From: Toby Bartels <toby+categories@ugcs.caltech.edu>
To: categories list <categories@mta.ca>
Subject: Re: terminology
Date: Tue, 25 May 2010 20:08:01 -0700 [thread overview]
Message-ID: <E1OHd8a-0005w3-KE@mailserv.mta.ca> (raw)
In-Reply-To: <E1OGxyx-0003OJ-KP@mailserv.mta.ca>
Vaughan Pratt wrote in part:
>Moreover most of us would agree that the proposition "the prime factors
>of M = 7^7^7^7 + 5^5^5^5 + 1 (7#4 + 5#4 + 1 where m#n denotes an
>exponential stack of n m's) are all greater than 2 billion and there are
>more than a thousand distinct such" not only makes perfect sense but is
>either true or false. However fewer might be willing to join me in
>insisting that it is certainly true.
Since I know very little about these issues,
I'm not ready to accept your claim that it is true.
(I know that you sketched a way for me to verify it
by performing some calculations on my laptop,
but it would take a while for me to figure out what to program
and then to convince myself that the output meant what you say.)
However, I am happy to agree that the statement is true or false.
>Those who question excluded middle for this proposition may have
>received different wisdom about N than the rest of us, though if I'm
>right then there's a constructive proof of the proposition that can be
>checked on any laptop in under an hour, which should then oblige the
>intuitionistic objectors to stand down.
Anyone who doubts excluded middle for *this* proposition
is not merely a constructivist, or even an intuitionist.
Excluded middle for this proposition is provable in Heyting arithmetic.
While a straightforward calculation of the factors of M
would not fit into the physical universe, it is still finite.
Those who doubt excluded middle (or meaningfulness) for this proposition
go beyond intuitionism; they have been called "ultra-intuitionists",
although the preferred term these days is "ultra-finitists".
As someone who is quite comfortable with constructivism,
I still find ultra-finitism a very strange way to think.
Ultra-finitists definitely have a different recieved wisdom about N
from what the rest of us have received.
Ob categories: Does anybody know any work on ultra-finitism
from the perspective of categorial logic? (somewhat in the way
that topos theory can provide a perspective on constructivism).
I doubt that any exists, but I would it would be nice if it did.
--Toby
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next prev parent reply other threads:[~2010-05-26 3:08 UTC|newest]
Thread overview: 83+ messages / expand[flat|nested] mbox.gz Atom feed top
2010-05-19 10:38 Re terminology: Ronnie Brown
2010-05-20 7:58 ` soloviev
2010-05-20 19:53 ` terminology Eduardo J. Dubuc
2010-05-20 22:15 ` Re terminology: Joyal, Andre
2010-05-20 11:58 ` Urs Schreiber
[not found] ` <AANLkTikre9x4Qikw0mqOl1qZs9DDSkcBu3CXWA05OTQT@mail.gmail.com>
2010-05-21 17:00 ` Ronnie Brown
2010-05-22 19:40 ` Joyal, André
[not found] ` <B3C24EA955FF0C4EA14658997CD3E25E370F5827@CAHIER.gst.uqam.ca>
2010-05-22 21:43 ` terminology Ronnie Brown
[not found] ` <4BF84FF3.7060806@btinternet.com>
2010-05-22 22:44 ` terminology Joyal, André
2010-05-23 15:39 ` terminology Colin McLarty
2010-05-24 13:42 ` equivalence terminology Paul Taylor
2010-05-24 15:53 ` we do meet isomorphisms of categories Marco Grandis
2010-05-26 15:21 ` Toby Bartels
2010-05-27 9:29 ` Prof. Peter Johnstone
[not found] ` <alpine.LRH.2.00.1005271007240.11352@siskin.dpmms.cam.ac.uk>
2010-05-27 10:08 ` Marco Grandis
2010-05-30 12:05 ` Joyal, André
2010-05-24 18:04 ` terminology Vaughan Pratt
2010-05-26 3:08 ` Toby Bartels [this message]
2010-05-24 23:06 ` Equality again Joyal, André
2010-05-26 2:27 ` Patrik Eklund
2010-05-27 11:30 ` Prof. Peter Johnstone
2010-06-01 6:36 ` Marco Grandis
