MIT Professor Michael Sipser has agreed that the following verbatim
paragraph is correct (he has not agreed to anything else in this paper):

(a) If simulating halt decider H correctly simulates its input D
until H correctly determines that its simulated D would never
stop running unless aborted then
(b) H can abort its simulation of D and correctly report that D
specifies a non-halting sequence of configurations.

01 int D(int (*x)())
02 {
03 int Halt_Status = H(x, x);
04 if (Halt_Status)
05 HERE: goto HERE;
06 return Halt_Status;
07 }
08
09 void main()
10 {
11 H(D,D);
12 }

Here is the sequence when H never aborts it simulation: proving (a)
main() calls H(D,D) that simulates D(D) at line 11
keeps repeating: simulated D(D) calls simulated H(D,D) that simulates
D(D) at line 03 ...

computation that halts…“the Turing machine will halt whenever it enters
a final state” (Linz:1990:234)

*When we focus on the actual behavior of the actual input* we see that D
correctly simulated by H cannot possibly reach past its own line 3 in
any finite number of steps of correct simulation thus never reaches its
own final state and halts whether or not its simulation is ever aborted.

Anything other than the actual behavior of D correctly simulated by H is
irrelevant to the halt status that H(D,D) computes.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 3/16/2023 11:04 AM, olcott wrote:
> MIT Professor Michael Sipser has agreed that the following verbatim
> paragraph is correct (he has not agreed to anything else in this paper):
>
>    (a) If simulating halt decider H correctly simulates its input D
>        until H correctly determines that its simulated D would never
>        stop running unless aborted then
>    (b) H can abort its simulation of D and correctly report that D
>        specifies a non-halting sequence of configurations.
>
> 01 int D(int (*x)())
> 02 {
> 03   int Halt_Status = H(x, x);
> 04   if (Halt_Status)
> 05     HERE: goto HERE;
> 06   return Halt_Status;
> 07 }
> 08
> 09 void main()
> 10 {
> 11   H(D,D);
> 12 }
>
> Here is the sequence when H never aborts it simulation: proving (a)
>   main() calls H(D,D) that simulates D(D) at line 11
>   keeps repeating: simulated D(D) calls simulated H(D,D) that simulates
> D(D) at line 03 ...
>
> computation that halts…“the Turing machine will halt whenever it enters
> a final state” (Linz:1990:234)
>
> *When we focus on the actual behavior of the actual input* we see that D
> correctly simulated by H cannot possibly reach past its own line 3 in
> any finite number of steps of correct simulation thus never reaches its
> own final state and halts whether or not its simulation is ever aborted.
>
> Anything other than the actual behavior of D correctly simulated by H is
> irrelevant to the halt status that H(D,D) computes.
>

Anything other that the behavior of D correctly simulated by H is
irrelevant because D correctly simulated by H is the only behavior
that H can see.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 3/16/2023 12:46 PM, Fritz Feldhase wrote:
> On Thursday, March 16, 2023 at 5:27:38 PM UTC+1, olcott wrote:
>
>> Anything other than the [actual] behavior of D [called with input D] is
>> irrelevant because [the actual behavior of D called with input D is
>> what we are interested in]
>
> Exactly!

01 int D(int (*x)())
02 {
03 int Halt_Status = H(x, x);
04 if (Halt_Status)
05 HERE: goto HERE;
06 return Halt_Status;
07 }
08
09 void main()
10 {
11 H(D,D);
12 }

Here is the sequence when H never aborts it simulation:
main() calls H(D,D) that simulates D(D) at line 11
keeps repeating: simulated D(D) calls simulated H(D,D) that simulates
D(D) at line 03 ... thus never reaching line 06 and halting.

Try and explain the detailed steps of exactly how H can see the behavior
of D(D) that is not its input on the basis of H(D,D) that is its input.

Failure to respond with every detail of these steps will be construed
as an admission that this cannot be done.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 3/16/23 12:04 PM, olcott wrote:
> MIT Professor Michael Sipser has agreed that the following verbatim
> paragraph is correct (he has not agreed to anything else in this paper):
>
>    (a) If simulating halt decider H correctly simulates its input D
>        until H correctly determines that its simulated D would never
>        stop running unless aborted then
>    (b) H can abort its simulation of D and correctly report that D
>        specifies a non-halting sequence of configurations.
>
> 01 int D(int (*x)())
> 02 {
> 03   int Halt_Status = H(x, x);
> 04   if (Halt_Status)
> 05     HERE: goto HERE;
> 06   return Halt_Status;
> 07 }
> 08
> 09 void main()
> 10 {
> 11   H(D,D);
> 12 }
>
> Here is the sequence when H never aborts it simulation: proving (a)
>   main() calls H(D,D) that simulates D(D) at line 11
>   keeps repeating: simulated D(D) calls simulated H(D,D) that simulates
> D(D) at line 03 ...
>

> computation that halts…“the Turing machine will halt whenever it enters
> a final state” (Linz:1990:234)

Right, so a "D" built on an "H" that doesn't abort will not halt. But
since THE H you are presenting DOES abort, we can see that THE D that is
build on it will halt.

You are just answering about something that isn't the input to H.

>
> *When we focus on the actual behavior of the actual input* we see that D
> correctly simulated by H cannot possibly reach past its own line 3 in
> any finite number of steps of correct simulation thus never reaches its
> own final state and halts whether or not its simulation is ever aborted.

And the input D INCLUDES the H that it calls, as programs include ALL of
their code, even "library" or "operating system".

Since that H aborts its simulation, and thus will return 0 to D, causing
D to halt, THE correct simulation of it must do so to, so H is proven

>
> Anything other than the actual behavior of D correctly simulated by H is
> irrelevant to the halt status that H(D,D) computes.

Nope, anthing other then the actual behavior of the machine D is
irrelevent BY THE DEFINITION.

Remember, the definition you quoted side "THE TURING MACHINE", not the
simulation by the decider.

