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Re: What databases have taught me

From: Keith H Duggar <duggar_at_alum.mit.edu>
Date: 1 Jul 2006 11:29:38 -0700
Message-ID: <1151778578.203807.299950@m79g2000cwm.googlegroups.com>


Ok, let me see if I can summarize, as it appears to me, the philosophical difference between your, my (and Marshall?), and Dmitry's viewpoints.

  1. All of us agree that there is an unlimited number of consistent operations O that can be defined on a set S.
  2. All of us agree that mathematicians and others often distinguish a subset OA of O as 'axioms'.

Let us call OD = O - OA 'derived' operations. And let us call a subset OS of OD 'scoped' operations which are operations that are currently "in scope".

3a) I (and Marshall?) say that S + OA defines a data type T.
3b) You (Bob) say that S + O defines a data type T.
3c) Dmitry says that S + OA + OS defines a data type T.

Do you Bob, Marshall, and Dmitry find this summary accurate?

> > > What is important is not which operations we consider
> > > fundamental and which we consider auxiliary. What is
> > > important is all of those operations exist and we can
> > > communicate them to each other.
> >
> > Not important? Well that is a large part of mathematics,
> > finding sets of operations (the smaller the better) we
> > consider fundamental and from which we can derive other
> > operations.
>
> Axiomatization is arbitrary. Mathematicians also spend
> time trying to find completely different sets of axioms
> for the same things and then trying to prove the
> equivalence between them.

It may be arbitrary (if by arbitrary you meant the "subject to judgment" and not "without reason") but it is obviously valuable. No?

Received on Sat Jul 01 2006 - 13:29:38 CDT

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