Re: Natural deduction?

> >
> > Whether that analogy applies depends on what you think makes a system
> > of natural deduction good, IOW what one wants to achieve with one.
> >

"The formalization of logical deduction, especially as it has been
developed by Frege, Russell, and Hilbert, is rather far removed from the
forms of deduction used in practice in mathematical proofs. ... In
contrast I intended first to set up a formal system which comes as close
as possible to actual reasoning. The result was a calculus of natural
deduction (NJ for intuitionist, NK for classical predicate logic)."

(Gentzen, Investigations into logical deduction)

It seems that Gentzen was rather successful in his attempt:

"[...] Gentzen's systems are also natural in the more
superficial sense of corresponding rather well to informal practices;
in other words, the structures of informal proofs are often preserved
rather well when formalized within the systems of natural deduction."

(Prawitz)


F.

--
"I do tend to feel Hughes & Cresswell is a more authoritative
source than you." (D. Ullrich)
.

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