XPost: comp.theory, sci.logic, sci.math

On 4/29/2022 4:42 PM, Richard Damon wrote:

On 4/29/22 4:25 PM, olcott wrote:

On 4/29/2022 3:17 PM, Mr Flibble wrote:

On Fri, 29 Apr 2022 15:42:49 -0400
Richard Damon <Richard@Damon-Family.org> wrote:

On 4/29/22 3:30 PM, olcott wrote:

On 4/29/2022 10:21 AM, Mikko wrote:

On 2022-04-29 14:07:07 +0000, Mr Flibble said:

A proof of an erroneous theory is, by implication, also
erroneous. The halting problem as stated is erroneous ergo all
currently extant halting problem proofs are, by implication, also >>>>>>> erroneous and do not require formal refutation to be considered
invalid.

Fix the halting problem itself before trying to refute Olcott, you >>>>>>> shower.

Apparently Mr Flibble does not know what "erroneous" mean.
Otherwise he would tell.

There is a common meaning that can be applied proofs: an
"erroneous proof"
is not a proof although it may look like one. Does this extend to
problems
or theories? Does "erroneous theory" mean something that looks
like a theory but isn't? Is Mr Flibble trying to say that the
halting problem is nor really any problem?

Mikko

A person that only cares about rebuttal and does not give a rat's
ass about truth would say that. You don't pay attention to what he
says you merely pick out some fake excuse for a rebuttal.

Flibble perfectly defined "erroneous proof" and "erroneous theory"
in that their basis is anchored in the well defined concept of
[category error]:

[category error]
a semantic or ontological error in which things belonging to a
particular category are presented as if they belong to a different
category,[1] or, alternatively, a property is ascribed to a thing
that could not possibly have that property.
https://en.wikipedia.org/wiki/Category_mistake

And exactly WHAT is the category error in the Halting Problem.

The infinitely recursive definition.

What is given the wrong category, and what category is it incorrectly
being given.

The two categories are the decider and that which is being decided.

If you can't state what the error is, you are just proving that YOU
are just in "Rebuttal Mode" and not caring about what is the actual
truth.

/Flibble

The Liar Paradox and Gödel's G are examples of infinitely recursive
definition.

LP := ~True(LP)
G := ~Provable(G)

This is totally obvious when they are encoded in Prolog.

https://www.researchgate.net/publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence

Except that isn't the actual statement of G, and G can't be written in
Prolog because Prolog only handles first order logic and G uses Higher
Order logic.

FAIL.

DIRECT QUOTE FROM page 40/43 OF Gödel's PAPER
The analogy between this result and Richard’s antinomy leaps to the eye; there is also a close relationship with the “liar” antinomy,^14 since
the undecidable proposition [R(q); q] states precisely that q belongs to
K, i.e. according to (1), that [R(q); q] is not provable. We are
therefore confronted with a proposition which asserts its own unprovability.

14 Every epistemological antinomy can likewise be used for a similar undecidability proof

https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf


Thus: G ⟷ ~Provable(G)
is sufficiently equivalent to Gödel's G.

When this is encoded in Prolog it is rejected as an infinite term as my
paper clearly shows.



--
Copyright 2022 Pete Olcott "Talent hits a target no one else can hit;
Genius hits a target no one else can see." Arthur Schopenhauer

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