From: "Martín Hötzel Escardó" <"escardo..."@gmail.com>
To: Homotopy Type Theory <HomotopyT...@googlegroups.com>
Subject: Re: [HoTT] Re: Where is the problem with initiality?
Date: Fri, 1 Jun 2018 10:07:32 -0700 (PDT) [thread overview]
Message-ID: <2b190a31-7985-4e6b-9f69-ed244ea64d7d@googlegroups.com> (raw)
In-Reply-To: <37CBB960-C4F1-4B97-92E6-28462A0591C1@gmail.com>
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On Thursday, 31 May 2018 20:02:51 UTC+1, Alexander Kurz wrote:
>
>
> > On 31 May 2018, at 12:05, Michael Shulman <shu...@sandiego.edu
> <javascript:>> wrote:
> >
> > It sounds like Thorsten and are both starting to repeat ourselves, so
> > we should probably spare the patience of everyone else on the list
> > pretty soon. I'll just make my own hopefully-final point by saying
> > that if "properties of the typed algebraic syntax" can imply that the
> > untyped stuff we write on the page has a *unique* typed denotation,
> > independent of a particular typechecking algorithm, as mentioned in my
> > last email, then I'll (probably) be satisfied.
>
> I am interested in this question of translating the untyped stuff we write
> on the page into type theory.
>
> To give a concrete example of what I am thinking of as untyped, but
> nevertheless conceptual and structural mathematics, I would point at Tom
> Leinster’s elegant description of the solution to the problem of Buffon’s
> needle, see the first paragraphs of the section “What is category theory?”
> at
> https://golem.ph.utexas.edu/category/2010/03/a_perspective_on_higher_catego.html
>
> I call this argument type free because I see no obvious or canonical way
> to make the types precise enough in order to implement the proof in, say,
> Agda. Even if this can be done, it is still important that mathematicians
> can discuss this argument first without having to make the types precise.
> So there will always be mathematics outside of type theory.
>
I don't understand why you call this argument untyped. Do you feel that a
formalization in set theory, which is untyped, would be easier than a
formalization in type theory? How is untypedness helping with this
argument?
Martin
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next prev parent reply other threads:[~2018-06-01 17:07 UTC|newest]
Thread overview: 57+ messages / expand[flat|nested] mbox.gz Atom feed top
2018-05-22 5:46 Michael Shulman
2018-05-22 16:47 ` Ambrus Kaposi
2018-05-23 16:26 ` [HoTT] " Thorsten Altenkirch
2018-05-24 5:52 ` Michael Shulman
2018-05-24 8:11 ` Thorsten Altenkirch
2018-05-24 9:53 ` Ambrus Kaposi
2018-05-24 17:26 ` Michael Shulman
2018-05-26 9:21 ` Thomas Streicher
2018-05-26 11:47 ` Michael Shulman
2018-05-26 16:47 ` stre...
2018-05-27 5:14 ` Bas Spitters
2018-05-28 22:39 ` Michael Shulman
2018-05-29 9:15 ` [HoTT] " Thorsten Altenkirch
2018-05-29 15:15 ` Michael Shulman
2018-05-30 9:33 ` Thomas Streicher
2018-05-30 9:37 ` Thorsten Altenkirch
2018-05-30 10:10 ` Thomas Streicher
2018-05-30 12:08 ` Thorsten Altenkirch
2018-05-30 13:40 ` Thomas Streicher
2018-05-30 14:38 ` Thorsten Altenkirch
2018-05-30 10:53 ` Alexander Kurz
2018-05-30 12:05 ` Thorsten Altenkirch
2018-05-30 19:07 ` Michael Shulman
2018-05-31 10:06 ` Thorsten Altenkirch
2018-05-31 11:05 ` Michael Shulman
2018-05-31 19:02 ` Alexander Kurz
2018-06-01 9:55 ` Martin Escardo
2018-06-01 17:07 ` Martín Hötzel Escardó [this message]
2018-06-01 17:43 ` Eric Finster
2018-06-01 19:55 ` Martín Hötzel Escardó
2018-06-01 20:59 ` András Kovács
2018-06-01 21:06 ` Martín Hötzel Escardó
2018-06-01 21:23 ` Michael Shulman
2018-06-01 21:53 ` Eric Finster
2018-06-01 22:09 ` Michael Shulman
2018-06-02 15:06 ` Eric Finster
2018-06-05 20:04 ` Michael Shulman
2018-06-02 5:13 ` Thomas Streicher
2018-06-01 21:52 ` Jasper Hugunin
2018-06-01 22:00 ` Eric Finster
2018-06-01 21:27 ` Matt Oliveri
2018-06-02 5:21 ` Ambrus Kaposi
2018-06-02 6:01 ` Thomas Streicher
2018-06-02 14:35 ` Thorsten Altenkirch
2018-05-30 13:30 ` Jon Sterling
2018-06-05 7:52 ` Andrej Bauer
2018-06-05 8:37 ` David Roberts
2018-06-05 9:46 ` Gabriel Scherer
2018-06-05 22:19 ` Martín Hötzel Escardó
2018-06-05 22:54 ` Martín Hötzel Escardó
2018-06-05 22:12 ` Richard Williamson
2018-06-06 15:05 ` Thorsten Altenkirch
2018-06-06 19:25 ` Richard Williamson
2018-05-29 14:00 ` Jon Sterling
2018-05-30 22:35 ` Michael Shulman
2018-05-31 10:48 ` Martín Hötzel Escardó
2018-05-31 11:09 ` Michael Shulman
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