You are just proving you are a liar.
>

On 3/16/2023 1:19 PM, olcott wrote:
> On 3/16/2023 12:46 PM, Fritz Feldhase wrote:
>> On Thursday, March 16, 2023 at 5:27:38 PM UTC+1, olcott wrote:
>>
>>> Anything other than the [actual] behavior of D [called with input D] is
>>> irrelevant because [the actual behavior of D called with input D is
>>> what we are interested in]
>>
>> Exactly!
>
> 01 int D(int (*x)())
> 02 {
> 03   int Halt_Status = H(x, x);
> 04   if (Halt_Status)
> 05     HERE: goto HERE;
> 06   return Halt_Status;
> 07 }
> 08
> 09 void main()
> 10 {
> 11   H(D,D);
> 12 }
>
> Here is the sequence when H never aborts it simulation:
>   main() calls H(D,D) that simulates D(D) at line 11
>   keeps repeating: simulated D(D) calls simulated H(D,D) that simulates
> D(D) at line 03 ...  thus never reaching line 06 and halting.
>
> Try and explain the detailed steps of exactly how H can see the behavior
> of D(D) that is not its input on the basis of H(D,D) that is its input.
>
> Failure to respond with every detail of these steps will be construed
> as an admission that this cannot be done.
>

When halting is defined as reaching the final state at line 6 and H
correctly predicts that D correctly simulated by every H that can
possibly exist will never halt then any element of the infinite set of
every H that can possibly exist is correct to reject D as non-halting.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 3/16/23 6:50 PM, olcott wrote:
> On 3/16/2023 1:19 PM, olcott wrote:
>> On 3/16/2023 12:46 PM, Fritz Feldhase wrote:
>>> On Thursday, March 16, 2023 at 5:27:38 PM UTC+1, olcott wrote:
>>>
>>>> Anything other than the [actual] behavior of D [called with input D] is
>>>> irrelevant because [the actual behavior of D called with input D is
>>>> what we are interested in]
>>>
>>> Exactly!
>>
>> 01 int D(int (*x)())
>> 02 {
>> 03   int Halt_Status = H(x, x);
>> 04   if (Halt_Status)
>> 05     HERE: goto HERE;
>> 06   return Halt_Status;
>> 07 }
>> 08
>> 09 void main()
>> 10 {
>> 11   H(D,D);
>> 12 }
>>
>> Here is the sequence when H never aborts it simulation:
>>    main() calls H(D,D) that simulates D(D) at line 11
>>    keeps repeating: simulated D(D) calls simulated H(D,D) that
>> simulates D(D) at line 03 ...  thus never reaching line 06 and halting.
>>
>> Try and explain the detailed steps of exactly how H can see the behavior
>> of D(D) that is not its input on the basis of H(D,D) that is its input.
>>
>> Failure to respond with every detail of these steps will be construed
>> as an admission that this cannot be done.
>>
>
> When halting is defined as reaching the final state at line 6 and H
> correctly predicts that D correctly simulated by every H that can
> possibly exist will never halt then any element of the infinite set of
> every H that can possibly exist is correct to reject D as non-halting.
>

So you admit to not working on the ACTUAL halting problem, as that isn't
how Halting is actually defined.

Or, are you just admitting that you are a liar about what you are doing?

Remember, Halting is DEFINED as the Behavior of the ACTUAL MACHINE, not
a "simulation of it".

On 3/16/2023 5:50 PM, olcott wrote:
> On 3/16/2023 1:19 PM, olcott wrote:
>> On 3/16/2023 12:46 PM, Fritz Feldhase wrote:
>>> On Thursday, March 16, 2023 at 5:27:38 PM UTC+1, olcott wrote:
>>>
>>>> Anything other than the [actual] behavior of D [called with input D] is
>>>> irrelevant because [the actual behavior of D called with input D is
>>>> what we are interested in]
>>>
>>> Exactly!
>>
>> 01 int D(int (*x)())
>> 02 {
>> 03   int Halt_Status = H(x, x);
>> 04   if (Halt_Status)
>> 05     HERE: goto HERE;
>> 06   return Halt_Status;
>> 07 }
>> 08
>> 09 void main()
>> 10 {
>> 11   H(D,D);
>> 12 }
>>
>> Here is the sequence when H never aborts it simulation:
>>    main() calls H(D,D) that simulates D(D) at line 11
>>    keeps repeating: simulated D(D) calls simulated H(D,D) that
>> simulates D(D) at line 03 ...  thus never reaching line 06 and halting.
>>
>> Try and explain the detailed steps of exactly how H can see the behavior
>> of D(D) that is not its input on the basis of H(D,D) that is its input.
>>
>> Failure to respond with every detail of these steps will be construed
>> as an admission that this cannot be done.
>>
>
> When halting is defined as reaching the final state at line 6 and H
> correctly predicts that D correctly simulated by every H that can
> possibly exist will never halt then any element of the infinite set of
> every H that can possibly exist is correct to reject D as non-halting.
>

When a decision problem is defined as what yes/no answer can Bill say
that correctly predicts the answer that Harry will provide when Harry
makes sure to always provide the opposite of whatever Bill predicts this
"decision problem" is equivalent to correctly determining whether the
Liar Paradox is true or false: "This sentence is not true".

*The diagonal argument of the halting theorem has this exact same form*

My work on the Halting Problem, Gödel's 1931 Incompleteness theorem,
the Tarski Undefinability theorem and the Liar Paradox is actually work
on the philosophical foundations of the notion of analytical truth
itself.

People that merely memorize what textbooks say don't have a clue about
these things. They are only capable of mindlessly conforming to dogma.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 3/16/23 7:34 PM, olcott wrote:
> On 3/16/2023 5:50 PM, olcott wrote:
>> On 3/16/2023 1:19 PM, olcott wrote:
>>> On 3/16/2023 12:46 PM, Fritz Feldhase wrote:
>>>> On Thursday, March 16, 2023 at 5:27:38 PM UTC+1, olcott wrote:
>>>>
>>>>> Anything other than the [actual] behavior of D [called with input
>>>>> D] is
>>>>> irrelevant because [the actual behavior of D called with input D is
>>>>> what we are interested in]
>>>>
>>>> Exactly!
>>>
>>> 01 int D(int (*x)())
>>> 02 {
>>> 03   int Halt_Status = H(x, x);
>>> 04   if (Halt_Status)
>>> 05     HERE: goto HERE;
>>> 06   return Halt_Status;
>>> 07 }
>>> 08
>>> 09 void main()
>>> 10 {
>>> 11   H(D,D);
>>> 12 }
>>>
>>> Here is the sequence when H never aborts it simulation:
>>>    main() calls H(D,D) that simulates D(D) at line 11
>>>    keeps repeating: simulated D(D) calls simulated H(D,D) that
>>> simulates D(D) at line 03 ...  thus never reaching line 06 and halting.
>>>
>>> Try and explain the detailed steps of exactly how H can see the behavior
>>> of D(D) that is not its input on the basis of H(D,D) that is its input.
>>>
>>> Failure to respond with every detail of these steps will be construed
>>> as an admission that this cannot be done.
>>>
>>
>> When halting is defined as reaching the final state at line 6 and H
>> correctly predicts that D correctly simulated by every H that can
>> possibly exist will never halt then any element of the infinite set of
>> every H that can possibly exist is correct to reject D as non-halting.
>>
>
> When a decision problem is defined as what yes/no answer can Bill say
> that correctly predicts the answer that Harry will provide when Harry
> makes sure to always provide the opposite of whatever Bill predicts this
> "decision problem" is equivalent to correctly determining whether the
> Liar Paradox is true or false: "This sentence is not true".

But that isn't the issue.

