Angels dancing on a pin

This came up in a discussion I had with Huenemann earlier today:

You’ve all heard the expression – ‘How many angels can dance on the head of a pin?’ – used to disparage the apparent waste of good brain-power in trying to sort out pointless problems.  

Two things:

a) What is the origin of this question?  I had long thought that no medieval philosopher really asked it, but that the question was made up later in order to lampoon those ‘silly’ Scholastics.  After doing a quick bit of research, I think I have identified the origin of the question:  It seems it was first asked in a satirical book called ‘Memoirs of the Extraordinary Life’, a book written under the pseudonym ‘Martinus Scriblerus’ (Alexander Pope, Johathan Swift, and others collaborated on the work).  They were making fun of Scholastic philosophers, and in particular Thomas Aquinas.  

Aquinas did produce a very sustained ‘angelology’, still thought by many to be the most complete investigation of angels.  He used both scriptural and non-scriptural (Aristotle) sources to try to sort things out, determining that angels were immaterial intellects of great power who can assume bodies and who learn through a kind of direct communion with the mind of God.  In fact, the way that Plato describes humans (learning through recollection, knowledge of the Forms) is pretty close to what Aquinas says about angels. 

But, as best as I can tell, it is not the case that Aquinas or any other medieval thinker asked this particular question regarding angels dancing on the head of a pin (though they did ask related questions).

b) That said, now that the question has been asked, it may turn out to be a decent question.   Aquinas does think that angels have locomotive powers (the ability to move from one place to another), and he debated whether or not they have to pass between all intermediate points when moving from A to B.  He thought they need not move through all points when traveling between two points but instead can ‘jump’ from one location to another in a non-continuous way (thus anticipating similar suggestions in contemporary string theory).  Read here.

And he wondered whether several angels could be in the same place at the same time.  In the end, he did not think that many angels could be in the same place at once.  Read here.

Now, no matter what we might think about Aquinas or angels, the issue raises some interesting questions.  Huenemann had recently read a book on early modern physiology that asked related questions: What is the relationship between matter and space?  Why does matter occupy space, and why can’t more than one object occupy the same space?   What is the relationship between matter, mass, and location?  Are mass and location essential qualities of space (that it is the ‘form’ of matter to have those attributes)?


This entry was posted in Uncategorized on by .

About Kleiner

Associate Vice Provost and Assistant Professor of Philosophy at Utah State University. I teach across the curriculum, but am most interested in continental philosophy, ancient and medieval philosophy as well as Catholic thought, all of which might be summed up as an interest in the ressourcement tradition (returning in order to make progress). I also enjoy spending time thinking about liberal education and its ends.

9 thoughts on “Angels dancing on a pin

  1. Huenemann

    Interesting story about the origin of the question. I had thought the medievals did discuss it.

    The book I had read (“Physiologia,” by Dennis Des Chene) is really good at getting anyone to think more carefully about different ways of carving up the world. The medievals he describes tried to go as far as they possibly could in working out the details of a broadly Aristotelian metaphysics. Their thought is ingenious.

    The questions they would have raised seem to be questions philosophers today largely ignore. What is it for a thing to have mass? What do two things have in common when they are both said to have mass? Does everything with location have mass? Does everything with mass have location?


  2. Anonymous

    Richard Feynman used a version of the question in his physics lectures taped for the BBC in the 1950’s. He was discussing physics theories as mathematical descriptions of the world that have at their core an undefinable quantity (i.e., What is mass? What is space?) He set up the audience by identifying the silly medieval theologians asking the question “How many angels does it take to push the earth around the sun with their beating wings?” Dr. Feynman praised Isaac Newton for correcting these silly people by creating the first gravitational theory. Newton showed that the angels were beating their wings and pushing the earth toward the sun not around the sun. Einstein would correct that by saying the beating of angel wings warps space.

    Angels can be the personification or poetic embodiment of the agents governing the world subject to God’s creative intent … very much like J.R.R. Tolkien’s creation Myth of the Silmarillion … the standard of reality and truth in literature.


  3. Huenemann

    Here’s another great Feynman story. He claims that, when he was a kid, he noticed that if he was pulling along a wagon with a ball in it, and suddenly stopped, the ball would roll to the front. He asked his dad why that happened. His dad wisely answered, “Nobody knows. It’s one of the deepest mysteries in the universe. People put a name on the phenomenon — they call it ‘inertia’ — but no one really knows why it happens.”

