[FOM] naive continuum metaphysics

[Jesse Alama]

> Following up on Steven's question regarding the continuum as a non-set:
>
> I was wondering if anyone on the list has seen mathematical or philosophical
> work on the continuum being a fundamental unity? To consider the continuum as a
> pointless entity where the reals are in some sense indiscernable from one
> another was proposed to me by a friend. This person regards the CH as a
> fundamentally meaningless question and claims that we make the mistake of
> thinking of the continuum as composed of objects (points or reals) when it is
> really a single, "solid" entity. Has anyone seen any writing on this or perhaps
> written something on this themselves?

A. Alexanderov discusses (briefly) the dialectical issue of
discreteness versus continuity in mathematics in his fine essay "A
general view of mathematics".  The essay can be found in volume 1 of
the three-volume collection _Mathematics: Its Content, Meaning, and
Methods_, which contains essays on various areas of mathematics
written by some really excellent Russian mathematicians.  See section
5 in Alexanderov's essay, "The conflict of opposites: discrete and
continuous".



Jesse