In article <6z_tg.837653$084.60584@attbi_s22>, Stephen Montgomery-Smith <firstname.lastname@example.org> wrote:
> Gene Ward Smith wrote: > > Kevin Karn wrote: > > > > > >>That's why this debate is so ironic. History has come full circle, and > >>now we are at the point where reality-based people who deny the > >>existence of angels are "cranks". > > > > > > I haven't seen constructivists, etc. called cranks in these > > discussions. However, suggesting > > the continuum hypothesis is like angels dancing on a pin seems to me to > > be backwards--it is the objectors who seem to have some kind of > > philosophical qualm which almost seems to amount to a religious one. > > I'm reminded of Kronecker's remarks about what God did and did not > > create in terms of mathematicals. > > I don't think Aquinas's argument over whether angels can occupy the same > space should be seen as having much to do with religion - rather I see > it as Aristotlean thinking taken to extremes. The question he poses, > and answers, bears no reality to anything, neither to an atheist nor to > a theist. Only the most ardent Aristotlean is going to be interested.
<pedantry> AIUI, the Scholastics' pondering on angels and pinheads presupposed that angels do each take up space; the question is HOW MUCH space per angel. This is an issue because Revelation gives the shape and dimensions of the eternal City of God, and if you divide its calculated volume by the minimum number of angels mentioned in the bible (at least ten thousand of ten thousands, IIRC), that leaves very little space per angel. Hence the question regarding pinheads.
Aquinas gives another take entirely, based (I guess) on the fact that at least some of the angels mentioned in the bible are clearly of human size. So if myriads of full-size angels are all to fit in that limited space, they must overlap somehow. </pedantry>