Sunday, December 04, 2011

Ockham on the continuum

Newly translated, for the first time on the Internet etc., here is chapter 45 of part I of Ockham's Summa Logicae.  Here, Ockham's applies his nominalism to the age-old question of the continuum.  Is a point something separate and indivisible from the line of which it is a point?  Is number something different from the things which are numbered?

Ockham says no. Aristotle’s intention, according to Ockham, was to deny that there is anything indivisible 'in this world below' (in istis inferioribus).  Continuous quantity is nothing other than a single thing having one part at a distance from another part, and discrete quantity (number) is nothing other than the numbered things themselves. The difference between continuous and discrete quantity is simply that the parts of continuous quantity mutally protude onto one another [ad se protensae mutuo], whereas the parts of discrete quantity (i.e. two men) can be as near or as far as you like, with no 'medium' between them.
... in the case of discrete quantity it does not matter whether or not the items which constitute the discrete quantity are distinct in place and situation or not, or whether there is a medium between them. Hence, for two men to be 'two', it does not matter whether there is a medium between those two men or not. For they are two when there is no medium between them, just as when they are distant from each other by a hundred leagues, nor does the predication 'two' of those men vary because of anything to do with nearness or distance. On the contrary, if they were in the same place at the same time they would be two, just as if they were not in the same place.
 The translation is new, and has not been through any of the review stages required in the Logic Museum, so all suggestions welcome.


William M. Connolley said...

If I look at your wiki page, all the English side is blank. Oddly, when I view it as a diff against the previous, all is well.

Edward Ockham said...

Thank you for that. I cleared the cache. Try it now.

I have to run

TRUNCATE TABLE wiki_objectcache;

for some bizarre reason. Wikis.

J said...
This comment has been removed by the author.