    Advocates of science need to be as honest as Feynman in pointing out the limits of their/our knowledge.


  4. Kleiner Post author

    So the buck stops – for everyone – at saying something like ‘well, it is just the nature of x to be that way’. This might suggest (and Huenemann and I sort of agreed to this yesterday), that Aristotle’s explanation might have the right ‘form’ even if it has the wrong ‘matter’ (he gets the details wrong).

    I suppose the hard-nosed materialist could still resist the nature talk, just leaving it unexplained (butting up against ‘mysteries’ after all, hah!!). And he could argue that Aristotelians are just slapping a name on the unknown. They might argue that the Aristotelian move is unnecessary. But I will continue to insist that the Aristotelian move (particularly final cause) has real explanatory power. And I don’t think there is anything in, for instance, the Darwinian view that disproves the Aristotelian view (he doesn’t think that final cause replaces efficient cause, and final cause is not used to fill in the gaps or to explain complexity). And, in fact, biologists use teleological language all the time. I just got my copy of National Geographic (a clearinghouse for reductionist and materialist views but I still read it), randomly flipped to a page, and read a sentence with teleological significance in the first paragraph I randomly chose (something like ‘these birds sharpen their beaks in order to use them to make holes in trees to store food’).


  5. Huenemann

    Just because the biologists use teleological locutions doesn’t mean they HAVE to use them. They’re just convenient shorthand for a long story about natural selection. And I for one won’t regard “nature” talk as explanatory until someone puts together a compelling ontology of natures (how many are there, how do you tell one from another, etc.), along with an explanation of how one thing comes to have one rather than another nature.

    But at the same time, I admit that materialists don’t have any better explanation for their basic substances or forces or properties. Everybody’s up against the wall on this one.


  6. Kleiner Post author

    We just disagree here. Final cause is not a replacement for efficient cause (Paley makes this mistake). But, to you, I say that efficient cause is not a replacement for final cause (as if teleology is just short-hand for complicated efficient causes).

    Let’s turn to The Philosopher (Aristotle):

    ‘Again, whenever there is plainly some final end, to which a motion [change] tends should nothing stand in its way, we always say that the one is for the sake of the other; and from this it is evident that there must be something of the kind, corresponding to what we call nature. For a given seed does not give rise to any chance living being, nor spring from any chance one; but each springs from a definite parent. And thus it is that from which the seed comes which is the origin and fabricator of its offspring. For these it is by nature, the offspring being at any rate that which in nature will spring from it.

    It is plain then that there are two modes of causation, and that both of these must, so far as possible, be taken into account, or that at any rate an attempt must be made to include them both; and that those who fail in this tell us in reality nothing about nature.’
    ~ Aristotle, On the Parts of Animals, I.1, 641-642

    Two things to say on this:

    First: What Aristotle is arguing is that biologists, if they are to tell us anything interesting about the natural world at all, have to include final cause in their account. I will borrow from Machuga for examples on this point.
    When a scientist tries to describe a turtle’s behavior, he can say one of two things:
    a) The turtle came ashore in order to lay her eggs.
    b) The turtle came ashore and laid some eggs.

    The first uses final cause, the second does not. But the second claim is pretty useless. There is no reason, without an appeal to final cause, to distinguish as more important any of the following descriptions:
    i) The turtle came ashore and laid some eggs.
    ii) The turtle came ashore and kicked some sand.
    iii) The turtle came ashore and kicked a piece of driftwood.

    But of course the biologist wants to – AND SHOULD – distinguish between these events, and for obvious reasons. That turtles come ashore in order to lay eggs tells us something about the nature of turtles! The other descriptions only describe accidental qualities of the lives of turtles.

    Second, you abandon final cause with no small amount of cost. I think, in order for you to be consistent, you would HAVE to say that it is possible for an oak tree to, in an instant, turn into an elephant. This would have to be the case because there is nothing (no nature) that is making the thing be what it is. In other words, you are denying the fairly obvious assertion that ‘a given seed does not give rise to any chance living being’. Rather, on your view, it is what it is thanks to a series of purely accidental relations between material parts. And there is nothing ‘securing’ those relations. So you must accept that out of an acorn could grow a giraffe, and that a full-grown oak could instantly turn into a gazelle. Maybe you are willing to bite that bullet, I am not.

