, Hegel’s orientation… is not from sentence or predicate negation, but from developments in the understanding of negative numbers and from Kant’s defense of Newton on positive and negative magnitudes. In general, then, mathematical, not logical negation” (pp. 243-244).

This is extremely important. The status of negative numbers was still controversial in Hegel’s time. Kant and Hegel contributed to their acceptance. Hegel struggled to invent new language to distinguish ambiguous cases in his Logic and to say reasonable things about them, but readers (certainly including myself) have found his unique idioms very hard to follow. Most of the ink spilled over “contradiction” in Hegel has been based on fundamental misunderstandings. (See also Negation and Negativity.)

“To use an empirical example, if the question is something like ‘Why did the ball fall to the ground?’ we want to avoid two kinds of answers: ‘because whenever a heavy object is dropped from a height, it falls’; and ‘it is in the nature of heavy things to fall’. Doing so, avoiding these alternatives, will allow us to see that the relation between a ‘ground’ and ‘what it grounds’ must be understood as a dynamic relation, one whereby the determinacy of the ground and that of the grounded cannot be fixed in isolation from each other” (pp. 245-246).

He quotes Hegel: “But the being that appears and essential being stand referred to each other absolutely. Thus concrete existence is, third, essential relation; what appears shows the essential, and the essential is in the appearance. — Relation is the still incomplete union of reflection into otherness and reflection into itself; the complete interpenetrating of the two is actuality” (p. 246).

“The general point [Hegel] keeps making is: a strict separation of the two moments, and an insistence that the nature of an appeal to an essence, or to a causal law, or to someone’s reason for acting cannot be understood as punctuated moments on the billiard-ball model of causation, but involve a kind of unity, the development of a kind of unity, much closer (yet again) to Aristotle on energeia. This essential-being-as-activity, manifesting itself in its appearances, is what should count as ‘actuality’. This has the implication that many existing things have no actuality, are not really ‘anything’. A lump of dirt, a cough, a strand of wire” (ibid).

“The question for Hegel is the question of ‘actuality’, not ‘existence’, or the sensibly apprehensible, just as for Aristotle, the question is the ‘really real’, to ontos on.” (p. 247).

Pippin quotes from the Encyclopedia Logic, “The logical is to be sought in a system of thought-determinations in which the antithesis between subjective and objective (in its usual meaning) disappears. This meaning of thinking and of its determinations is more precisely expressed by the ancients when they say that nous [“intellect”, or thought in a non-psychological sense] governs the world” (p. 248).

Here “governs” is meant in a constitutive sense. The important point is that the “thought-determinations” here are indifferent to the ordinary distinction between a subjective “thinker” and an objective “thought content”.

In this context he speaks of “this dynamical relation, this Ur-relation of all relations” (ibid).

“I have tried to show in another book that the most important, most clarifying implications of this Ur-relation occur in Hegel’s practical philosophy, both in his account of human agency, and in the implications of that account for the practical theory of freedom in his Philosophy of Right and theory of objective spirit in general (ibid).

“[T]he full demonstration of the truth of this Ur-relation lies in what it actually illuminates, in the cogency and credibility of, for example, an account of agency based on it” (p. 249).

It was the outstanding (and very Aristotelian) account of Hegel’s view of agency in Hegel’s Practical Philosophy that first attracted me to Pippin’s work.

In his own idiom, Hegel says “thus the inner is immediately the outer, and it is this determinateness of externality for the reason that it is the inner; conversely, the outer is only an inner because it is only an outer” (quoted, ibid.)

Pippin comments, “He does not mean here anything as obvious as: when I do something, my ex ante intention is fulfilled and so becomes something outer, just as what was done, the bodily movement, counts as an action because it expressed this ex ante intention. The passage does not say that the inner becomes the outer, nor that the outer is the expression of the inner. It says: there is no ex ante intention except as outer. It is the outer. And there is no outer except as what must count as inner, nor that it expresses a separable inner. There is no such separation” (pp. 249-250; see also Hegel on Willing).

