Re: Undecidability based on epistemological antinomies V2 --H(D,D)--

On 4/28/24 11:27 AM, olcott wrote:

On 4/28/2024 10:10 AM, Richard Damon wrote:

On 4/28/24 10:48 AM, olcott wrote:

On 4/28/2024 9:31 AM, Ross Finlayson wrote:

On 04/28/2024 06:10 AM, olcott wrote:

On 4/28/2024 3:36 AM, Mikko wrote:

On 2024-04-27 13:39:50 +0000, olcott said:
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On 4/27/2024 3:24 AM, Mikko wrote:

On 2024-04-26 13:54:05 +0000, olcott said:
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On 4/26/2024 3:32 AM, Mikko wrote:

On 2024-04-25 14:15:20 +0000, olcott said:
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On 4/25/2024 3:16 AM, Mikko wrote:

On 2024-04-25 00:17:57 +0000, olcott said:
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On 4/24/2024 6:01 PM, Richard Damon wrote:

On 4/24/24 11:33 AM, olcott wrote:

On 4/24/2024 3:35 AM, Mikko wrote:

On 2024-04-23 14:31:00 +0000, olcott said:
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On 4/23/2024 3:21 AM, Mikko wrote:

On 2024-04-22 17:37:55 +0000, olcott said:
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On 4/22/2024 10:27 AM, Mikko wrote:

On 2024-04-22 14:10:54 +0000, olcott said:
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On 4/22/2024 4:35 AM, Mikko wrote:

On 2024-04-21 14:44:37 +0000, olcott said:
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On 4/21/2024 2:57 AM, Mikko wrote:

On 2024-04-20 15:20:05 +0000, olcott said:
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On 4/20/2024 2:54 AM, Mikko wrote:

On 2024-04-19 18:04:48 +0000, olcott said:
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When we create a three-valued logic system that
has these
three values: {True, False, Nonsense}
https://en.wikipedia.org/wiki/Three-valued_logic

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Such three valued logic has the problem that a
tautology of the
ordinary propositional logic cannot be trusted to
be true. For
example, in ordinary logic A ∨ ¬A is always true.
This means that
some ordinary proofs of ordinary theorems are no
longer valid and
you need to accept the possibility that a theory
that is complete
in ordinary logic is incomplete in your logic.
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I only used three-valued logic as a teaching
device. Whenever an
expression of language has the value of {Nonsense}
then it is
rejected and not allowed to be used in any logical
operations. It
is basically invalid input.

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You cannot teach because you lack necessary skills.
Therefore you
don't need any teaching device.
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That is too close to ad homimen.
If you think my reasoning is incorrect then point to
the error
in my reasoning. Saying that in your opinion I am a
bad teacher
is too close to ad hominem because it refers to your
opinion of
me and utterly bypasses any of my reasoning.

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No, it isn't. You introduced youtself as a topic of
discussion so
you are a legitimate topic of discussion.
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I didn't claim that there be any reasoning, incorrect
or otherwise.
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If you claim I am a bad teacher you must point out what
is wrong with
the lesson otherwise your claim that I am a bad teacher
is essentially
an as hominem attack.

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You are not a teacher, bad or otherwise. That you lack
skills that
happen to be necessary for teaching is obvious from you
postings
here. A teacher needs to understand human psychology but
you don't.
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You may be correct that I am a terrible teacher.
None-the-less Mathematicians might not have very much
understanding
of the link between proof theory and computability.

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Sume mathematicians do have very much understanding of
that. But that
link is not needed for understanding and solving problems
separately
in the two areas.
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When I refer to rejecting an invalid input math would
seem to construe
this as nonsense, where as computability theory would
totally understand.

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People working on computability theory do not understand
"invalid input"
as "impossible input".

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The proof then shows, for any program f that might
determine whether
programs halt, that a "pathological" program g, called with
some input,
can pass its own source and its input to f and then
specifically do the
opposite of what f predicts g will do. No f can exist that
handles this
case, thus showing undecidability.
https://en.wikipedia.org/wiki/Halting_problem#
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So then they must believe that there exists an H that does
correctly
determine the halt status of every input, some inputs are
simply
more difficult than others, no inputs are impossible.

