From: Andrew Polonsky <andrew....@gmail.com>
To: Michael Shulman <shu...@sandiego.edu>
Cc: Homotopy Type Theory <HomotopyT...@googlegroups.com>
Subject: Re: [HoTT] Different notions of equality; terminology
Date: Tue, 19 Jul 2016 01:01:12 +0200 [thread overview]
Message-ID: <CABcT7WCxdHSuWdHc+5DwO98ovHx_-9bszE=kOJuuDPg5ZfyZxQ@mail.gmail.com> (raw)
In-Reply-To: <CAOvivQw15pOvi9wzWFpB2WcwmgxB=uw-826xNmxUck57VagEQA@mail.gmail.com>
>>> case I think it better to use a word that conveys *exactly* what the
>>> distinction is,
>>
>> The distinction is that it is the equality
>> predicate/formula/thing-you-can-prove-or-inhabit.
>
> "Predicate/formula/thing-you-can-prove-or-inhabit" is a long-winded
> way of saying "type".
However, that distinction was present before types. It is indeed
illogical to call "typal" something which was there before types were
invented.
>> In type theory with reflection rule, one can think of all equalities
>> as "definitional", including those that appear in the hypothesis of
>> the reflection rule.
>
> Only if you are willing to redefine the word "definition".
I am quite happy with it as is.
Andrew
next prev parent reply other threads:[~2016-07-18 23:01 UTC|newest]
Thread overview: 17+ messages / expand[flat|nested] mbox.gz Atom feed top
2016-07-18 20:45 Andrew Polonsky
2016-07-18 21:03 ` [HoTT] " Andrej Bauer
2016-07-18 21:05 ` Vladimir Voevodsky
2016-07-18 21:13 ` Andrew Polonsky
[not found] ` <2506A3A8-8AC0-4B49-AD1E-D660A7A15245@ias.edu>
[not found] ` <CABcT7WDYqUY=efCTvdRpdW98aDSXpjfHGo9pJz2jBNa3yNXCgQ@mail.gmail.com>
[not found] ` <085E4ACF-BD06-484F-ACA3-17DD6249CF76@ias.edu>
[not found] ` <CABcT7WBKxFhcvuBP66wOcUzU1uPNUqPqXoSYW4aCJv4c8U7iuQ@mail.gmail.com>
2016-07-18 21:45 ` Vladimir Voevodsky
2016-07-18 21:16 ` Dimitris Tsementzis
2016-07-18 21:17 ` Jon Sterling
2016-07-18 21:24 ` Andrew Polonsky
[not found] ` <CAOvivQyZzdyhFFPfqkH4W+Z--78t0LEVWtthLhCpDxUkJNUrMQ@mail.gmail.com>
2016-07-18 22:20 ` Andrew Polonsky
2016-07-18 22:24 ` Jon Sterling
[not found] ` <CAOvivQy44FvN_bVD+nby8t0BnnTYf38dR5=s31_Yv_VsDOzLCA@mail.gmail.com>
2016-07-18 22:43 ` Andrew Polonsky
[not found] ` <CAOvivQw15pOvi9wzWFpB2WcwmgxB=uw-826xNmxUck57VagEQA@mail.gmail.com>
2016-07-18 23:01 ` Andrew Polonsky [this message]
2016-07-19 12:53 ` Michael Shulman
2016-07-19 16:49 ` Jon Sterling
2016-07-19 19:07 ` Egbert Rijke
2016-07-20 2:45 ` Dan Licata
2016-07-19 23:19 ` Martin Hotzel Escardo
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='CABcT7WCxdHSuWdHc+5DwO98ovHx_-9bszE=kOJuuDPg5ZfyZxQ@mail.gmail.com' \
--to="andrew...."@gmail.com \
--cc="HomotopyT..."@googlegroups.com \
--cc="shu..."@sandiego.edu \
/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).