FOM: listing foundational issues

[Larry Stout]

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.  

Larry Stout