[FOM] Why inclusive disjunction

Leo Meyerovich Leo_Meyerovich at brown.edu
Wed Jan 10 16:53:17 EST 2007

Most representations of logic will have drawbacks as it seems that
whatever cognitive model we follow, in practice the model seems to be
making approximations to represent logical forms -
http://cogdev.cog.ohio-state.edu/2-2.pdf . This leads to bad recall
unless we think really hard about it, defeating the purpose of an
'intuitive' base set of operators. Once a person sits down to learn a
formal system, the question becomes somewhat moot as there may be many
similarly unnatural forms. Cognitive scientists may want to correct me
here. I suspect this topic gets even more interesting once we
introduce temporal logic (sequencing is important to memory).

Begriffsschrift didn't have disjunction as a base operator. Wikipedia
notes Boole used exclusive, while Jevons and those after him,
inclusive. My naive guess is the similarity with 'union' was
appealing. Perhaps you could contact the wikipedia author of the
'disjunction' entry for his/her findings..

- Leo

[note to editor: you may want to censor this one out - I'm not sure
about the effectiveness of its informational content]

On 1/10/07, fom-request at cs.nyu.edu <fom-request at cs.nyu.edu> wrote:
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>    1. Why inclusive disjunction? (John Baldwin)
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> Message: 1
> Date: Tue, 9 Jan 2007 22:38:30 -0600 (Central Standard Time)
> From: John Baldwin <jbaldwin at uic.edu>
> Subject: [FOM] Why inclusive disjunction?
> To: Foundations of Mathematics <fom at cs.nyu.edu>
> Message-ID: <Pine.WNT.4.61.0701092235470.3024 at ALFREDTARSKI>
> Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed
> I am preparing to teach a course in `proof'.
> Can anyone provide a principled reason for why logicians choose to
>   interpret "or" as inclusive disjunction?
> I understand that in the interpretations of statutes, the exclusive or
> is the default.  So attorney's have made a different choice of
> `formalization'.
> John T. Baldwin
> Director, Office of Mathematics Education
> Department of Mathematics, Statistics,
> and Computer Science  M/C 249
> jbaldwin at uic.edu
> 312-413-2149
> Room 327 Science and Engineering Offices (SEO)
> 851 S. Morgan
> Chicago, IL 60607
> Assistant to the director
> Jan Nekola: 312-413-3750
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