Re: "Friendly Premises"

Acme Diagnostics wrote:
> Torkel Franzen <torkel@xxxxxxxxxx> wrote:
> >"Acme Diagnostics" <LFinezapthis@xxxxxxxxxxxxxxxx> writes:
> >
> >I don't know why you should be
> >interested in the logic of Frege and Russell,
>
> I have a great reason to be interested in the difference
> between premise/conclusion/valid logic (PCVL) and
> axiom/theorem/proof logic (ATPL) if it is affecting mental
> combat skills, and here I'm only using that term to avoid
> quite socially admirable but pretentious alternatives.
>
> My training is old news here for anyone paying attention and
> doesn't involve Trekkian glamour. "Playing against myself" is
> just the theatrical version of "argue both sides," and "force"
> the theatrical version of "too fun."

The Jesuits used to do that, and it was standard in debates when I was
a lad: two teams of students would debate a topic, and then switch
positions and debate it again.

> Obviously, in my case, training involved PCVL but not
> ATPL. If those two involve subtle rule differences that would
> operate on an intuitive level, such as existential import, then
> there would be a difference in the mental combat result.

> I'm
> asked to participate in a project intended for young people.
> I trust you see my dilemma at this point.
>
> You could help by recommending a book that explains such
> subtle departures from PCVL as existential import.

The rule difference is not that big a deal, though it has a large
effect (even, as I've argued, on Torkel's own students). The
difference was to redefine "All A are B" as (x)(Ax -> Bx), which
(unlike Aristotle's "All A are B") is true when there are no A's. The
effect was to render some valid inferences from Ari's Square of
Opposition such as subalternation ("All A are B; therefore some A are
B") invalid.

That's really all you need to know (though of course you can check it
for yourself, rather than simply taking my word for it - I'm not
interested in the latter in any case). There's a couple of Stanford
articles on the Square of Opposition; you might wish to google them.

> >but if you are,
> >why not go through with your plan of reading a good book
> >about it?
>
> Because you backed off your previous recommendation
> and did not respond to my clarified request. Perhaps now
> something jogs your memory.
>
> As a programmer, if someone asked me what some of the
> subtle differences were between "subroutine languages"
> and "procedure languages," and even though the
> subroutine/procedure distinction itself is only a trivial
> terminological one, I would have no problem listing a dozen most
> subtle differences not included in introductory textbooks and
> explaining them in common language. I don't see why a teacher of
> logic can't do the same in that area.

Doing that would require a willingness to explain the difference; which
appears to be what's lacking here.

.

Relevant Pages

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