Giove a definition of what H actually does, there IS a correct answer
for the halting question of D(D). Thus it ISN'T the Liar's Paradox

>
> *The diagonal argument of the halting theorem has this exact same form*

The diagonal arguement is a method of PROOF, not of definition.

Sipser H has a simple job, if the machine will accept its input, it
answers Accept, and if it will reject the input, or fail to answer, it
answers Reject.

Sipser D is a simple machine that will ALWAYS answer as long as the H
gives an answer (which it must), so the "fail to answer" clause can
never happen.

Your arguement about H getting caught in a recursive loop is just an
admission that you H will fail, or you built D on the wrong H.

>
> My work on the Halting Problem, Gödel's 1931 Incompleteness theorem,
> the Tarski Undefinability theorem and the Liar Paradox is actually work
> on the philosophical foundations of the notion of analytical truth
> itself.
>

So, why aren't you talking about that fundamental foundation of
analytical truth?

Instead, you break your own rules as in the field, there ARE defined
"Truth Makers" and "Rules of Inference" so you can't change them and be
in the field.

I think the problem is you just don't understand the basics well enough
to actually talk about them.

> People that merely memorize what textbooks say don't have a clue about
> these things. They are only capable of mindlessly conforming to dogma.
>

No, people are quoting the RULES that apply to the problems.

You aren't ALLOWED to change the defintion of a FORMAL SYSTEM and remain
in it.

You are just showing you don't understand the basics of logic.

If you want to disagree with the foundation, talk about the foundation,
not show that there is something wrong with the penthouse.

This is your fundamental problem.

On 3/16/2023 6:34 PM, olcott wrote:
> On 3/16/2023 5:50 PM, olcott wrote:
>> On 3/16/2023 1:19 PM, olcott wrote:
>>> On 3/16/2023 12:46 PM, Fritz Feldhase wrote:
>>>> On Thursday, March 16, 2023 at 5:27:38 PM UTC+1, olcott wrote:
>>>>
>>>>> Anything other than the [actual] behavior of D [called with input
>>>>> D] is
>>>>> irrelevant because [the actual behavior of D called with input D is
>>>>> what we are interested in]
>>>>
>>>> Exactly!
>>>
>>> 01 int D(int (*x)())
>>> 02 {
>>> 03   int Halt_Status = H(x, x);
>>> 04   if (Halt_Status)
>>> 05     HERE: goto HERE;
>>> 06   return Halt_Status;
>>> 07 }
>>> 08
>>> 09 void main()
>>> 10 {
>>> 11   H(D,D);
>>> 12 }
>>>
>>> Here is the sequence when H never aborts it simulation:
>>>    main() calls H(D,D) that simulates D(D) at line 11
>>>    keeps repeating: simulated D(D) calls simulated H(D,D) that
>>> simulates D(D) at line 03 ...  thus never reaching line 06 and halting.
>>>
>>> Try and explain the detailed steps of exactly how H can see the behavior
>>> of D(D) that is not its input on the basis of H(D,D) that is its input.
>>>
>>> Failure to respond with every detail of these steps will be construed
>>> as an admission that this cannot be done.
>>>
>>
>> When halting is defined as reaching the final state at line 6 and H
>> correctly predicts that D correctly simulated by every H that can
>> possibly exist will never halt then any element of the infinite set of
>> every H that can possibly exist is correct to reject D as non-halting.
>>
>
> When a decision problem is defined as what yes/no answer can Bill say
> that correctly predicts the answer that Harry will provide when Harry
> makes sure to always provide the opposite of whatever Bill predicts this
> "decision problem" is equivalent to correctly determining whether the
> Liar Paradox is true or false: "This sentence is not true".
>
> *The diagonal argument of the halting theorem has this exact same form*
>
> My work on the Halting Problem, Gödel's 1931 Incompleteness theorem,
> the Tarski Undefinability theorem and the Liar Paradox is actually work
> on the philosophical foundations of the notion of analytical truth
> itself.
>
> People that merely memorize what textbooks say don't have a clue about
> these things. They are only capable of mindlessly conforming to dogma.
>

When there are actual errors in the foundation of the notion of
analytical truth these same errors are carried over to mathematics,
logic, and computer science with no one that merely follows the rules as
given ever noticing the inconsistency and incoherence.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 3/16/23 9:24 PM, olcott wrote:
> On 3/16/2023 6:34 PM, olcott wrote:
>> On 3/16/2023 5:50 PM, olcott wrote:
>>> On 3/16/2023 1:19 PM, olcott wrote:
>>>> On 3/16/2023 12:46 PM, Fritz Feldhase wrote:
>>>>> On Thursday, March 16, 2023 at 5:27:38 PM UTC+1, olcott wrote:
>>>>>
>>>>>> Anything other than the [actual] behavior of D [called with input
>>>>>> D] is
>>>>>> irrelevant because [the actual behavior of D called with input D is
>>>>>> what we are interested in]
>>>>>
>>>>> Exactly!
>>>>
>>>> 01 int D(int (*x)())
>>>> 02 {
>>>> 03   int Halt_Status = H(x, x);
>>>> 04   if (Halt_Status)
>>>> 05     HERE: goto HERE;
>>>> 06   return Halt_Status;
>>>> 07 }
>>>> 08
>>>> 09 void main()
>>>> 10 {
>>>> 11   H(D,D);
>>>> 12 }
>>>>
>>>> Here is the sequence when H never aborts it simulation:
>>>>    main() calls H(D,D) that simulates D(D) at line 11
>>>>    keeps repeating: simulated D(D) calls simulated H(D,D) that
>>>> simulates D(D) at line 03 ...  thus never reaching line 06 and halting.
>>>>
>>>> Try and explain the detailed steps of exactly how H can see the
>>>> behavior
>>>> of D(D) that is not its input on the basis of H(D,D) that is its input.
>>>>
>>>> Failure to respond with every detail of these steps will be construed
>>>> as an admission that this cannot be done.
>>>>
>>>
>>> When halting is defined as reaching the final state at line 6 and H
>>> correctly predicts that D correctly simulated by every H that can
>>> possibly exist will never halt then any element of the infinite set of
>>> every H that can possibly exist is correct to reject D as non-halting.
>>>
>>
>> When a decision problem is defined as what yes/no answer can Bill say
>> that correctly predicts the answer that Harry will provide when Harry
>> makes sure to always provide the opposite of whatever Bill predicts this
>> "decision problem" is equivalent to correctly determining whether the
>> Liar Paradox is true or false: "This sentence is not true".
>>
>> *The diagonal argument of the halting theorem has this exact same form*
>>
>> My work on the Halting Problem, Gödel's 1931 Incompleteness theorem,
>> the Tarski Undefinability theorem and the Liar Paradox is actually work
>> on the philosophical foundations of the notion of analytical truth
>> itself.
>>
>> People that merely memorize what textbooks say don't have a clue about
>> these things. They are only capable of mindlessly conforming to dogma.
>>
>
> When there are actual errors in the foundation of the notion of
> analytical truth these same errors are carried over to mathematics,
> logic, and computer science with no one that merely follows the rules as
> given ever noticing the inconsistency and incoherence.
>
>
>

So, if the problem is in the Foundation, you work on the Foundation, not
the attic.