This concludes Pippin’s chapter on the logic of essence. Unsurprisingly, we have not uncovered any magic formula that would tell us which appearances manifest the essence in particular cases. Such a thing seems completely impossible to me; we should not expect to be able to find any general formula covering an unspecified collection of particulars. Any judgments involving particulars must in part at least come back to something like Aristotelian deliberation and practical judgment, which yield only particular results.

Nonetheless, in discussing the logic of essence we have ruled out some important classes of misunderstandings, and we have set the stage for the climax of Hegel’s Logic in the “logic of the concept”. The logic of the concept will take as a starting point the non-separation of “inner” and “outer” that has been shown in the logic of essence.

Next in this series: “The” Concept?

Toward Essence

What does it mean to really explain something, as opposed to just making claims about it? According to Robert Pippin, this question underlies what he calls the key transition of Hegel’s Logic, between the “logic of being” addressed in several recent posts and what Hegel calls the “logic of essence”.

The logic of essence will itself eventually be superseded by the logic of the concept. With very broad brush, it seems to me one might expect that the logic of essence will be a representation of important insights Hegel attributes to Aristotle, whereas the logic of the concept is supposed to be a representation of what he claims as his own (and Kant’s).

“[Hegel’s] general approach [is] to begin with the least ‘mediated’, least theoretically committed determination and argue for the further determinations, further theoretical commitments, without which even these relatively simpler determinations would not be possible” (Hegel’s Realm of Shadows, p. 211).

Hegel assimilates all simple predications or assertions to the logic of being, the inadequacy of which we have seen in some detail. Every word, phrase, or assertion taken in strict isolation reduces to meaningless noise, just like the attempt to “say” indeterminate Being. Only taken together and in some sort of context do words and assertions begin to mean something.

According to Pippin, “a mere list of contingent properties and quantitative measures cannot count as having determined any subject of those determinations as such” (ibid). Hegel “summarizes this problem by calling it the problem of indifference” (ibid). We still lack any even quasi-stable things to talk about.

An explanation is more than just a generalization. Explanation requires distinguishing the essential from the nonessential.

Hegel thinks that even something as sophisticated as the use of Newton’s inverse square law to account for the elliptical shape of planetary orbits is still only a compact way of making a complex assertion about relational properties, and does not give us a reason. This corresponds to the level of the “force and understanding” chapter of the Phenomenology, which reaches a purely relational point of view on mathematical physics, but still lacks the features Hegel associates with self-consciousness.

“[A] distinction between what is truly real or essential and what appears, or that way of thinking, is now on the Logic‘s agenda…. A practice exists, and we want to know not merely what happens or whether it exists but whether the practice is actually a religious practice. Or a computer wins at chess, but is it actually thinking? Something is displayed in a gallery, but is it actually art?” (p. 218).

“These questions are just examples. The Logic is not concerned with them, and, we should say, is concerned with actuality as such, the possible actuality of anything intelligible” (ibid). “These example questions… depend on ‘the logic of actuality’ as such, which simply means: how we think about what anything ‘really is’. As we have seen, the determinations of such conceptuality cannot be empirical; they must be understood, according to Hegel, as ‘products’ of thought’s self-determination of itself, a process that continually realizes thought’s apperceptive nature. Or: the concept gives itself its own actuality. Hegelian conceptuality has this subjective dimension (‘thought’s autonomy‘), even while also being the articulation of the conceptual structure of reality. This has nothing to do with spinning every actual, contingent species-form out of thought’s self-examination. The topic… is logical or categorical formality as such, not ‘what are the existing species-forms?’ ” pp. 218-219).

“The very title of a ‘logic of essence’ suggests (yet again) immediately the philosopher whom Hegel seems most to admire, Aristotle” (p. 219). “We found in the logic of being that, according to Hegel, it was not possible to specify a thing’s ‘actual’ being by qualitative and quantitative markers…. Since Hegel accepts the Aristotelian premise that actually to be is to be a this-such, where that means it is identifiable by being an instance of a kind, this means we have failed with respect to the question of actuality. We are thereby compelled, in the prosecution of the original task, to consider that, ‘actually’, a thing is not how it simply appears, looks, sensibly manifests itself, however regular or predictable. We have to say that in some way, what a thing actually is lies hidden, must be uncovered, posited, a product of thought, not a simple empirical apprehension as such” (p. 220).

