Re: The Idea of Structure as Data and Conditions

[Vaughan Pratt <pratt@cs.stanford.edu>]

The proposition that "mathematical structure is given by data and
conditions" is so broad as to be vacuous from a foundational standpoint.
   While there may be disagreement between mathematical camps over
whether algebraic frameworks rest on logical or vice versa, common to
both is the idea that one starts with a (non-logical) language and
equips it with a theory.  I don't see how "data and conditions" can be
interpreted as giving undue weight to either the equational or
first-order starting points.    The sentiment could just as validly
preface a graduate course on first order model theory.

Vaughan Pratt

On 5/25/2012 3:09 PM, Ellis D. Cooper wrote:
> I was permitted to audit a graduate course on category theory guided
> by Sammy at Columbia University in the early 1960s.
> I recall his insistence that mathematical structure is given by data
> and conditions. Is that idea
> implicit or explicit in Bourbaki? Has that idea been superceded? How
> does it relate to the
> development of algebraic theories as understood by Lawvere, Linton,
> Barr-Wells, the Elephant, and so on?


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