FOM: listing foundational issues
lstout at sun.iwu.edu
Mon Mar 9 18:30:42 EST 1998
Vaughn Pratt wrote that
> But in that case it would seem equally reasonable to include "object" as
> an equally generic term that includes "relational structure", "topological
> space", "manifold", etc. After all, what would the first-order definition
> of "set" mean without a relational structure to furnish it with a meaning?
> Just how basic objects are depends on where one views mathematics as
> beginning. While it is reasonable to consider objects as being not so
> basic when they are defined set theoretically, it seems unreasonable
> to insist that this perspective is absolute. From the categorical
> perspective on mathematics, objects are the most basic of all entities,
> being the first thing a typical categorical foundation talks about.
As a categorist I would have said that the notion of morphism, of which function
is a special case, is what is most fundamental. The most fundamental role of
objects is to be what the morphisms are between.
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