Tuesday, August 28, 2012

Are infinite and infinitesimal sizes relational?

Suppose that Leibniz is right, and in addition us (call us "macros") there are infinitesimal embodied beings ("micros") and infinite embodied beings ("megas"). Suppose we are teaching English to one of the micros. Should we tell her to say:

  1. The micros are infinitesimal, the macros are finite and non-infinitesimal, and the megas are infinite,
as we do, or should she say:
  1. The micros are finite and non-infinitesimal, the macros are infinite, and the megas are infinitely many times bigger than the infinite macros?
I am inclined to think she should say (2), and so infinite and infinitesimal sizes are merely relational or indexical.

2 comments:

Kenny said...

Leibniz interpretation wasn't the main point of your post, so this is a little nitpicky, I suppose, but I don't think Leibniz holds that there are infinite or infinitesimal embodied beings. Rather, there are arbitrarily large and arbitrarily small embodied beings. The monads are, of course, located at points, though they are not strictly and literally spatial entities, but every monad has a finite body. In fact, I don't think that for Leibniz the notion of an infinite or infinitesimal body even makes sense.

Alexander R Pruss said...

You might be right. I thought I read a passage that supported my view, but I searched through Gerhardt and couldn't find any that did.