The “original task” is the determination of meaning, which didn’t get very far in the logic of being, even though in the parts Pippin has skipped over, Hegel did develop resources for making broad classes of simple assertions or claims about appearance.

“What we will need is a comprehension of the difference… between the ‘essential’ and the ‘unessential’, and the basis for this differentiation” (p. 221). “[W]hatever seemings are, (in not ‘actually’ being), they exist and are determinate, a determinacy inexplicable, Hegel claims, by the ‘skeptics and idealists’ who claim that the distinction cannot be made, and therefore say, ‘everything is illusory'” (ibid).

Whoever claims that “everything is only mere appearance” turns out to have no basis for making any distinctions within the so-called appearance.

“Someone who had understood everything said onstage, the plot of Shakespeare’s King Lear, and the basic motivations of the characters, as those characters and others voice them, and had understood only that, would not, we feel entitled to say, have understood ‘the play’. Put in the simplest possible way, to understand the play, one has to do more than listen to it; one must think about it, or we can say, using the word most important for Hegel, ‘reflect’ on it, understand what lies ‘beneath’… these facts about plots and characters…. There is no such thing as a hidden meaning in King Lear; there are just the words spoken or found on the page. How we get from this clumsy metaphor to the ‘concept’ of King Lear in itself is the underlying story of the logic of essence” (pp. 223-224).

All meaning that is worth talking about has this same kind of non-thing-like character. It is constituted from relations of connection and disconnection.

“It would be a mistake to sum a person up, attempt to ‘understand’ her in the distinct way persons should be understood, simply by adding up or listing everything she did, from what she had for breakfast to volunteering for a dangerous mission. A person would not be properly understood by attention to such ‘immediacy’ alone (or her qualitative/quantitative/measured appearances, as in the logic of being). We need to understand her deeds as ‘mediated’ by what Hegel calls her ‘inwardness’…, something (and now in the most important difference with the logic of being) that we cannot see, that does not simply present itself” (p. 224).

The relations that constitute meaning do not themselves directly appear. This applies as much to things in general as to human character.

It is certainly ubiquitous that people and things also respond differentially to direct appearances, without anything deeper than a qualitative or quantitative appearance being involved. Mid-20th century behaviorism claimed that was all there is, that the meaning at issue here was a mere figment or conceit.

Pippin continues his previous example, “For example, we can’t really understand what she did except by some attention to her own formulation of the act description and to her avowed motive (her ‘intention’). Sometimes what happens should not count as a deed because there is not the proper connection of inner and outer. An accident happens. Something prevents her from realizing her intention; that is, something happens to her. She does not do something. What happens is not an expression of her character. On the other hand, as Hegel states the central claim of the entire logic of essence in a phrase, we must concede that any such inner self-construal can ‘prove itself’… only in what manifests that outwardly, in the deeds. (It is immediately important that this ‘test’ can fail.) Too radical a separation and we have someone trying to disown what she in fact did, to fabricate excuses. (‘Mistakes were made’; ‘It was never my intention to deceive/hurt/offend anyone’, etc.) We need this distinction, but we can’t establish which deeds are true manifestations of essence and which are merely aberrations by any statistical analysis of frequency, any simple inspection of what happens. We need to understand how ‘what shows’, ‘what manifests itself’ (Schein), can be said to reflect these deeds’ essence when it does (if it does, then as Erscheinung, appearance), even if, as appearance, no one deed is ever a manifestation or simple representation of essence as such ” (pp. 224-225).

It was this sort of point about the ethical meaning and use of actuality in Hegel’s Practical Philosophy that initially greatly impressed me in Pippin’s work (see especially Hegel on Willing). According to Pippin, this kind of question about the relation of actuality to appearances is just what Hegel’s “logic of essence” is all about.

