Re: Turing Machine computable functions apply finite string transformations to inputs

On 5/4/2025 9:00 PM, Keith Thompson wrote:

Ben Bacarisse <ben@bsb.me.uk> writes:

Richard Heathfield <rjh@cpax.org.uk> writes:

On 04/05/2025 23:34, Mr Flibble wrote:

The function is neither computable nor incomputable because there is no
function at all, just a category error.

>
It's a point of view.

>
It's a point of view only in the sense that there is no opinion so daft
that it's not someone's point of view.  The technical-sounding waffle
about it being a "category error" is simply addressed by asking where
the supposed category error is in other perfectly straightforward
undecidable problems.  For example, whether or not a context-free
grammar is ambiguous or not, or the very simple to pose Post
correspondence problem.

 There's a program called "cksum" that computes a checksum of its input
(not a very secure one, but that's irrelevant).  I wonder if Mr Flibble
would consider applying cksum to its own source code, or to its own
executable file, would be a "category error".  (The second number is the
size in bytes of the input.)
      $ cksum /usr/bin/cksum
     1102087032 104984 /usr/bin/cksum
     $ cksum src/cksum.c
     1844242843 7449 src/cksum.c
 

There is self-reference and then there is pathological self-reference.
My primary research focus for the last 22 years is the latter.
This sentence has five words. // Is true and not pathological
This sentence is not true.    // Is neither true nor false
                               // because it <is> pathological
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer