From: Lawrence Paulson <lp15@cam.ac.uk>
To: Categories <categories@mta.ca>
Subject: Re: Topos logic arises naturally
Date: Tue, 3 Jun 2003 10:24:35 +0100 [thread overview]
Message-ID: <30CB5DA5-95A5-11D7-BEF0-00039384D4B8@cam.ac.uk> (raw)
> -----Original Message-----
> From: Elwood Wilkins [mailto:elwood@essex.ac.uk]
> Sent: Friday, May 30, 2003 4:35 AM
> To: Categories
> Subject: categories: Re: Topos logic arises naturally
>
> Isabelle's internal logic is not constructive. The existential clause
> of the BHK-interpretation is violated so that a consquence of "all
> unicorns have horns" is that "some unicorn has a horn". The moral
> (biased towards
> theorists): software engineering considerations are not enough, a
> coherant philosophy of mathematics is also needed.
Isabelle's internal logic comes from Lambek and Scott. It is an
instance of Example 1.1 on page 132, where all types are assumed to be
non-empty. However, even their full system is unacceptable to many
constructivists because it is impredicative. Constructive theories,
like a certain commuting diagrams package, have a surprising tendency
to "time out".
Larry Paulson
next reply other threads:[~2003-06-03 9:24 UTC|newest]
Thread overview: 8+ messages / expand[flat|nested] mbox.gz Atom feed top
2003-06-03 9:24 Lawrence Paulson [this message]
2003-06-03 16:04 ` Todd Wilson
2003-06-04 9:25 ` Lawrence Paulson
-- strict thread matches above, loose matches on Subject: below --
2003-06-02 18:11 Valeria.dePaiva
2003-05-27 10:44 Till Mossakowski
2003-05-30 11:35 ` Elwood Wilkins
2003-05-30 14:37 ` Till Mossakowski
2003-06-01 16:05 ` Toby Bartels
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