Re: HP undecidability is not an axiom

From	Ben Bacarisse <ben.usenet@bsb.me.uk>
Newsgroups	comp.theory
Subject	Re: HP undecidability is not an axiom
Date	2021-07-16 23:21 +0100
Organization	A noiseless patient Spider
Message-ID	<87fswdq4rf.fsf@bsb.me.uk> (permalink)
References	<20210716223332.000031bf@reddwarf.jmc>

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Mr Flibble <flibble@reddwarf.jmc> writes:

> The halting problem being undecidable is NOT a fucking axiom;

Agreed.  It follows logically from most reasonable sets of axioms.

Interestingly, halting being decidable /can/ be taken as an axiom
without introducing any inconsistency.

> you can't go about saying:
>
> "Since the halting problem is known to be undecidable blah blah fucking
> blah" in your fucking proofs.

It's perfectly reasonable to state theorems as being known.  We know
there is no largest prime.  We know that a^2 + b^2 = c^2 for right
triangles...

-- 
Ben.

Thread

HP undecidability is not an axiom Mr Flibble <flibble@reddwarf.jmc> - 2021-07-16 22:33 +0100
  Re: HP undecidability is not an axiom olcott <NoOne@NoWhere.com> - 2021-07-16 17:02 -0500
  Re: HP undecidability is not an axiom Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-16 23:21 +0100
    Re: HP undecidability is not an axiom Jeff Barnett <jbb@notatt.com> - 2021-07-16 16:48 -0600
      Re: HP undecidability is not an axiom Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-17 00:11 +0100
        Re: HP undecidability is not an axiom Jeff Barnett <jbb@notatt.com> - 2021-07-16 23:07 -0600
          Re: HP undecidability is not an axiom Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-17 21:15 +0100
            Re: HP undecidability is not an axiom Jeff Barnett <jbb@notatt.com> - 2021-07-17 17:30 -0600
  Re: HP undecidability is not an axiom Alan Mackenzie <acm@muc.de> - 2021-07-17 12:00 +0000
    Re: HP undecidability is not an axiom Mr Flibble <flibble@reddwarf.jmc> - 2021-07-17 13:03 +0100
      Re: HP undecidability is not an axiom Alan Mackenzie <acm@muc.de> - 2021-07-17 12:30 +0000

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