Unexpectedly for me at least, this now provides the occasion for Pippin to tell us more specifically what he thinks “mediated immediacy” means in Hegel. As I mentioned before, I have always thought first of things like the experience of riding a bicycle or recognizing an object, which properly speaking are examples of “immediatized mediation”, bridging the gap between the intrinsic emptiness of immediacy in itself and our undoubtedly non-empty “immediate” uptake of things in ordinary experience. In other words, my attention was drawn to the way in which complex results of some previous synthesis can be pre-consciously associated to what we experience “immediately” in a new synthesis of imagination.

Hitherto, in thinking about the term “mediated immediacy”, I have focused on ordinary appearances of meaning, in contexts that according to Hegel are not adequate to “immediately” support the constitution of that apparent meaning. This is admittedly to disregard the surface grammar of the phrase.

Pippin here starts to give “mediated immediacy” a sense that is aligned with the surface grammar, and is also closely aligned with what he has just said the logic of essence is all about.

He continues, “Understanding this relation properly is what Hegel thinks allows him to speak of a mediated immediacy. The appearances are not denied as unreal. They ‘shine’ in their immediacy. But they can be understood in their determinate immediacy only as the manifestation of the thing that they are appearances of, and so are always mediated…. We can’t derive the appearances from a mediated (‘posited’, ‘reflected’, ‘thought-over’) essence. That would be a denial of their immediacy. But we don’t apprehend such appearances on their own, in pure immediacy, and then infer what appears. What appears is appearing in what manifests itself…. What a person does is tied to that person’s character, whatever it is. And understanding that character is nothing other than rightly understanding what that person has done. With respect to all the reflected dualisms introduced in the logic of essence, this thought in various forms remains the kernel of that logic throughout” (p. 225).

This is Hegel’s recovery of something like Aristotle’s qualified common-sense realism about experience. We say that we experience not just phenomena but also things, even if we are wrong about them sometimes. At the simplest level, though not itself thing-like, essence is what enables the distinction of things from arbitrary collections of appearances.

“This is also why essence is a retrospective reflection of what has been made manifest, why it is rooted in gewesen, the past participle of sein [to be] or ‘what has been’, a feature somewhat counterintuitive in an account of action. It is also why Hegel is happy to accept the Wesen/gewesen suggestion of temporality. It links his account with one he admired, Aristotle’s, whose term for what has often been translated as essence is to ti en einai, something like ‘the what it was to be’ of a thing” (p. 226).

Essence, I would suggest, subsists independent of time once constituted, but the constitution of essence for both Aristotle and Hegel has a dependency on appearances in time. It therefore could not be pre-given. We have to actively discover or construct it, often taking into account long sequences of appearances in time. These may wander in various directions or sharply reverse our previous expectation. Parts of them we will judge to be irrelevant. This is only the beginning of the story of essence, not the end.

“Ultimately on Hegel’s account, if we want to know whether this lie reveals a person to be a ‘liar’, what we need is not to have deeper insight into some thinglike essence, but to observe what else the person does over time and to understand the relation among these deeds, to interpret them or ‘think them over’ in their relation to each other. This will be a crucial point throughout the logic of essence, and it obviously raises the question of how to make, what guides us in making, this relational connection.”

It is relatively easy to express the openness of Aristotelian practical judgment. But we still have to do the work of judgment in each case, and due to the openness we will have committed to with Aristotle, there could not be a precise roadmap telling us how to do the work. But Kant already argued that at least at a sufficiently high level of abstraction, universals can meaningfully guide practical judgment, so perhaps something more could be achieved. Any such progress on how to judge what is essential would be priceless indeed.

“Finally, it is important to stress that this topic is being introduced very broadly. No particular theory of ‘essentialism’ is being entertained, and as already noted, making the general distinction just discussed could be achieved even by an account of the difference between transcendental and empirical subjectivity, or between categories and empirical concepts” (ibid).

Essence as such need not be taken as a specific “ontological commitment”. It means what is reasonably, reflectively judged to be important. That is part of the hermeneutics of things and of life, which we encounter as soon as we begin asking if someone or something is really or actually something-or-other. (See also Essence and Explanation; Hegel on Reflection.)

Next in this series: Essence and Explanation