2010-06-01 14:38 ` Joyal, André
2010-05-25 14:08 ` terminology John Baez
2010-05-25 19:39 ` terminology Colin McLarty
2010-05-29 21:47 ` terminology Toby Bartels
2010-05-30 19:15 ` terminology Thorsten Altenkirch
[not found] ` <A46C7965-B4E7-42E6-AE97-6C1D930AC878@cs.nott.ac.uk>
2010-05-30 20:51 ` terminology Toby Bartels
2010-06-01 7:39 ` terminology Thorsten Altenkirch
2010-06-01 13:33 ` terminology Peter LeFanu Lumsdaine
[not found] ` <7BF50141-7775-4D3C-A4AF-D543891666B9@cs.nott.ac.uk>
2010-06-01 18:22 ` terminology Toby Bartels
2010-05-26 8:03 ` terminology Reinhard Boerger
[not found] ` <4BF6BC2C.2000606@btinternet.com>
2010-05-21 18:48 ` Re terminology: Urs Schreiber
[not found] ` <AANLkTilG69hcX7ZV8zrLpQ_nf1pCmyktsnuE0RyJtQYF@mail.gmail.com>
2010-05-26 8:28 ` terminology John Baez
-- strict thread matches above, loose matches on Subject: below --
2017-02-11 20:42 Terminology Fred E.J. Linton
2017-02-14 8:48 ` Terminology Steve Vickers
[not found] ` <02568D97-0A72-4CA8-8900-BDE11E890890@cs.bham.ac.uk>
2017-02-14 9:39 ` Terminology Jean Benabou
2017-02-09 22:03 Terminology Andrée Ehresmann
2017-02-08 8:03 Terminology Jean Benabou
2017-02-08 16:34 ` Terminology Jirí Adámek
2017-02-10 1:42 ` Terminology George Janelidze
2017-02-08 21:40 ` Terminology Carsten Führmann
2017-02-09 11:31 ` Terminology Thomas Streicher
[not found] ` <20170208180636.18346065.28939.42961@rbccm.com>
2017-02-09 16:38 ` Terminology Jean Benabou
2017-02-11 15:07 ` Terminology Steve Vickers
2013-05-02 3:57 Terminology Fred E.J. Linton
2013-05-02 3:57 Terminology Fred E.J. Linton
2013-05-03 11:53 ` Terminology Robert Dawson
2013-04-30 1:20 Terminology Fred E.J. Linton
2013-04-24 17:13 Terminology Jean Bénabou
2013-04-24 23:04 ` Terminology David Roberts
2013-04-27 13:08 ` Terminology Thomas Streicher
[not found] ` <20130427130857.GC16801@mathematik.tu-darmstadt.de>
2013-04-28 3:49 ` Terminology Jean Bénabou
2013-04-28 22:47 ` Terminology Olivier Gerard
[not found] ` <557435A6-4568-4012-8C63-E031931F41FB@wanadoo.fr>
2013-04-28 14:17 ` Terminology Thomas Streicher
2013-04-29 20:05 ` Terminology Toby Bartels
2013-04-30 0:58 ` Terminology Peter May
2010-09-29 2:03 terminology Todd Trimble
2010-09-28 4:38 terminology Eduardo J. Dubuc
2010-05-27 18:31 terminology Colin McLarty
2010-05-16 12:44 terminology Peter Selinger
2010-05-13 17:17 bilax_monoidal_functors Michael Shulman
2010-05-14 14:43 ` terminology (was: bilax_monoidal_functors) Peter Selinger
2010-05-15 19:52 ` terminology Toby Bartels
2010-05-08 3:27 RE : bilax monoidal functors John Baez
2010-05-10 18:16 ` bilax_monoidal_functors?= John Baez
2010-05-11 8:28 ` bilax_monoidal_functors?= Michael Batanin
2010-05-12 3:02 ` bilax_monoidal_functors?= Toby Bartels
2010-05-13 23:09 ` bilax_monoidal_functors?= Michael Batanin
2010-05-15 16:05 ` terminology Joyal, André
2007-01-27 17:06 terminology wlawvere
2007-01-26 23:30 terminology Eduardo Dubuc
2005-12-30 1:16 terminology vs27
2005-12-29 19:09 terminology Nikita Danilov
2005-12-10 3:51 Terminology jean benabou
2005-12-21 20:04 ` Terminology Eduardo Dubuc
2005-12-26 19:47 ` terminology Vaughan Pratt
2005-12-29 23:17 ` terminology Eduardo Dubuc
2006-01-04 14:59 ` terminology Eduardo Dubuc
2003-10-17 15:19 terminology Marco Grandis
2003-10-16 21:39 terminology James Stasheff
2001-04-09 11:06 Terminology Krzysztof Worytkiewicz
2000-12-14 6:17 Terminology Max Kelly
[not found] <3a35cdd73a39f901@amyris.wanadoo.fr>
2000-12-13 11:10 ` Terminology Dr. P.T. Johnstone
2000-12-13 1:17 Terminology Steve Lack
2000-12-12 8:19 Terminology Jean Benabou
2000-01-28 12:02 terminology James Stasheff
2000-01-28 9:57 terminology Marco Grandis
2000-01-27 19:28 terminology James Stasheff
2000-01-27 21:04 ` terminology Paul Glenn
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