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That "must" is false as it does not follow from anything.
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Sure it does. If there are no "impossible" inputs that entails
that all inputs are possible. When all inputs are possible then
the halting problem proof is wrong.
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*Termination Analyzer H is Not Fooled by Pathological Input D*
https://www.researchgate.net/publication/369971402_Termination_Analyzer_H_is_Not_Fooled_by_Pathological_Input_D
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Everyone that objects to the statement that H(D,D) correctly
determines the halt status of its inputs say that believe
that H(D,D) must report on the behavior of the D(D) that
invokes H(D,D).

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Right, because that IS the definition of a Halt Decider.
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Everyone here takes the definition of a halt decider to be
required to determine the halt status of the program that
invokes this halt decider, knowing full well that the program
that invokes this halt decider IS NOT ITS INPUT.
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All these same people also know the computable functions only
operate on their inputs and are not allowed to consider anything
else.
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Computable functions are the formalized analogue of the
intuitive notion
of algorithms, in the sense that a function is computable if there
exists an algorithm that can do the job of the function, i.e.
given an
input of the function domain it can return the corresponding
output.
https://en.wikipedia.org/wiki/Computable_function
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When the definition of a halt decider contradicts the
definition of
a computable function they can't both be right.

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When the definitions of a term contradicts the definition of
another term
then both of them are wrong. A correct definition does not
contradict
anything other than a different definition of the same term.
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*Wrong*

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That "Wrong" is wrong as it refers to a true statement.
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 >>> then both of them are wrong.
No it only proves that at least one of them are wrong.

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A correct definition cannot contradict any other sentence, including
other defintions as well as any true and false claims. If a "defintion"
contradicts something then it is not really a definition.
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*That is not the way that it works*

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Yes, it is. A correct definition does not claim anything, so it cannot
contradict anything.
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If a pair of existing definitions
contradict each other then at least one of them is incorrect.

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If a definition contradicts anything then it is incorrect.
If both of them contradict something then both are incorrect.
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Are you actually paying attention or just glancing at a few
words and then spouting off something?
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*Here is your reasoning*
Cats are animals
Cats are not animals
therefore Cats are Neither Animals nor Not Animals
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It might
be the one that you thought was correct.

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One should not think it was correct as it is not.
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There are at least two kinds of Tertium Non Datur,
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A xor B
both A and B
neither A nor B
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Notice that it's just Tertium Non Datur about Tertium Non Datur,
and exhausts all possibilities.
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If you replace terms that are so referential in their types,
or aren't, or in consequence otherwise of the entire structure
of relation all of them together, are and aren't, they do
not model each other and it's thusly not a proof, the same.
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You never got around to saying that I am correct.
When a contradiction arises between two expressions
then at most one of them is correct.

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Depends on the logic system.
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Some logic systems allow for two contradictory expressions to both be correct.
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Of course, those logic system have a lot of different rules for how you do logic in them.
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 Language can be a mere game where incoherence is allowed or it
can establish the foundation for {true on the basis of meaning}.
In the latter contradictions prove falsehood.

But there CAN be real meaning even in the presence of "Contradiction".
For instance, take the statements:
Light Behaves like a Particle
Light Behaves like a Wave
These are contradictory, as things acting like a particle do not act like waves.
But it is also true that both sides of the contradiction are TRUE, Light DOES act like a particle, and Light DOES act like a wave, sometimes more the first, and sometimes more the second, and sometimes acts as both at once.
This shows the limitation of trying to work on too simple of a foundation, like the simple meaning of words.
All you are doing is showing that you do not fully understand how logic actually works, and that you mind can only handle the simplest of logical systems, and you presume that is all that can exist.

 

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I.e., to exhaust all possibilities, when possible via induction
to arrive at each and when possible via deduction to detach
from each, and each and every and any and all, for the universal
quantifier at least so many ways, and to arrive at what exists
and what exists uniquely, the existential quantifier exactly
one way, has that what you should do is entirely rely on
a _constructivist_ approach for your own setting, insofar
as _all the ways_ it's arrived at, then also to show for
the other _constructivist_ approach, the quickest way to
the "inductive impasse", then show how deduction arrives
at what cleaves to detach, the separate concerns.
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