[FOM] Why inclusive disjunction?
Richard Heck
rgheck at brown.edu
Thu Jan 11 16:29:15 EST 2007
Thanks, Neil. But in my book, the absurdity sign is a zero-place
connective. What I had in mind---perhaps this was obvious---had
something to do with harmony and all that, and, since the absurdity sign
is as much in need of introduction and elimination rules as anything
else, any worries one had about mixing connectives in rules will surface
with it, too. I'm not, to be sure, saying such worries can't be
resolved. Just asking whether they would need to be.
Richard
Neil Tennant wrote:
> On Wed, 10 Jan 2007, Richard Heck wrote:
>
>
>> [A]re there introduction and elimination rules for exclusive or that
>> don't involve other connectives?
>>
>
> Yes.
>
> Neil Tennant
> ______________________________________________________
>
> [#: absurdity sign]
>
> (i)__ __(i) (i)__ __(i)
> A , B A , B
> Intro : :
> A # B #
> __________(i) _________(i)
> A aut B A aut B
>
> [In the relevant logics CR and IR, specify that in applications
> of the first half of aut-Intro, the assumption B must be used; and
> that in applications of the second half of aut-Intro, the assumption A
> must be used.]
>
> (i)__ __(i)
> Elim A B
> : :
> A aut B C C A aut B A B
> ___________________(i) __________________
> C #
>
> [In the relevant logics CR and IR, specify that in applications
> of the first half of aut-Elim, the assumption A must be used in
> the first case-proof, and the assumption B must be used in the second
> case-proof.]
>
>
--
==================================================================
Richard G Heck, Jr
Professor of Philosophy
Brown University
http://bobjweil.com/heck/
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