[FOM] Early views infinity
William Tait
wwtx at earthlink.net
Thu Nov 6 11:24:13 EST 2003
On Nov 5, 2003, at 4:20 AM, José Félix Costa wrote:
> About infinity:
>
> Interesting is without doubt the book by A. W. Moore, The Infinite.
>
> I also suggest authors such as
>
> Pierre Duhem, in Medieval Cosmology (a short account on the 12 volumes
> on
> the subject writen by Duhem)
The Duhem book is useful: it has lots of quotations, whereas in general
it is difficult to find the actual words of many of the important
medieval authors concerning foundational matters. But the edited and
translated version at least does not contain much detail concerning
mathematical work in the late middle ages. Also, perhaps because of
European tribalism, he makes rather less than he ought of the
Mertonians, including my guy Swineshead, charging that they were more
interested in playing meaningless word games, in favor of the slightly
later Parisians. Finally, he continually blunders over logical matters:
e.g. on pp. 36-7 he quotes Aquinas' statement that, although one can
divide a (finite) line segment into an infinite number of unequal
segments, one cannot divide it into an infinite number of equal line
segments (a reference to Archimedes' axiom, which had already been
expressed by Aristotle). Duhem comments that Aquinas overlooked the
fact that one can divide the line segment into thirds, then each part
into thirds ``and so forth indefinitely''! [On the other hand, he did
quote Aquinas.]
Worth looking at on this topic are
author = {J. Murdoch},
title = {Infinity and continuity},
pages = {564-591}
in
editor = {N. Kretzmann and A. Kenny and J. Pinborg},
title = {The Cambridge History of Later Medieval
Philosophy},
publisher = {Cambridge: Cambridge University Press},
year = {1982}
There are also a number of useful papers in
editor = {N. Kretzmann},
title = {Infinity and Contiunuity in Ancient and Medieval
Thought},
publisher = {Ithica: Cornell University Press},
year = {1982.
including one by Murdoch on Ockham.
Bill Tait
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