You can't touch the foundation while in the attic.

That you can't understand that makes it seem like YOU don't notice your
inconsistency and incoherence.

I've told you this before, if you want to change the foundation, sit
down a fully define what you new foundation is and then start to build
up from it. You can't just assume that you can change the foundation and
it won't change anything between it and the attic, because it most
likely will, and until you work your way up, you don't know what that
will look like.

But, based on how many flaws you put into your arguments, I don't think
you know enough to do that, or even to actually have a clear idea what
your foundations should be.

On 3/16/2023 8:24 PM, olcott wrote:
> On 3/16/2023 6:34 PM, olcott wrote:
>> On 3/16/2023 5:50 PM, olcott wrote:
>>> On 3/16/2023 1:19 PM, olcott wrote:
>>>> On 3/16/2023 12:46 PM, Fritz Feldhase wrote:
>>>>> On Thursday, March 16, 2023 at 5:27:38 PM UTC+1, olcott wrote:
>>>>>
>>>>>> Anything other than the [actual] behavior of D [called with input
>>>>>> D] is
>>>>>> irrelevant because [the actual behavior of D called with input D is
>>>>>> what we are interested in]
>>>>>
>>>>> Exactly!
>>>>
>>>> 01 int D(int (*x)())
>>>> 02 {
>>>> 03   int Halt_Status = H(x, x);
>>>> 04   if (Halt_Status)
>>>> 05     HERE: goto HERE;
>>>> 06   return Halt_Status;
>>>> 07 }
>>>> 08
>>>> 09 void main()
>>>> 10 {
>>>> 11   H(D,D);
>>>> 12 }
>>>>
>>>> Here is the sequence when H never aborts it simulation:
>>>>    main() calls H(D,D) that simulates D(D) at line 11
>>>>    keeps repeating: simulated D(D) calls simulated H(D,D) that
>>>> simulates D(D) at line 03 ...  thus never reaching line 06 and halting.
>>>>
>>>> Try and explain the detailed steps of exactly how H can see the
>>>> behavior
>>>> of D(D) that is not its input on the basis of H(D,D) that is its input.
>>>>
>>>> Failure to respond with every detail of these steps will be construed
>>>> as an admission that this cannot be done.
>>>>
>>>
>>> When halting is defined as reaching the final state at line 6 and H
>>> correctly predicts that D correctly simulated by every H that can
>>> possibly exist will never halt then any element of the infinite set of
>>> every H that can possibly exist is correct to reject D as non-halting.
>>>
>>
>> When a decision problem is defined as what yes/no answer can Bill say
>> that correctly predicts the answer that Harry will provide when Harry
>> makes sure to always provide the opposite of whatever Bill predicts this
>> "decision problem" is equivalent to correctly determining whether the
>> Liar Paradox is true or false: "This sentence is not true".
>>
>> *The diagonal argument of the halting theorem has this exact same form*
>>
>> My work on the Halting Problem, Gödel's 1931 Incompleteness theorem,
>> the Tarski Undefinability theorem and the Liar Paradox is actually work
>> on the philosophical foundations of the notion of analytical truth
>> itself.
>>
>> People that merely memorize what textbooks say don't have a clue about
>> these things. They are only capable of mindlessly conforming to dogma.
>>
>
> When there are actual errors in the foundation of the notion of
> analytical truth these same errors are carried over to mathematics,
> logic, and computer science with no one that merely follows the rules as
> given ever noticing the inconsistency and incoherence.

The foundation of the notion of analytic true can be so succinctly
stated that it can be far too easily misconstrued as simplistic.

Expression X of language L is true iff there is a semantic connection
from expressions of language L that are stipulated as true to X
otherwise X is untrue. Untrue does not entail false.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 3/16/2023 9:02 PM, olcott wrote:
> On 3/16/2023 8:24 PM, olcott wrote:
>> On 3/16/2023 6:34 PM, olcott wrote:
>>> On 3/16/2023 5:50 PM, olcott wrote:
>>>> On 3/16/2023 1:19 PM, olcott wrote:
>>>>> On 3/16/2023 12:46 PM, Fritz Feldhase wrote:
>>>>>> On Thursday, March 16, 2023 at 5:27:38 PM UTC+1, olcott wrote:
>>>>>>
>>>>>>> Anything other than the [actual] behavior of D [called with input
>>>>>>> D] is
>>>>>>> irrelevant because [the actual behavior of D called with input D is
>>>>>>> what we are interested in]
>>>>>>
>>>>>> Exactly!
>>>>>
>>>>> 01 int D(int (*x)())
>>>>> 02 {
>>>>> 03   int Halt_Status = H(x, x);
>>>>> 04   if (Halt_Status)
>>>>> 05     HERE: goto HERE;
>>>>> 06   return Halt_Status;
>>>>> 07 }
>>>>> 08
>>>>> 09 void main()
>>>>> 10 {
>>>>> 11   H(D,D);
>>>>> 12 }
>>>>>
>>>>> Here is the sequence when H never aborts it simulation:
>>>>>    main() calls H(D,D) that simulates D(D) at line 11
>>>>>    keeps repeating: simulated D(D) calls simulated H(D,D) that
>>>>> simulates D(D) at line 03 ...  thus never reaching line 06 and
>>>>> halting.
>>>>>
>>>>> Try and explain the detailed steps of exactly how H can see the
>>>>> behavior
>>>>> of D(D) that is not its input on the basis of H(D,D) that is its
>>>>> input.
>>>>>
>>>>> Failure to respond with every detail of these steps will be construed
>>>>> as an admission that this cannot be done.
>>>>>
>>>>
>>>> When halting is defined as reaching the final state at line 6 and H
>>>> correctly predicts that D correctly simulated by every H that can
>>>> possibly exist will never halt then any element of the infinite set of
>>>> every H that can possibly exist is correct to reject D as non-halting.
>>>>
>>>
>>> When a decision problem is defined as what yes/no answer can Bill say
>>> that correctly predicts the answer that Harry will provide when Harry
>>> makes sure to always provide the opposite of whatever Bill predicts this
>>> "decision problem" is equivalent to correctly determining whether the
>>> Liar Paradox is true or false: "This sentence is not true".
>>>
>>> *The diagonal argument of the halting theorem has this exact same form*
>>>
>>> My work on the Halting Problem, Gödel's 1931 Incompleteness theorem,
>>> the Tarski Undefinability theorem and the Liar Paradox is actually work
>>> on the philosophical foundations of the notion of analytical truth
>>> itself.
>>>
>>> People that merely memorize what textbooks say don't have a clue about
>>> these things. They are only capable of mindlessly conforming to dogma.
>>>
>>
>> When there are actual errors in the foundation of the notion of
>> analytical truth these same errors are carried over to mathematics,
>> logic, and computer science with no one that merely follows the rules as
>> given ever noticing the inconsistency and incoherence.
>
> The foundation of the notion of analytic true can be so succinctly
> stated that it can be far too easily misconstrued as simplistic.
>
> Expression X of language L is true iff there is a semantic connection
> from expressions of language L that are stipulated as true to X
> otherwise X is untrue. Untrue does not entail false.
>