    One side question: why be willing to swim upstream of common sense here, why be willing to bite that bullet? As Machuga suggests in his book, ‘fear of religion’ is a really bad reason to strip yourself of the explanatory power of final causes. (I don’t think that is Huenemann’s reason, and I hope it isn’t. But I do think it is the secret fear of many who refuse to take teleology seriously).


  7. Huenemann

    Re. turtles, I am inclined to say: “The turtle came to shore and laid her eggs, and all of her ancestors who did not do the same did not have equal reproductive success.” That also sidesteps the driftwood counterexample, assuming that kicking or not kicking driftwood did not have any effect on reproductive success.

    I don’t see why the observation of patterns should impel us to affirm the existence of “natures” which are causally responsible for those patterns, particularly if those “natures” are understood to be something other than the efficient causes which, by themselves, plus natural selection, are enough to explain the presence of apparent patterns.

    Let me try to handle the acorn/elephant in the following way. A devotee of Aristotelian species would make the same objection regarding the possibility of, say, some early hominid like australopithicus aferensis giving birth to a homo sapien, or, indeed, a shrew-like critter giving birth to a human. “Impossible!” But given a heckuva long time, and many random changes in genetics, and many lives lost, behold! The impossible becomes actual. Now could I say the same of acorn/elephant? Probably not; I think the genetic space is not infinitely malleable. But acorn/fir tree, maybe, acorn/corn plant, maybe. Tinker enough with the efficient causes and you seem to change the thing’s “nature.” That should be enough to show that “natures” actually reduce to these efficient causes.


  8. Kleiner Post author

    We should just sit down and read Machuga’s book together. He treats your first response in his very next section from the one I cited above!

    I must admit I find it hard to believe that you don’t see one of these explanations as more complete:
    a) The sight of an encroaching animal caused the wolf’s blood temperature to increase, and his muscles tensed up and this made its hair stand on end.
    b) The wolf’s hair raised on end in order to scare off the other animal AND the sight of an encroaching animal caused the wolf’s blood temperature to increase, and his muscles tensed up and this made its hair stand on end.
    I would need to do better than this, Aristotle wants the two causes explained in a ‘single formula’.

    Here are three responses to your last post:

    1) I think you are committed to saying that the ‘genetic space’ is more malleable than you say. Ultimately you’ll have to get ‘behind’ the genes. Ultimately you’ll have to appeal to the relation of material parts at the lowest level. Why couldn’t the genetic sequence be completely scattered from one instant to another (so that a gazelle turns immediately into a cactus)? There is no ‘nature’ holding the relations in place, they are purely accidental.

    This point, I might add, perhaps distinguishes pre-modern from modern philosophy more than any other point. Pre-moderns tend to say that the form explains why the matter is the way it is (that there is some ‘nature’ that is the principle of unity in the organism that makes it stable and one). Moderns tend to say that it is the matter that makes the form be the way it is.

    2) Does natural selection show that final causes are unnecessary? No, in fact, they underline the need for them! Machuga turns back, again, to the word. He denies that something can be a word if it is not intentional. If driftwood floats ashore in the shape of an arrow, it is not actually an arrow (a sign) since it does not point to anything. Words are not heaps of letters, so cannot be explained by efficient cause. Form is not the same as shape.
    The same goes for genetic codes. Your explanation suggests that the turtles who were the sorts of things that came ashore and laid eggs (I guess because of some genetic trait) had better reproductive success. This trait was then inherited. The DNA is really a code then, and it can explain the inherited traits. But if it really is a code (has meaning), then it could not have arisen out of purely efficient causation. If it did arise out of efficient causation, then it is not really a code, and so cannot explain inherited traits.

    3) Your latter example (biological reductionism) assumes that the whole is nothing more than the sum of its parts. Music is not merely a collection of sound waves. Man is not merely his genetics. The best explanations explain the thing both in terms of its efficient causes and its final causes (see Machuga’s wolf example that I appeal to above). And I think we have good reason for appealing to something beyond the parts – human understanding. You know the argument: no soul, no words. Humans can grasp the ‘whys’ of things, and one cannot give an account of that in merely material terms.



Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s