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## Sorry, Aristotle (and Aquinas), but I still don’t understand formal causes

Subtitle: how a modern physicist is liable to misunderstand Aristotle. This post was inspired by a very interesting post by Edward Feser here.

I have tried. What follows is my attempt to give full expression of my own ignorance. One of the conclusions I have drawn from my forays into Ancient and Medieval philosophy is that these are great thinkers.

Here is the standard illustration for Aristotle’s four causes. Consider a marble statue. The statue has four causes. The material cause is the marble, the material out of which the thing is made. The formal cause is the arrangement of the statue, its geometrical shape. The efficient cause is the “doer”, the sculptor, who arranges the material into the desired shape. The final cause of the statue is the purpose for which the sculptor has created the statue, e.g. to look beautiful in the garden.

### Aristotle and Newton

Right, I think. My physicist training naturally has me try to cast my Newtonian (occasionally Einsteinian, sometimes quantum) view of the world in these categories. (This might be a bad idea, I think, given the discontinuity between Aristotle and Newton. Still, I’ll give it a go. Also, I’ll worry about relativity and quantum mechanics later, if at all.) So,

• Material cause – the particles of matter out of which physical things are made.
• Formal cause – the arrangement of those particles. Mathematically, a list of the position and velocity of each particle at some time $(x_i(t), v_i(t))$
• Efficient cause – Newtonian forces, which move particles around.
• Final causes – an emergent, higher-level property of minds, who can make and execute plans.

(This is not the correct way to understand Aristotle, so stay tuned.) So far, so good, I think. The “Newtonian” material, formal and efficient causes give all the information one needs to solve Newton’s laws of motion. But now the confusion starts.

A lecturer giving an introduction to the history of science talks about Plato’s theory of forms as a realm of abstract but still “really” existing ideas. He later seems to suggest that the formal cause of a chalk circle drawn on the board is the idea of the circle in the mind of the lecturer. I ask, “For the circle on the board: is the formal cause the idea in the mind, or the idea of a circle floating out there somewhere in Plato’s realm?”. “Uh … have you been reading the Scholastics?”, he replies. “Nope”. I can’t remember the rest of his answer – it was rather vague. I’ve had a chance to ask a few other philosophers about formal causes since, and their reply usually starts with a grimace.

### Enter Feser

So it was that I came to Edward Feser’s Aquinas (A Beginner’s Guide). His exposition is admirably clear, and it is obvious that I must change my understanding of the four causes. In particular, final causes are more than just intentions of minds. There are natural final causes. When a match is struck and fire is created, the efficient cause of the fire is the match. At the same time, the final cause of the match is the fire. The properties of the match “point to” or “are directed at” the creation of fire. Fire is what matches do. The match isn’t just a generic efficient cause that could cause any old thing but just happens to cause fire every time. Its ability to do something is controlled by fire as its final cause. I picture this as the efficient cause being the engine, and the final cause as the steering wheel. The efficient cause does the causing, and the final cause directs the efficient cause towards the production of its effect.

The shocking thing about this, as Feser points out, is that the scientific revolution, despite its PR, didn’t get rid of final causes. Final causes are how Aristotelian metaphysics explains the orderliness of nature. The fact that things keep doing the same kind of things – trees grow, the sun shines, fire burns, dropped stones fall – is because the efficient causes in the world are conjoined (is that the right word?) to final causes, ensuring that they produce consistent effects. The “laws of nature”, to use an slight anachronism, are more about final causes than efficient ones. But that is a topic for another day.

Despite Feser’s clarity, formal causes now get even more confusing. Feser argues that things can be imperfect instantiations of their form. Their form isn’t just how their parts are arranged. It is, in some sense, how they should be arranged, what their essential arrangement is. For example, when a person loses a leg, they don’t take the form of a one-legged person. Their true, two-legged human nature is still there in the person, but it is instantiated imperfectly.

Note that Aristotle differs from Plato in locating the form of a thing in the thing itself, not in some ideal external realm of forms. It isn’t just that the person fails to replicate the ideal of a  two-legged Platonic person “up there”. The one-legged person still has the form of a  two-legged human. Two-legged-ness is still in there, somewhere.