The above terse little paragraph totally refutes the Tarski
undefinability theorem.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 3/16/23 10:02 PM, olcott wrote:
> On 3/16/2023 8:24 PM, olcott wrote:
>> On 3/16/2023 6:34 PM, olcott wrote:
>>> On 3/16/2023 5:50 PM, olcott wrote:
>>>> On 3/16/2023 1:19 PM, olcott wrote:
>>>>> On 3/16/2023 12:46 PM, Fritz Feldhase wrote:
>>>>>> On Thursday, March 16, 2023 at 5:27:38 PM UTC+1, olcott wrote:
>>>>>>
>>>>>>> Anything other than the [actual] behavior of D [called with input
>>>>>>> D] is
>>>>>>> irrelevant because [the actual behavior of D called with input D is
>>>>>>> what we are interested in]
>>>>>>
>>>>>> Exactly!
>>>>>
>>>>> 01 int D(int (*x)())
>>>>> 02 {
>>>>> 03   int Halt_Status = H(x, x);
>>>>> 04   if (Halt_Status)
>>>>> 05     HERE: goto HERE;
>>>>> 06   return Halt_Status;
>>>>> 07 }
>>>>> 08
>>>>> 09 void main()
>>>>> 10 {
>>>>> 11   H(D,D);
>>>>> 12 }
>>>>>
>>>>> Here is the sequence when H never aborts it simulation:
>>>>>    main() calls H(D,D) that simulates D(D) at line 11
>>>>>    keeps repeating: simulated D(D) calls simulated H(D,D) that
>>>>> simulates D(D) at line 03 ...  thus never reaching line 06 and
>>>>> halting.
>>>>>
>>>>> Try and explain the detailed steps of exactly how H can see the
>>>>> behavior
>>>>> of D(D) that is not its input on the basis of H(D,D) that is its
>>>>> input.
>>>>>
>>>>> Failure to respond with every detail of these steps will be construed
>>>>> as an admission that this cannot be done.
>>>>>
>>>>
>>>> When halting is defined as reaching the final state at line 6 and H
>>>> correctly predicts that D correctly simulated by every H that can
>>>> possibly exist will never halt then any element of the infinite set of
>>>> every H that can possibly exist is correct to reject D as non-halting.
>>>>
>>>
>>> When a decision problem is defined as what yes/no answer can Bill say
>>> that correctly predicts the answer that Harry will provide when Harry
>>> makes sure to always provide the opposite of whatever Bill predicts this
>>> "decision problem" is equivalent to correctly determining whether the
>>> Liar Paradox is true or false: "This sentence is not true".
>>>
>>> *The diagonal argument of the halting theorem has this exact same form*
>>>
>>> My work on the Halting Problem, Gödel's 1931 Incompleteness theorem,
>>> the Tarski Undefinability theorem and the Liar Paradox is actually work
>>> on the philosophical foundations of the notion of analytical truth
>>> itself.
>>>
>>> People that merely memorize what textbooks say don't have a clue about
>>> these things. They are only capable of mindlessly conforming to dogma.
>>>
>>
>> When there are actual errors in the foundation of the notion of
>> analytical truth these same errors are carried over to mathematics,
>> logic, and computer science with no one that merely follows the rules as
>> given ever noticing the inconsistency and incoherence.
>
> The foundation of the notion of analytic true can be so succinctly
> stated that it can be far too easily misconstrued as simplistic.
>
> Expression X of language L is true iff there is a semantic connection
> from expressions of language L that are stipulated as true to X
> otherwise X is untrue. Untrue does not entail false.
>

So, starting from that definition, show what your logic system can do.

Note, since Untrue does not entail false, this seems to be a tri-state
(or higher) logic system, what are ALL the rules for working with this?

Remember, you can't use any thing that was proven in the old system, you
have to show you can derive it with your logic.

I think your problem is you don't understand the basics well enough to
even know what you need to do.

Do anything change with the basic rules of logic?
(You have stated problem with the rules of inference)

Can you establish categorical logic with this definition?

Does induction work in with this notion of logic?

Can you establish something similar to Mathematics with your logic?

What changes?

(Something needs to, or Godel's proof still holds)

Can you show your system is actually USEFUL?

On 3/16/23 10:11 PM, olcott wrote:
> On 3/16/2023 9:02 PM, olcott wrote:
>> On 3/16/2023 8:24 PM, olcott wrote:
>>> On 3/16/2023 6:34 PM, olcott wrote:
>>>> On 3/16/2023 5:50 PM, olcott wrote:
>>>>> On 3/16/2023 1:19 PM, olcott wrote:
>>>>>> On 3/16/2023 12:46 PM, Fritz Feldhase wrote:
>>>>>>> On Thursday, March 16, 2023 at 5:27:38 PM UTC+1, olcott wrote:
>>>>>>>
>>>>>>>> Anything other than the [actual] behavior of D [called with
>>>>>>>> input D] is
>>>>>>>> irrelevant because [the actual behavior of D called with input D is
>>>>>>>> what we are interested in]
>>>>>>>
>>>>>>> Exactly!
>>>>>>
>>>>>> 01 int D(int (*x)())
>>>>>> 02 {
>>>>>> 03   int Halt_Status = H(x, x);
>>>>>> 04   if (Halt_Status)
>>>>>> 05     HERE: goto HERE;
>>>>>> 06   return Halt_Status;
>>>>>> 07 }
>>>>>> 08
>>>>>> 09 void main()
>>>>>> 10 {
>>>>>> 11   H(D,D);
>>>>>> 12 }
>>>>>>
>>>>>> Here is the sequence when H never aborts it simulation:
>>>>>>    main() calls H(D,D) that simulates D(D) at line 11
>>>>>>    keeps repeating: simulated D(D) calls simulated H(D,D) that
>>>>>> simulates D(D) at line 03 ...  thus never reaching line 06 and
>>>>>> halting.
>>>>>>
>>>>>> Try and explain the detailed steps of exactly how H can see the
>>>>>> behavior
>>>>>> of D(D) that is not its input on the basis of H(D,D) that is its
>>>>>> input.
>>>>>>
>>>>>> Failure to respond with every detail of these steps will be construed
>>>>>> as an admission that this cannot be done.
>>>>>>
>>>>>
>>>>> When halting is defined as reaching the final state at line 6 and H
>>>>> correctly predicts that D correctly simulated by every H that can
>>>>> possibly exist will never halt then any element of the infinite set of
>>>>> every H that can possibly exist is correct to reject D as non-halting.
>>>>>
>>>>
>>>> When a decision problem is defined as what yes/no answer can Bill say
>>>> that correctly predicts the answer that Harry will provide when Harry
>>>> makes sure to always provide the opposite of whatever Bill predicts
>>>> this
>>>> "decision problem" is equivalent to correctly determining whether the
>>>> Liar Paradox is true or false: "This sentence is not true".
>>>>
>>>> *The diagonal argument of the halting theorem has this exact same form*
>>>>
>>>> My work on the Halting Problem, Gödel's 1931 Incompleteness theorem,
>>>> the Tarski Undefinability theorem and the Liar Paradox is actually work
>>>> on the philosophical foundations of the notion of analytical truth
>>>> itself.
>>>>
>>>> People that merely memorize what textbooks say don't have a clue about
>>>> these things. They are only capable of mindlessly conforming to dogma.
>>>>
>>>
>>> When there are actual errors in the foundation of the notion of
>>> analytical truth these same errors are carried over to mathematics,
>>> logic, and computer science with no one that merely follows the rules as
>>> given ever noticing the inconsistency and incoherence.
>>
>> The foundation of the notion of analytic true can be so succinctly
>> stated that it can be far too easily misconstrued as simplistic.
>>
>> Expression X of language L is true iff there is a semantic connection
>> from expressions of language L that are stipulated as true to X
>> otherwise X is untrue. Untrue does not entail false.
>>
>
> The above terse little paragraph totally refutes the Tarski
> undefinability theorem.
>

