Discussion of Homotopy Type Theory and Univalent Foundations
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From: Thorsten Altenkirch <Thorsten....@nottingham.ac.uk>
To: Michael Shulman <shu...@sandiego.edu>
Cc: "homotopyt...@googlegroups.com" <homotopyt...@googlegroups.com>
Subject: Re: [HoTT] "Identifications" ?
Date: Mon, 4 May 2020 14:17:23 +0000	[thread overview]
Message-ID: <7A5CCED7-4FFC-43EE-AD3C-699899C19520@nottingham.ac.uk> (raw)
In-Reply-To: <CAOvivQz1avq5PgK1FHWp1d4-U6UzV=Vdvo9iRp_3WjaXxNUskg@mail.gmail.com>

This seems reasonable. I usually say "equality proofs" but the word proof also has other conotations. Also what is an element of 3 <= 4, if not a proof or evidence? Maybe it is a inidentification? __

Thorsten

On 04/05/2020, 14:17, "Michael Shulman" <shu...@sandiego.edu> wrote:

    I don't think using "identification" necessarily implies any
    difference between "identification" and "equality".  I don't think of
    it that way.  For me the point is just to have a word that refers to
    an *element* of an identity type.  Calling it "an equality" can have
    the wrong connotation because classically, an equality is just a
    proposition (or a true proposition), whereas an element of an identity
    type carries information.  Calling it "an identification" suggests
    exactly the information that it carries: a way of identifying two
    things.

    On Mon, May 4, 2020 at 2:35 AM Thorsten Altenkirch
    <Thorsten....@nottingham.ac.uk> wrote:
    >
    > I am just reading a paper which uses the word “Identification” instead of equality. I think this has been proposed by Bob Harper. Can anybody enlighten me what is the difference between identifications and equality? Maybe there is an identification between them but they are not equal? Are the real numbers 0.999… identified or are they equal?
    >
    >
    >
    > Thorsten
    >
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  reply	other threads:[~2020-05-04 14:17 UTC|newest]

Thread overview: 26+ messages / expand[flat|nested]  mbox.gz  Atom feed  top
2020-05-04  9:35 Thorsten Altenkirch
2020-05-04 10:59 ` [HoTT] " stre...
2020-05-04 11:04   ` Steve Awodey
2020-05-04 11:17   ` Thorsten Altenkirch
2020-05-04 11:42     ` Nicolai Kraus
2020-05-04 12:04       ` Thorsten Altenkirch
2020-05-04 12:06     ` Thomas Streicher
2020-05-04 12:12       ` Thorsten Altenkirch
2020-05-04 12:39         ` Thomas Streicher
2020-05-04 13:16 ` Michael Shulman
2020-05-04 14:17   ` Thorsten Altenkirch [this message]
2020-05-04 14:48   ` Stefan Monnier
2020-05-04 15:46     ` Nicolai Kraus
2020-05-04 15:57       ` Thorsten Altenkirch
2020-05-04 15:59     ` Michael Shulman
2020-05-04 16:07       ` Steve Awodey
2020-05-04 16:17         ` Thorsten Altenkirch
2020-05-04 16:53           ` Steve Awodey
2020-05-04 17:25             ` Thorsten Altenkirch
2020-05-04 17:43               ` Michael Shulman
2020-05-04 17:55               ` Steve Awodey
2020-05-04 16:21         ` Peter LeFanu Lumsdaine
2020-05-04 16:16       ` Joyal, André
2020-05-04 20:38         ` Joyal, André
2020-05-07 19:43 ` Martín Hötzel Escardó
2020-05-08 10:41   ` [HoTT] " Thorsten Altenkirch

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