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This question became a symbol for the silly and pointless sophistry of medieval scholastics. But as modern scholarship has shown scholastics was not such a thoughtless desert as some of its caricatures: the role of Duns Scotus and Ockham in the development of epistemology and modal logic is well known, as is the influence of Buridan and Oresme on science and philosophy of Descartes and Galileo, the problem of universals is still actively discussed. Still I was surprised to read this in Butterfield-Isham's paper (p.46) on modern physics:

"This situation inevitably prompts the sceptical question why we are spending time and effort discussing possible philosophical implications of an equation [the Wheeler-DeWitt equation in quantum gravity] that is mathematically meaningless! Are we as misguided as the medieval scholastics are often taken to have been, in their discussions of how many angels can dance on the head of a pin? We believe not. Indeed, as philosophers know well, the scholastics’ discussions were not as misdirected as folklore suggests. They addressed deep, maybe perennial, issues about personal identity and spatiotemporal location, in terms of their era’s accepted ontology; which included angels".

Wikipedia has an article on the title question that mentions Duns Scotus and Acquinas, but is thin on philosophy. Can someone fill in the details. In what philosophical context was the question originally discussed? What "deep, maybe perennial, issues about personal identity and spatiotemporal location" were addressed by it? What were the positions and the arguments? Does it resonate with some modern discussions?

Conifold
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    The question, also it seems pointless at first glance, was not. It was actually a question on the corporeality or non-corporeality of spiritual beings. If angels have a corporeal body, then only one can dance on the head of a pin. If angels have non-corporeal bodies - spiritual bodies - than an infinite number can dance on the head of a pin. Are the heavens of Christian theology a material location or a spiritual location? – Swami Vishwananda Jan 07 '16 at 05:11
  • I had always imagined this was a version of Cantor's "how many points are on a line?" – Nelson Alexander Jan 07 '16 at 16:30
  • As the wikipedia article you link to says, much of the dismissal of medieval philosophy (and things medieval in general) come from people with a pretty clear anti-Catholic bias. – James Kingsbery Jan 07 '16 at 20:09
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    This makes tons more sense in terms of the **point** of the pin, a projected point of radius zero, than the **head**. Is anyone sure this was even the original question? –  Jan 07 '16 at 21:21
  • This is tangential to the issue but there was a tradition among medieval universities where one day a year was set aside for students to ask the faculty any question. The competition to 'stump the prof' was fierce and groups labored hard and long to produce the most difficult. the answers were given in a lecture hall and if records were found, I think they would be fascinating. – jim sekerak Mar 28 '17 at 23:27

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I'm a medievalist. I don't know of any discussion of angels dancing on pinheads, probably because literally every medieval theologian (at least in the Christian tradition) would have regarded angels as immaterial beings. So they don't occupy space (or at the very least, not in the same way bodies do).

Aquinas argues in Summa Theologica I q. 52 a. 3 ("Whether several angels can be at the same time in the same place?") c. that two angels can't be in the same place, but not for the same reason two bodies can't be in the same place:

There are not two angels in the same place. The reason of this is because it is impossible for two complete causes to be the causes immediately of one and the same thing. This is evident in every class of causes: for there is one proximate form of one thing, and there is one proximate mover, although there may be several remote movers. Nor can it be objected that several individuals may row a boat, since no one of them is a perfect mover, because no one man's strength is sufficient for moving the boat; while all together are as one mover, in so far as their united strengths all combine in producing the one movement. Hence, since the angel is said to be in one place by the fact that his power touches the place immediately by way of a perfect container, as was said (Article [1]), there can be but one angel in one place.

He writes in Article [1]:

It is befitting an angel to be in a place; yet an angel and a body are said to be in a place in quite a different sense. A body is said to be in a place in such a way that it is applied to such place according to the contact of dimensive quantity; but there is no such quantity in the angels, for theirs is a virtual one. Consequently an angel is said to be in a corporeal place by application of the angelic power in any manner whatever to any place.

Accordingly there is no need for saying that an angel can be deemed commensurate with a place, or that he occupies a space in the continuous; for this is proper to a located body which is endowed with dimensive quantity. In similar fashion it is not necessary on this account for the angel to be contained by a place; because an incorporeal substance virtually contains the thing with which it comes into contact, and is not contained by it: for the soul is in the body as containing it, not as contained by it. In the same way an angel is said to be in a place which is corporeal, not as the thing contained, but as somehow containing it.

There are important medieval questions that do exhibit the phenomenon that the author you've quoted is interested in. One case in point: medieval debate about how God knows things involve some very interesting speculation about philosophical psychology.

Community
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  • Acquinas's answer is a bit cryptic:"*The reason of this is because it is impossible for two complete causes to be the causes immediately of one and the same thing... the angel is said to be in one place by the fact that his power touches the place immediately by way of a perfect container...*" Why "touching" a place involves being a complete cause, or does it refer to being an angel? Does it mean that several demons can "touch" the same place at once? How does immaterial power "touch" a place? Are there authors to objections he responds to, did Duns Scotus, etc., see it differently? – Conifold Jan 07 '16 at 04:35
  • What Aquinas means by a power "touching" a place is causing an event *at* that place. So the sun's power of heating "touches" the stone in the field at one determinate place. So the idea here is that (at least when the angels are causing something--for instance, causing someone to hear words, etc) they have to be in distinct places in the sense that it needs to be the Angel Michael causing this event in this place, rather than the Angel Gabriel. At least, that's the most sense I can make out of the passage you've cited. I don't know what Scotus thought about the issue. –  Jan 07 '16 at 13:31
  • Regarding the source of Aquinas's view. In the previous article, he cites John Damascene as saying, "An Angel is present wherever he is at work." Kenelm Foster (in the Benzinger edition of the ST) also conjectures that Aquinas's motivation in discussing this question is probably to make sense of the Church's teaching about guardian angels. –  Jan 07 '16 at 13:33
  • Foster continues: "To say that only one angel at a time can be present (i.e. active) at a given place is only to say that just so far as the activity is one, it must proceed from one cause. What, in effect, this unification declares is not the incapacity of several angels to be thus 'present' in one place but rather the capacity of the single angel to do, of himself, whatever it is he can do in that place." (ST, vol 9, p. 49, note c) –  Jan 07 '16 at 13:35
  • Until the concepts of fields and waves were developed after the medieval period, superposition was something that people had difficulty even thinking about. People who are not trained in physics or engineering today still have difficulty thinking about superposition. Understanding superposition, leads to an answer of infinity. Aquinas's reasons for why only one angel could ACT at one place, are not valid, as superposition of causal influence is another case of superposition. Multiple causes act on pretty much everything, all the time. – Dcleve Jun 28 '22 at 16:00
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Thomas Aquinas discusses in Question 52 The angels in relation to place in Summa Theologiae

Whether several angels can be at the same time in the same place?“ (Article 3).

He concludes that there are not two angels at the same place. His argumentation employs a general principle of causation. He does not argue with the lack of space (Reply to objection 1)

As a consequence the discussion just does not deal with „personal identity and spatiotemporal location“

Instead the point of his discussion can be easily separated from the special case of angles. On a very general level Thomas invokes sophisticated philosophical principles. But the sophistication of these principles prompts the question:

  • Are these principles expressed precisely and sharp enough to apply to real world problems?
Jo Wehler
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  • Could it be the case that the question came from a jibe at Aquinas: the asertion "there are not two angels in the same place" invites to aks "how many (different) places are there on a pinhead"? – sand1 Jan 07 '16 at 19:19