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: Tue, 5 Jun 2018 15:54:39 -0700 (PDT) [thread overview]
Message-ID: <581e9092-7f93-4915-8752-ec68e80c4a6f@googlegroups.com> (raw)
In-Reply-To: <299441c8-2760-48cd-b052-02b2bb4d361f@googlegroups.com>
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("Imprecisely mirrored by 0-groupoids" - apologies for the typo.)
On Tuesday, 5 June 2018 23:19:20 UTC+1, Martín Hötzel Escardó wrote:
>
>
>
> On Tuesday, 5 June 2018 09:37:41 UTC+1, David Roberts wrote:
>>
>> There is an... "interesting" discussion going on at the fom mailing
>> list at present, the usual suspects included, about set theory-based
>> proof assistants, which might provide either a source of entertainment
>> or frustration. It is enlightening when considering what people think
>> about typed vs untyped.
>>
>> Univalent foundations gets a mention here:
>> https://cs.nyu.edu/pipermail/fom/2018-May/021012.html
>> The 'ideal proof assistant' is described as being based on ZFC here:
>> https://cs.nyu.edu/pipermail/fom/2018-May/021026.html
>> Friedman proclaims he is completely ignorant of the issues and that he
>> has never gotten close to getting dirty with details, but is happy to
>> weigh in: https://cs.nyu.edu/pipermail/fom/2018-May/021023.html
>> The discussion continues this month here:
>> https://cs.nyu.edu/pipermail/fom/2018-June/021030.html
>>
>>
> May I humbly say that the FOM list is mainly concerned with the
> foundations of mathematics of hlevel 2, or 0-types.
>
> And that they are concerned with "how much" a foundation can prove, rather
> than "what" a foundation talks about *natively*? (As opposed to via
> ZFC-set avatars.)
>
> What univalent mathematics proposes is that infty-groupoids are the
> primitive objects of mathematics, rather than ZFC sets (imprecisely
> mirrored by 1-groupoids).
>
> We call these things types (bad terminology, inherited from history).
>
> From this point of view, the above FOM discussion is completely misguided.
> (As you already know.)
>
> The point of univalent foundations is that we should be able to talk about
> the objects we have in mind directly as they are, rather than via ZFC
> avatars.
>
> It is not that we worship types.
>
> Martin
>
>
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next prev parent reply other threads:[~2018-06-05 22:54 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
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 [this message]
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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