Re: Extending my question. Was: The relational model and relationalalgebra - why did SQL become the industry standard?

From: Mikito Harakiri <>
Date: Thu, 13 Feb 2003 15:23:48 -0800
Message-ID: <wTV2a.14$>

In short, logic and set theory together are only a tiny part of mathematics.
Don't evangelize them.

Well, not being a mathematician,
but having studied some mathematics I was and
still am under the impression that all modern mathematics
is based on set theory which is equivalent with logic.
Set Reductionalism is a dicease that I was ill when being a student. Although Sets and Logic certainly spice mathematics with rigour, they are mostly irrelevant for practioner mathematician not working in those fields.
Here is a quote from Wikipedia


The current dominant mathematical paradigm is based on axiomatic set theory and formal logic. Virtually all mathematical theorems today can be formulated as theorems of set theory. The truth of a mathematical statement, in this view, is then nothing but the claim that the statement can be derived from the axioms of set theory using the rules of formal logic.


There is a difference between "can" and "have to". Reductionalizm to sets might be unnatural, unpractical, etc. The famous example is the ordered pair definition
(a, b) := {{a}, {a, b}}
AFAIK, no mathematical theorem is reformulated to use the above set based definition instead of ordered pairs. Ordered tuple is widely considered to be a basic concept (including Relational Theory;-).
Received on Fri Feb 14 2003 - 00:23:48 CET

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