### How do we see the form?

Here is my specific confusion. Feser asks us to consider a drawing of a triangle. This drawing of a triangle has the form of a perfect triangle. That is, its form is perfect triangularity. It can instantiate this form more perfectly (a sharp pencil, a straight edge and some graph paper) or less perfectly (a crayon, free hand, on a cracked plastic bus seat). Remember: we’re talking about the form of that specific collection of ink/crayon, not the abstract idea that it usually represents.

Now consider a triangle with sides sides that bow outwards slightly. Why say that this is a mildly imperfect triangle, rather than a slightly imperfect Reuleaux triangle? Consider a sequence of geometrical shapes (below), starting with a circle and smoothly merging into a triangle. (Consider these as real, physical things, not as mathematical abstractions. Print them off, and then consider the arrangement of ink on the page). At what point does it cease to be an imperfect circle and start to be an imperfect triangle? All we have is an arrangement of ink. How do we see through it into the perfect form behind it?

The forms of things can change. How do we know that Terri Schiavo (Aquinas, pg 203), having entered a vegetative state from which a return to consciousness was not physically possible, still had the form of a human (a rational animal) even though she could no longer exercise her rational capacity? Why not instead believe that she had, in having brain damage cause by a cardiac arrest, changed her form to become something else, something less than human? (I wish I had an example which didn’t have such strong moral consequences, but that is the example Feser uses.)

Feser criticises Descartes’ dualism on the grounds that it creates the problem of personal identity: since a person’s soul is immaterial, it is imperceptible. “All we ever observe or can observe are people’s bodies, not their souls, not them. How we can ever know whether other minds or persons even exist at all thus becomes problematic.” (pg 204). But it seems that Aristotle has the same problem. Given that “any material thing is bound to fail perfectly to instantiate its form in some respect or another”, it becomes somewhat arbitrary to decide which particular perfect form a particular object is failing to instantiate. What would you expect to find inside a packet of “Almost Bacon”?

Sometimes, when something changes, we are to say that the matter has taken on a different form, as when a rubber ball is melted down into an eraser. Other times, when something changes, we are to say that it has become a more or less perfect instantiation of the same form, as when a person loses a leg but remains the same person. The choice between these two characterisations seems to be somewhat arbitrary. For every clear example, there will be a thousand ambiguous ones.

Another problem. According to Aristotle, one of the features of formal causes is that they permit one to truly think about something, since the form of a thing can exist in the object and in the mind at the same time and be the same thing. However, if, when I consider a triangle, the same form exists both in my mind and in reality, then we have a problem. If the crayon triangle on a seat is an imperfect instantiation of a perfect triangle, then its form is that of a perfect triangle. So if I think about the crayon triangle, what I am really thinking about is perfect triangularity. But then I am not thinking about the crayon triangle on the seat. I cannot think about the triangle on the seat. I can only abstract from that triangle to perfect triangularity.

### The problem for the physicist

Feser wants to return modern science to an Aristotelian metaphysic. It is, despite my misgivings, a project for which I have some sympathy. I can see, or I think I can see, some of the benefits for such a system.

The problem is that I can’t see how to analyse the theories of modern physics in Aristotelian terms. The examples used – sticks and hands and stones and fires and matches and such – are somewhat useful, once one has a firm idea in mind of what they are trying to illustrate. But I can’t translate the principles into, say, quantum field theory. What, in a quantum field theory, corresponds to “form”? What are the “potentialities” and what are the “actualities” in a given configuration of fields? How do we understand causes in spacetime? If I had two bodies in otherwise empty space orbiting each other (according to Newtonian gravity), what is the first cause?

The problem with something like the triangle example is that these ideas seem to be adding structure on top of the physical theory. As well as the atoms and such that make up the crayon triangle, there is also “perfect triangularity” hanging around, somewhere. The physicist in me wants, to make these ideas precise, a function that takes a certain configuration of fields as an input, and outputs its true essence, or form, or whatever. This would seem to have to make arbitrary distinctions – if the sides bow by 4.7% or less then it’s an imperfect triangle, more than 4.7% and it’s something else. Physicists, for obvious Occam’s razor reasons, are loathe to add empirically unobservable structure to their theories. General relativity is hard enough as it is without having to analyse the true form that inhabits some spacetime.

