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Re: In an RDBMS, what does "Data" mean?

From: Paul <paul_at_test.com>
Date: Fri, 18 Jun 2004 22:55:48 +0100
Message-ID: <cxJAc.16643$NK4.2898559@stones.force9.net>


Eric Kaun wrote:

>>Logic as a branch of mathematics most definitely requires axioms.  --dawn

>
> I'll posit that it doesn't; I would regard mathematics as a derivation of
> (wrong term, I know) logic. Logic is a system or metasystem of symbolic
> manipulation, and can be applied to many different "maths".
>
> As I think of it, I'd say math has axioms and logic doesn't, and derives its
> power for precisely that reason; it can be applied to different sets of
> axioms. At least that's how I've always thought of it... I could be dead
> wrong, and would expect this to be contested.

This is from http://en.wikipedia.org/wiki/First-order_predicate_calculus

---
Like any logical theory, first-order calculus consists of
* a specification of how to construct syntactically correct statements
   (the well-formed formulas)
* a set of axioms, each axiom being a well-formed formula itself
* a set of inference rules which allow one to prove theorems from axioms
   or earlier proven theorems.

There are two types of axioms: the logical axioms which embody the 
general truths about proper reasoning involving quantified statements, 
and the axioms describing the subject matter at hand, for instance 
axioms describing sets in set theory or axioms describing numbers in 
arithmetic.
---

Now ultimately set theory is used for the foundation of everything in 
mathematics. So you use set theory to build your logical theory.

You might ask how do you specify your set theory without using logic, 
otherwise you've got a chicken and egg situation. I'm not too sure what 
the answer is there, I think there is some kind of hand-waving appeal to 
"naive logic". Or maybe it is more rigorous, I don't know.

Very philosophically interesting these questions of foundation though.

Paul.
Received on Fri Jun 18 2004 - 16:55:48 CDT

Original text of this message

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