From: Michael Shulman <shu...@sandiego.edu>
To: Matt Oliveri <atm...@gmail.com>
Cc: Homotopy Type Theory <HomotopyT...@googlegroups.com>
Subject: Re: [HoTT] A puzzle about "univalent equality"
Date: Wed, 7 Sep 2016 21:14:50 -0700 [thread overview]
Message-ID: <CAOvivQxFDPaVL0iwDR=sBMWa+Zmh56jatW24-Bv7n0ar4FvaSA@mail.gmail.com> (raw)
In-Reply-To: <a88b7834-5ce8-47d6-803a-d2a98ed27084@googlegroups.com>
Does "Zermelo-style set-theoretic equality" even make sense in MLTT?
Types don't have the global membership structure that Zermelo-sets do.
On Wed, Sep 7, 2016 at 4:18 PM, Matt Oliveri <atm...@gmail.com> wrote:
> On Tuesday, September 6, 2016 at 6:14:24 PM UTC-4, Martin Hotzel Escardo
> wrote:
>>
>> Some people like the K-axiom for U because ... (let them fill the answer).
>
>
> It allows you to interpret (within type theory) the types of ITT + K as
> types of U, and their elements as the corresponding elements. (Conjecture?)
> Whereas without K, we don't know how to interpret ITT types as types of U.
> In other words, K is a simple way to give ITT reflection.
>
>> Can we stare at the type (Id U X Y) objectively, mathematically, say
>> within intensional MLTT, where it was introduced, and, internally in
>> MLTT, ponder what it can be, and identify the only "compelling" thing it
>> can be as the type of equivalences X~Y, where "compelling" is a notion
>> remote from univalence?
>
>
> How does Zermelo-style set-theoretic equality get ruled out as a potential
> "compelling" meaning for identity? Of course, there's a potential argument
> about what "compelling" ought to be getting at. You seem to not consider
> set-theoretic equality compelling, which I can play along with.
>
> --
> You received this message because you are subscribed to the Google Groups
> "Homotopy Type Theory" group.
> To unsubscribe from this group and stop receiving emails from it, send an
> email to HomotopyTypeThe...@googlegroups.com.
> For more options, visit https://groups.google.com/d/optout.
next prev parent reply other threads:[~2016-09-08 4:15 UTC|newest]
Thread overview: 18+ messages / expand[flat|nested] mbox.gz Atom feed top
2016-09-05 16:54 Andrew Polonsky
2016-09-05 21:40 ` [HoTT] " Michael Shulman
2016-09-05 21:51 ` Dan Licata
2016-09-06 7:30 ` Andrew Polonsky
2016-09-06 12:32 ` Michael Shulman
2016-09-06 12:56 ` Dan Licata
2016-09-06 12:57 ` Peter LeFanu Lumsdaine
2016-09-06 13:44 ` Andrew Polonsky
2016-09-06 22:14 ` Martin Escardo
2016-09-07 23:18 ` Matt Oliveri
2016-09-08 4:14 ` Michael Shulman [this message]
2016-09-08 6:06 ` Jason Gross
2016-09-08 9:11 ` Martin Escardo
2016-09-08 6:34 ` Matt Oliveri
2016-09-08 6:45 ` Michael Shulman
2016-09-08 9:07 ` Martin Escardo
2016-09-08 9:51 ` Thomas Streicher
2016-09-19 12:40 ` Robin Adams
Reply instructions:
You may reply publicly to this message via plain-text email
using any one of the following methods:
* Save the following mbox file, import it into your mail client,
and reply-to-all from there: mbox
Avoid top-posting and favor interleaved quoting:
https://en.wikipedia.org/wiki/Posting_style#Interleaved_style
* Reply using the --to, --cc, and --in-reply-to
switches of git-send-email(1):
git send-email \
--in-reply-to='CAOvivQxFDPaVL0iwDR=sBMWa+Zmh56jatW24-Bv7n0ar4FvaSA@mail.gmail.com' \
--to="shu..."@sandiego.edu \
--cc="HomotopyT..."@googlegroups.com \
--cc="atm..."@gmail.com \
/path/to/YOUR_REPLY
https://kernel.org/pub/software/scm/git/docs/git-send-email.html
* If your mail client supports setting the In-Reply-To header
via mailto: links, try the mailto: link
Be sure your reply has a Subject: header at the top and a blank line
before the message body.
This is a public inbox, see mirroring instructions
for how to clone and mirror all data and code used for this inbox;
as well as URLs for NNTP newsgroup(s).