In particular, as physicists we are taught to avoid debates over names and labels. Feynmann summarises this view perfectly

You can know the name of a bird in all the languages of the world, but when you’re finished, you’ll know absolutely nothing whatever about the bird… So let’s look at the bird and see what it’s doing — that’s what counts. I learned very early the difference between knowing the name of something and knowing something.

These discussions of instantiations of triangularity strike me as debates over the name of something. “I say it’s a more perfect Reuleaux triangle”. “Well I say it’s a less perfect triangle.” This, and all other discussions of forms and patterns, seems like a debate about how I will classify something in my mind. Such classifications can be more or less useful but, like our naming of a bird species, don’t reflect anything about the real world.

### Confusion, not criticism

Anyway, such are my confusions. Note well: these are not necessarily criticisms. I’m pretty sure I’m just not getting it. Aristotle and Aquinas were geniuses, and so presumably have answers to my questions. Still, I think that the points made above are somewhat typical of how physicists react to Aristotle’s ideas. The neo-Aristotelian project, to recruit physicists, will have to deal with these kinds of confusions. I couldn’t help thinking throughout Feser’s “Aquinas” that I would be greatly helped by an appendix titled: “1001 examples of how Aristotelian metaphysics analyses familiar and fundamental physical systems”.

### 11 Responses

1. Hi, Luke. As a junior Scholastic, I’d like to have a crack at your worries.

Let’s give an account of what Forms are, to begin with, then consider them in light of your worries. Form is the principle of actuality of a thing- what makes a thing itself. You might call it the “metaphysical pattern” intrinsic to a thing, in virtue of which it is itself.

Form is usually contrasted with Matter, which is what “limits” Form, which is of itself universal, to the individual, and, insofar as it grounds the capacity to receive Form, also grounds the possibility of change. It is that in which the abstraction needs to inhere, in order for there to be an individual instance of that which the abstraction describes. (For the Scholastic, not all Forms are multiply-instantiable, so not all Forms need Matter to be instantiated).

To use a scientific example, when one mathematically describes a field, one is elucidating its Formal, intelligible structure, in virtue of which one would actually have a field of that kind. When one goes out into the world to look for it, one is looking for an individual instance of that structure- a combination of that Form described in theory, and matter.

The “drawing of a triangle” example has certain limits, from the Scholastic point of view, and I think that you are running up against them when you question the determinacy of language-tokens. Feser puts forth the perfect/imperfect representation of a triangle example to introduce the idea of the normativity of Form- that is, how a thing can be more or less perfect by being a better or worse approximation of a perfect Form. When you ask what makes the target Form of a particular representation that of a triangle rather than a Reuleaux triangle, you are invoking the indeterminacy of the particular. This is where there is no intrinsic right answer to the question of what the particular marks on a surface represent- the triangle you draw might be an imperfect representation of a Christmas tree or a campfire. I think one can rescue this analogy by considering it as an instance of the universal, “representation of a triangle.” In that sense, it clearly does become more or less perfect qua what it is the better it approximates triangularity.

What the conditions are in virtue of which a Form is lost is a complicated matter, because different natures have different conditions of instantiation.That the hard cases outnumber the easy ones should be no surprise, given our ignorance of the world. The fact that there are hard cases doesn’t imply that there is no such thing as Form, since change itself presupposes Form. Change requires Form because it is necessary to ground the metaphysical distinction between the start and end of the change.

As to imperfection vis. Form, it doesn’t seem that imperfection is a formidable obstacle to things having Forms which contain the conditions of their perfection. One doesn’t have to perfectly instantiate human-ness to be human- in fact, to be an imperfect human actually requires having the Form of humanity. There are, then, two senses in which one can “be” human: one is having the Form of humanity at all, and the second is in the degree to which one satisfies the Form one has. Whether a particular is failing to instantiate humanity or tree-ness perfectly is a matter of determining which of these forms it actually has, which one understands through observing the particular and asking whether it exhibits any behaviour that is specifically referrable only to one nature or the other.

