From: Toby Bartels <toby+categories@math.ucr.edu>
To: Categories <categories@mta.ca>
Subject: Re: Topos logic arises naturally
Date: Sun, 1 Jun 2003 09:05:31 -0700 [thread overview]
Message-ID: <20030601160531.GH20845@math-rs-n01.ucr.edu> (raw)
In-Reply-To: <002801c326a1$05dc0000$f112fea9@essex.ac.uk>
Elwood Wilkins wrote:
>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.
Is this a failure of constructivism as such, or just a bug?
No doubt that a coherent philosophy of mathematics
helps to avoid such mistakes, but would anybody ever claim
that it's *not* a mistake?
-- Toby
next prev parent reply other threads:[~2003-06-01 16:05 UTC|newest]
Thread overview: 8+ messages / expand[flat|nested] mbox.gz Atom feed top
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 [this message]
2003-06-02 18:11 Valeria.dePaiva
2003-06-03 9:24 Lawrence Paulson
2003-06-03 16:04 ` Todd Wilson
2003-06-04 9:25 ` Lawrence Paulson
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