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From: Andrej Bauer <andrej.bauer@andrej.com>
To: David Leduc <david.leduc6@googlemail.com>
Cc: categories <categories@mta.ca>
Subject: Re: The boringness of the dual of exponential
Date: Wed, 9 Nov 2011 12:28:51 +0100	[thread overview]
Message-ID: <E1RO8sG-0000dv-Uq@mlist.mta.ca> (raw)
In-Reply-To: <E1RNo1R-00088Q-MC@mlist.mta.ca>

> Also, in logic, "and" goes in pair with "or", "for all" goes in pair
> with "there exists". But implication is always left alone. Why is it
> so?

I am afraid logic is polyamorous:

1. "and" goes with "implies" because they are adjoint.
2. "and" goes with "or" because they are dual.

By the way:

1. "forall" goes with "weakening" because it is adjoint to it on the right.
2. "exists" goes with "weakening" because it is adjoint to it on the left.

But why is "forall" dual to "exists"?

With kind regards,

Andrej


[For admin and other information see: http://www.mta.ca/~cat-dist/ ]


  parent reply	other threads:[~2011-11-09 11:28 UTC|newest]

Thread overview: 22+ messages / expand[flat|nested]  mbox.gz  Atom feed  top
2011-11-05 12:52 David Leduc
2011-11-06 20:22 ` FEJ Linton
2011-11-06 21:55 ` Thomas Streicher
2011-11-07 16:32   ` F. William Lawvere
2011-11-06 22:59 ` Ross Street
     [not found] ` <F284B070-BBE5-4187-BA3C-E1A3EA560E6A@mq.edu.au>
2011-11-07 12:52   ` David Leduc
2011-11-08 16:20     ` Paul Taylor
2011-11-09 20:57       ` Uwe.Wolter
2011-11-10  9:29       ` Prof. Peter Johnstone
2011-11-11  7:47         ` Vaughan Pratt
2011-11-11 21:08           ` Robert Seely
2011-11-09 11:28     ` Andrej Bauer [this message]
2011-11-10  0:45       ` Jocelyn Ireson-Paine
2011-11-13  7:57         ` Vaughan Pratt
2011-11-14 13:36           ` Patrik Eklund
2011-11-15 13:03             ` Robert Dawson
     [not found]               ` <07D33522-CA8F-4133-A8E8-4B3BF6DFCCB4@cs.ox.ac.uk>
2011-11-16 18:06                 ` Robert Dawson
2011-11-10  2:17     ` Peter Selinger
2011-11-07 21:23 ` Michael Shulman
2011-11-10  1:11 ` Andrej Bauer
2011-11-09  9:19 Reinhard Boerger
2011-11-09 18:58 RJ Wood

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