Re: Help with a problem

On 25 Nov 2005 04:18:53 -0800, "George Dance" <georgedance04@xxxxxxxx>
wrote:


"It is practically impossible to teach good proving style
to students that have had prior exposure to Copi's system:
as potential logicians they are mentally mutilated beyond
hope of regeneration."

(G. Frege)

>
> Whether that analogy applies depends on what you think makes a system
> of natural deduction good, IOW what one wants to achieve with one.
>
> If one's aim is to use nd to formalize the inferences of informal
> reasoning, then a system like Copi's would work best. If OTOH (as per
> your analogy) one's aim is to train people to reason in a certain
> 'style' only, then a system like Gentzen's would clearly be better.
>

Well...

"The claim that the essential deductive operations have been isolated
[in Gentzen's calculi] is not to be understood as the claim that these
operations mirror all informal deductive practices, which would be an
unreasonable demand in view of the fact that informal practices may
sometimes contain logically insignificant irregularities. What is
claimed is that the essential logical content of intuitive logical
operations that can be formulated in the language considered can be
understood as composed of the atomic inferences isolated by Gentzen.
It is in this sense that we may understand the terminology _natural_
deduction.
Nevertheless, 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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