As to accessibility of the particular, you understand the particular through its Forms- not only its substantial Forms, but its accidental ones too- while considered abstractly and on its own each Form gives you only the universal, one gets the particulars through understanding what the collection of universals you abstract entail in conjunction. So I understand you not only through the universal “human,” but the accidental forms of shape and dimension and location and colour, etc. that you take on in virtue of your matter.

Not sure if this makes things too clear, but I hope it’s been somewhat helpful!

2. I’m no expert yet but it does seem like your difficulties stem from pressing Feser’s examples too far, that are only illustrative rather than actual. A triangle drawn on a blackboard or the bouncy ball do not strictly speaking have substantial forms because they are not actually substances. From what I can tell the drawn triangle would more or less be in the same category as a pile of stones, while the ball is an artifact and so only has the form and end given to it by human agents. In both cases we are dealing with accidental forms, and from what I can tell those are endlessly vague and indeterminate. In Scholastic Metaphysics Feser mentions the Ship of Theseus. From a Scholastic point of view there is no fact of the matter as to whether the ship remains the same when it is replaced plank by plank, because the ship is merely an accidental configuration of parts and is not a true substance. Proper examples of substantial forms but harder to grasp are things like electrons, the rubber the ball is made of or human beings. Whenever you have a ‘thing’ or ‘stuff’ that can be reliably differentiated from other things or stuff by virtue of its distinctive properties that flow from within itself and not imposed on it from outside, you’ve got yourself a substance and along with it a substantial form.

Don’t know if that helps, I’m just starting out with the Scholastic worldview myself. What I will say though is that the Scholastic would agree wholeheartedly with Feynman’s quote. It is a caricature to think that Scholastic philosophy of nature is only about attaching the right labels to things. According to the Scholastic essence is known from the empirically observable properties of a substance, not from parsing language. And I would be careful about identifying form simply with structure, as they are not the same thing. Form is a metaphysical principle. Structure, again if I’m understanding this correctly, will often be the result of form but not identical to it.

I’m currently reading William A. Wallace’s The Modeling of Nature, which is an exposition of natural science, philosophy of nature and philosophy of science from an Aristotelian point of view. That might help with some of your questions about how exactly Scholasticism intersects with modern science. That’s why I’m reading it:

http://www.amazon.com/The-Modeling-Nature-Philosophy-Synthesis/dp/0813208602/ref=sr_1_1?ie=UTF8&qid=1408716231&sr=8-1&keywords=the+modeling+of+nature

3. Consider this a complementary or supplementary answer to Matthew’s answer. He probably described things more eloquently than I will but sometimes it helps to hear different wordings.

The formal cause is that which determines a thing to be this kind of thing and not another. It is the what-ness of a thing. I think of it as the nature of a thing.

The choice between these two characterisations seems to be somewhat arbitrary. For every clear example, there will be a thousand ambiguous ones.

It may very well be the case that we don’t know the formal cause of a substance. There are difficult cases. But that does not mean the substance in question has no what-ness or nature at all. We can say that things have formal causes without knowing the formal cause of every single thing. Even if we are familiar with an object we may not know its entire formal cause.

So if I think about the crayon triangle, what I am really thinking about is perfect triangularity. But then I am not thinking about the crayon triangle on the seat. I cannot think about the triangle on the seat. I can only abstract from that triangle to perfect triangularity.

The triangle example is useful for illustrating how something can imperfectly instantiate a form. But any humanly drawn triangle is not a substance with a substantial form. A drawing is really an accidental form created by a human. When you think of the imperfect triangle you are thinking of the imperfect triangle, not perfect triangularity. But you are also able to abstract from individual triangles and consider triangularity in itself in a separate thought.

But I can’t translate the principles into, say, quantum field theory. What, in a quantum field theory, corresponds to “form”? What are the “potentialities” and what are the “actualities” in a given configuration of fields? How do we understand causes in spacetime? If I had two bodies in otherwise empty space orbiting each other (according to Newtonian gravity), what is the first cause?

A general approach to such questions might go as follows:

(1) What are the substances and what are the accidents in question?