Nope, because you don't understand what Tarksi meant by his statement.

On 3/16/2023 9:02 PM, olcott wrote:
> On 3/16/2023 8:24 PM, olcott wrote:
>> On 3/16/2023 6:34 PM, olcott wrote:
>>> On 3/16/2023 5:50 PM, olcott wrote:
>>>> On 3/16/2023 1:19 PM, olcott wrote:
>>>>> On 3/16/2023 12:46 PM, Fritz Feldhase wrote:
>>>>>> On Thursday, March 16, 2023 at 5:27:38 PM UTC+1, olcott wrote:
>>>>>>
>>>>>>> Anything other than the [actual] behavior of D [called with input
>>>>>>> D] is
>>>>>>> irrelevant because [the actual behavior of D called with input D is
>>>>>>> what we are interested in]
>>>>>>
>>>>>> Exactly!
>>>>>
>>>>> 01 int D(int (*x)())
>>>>> 02 {
>>>>> 03   int Halt_Status = H(x, x);
>>>>> 04   if (Halt_Status)
>>>>> 05     HERE: goto HERE;
>>>>> 06   return Halt_Status;
>>>>> 07 }
>>>>> 08
>>>>> 09 void main()
>>>>> 10 {
>>>>> 11   H(D,D);
>>>>> 12 }
>>>>>
>>>>> Here is the sequence when H never aborts it simulation:
>>>>>    main() calls H(D,D) that simulates D(D) at line 11
>>>>>    keeps repeating: simulated D(D) calls simulated H(D,D) that
>>>>> simulates D(D) at line 03 ...  thus never reaching line 06 and
>>>>> halting.
>>>>>
>>>>> Try and explain the detailed steps of exactly how H can see the
>>>>> behavior
>>>>> of D(D) that is not its input on the basis of H(D,D) that is its
>>>>> input.
>>>>>
>>>>> Failure to respond with every detail of these steps will be construed
>>>>> as an admission that this cannot be done.
>>>>>
>>>>
>>>> When halting is defined as reaching the final state at line 6 and H
>>>> correctly predicts that D correctly simulated by every H that can
>>>> possibly exist will never halt then any element of the infinite set of
>>>> every H that can possibly exist is correct to reject D as non-halting.
>>>>
>>>
>>> When a decision problem is defined as what yes/no answer can Bill say
>>> that correctly predicts the answer that Harry will provide when Harry
>>> makes sure to always provide the opposite of whatever Bill predicts this
>>> "decision problem" is equivalent to correctly determining whether the
>>> Liar Paradox is true or false: "This sentence is not true".
>>>
>>> *The diagonal argument of the halting theorem has this exact same form*
>>>
>>> My work on the Halting Problem, Gödel's 1931 Incompleteness theorem,
>>> the Tarski Undefinability theorem and the Liar Paradox is actually work
>>> on the philosophical foundations of the notion of analytical truth
>>> itself.
>>>
>>> People that merely memorize what textbooks say don't have a clue about
>>> these things. They are only capable of mindlessly conforming to dogma.
>>>
>>
>> When there are actual errors in the foundation of the notion of
>> analytical truth these same errors are carried over to mathematics,
>> logic, and computer science with no one that merely follows the rules as
>> given ever noticing the inconsistency and incoherence.
>
> The foundation of the notion of analytic true can be so succinctly
> stated that it can be far too easily misconstrued as simplistic.
>
> Expression X of language L is true iff there is a semantic connection
> from expressions of language L that are stipulated as true to X
> otherwise X is untrue. Untrue does not entail false.
>

This system is the foundation of all other systems I have not
worked out all the details.

My system can handle any expression of language thus it screens out
semantic gibberish.

Provable required the same semantic connection from the premises to the
conclusion, yet the premises need not be true.

The conclusion must be a semantically necessary consequence of its
premises. Some things stay the same A & B proves A at the level of
propositional variables is still valid.

We still need to have some way to define the meaning of terms so that
semantics can become much deeper. Syllogisms tend to use natural
language for this.

Categorical logic is fine the way that it is.

Everything that supports the principle of explosion is abolished by the
semantic connection requirement.

Implication may be abolished or changed.
We may overload this □⊨ as the semantically necessary operator.

(a) □⊨ (b) (b) is a semantically necessary consequence of (a)

I don't see any definite reason to change much of mathematics.

