Discussion of Homotopy Type Theory and Univalent Foundations
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From: stre...@mathematik.tu-darmstadt.de
To: "\"Joyal, André\"" <"joyal..."@uqam.ca>
Cc: "Thomas Streicher" <stre...@mathematik.tu-darmstadt.de>,
	"Ulrik Buchholtz" <ulrikbu...@gmail.com>,
	"Homotopy Type Theory" <homotopyt...@googlegroups.com>
Subject: RE: [HoTT] Identity versus equality
Date: Mon, 11 May 2020 18:37:42 +0200	[thread overview]
Message-ID: <0388695a1dfc717f9c5e458937dff760.squirrel@webmail.mathematik.tu-darmstadt.de> (raw)
In-Reply-To: <8C57894C7413F04A98DDF5629FEC90B1652F5861@Pli.gst.uqam.ca>

> Thank you for pointing out the case of the universe of constructible sets
> L.
> It is internal to ZF because it is was constructed from ordinals in ZF.
> Could it be also external to ZF ?

Anything internal can be externalized but not the other way round.

The point I tried to make was that in the usual models of 2-level type
theory the homotopical part is not internal to the ambient nonhomotopical
part.

> Gödel thought that ordinals and sets are real, like matter, but of a
> different kind.
> He was the first to use the full power of mathematics for studying formal
> logic.
> Most logicians believe that natural numbers are real.
> They use natural numbers and induction for studying formal systems.

Indeed, Goedel was the first one who took serious the difference between
syntax and semantics. This was crucial for his findings.
That he nevertheless was a dyed in the wool Platonist was a bit inconsequent
but nobody is perfect :-)

Thomas


  reply	other threads:[~2020-05-11 16:37 UTC|newest]

Thread overview: 61+ messages / expand[flat|nested]  mbox.gz  Atom feed  top
2020-05-05  8:47 Ansten Mørch Klev
2020-05-06 16:02 ` [HoTT] " Joyal, André
2020-05-06 19:01   ` Steve Awodey
2020-05-06 19:18     ` Michael Shulman
2020-05-06 19:31       ` Steve Awodey
2020-05-06 20:30         ` Joyal, André
2020-05-06 22:52         ` Thorsten Altenkirch
2020-05-06 22:54       ` Thorsten Altenkirch
2020-05-06 23:29         ` Joyal, André
2020-05-07  6:11           ` Egbert Rijke
2020-05-07  6:58           ` Thorsten Altenkirch
2020-05-07  9:04             ` Ansten Mørch Klev
2020-05-07 10:09             ` Thomas Streicher
2020-05-07 16:13               ` Joyal, André
2020-05-07 21:41                 ` David Roberts
2020-05-07 23:43                   ` Joyal, André
2020-05-07 23:56                     ` David Roberts
2020-05-08  6:40                       ` Thomas Streicher
2020-05-08 21:06                         ` Joyal, André
2020-05-08 23:44                           ` Steve Awodey
2020-05-09  2:46                             ` Joyal, André
2020-05-09  3:09                               ` Jon Sterling
     [not found]                             ` <CADZEZBY+3z6nrRwsx9p-HqYuTxAnwMUHv7JasHy8aoy1oaGPcw@mail.gmail.com>
2020-05-09  2:50                               ` Steve Awodey
2020-05-09  8:28                           ` Thomas Streicher
2020-05-09 15:53                             ` Joyal, André
2020-05-09 18:43                               ` Thomas Streicher
2020-05-09 20:18                                 ` Joyal, André
2020-05-09 21:27                                   ` Jon Sterling
2020-05-10  2:19                                     ` Joyal, André
2020-05-10  3:04                                       ` Jon Sterling
2020-05-10  9:09                                         ` Thomas Streicher
2020-05-10 11:59                                           ` Thorsten Altenkirch
2020-05-10 11:46                                     ` Thorsten Altenkirch
2020-05-10 14:01                                       ` Michael Shulman
2020-05-10 14:20                                         ` Nicolai Kraus
2020-05-10 14:34                                           ` Michael Shulman
2020-05-10 14:52                                             ` Nicolai Kraus
2020-05-10 15:16                                               ` Michael Shulman
2020-05-10 15:23                                                 ` Nicolai Kraus
2020-05-10 16:13                                                   ` Nicolai Kraus
2020-05-10 16:28                                                     ` Michael Shulman
2020-05-10 18:18                                                       ` Nicolai Kraus
2020-05-10 19:15                                             ` Thorsten Altenkirch
2020-05-10 19:20                                         ` Thorsten Altenkirch
2020-05-10 12:53                                   ` Ulrik Buchholtz
2020-05-10 14:01                                     ` Michael Shulman
2020-05-10 14:27                                       ` Nicolai Kraus
2020-05-10 15:35                                         ` Ulrik Buchholtz
2020-05-10 16:30                                           ` Michael Shulman
2020-05-10 18:56                                           ` Nicolai Kraus
2020-05-10 18:04                                     ` Joyal, André
2020-05-11  7:33                                       ` Thomas Streicher
2020-05-11 14:54                                         ` Joyal, André
2020-05-11 16:37                                           ` stre... [this message]
2020-05-11 16:42                                             ` Michael Shulman
2020-05-11 17:27                                               ` Thomas Streicher
2020-05-10 16:51                                   ` Nicolai Kraus
2020-05-10 18:57                                     ` Michael Shulman
2020-05-10 19:18                                     ` Nicolai Kraus
2020-05-10 20:22                                       ` Michael Shulman
2020-05-10 22:08                                         ` Joyal, André

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