(2) What causes X to exist? (efficient cause)

(3) What kind of thing is X? What is its nature? (formal cause)

(4) What is X made of? (material cause)

(5) What powers does X have? (final causes)

(6) What state is X in now? (act)

(7) What state could X be in? (potency)

Such classifications can be more or less useful but, like our naming of a bird species, don’t reflect anything about the real world.

If that were the case, wouldn’t induction be impossible? If hydrogen atom #1 does not have the same formal cause as hydrogen atom #2 then how can I predict the behavior of #1 based on the behavior of #2?

But induction is possible beecause the two atoms share the same formal cause. Knowing their formal cause, knowing their nature, does reflect something about the real world.

I couldn’t help thinking throughout Feser’s “Aquinas” that I would be greatly helped by an appendix titled: “1001 examples of how Aristotelian metaphysics analyses familiar and fundamental physical systems”.

You might want to look for philosophy of nature resources written from a Thomist perspective.

4. A series of lectures by Wallace and based on his book noted above can be found here:
http://home.comcast.net/~icuweb/c02001.htm
Wallace held a masters degree in physics and doctorates in philosophy and theology.

5. That’s a great set of comments, one and all. I’ll have another read and see if I have any more questions.

6. Hi, I am from Melbourne.
Please find a completely different Illuminated Understanding of Reality via this extraordinary essay.
http://www.dabase.org/Reality_Itself_Is_Not_In_The_Middle.htm

7. […] Metaphysics: A Contemporary Introduction by Edward Feser, maybe starting to get a grip on what a formal cause is supposed to be), I’d had a few idle thoughts about what a mathematical formalisation of Aristotle’s physics […]

8. Hi Luke,

I wanted to make a comment on your question about “changing forms” where you used the example of a triangle slowly changing into a circle.

The key thing to understand is you brought up an epistemological question rather than a metaphysical question.

Your epistemological question was: At what point does the triangle cease to exhibit the form of triangle and become something else as it moves into becoming a circle.

Epistemologically, it is possible that we could never pinpoint the exact point at which the triangle is objectively no longer an “imperfect triangle” and it becomes an “imperfect circle”. What we can say, metaphysically, is if a triangle very slowly turns into a circle, then objectively there is some point where it ceases to be an imperfect triangle and becomes something else. Again, it doesn’t matter if one could never know exactly where this point happens. One does not need to mathematically or scientifically analyze the specifics or the percentages of how close this imperfect triangle is to a triangle to say that this is the case metaphysically.

——

Now in regards to science and metaphysics–part of the essay above seemed like it wanted to turn metaphysics into physics. This is exactly what you don’t want to do, less you end up very confused and make some very bad philosophical (more specifically metaphysical) statements.

The key is to understand how to do metaphysics properly, because it is an area of study with its own methods and proper way of discovering underlying truths about reality. If you try and do metaphysics using science, it is Iike using a hammer to try and saw a board in half.

So what you are going to have to do is keep studying the method of metaphysics while leaving the scientific method at the door since science is not metaphysics (I know this may be hard for some). The key to remember is that metaphysics is not “unscientific”. It simply is a study that seeks to discover the underlying structure of reality. A rational account of the physical sciences relies on a good underlying metaphysics in the first place. Though many scientists do do science without a clue about their unconscious metaphysical assumptions, and that’s okay. They can still do science, in the proper sense of the word, without this knowledge.

So keep up the the asking of questions and your study of how to do metaphysics. Then once you have established a coherent metaphysics, then you will be well equipped to understand how to analyze the things that the physical sciences are studying (like quantum fields and such). I personally hold that the general Aristotelian-Thomistic metaphysics framework is the most coherent and correct description of reality, and I would have no problem describing any actual truth or entity that science discovers in terms of formal, material, efficient, and final causality.

9. Luke, I’ve been reading Feser’s book The Last Superstition. I too have for some time been trying to wrap my head around final causality (and for that matter Aristotelian causality in general) and for me at least, chaps. 2 and 3 were very helpful–Not only with a deeper understanding of these concepts, but with how misunderstandings of them have led to much of modern (and Postmodern) philosophy and the way they’ve been mangled by New Atheists. A lot of the book is a rant, but a pretty good one I think. I’ve got a ways to go still, but so far he’s been spot-on in his criticisms of New Atheism. If you haven’t read it yet I’d recommend it!