Godels proof can no longer possibly exist because provable is an aspect
of true there can be no true and unprovable.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 3/16/2023 9:11 PM, olcott wrote:
> On 3/16/2023 9:02 PM, olcott wrote:
>> On 3/16/2023 8:24 PM, olcott wrote:
>>> On 3/16/2023 6:34 PM, olcott wrote:
>>>> On 3/16/2023 5:50 PM, olcott wrote:
>>>>> On 3/16/2023 1:19 PM, olcott wrote:
>>>>>> On 3/16/2023 12:46 PM, Fritz Feldhase wrote:
>>>>>>> On Thursday, March 16, 2023 at 5:27:38 PM UTC+1, olcott wrote:
>>>>>>>
>>>>>>>> Anything other than the [actual] behavior of D [called with
>>>>>>>> input D] is
>>>>>>>> irrelevant because [the actual behavior of D called with input D is
>>>>>>>> what we are interested in]
>>>>>>>
>>>>>>> Exactly!
>>>>>>
>>>>>> 01 int D(int (*x)())
>>>>>> 02 {
>>>>>> 03   int Halt_Status = H(x, x);
>>>>>> 04   if (Halt_Status)
>>>>>> 05     HERE: goto HERE;
>>>>>> 06   return Halt_Status;
>>>>>> 07 }
>>>>>> 08
>>>>>> 09 void main()
>>>>>> 10 {
>>>>>> 11   H(D,D);
>>>>>> 12 }
>>>>>>
>>>>>> Here is the sequence when H never aborts it simulation:
>>>>>>    main() calls H(D,D) that simulates D(D) at line 11
>>>>>>    keeps repeating: simulated D(D) calls simulated H(D,D) that
>>>>>> simulates D(D) at line 03 ...  thus never reaching line 06 and
>>>>>> halting.
>>>>>>
>>>>>> Try and explain the detailed steps of exactly how H can see the
>>>>>> behavior
>>>>>> of D(D) that is not its input on the basis of H(D,D) that is its
>>>>>> input.
>>>>>>
>>>>>> Failure to respond with every detail of these steps will be construed
>>>>>> as an admission that this cannot be done.
>>>>>>
>>>>>
>>>>> When halting is defined as reaching the final state at line 6 and H
>>>>> correctly predicts that D correctly simulated by every H that can
>>>>> possibly exist will never halt then any element of the infinite set of
>>>>> every H that can possibly exist is correct to reject D as non-halting.
>>>>>
>>>>
>>>> When a decision problem is defined as what yes/no answer can Bill say
>>>> that correctly predicts the answer that Harry will provide when Harry
>>>> makes sure to always provide the opposite of whatever Bill predicts
>>>> this
>>>> "decision problem" is equivalent to correctly determining whether the
>>>> Liar Paradox is true or false: "This sentence is not true".
>>>>
>>>> *The diagonal argument of the halting theorem has this exact same form*
>>>>
>>>> My work on the Halting Problem, Gödel's 1931 Incompleteness theorem,
>>>> the Tarski Undefinability theorem and the Liar Paradox is actually work
>>>> on the philosophical foundations of the notion of analytical truth
>>>> itself.
>>>>
>>>> People that merely memorize what textbooks say don't have a clue about
>>>> these things. They are only capable of mindlessly conforming to dogma.
>>>>
>>>
>>> When there are actual errors in the foundation of the notion of
>>> analytical truth these same errors are carried over to mathematics,
>>> logic, and computer science with no one that merely follows the rules as
>>> given ever noticing the inconsistency and incoherence.
>>
>> The foundation of the notion of analytic true can be so succinctly
>> stated that it can be far too easily misconstrued as simplistic.
>>
>> Expression X of language L is true iff there is a semantic connection
>> from expressions of language L that are stipulated as true to X
>> otherwise X is untrue. Untrue does not entail false.
>>
>
> The above terse little paragraph totally refutes the Tarski
> undefinability theorem.
>

When I provide the analytical framework by which any analytical truth
can be defined and verified then any proof that this cannot be done has
been refuted.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 3/17/23 12:29 AM, olcott wrote:
> On 3/16/2023 9:02 PM, olcott wrote:
>> On 3/16/2023 8:24 PM, olcott wrote:
>>> On 3/16/2023 6:34 PM, olcott wrote:
>>>> On 3/16/2023 5:50 PM, olcott wrote:
>>>>> On 3/16/2023 1:19 PM, olcott wrote:
>>>>>> On 3/16/2023 12:46 PM, Fritz Feldhase wrote:
>>>>>>> On Thursday, March 16, 2023 at 5:27:38 PM UTC+1, olcott wrote:
>>>>>>>
>>>>>>>> Anything other than the [actual] behavior of D [called with
>>>>>>>> input D] is
>>>>>>>> irrelevant because [the actual behavior of D called with input D is
>>>>>>>> what we are interested in]
>>>>>>>
>>>>>>> Exactly!
>>>>>>
>>>>>> 01 int D(int (*x)())
>>>>>> 02 {
>>>>>> 03   int Halt_Status = H(x, x);
>>>>>> 04   if (Halt_Status)
>>>>>> 05     HERE: goto HERE;
>>>>>> 06   return Halt_Status;
>>>>>> 07 }
>>>>>> 08
>>>>>> 09 void main()
>>>>>> 10 {
>>>>>> 11   H(D,D);
>>>>>> 12 }
>>>>>>
>>>>>> Here is the sequence when H never aborts it simulation:
>>>>>>    main() calls H(D,D) that simulates D(D) at line 11
>>>>>>    keeps repeating: simulated D(D) calls simulated H(D,D) that
>>>>>> simulates D(D) at line 03 ...  thus never reaching line 06 and
>>>>>> halting.
>>>>>>
>>>>>> Try and explain the detailed steps of exactly how H can see the
>>>>>> behavior
>>>>>> of D(D) that is not its input on the basis of H(D,D) that is its
>>>>>> input.
>>>>>>
>>>>>> Failure to respond with every detail of these steps will be construed
>>>>>> as an admission that this cannot be done.
>>>>>>
>>>>>
>>>>> When halting is defined as reaching the final state at line 6 and H
>>>>> correctly predicts that D correctly simulated by every H that can
>>>>> possibly exist will never halt then any element of the infinite set of
>>>>> every H that can possibly exist is correct to reject D as non-halting.
>>>>>
>>>>
>>>> When a decision problem is defined as what yes/no answer can Bill say
>>>> that correctly predicts the answer that Harry will provide when Harry
>>>> makes sure to always provide the opposite of whatever Bill predicts
>>>> this
>>>> "decision problem" is equivalent to correctly determining whether the
>>>> Liar Paradox is true or false: "This sentence is not true".
>>>>
>>>> *The diagonal argument of the halting theorem has this exact same form*
>>>>
>>>> My work on the Halting Problem, Gödel's 1931 Incompleteness theorem,
>>>> the Tarski Undefinability theorem and the Liar Paradox is actually work
>>>> on the philosophical foundations of the notion of analytical truth
>>>> itself.
>>>>
>>>> People that merely memorize what textbooks say don't have a clue about
>>>> these things. They are only capable of mindlessly conforming to dogma.
>>>>
>>>
>>> When there are actual errors in the foundation of the notion of
>>> analytical truth these same errors are carried over to mathematics,
>>> logic, and computer science with no one that merely follows the rules as
>>> given ever noticing the inconsistency and incoherence.
>>
>> The foundation of the notion of analytic true can be so succinctly
>> stated that it can be far too easily misconstrued as simplistic.
>>
>> Expression X of language L is true iff there is a semantic connection
>> from expressions of language L that are stipulated as true to X
>> otherwise X is untrue. Untrue does not entail false.
>>
>
> This system is the foundation of all other systems I have not
> worked out all the details.

