[FOM] Early views infinity

[William Tait]

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