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Re: Programming is the Engineering Discipline of the Science that is Mathematics

From: Keith H Duggar <duggar_at_alum.mit.edu>
Date: 7 Jun 2006 13:11:22 -0700
Message-ID: <1149711078.211562.251250@i39g2000cwa.googlegroups.com>


erk wrote:
> Cimode wrote:
> > Interresting..you make a distinction between logic and
> > math. What better than math validates logic?
>
> I didn't intend to make this distinction here; I thought
> you were. If not, never mind. I'd say your question is
> reversed, though - the better statement might be that
> logic validates math, rather than vice versa.

Yeah it was a little unclear what he was saying there. Did he mean mathematics is an example of the application of logic and thus validates the usefulness of logic? Or did he literally mean mathematics is used to validate logic?

If the latter, than as you point out he is at odds with current dogma which views formal logic + axiomatic set theory as the foundation of mathematics. And interestingly, one view of logic is as a specialization of conditional probability theory. One that deals only with certainty (1) and impossibility (0) rather than a range of probability. Probability theory as a generalization of logic is useful because in addition to the logically valid modus ponens and modus tollens, it also gives a foundation for applying the weak syllogisms which in the limiting case of logic are treated as fallacies (affirming the consequent and denying the antecedent).

So ... perhaps conditional probability theory is the foundation of all :-)

Received on Wed Jun 07 2006 - 15:11:22 CDT

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