And that IS your problem.

>
> My system can handle any expression of language thus it screens out
> semantic gibberish.

Then why doesn't it screen out H calling an input non-halting when it Halts.

>
> Provable required the same semantic connection from the premises to the
> conclusion, yet the premises need not be true.

Nope, as statement is only proven when you show that it MUST be true due
to a connection to the axioms of the system.

An ARGUEMENT (also called a PROOF) can be VALID, independent on the
truthfullness of its premises, but is unsound if any of its premises are
not true.

So, is your whole arguement based on a simple misunderstanding of how
logic works.

>
> The conclusion must be a semantically necessary consequence of its
> premises. Some things stay the same A & B proves A at the level of
> propositional variables is still valid.

And as I have asked before, how do you define "semantically necessary
consquence"? If you mean "By the meaning of the words", then your system
doesn't allow non-trivial proofs, like the Pythagorean theorem, since
the conclusion doesn't derive just from the meaning of the words (and in
fact is only conditionally true, as it is only true for fields where
Euclid's Fifth Postulate holds).

>
> We still need to have some way to define the meaning of terms so that
> semantics can become much deeper. Syllogisms tend to use natural
> language for this.
>
> Categorical logic is fine the way that it is.
>
> Everything that supports the principle of explosion is abolished by the
> semantic connection requirement.

Which means that you can't support any of the higher forms of logic.

IN fact, categorical logic which you said is fine, has to be removed, as
it supports the principle of explosion.

>
> Implication may be abolished or changed.
> We may overload this □⊨ as the semantically necessary operator.

Which means that you need to either remove the "NOT" operator or the
"AND" and "OR" operator from your logic as A -> B is nothing more than
(~A | B) or
~(A & ~B)

>
> (a) □⊨ (b)    (b) is a semantically necessary consequence of (a)
>
> I don't see any definite reason to change much of mathematics.

Only because you don't understand that you defined most of it out of
existance.

Mathematics does support the principle of Explosion, because the logic
system it use it rich enough to enable it.

>
> Godels proof can no longer possibly exist because provable is an aspect
> of true there can be no true and unprovable.
>

And it doesn't exist because you have removed Mathematics as a valid system.

You just don't understand the depth of what you are talking about.

On 3/17/23 12:31 AM, olcott wrote:
> On 3/16/2023 9:11 PM, olcott wrote:
>> On 3/16/2023 9:02 PM, olcott wrote:
>>> On 3/16/2023 8:24 PM, olcott wrote:
>>>> On 3/16/2023 6:34 PM, olcott wrote:
>>>>> On 3/16/2023 5:50 PM, olcott wrote:
>>>>>> On 3/16/2023 1:19 PM, olcott wrote:
>>>>>>> On 3/16/2023 12:46 PM, Fritz Feldhase wrote:
>>>>>>>> On Thursday, March 16, 2023 at 5:27:38 PM UTC+1, olcott wrote:
>>>>>>>>
>>>>>>>>> Anything other than the [actual] behavior of D [called with
>>>>>>>>> input D] is
>>>>>>>>> irrelevant because [the actual behavior of D called with input
>>>>>>>>> D is
>>>>>>>>> what we are interested in]
>>>>>>>>
>>>>>>>> Exactly!
>>>>>>>
>>>>>>> 01 int D(int (*x)())
>>>>>>> 02 {
>>>>>>> 03   int Halt_Status = H(x, x);
>>>>>>> 04   if (Halt_Status)
>>>>>>> 05     HERE: goto HERE;
>>>>>>> 06   return Halt_Status;
>>>>>>> 07 }
>>>>>>> 08
>>>>>>> 09 void main()
>>>>>>> 10 {
>>>>>>> 11   H(D,D);
>>>>>>> 12 }
>>>>>>>
>>>>>>> Here is the sequence when H never aborts it simulation:
>>>>>>>    main() calls H(D,D) that simulates D(D) at line 11
>>>>>>>    keeps repeating: simulated D(D) calls simulated H(D,D) that
>>>>>>> simulates D(D) at line 03 ...  thus never reaching line 06 and
>>>>>>> halting.
>>>>>>>
>>>>>>> Try and explain the detailed steps of exactly how H can see the
>>>>>>> behavior
>>>>>>> of D(D) that is not its input on the basis of H(D,D) that is its
>>>>>>> input.
>>>>>>>
>>>>>>> Failure to respond with every detail of these steps will be
>>>>>>> construed
>>>>>>> as an admission that this cannot be done.
>>>>>>>
>>>>>>
>>>>>> When halting is defined as reaching the final state at line 6 and H
>>>>>> correctly predicts that D correctly simulated by every H that can
>>>>>> possibly exist will never halt then any element of the infinite
>>>>>> set of
>>>>>> every H that can possibly exist is correct to reject D as
>>>>>> non-halting.
>>>>>>
>>>>>
>>>>> When a decision problem is defined as what yes/no answer can Bill say
>>>>> that correctly predicts the answer that Harry will provide when Harry
>>>>> makes sure to always provide the opposite of whatever Bill predicts
>>>>> this
>>>>> "decision problem" is equivalent to correctly determining whether the
>>>>> Liar Paradox is true or false: "This sentence is not true".
>>>>>
>>>>> *The diagonal argument of the halting theorem has this exact same
>>>>> form*
>>>>>
>>>>> My work on the Halting Problem, Gödel's 1931 Incompleteness theorem,
>>>>> the Tarski Undefinability theorem and the Liar Paradox is actually
>>>>> work
>>>>> on the philosophical foundations of the notion of analytical truth
>>>>> itself.
>>>>>
>>>>> People that merely memorize what textbooks say don't have a clue about
>>>>> these things. They are only capable of mindlessly conforming to dogma.
>>>>>
>>>>
>>>> When there are actual errors in the foundation of the notion of
>>>> analytical truth these same errors are carried over to mathematics,
>>>> logic, and computer science with no one that merely follows the
>>>> rules as
>>>> given ever noticing the inconsistency and incoherence.
>>>
>>> The foundation of the notion of analytic true can be so succinctly
>>> stated that it can be far too easily misconstrued as simplistic.
>>>
>>> Expression X of language L is true iff there is a semantic connection
>>> from expressions of language L that are stipulated as true to X
>>> otherwise X is untrue. Untrue does not entail false.
>>>
>>
>> The above terse little paragraph totally refutes the Tarski
>> undefinability theorem.
>>
>
> When I provide the analytical framework by which any analytical truth
> can be defined and verified then any proof that this cannot be done has
> been refuted.
>

So, you admit that you don't know what Tarski is talking about by a
"Definition of Truth".

Note, he DOESN'T mean just a "dictionary" definition of the word.