For a simulating halt decider, HHH, simulating the program from the
classic diagonalization proof, DD, using a description of DD, a finite string, there are only three possibilities:
1) HHH(DD) == 0 (non-halting), DD() halts, Halting Problem undecidable.
2) HHH(DD) == 1 (halting), DD() doesn't halt, Halting Problem undecidable.
3) HHH(DD) doesn't report, Halting Problem undecidable.
Olcott's smoke and mirrors cannot obscure this reality.
/Flibble
On 8/17/25 2:13 PM, Mr Flibble wrote:
For a simulating halt decider, HHH, simulating the program from the
classic diagonalization proof, DD, using a description of DD, a finite
string, there are only three possibilities:
1) HHH(DD) == 0 (non-halting), DD() halts, Halting Problem undecidable.
2) HHH(DD) == 1 (halting), DD() doesn't halt, Halting Problem
undecidable.
3) HHH(DD) doesn't report, Halting Problem undecidable.
Olcott's smoke and mirrors cannot obscure this reality.
/Flibble
It is probably worht point out that the version of the proof that Olcott
is looking at is NOT a "Diagonalization" proof, but a proof by
contradiction.
There *IS* a verision of the proof based on diagonalization but it is
more complicated and harder to understand, but does avoid the proof by contradiction. It does require accepting the proof of the construction
of the target machine.
On Sun, 17 Aug 2025 15:28:42 -0400, Richard Damon wrote:
On 8/17/25 2:13 PM, Mr Flibble wrote:
For a simulating halt decider, HHH, simulating the program from the
classic diagonalization proof, DD, using a description of DD, a finite
string, there are only three possibilities:
1) HHH(DD) == 0 (non-halting), DD() halts, Halting Problem undecidable.
2) HHH(DD) == 1 (halting), DD() doesn't halt, Halting Problem
undecidable.
3) HHH(DD) doesn't report, Halting Problem undecidable.
Olcott's smoke and mirrors cannot obscure this reality.
/Flibble
It is probably worht point out that the version of the proof that Olcott
is looking at is NOT a "Diagonalization" proof, but a proof by
contradiction.
There *IS* a verision of the proof based on diagonalization but it is
more complicated and harder to understand, but does avoid the proof by
contradiction. It does require accepting the proof of the construction
of the target machine.
Diagonalization is a specific method used to achieve the contradiction in
the most common presentations of the proof.
/Flibble
On 8/17/25 4:11 PM, Mr Flibble wrote:
On Sun, 17 Aug 2025 15:28:42 -0400, Richard Damon wrote:The Linz method that Peter quotes is not a diagonalization proof, but a
On 8/17/25 2:13 PM, Mr Flibble wrote:
For a simulating halt decider, HHH, simulating the program from the
classic diagonalization proof, DD, using a description of DD, a
finite string, there are only three possibilities:
1) HHH(DD) == 0 (non-halting), DD() halts, Halting Problem
undecidable.
2) HHH(DD) == 1 (halting), DD() doesn't halt, Halting Problem
undecidable.
3) HHH(DD) doesn't report, Halting Problem undecidable.
Olcott's smoke and mirrors cannot obscure this reality.
/Flibble
It is probably worht point out that the version of the proof that
Olcott is looking at is NOT a "Diagonalization" proof, but a proof by
contradiction.
There *IS* a verision of the proof based on diagonalization but it is
more complicated and harder to understand, but does avoid the proof by
contradiction. It does require accepting the proof of the construction
of the target machine.
Diagonalization is a specific method used to achieve the contradiction
in the most common presentations of the proof.
/Flibble
proof by contradiction of showing that the decider can exist as it
creates a direct logical contradiction.
The diagonalization method isn't as dependent on the contradiction, but typically starts with an enumeration of all possible deciders on one
axis, and the enumerated equivalent pathological programs, in the same
order, on the other, with its answer, and then shows that no where on
the diagonal is a correct answer (since the behavior of the pathological program will be the opposite of what is on that diagonal).
While it shows "a contradiction", that contradiction is an immediate
result of the question, and to as is typical of a proof by
contradiction, beginning with an assumption that is much later proved to
not possible to have been made.
Olcott's logic doesn't seem to be able to support a proof by
contradiction, as he doesn't allow the reversing of the implication.
Of course, it also just allows starting with lies and proving false statements from lies, but he tries to hide that part.
On Sun, 17 Aug 2025 16:45:45 -0400, Richard Damon wrote:
On 8/17/25 4:11 PM, Mr Flibble wrote:
On Sun, 17 Aug 2025 15:28:42 -0400, Richard Damon wrote:The Linz method that Peter quotes is not a diagonalization proof, but a
On 8/17/25 2:13 PM, Mr Flibble wrote:
For a simulating halt decider, HHH, simulating the program from the
classic diagonalization proof, DD, using a description of DD, a
finite string, there are only three possibilities:
1) HHH(DD) == 0 (non-halting), DD() halts, Halting Problem
undecidable.
2) HHH(DD) == 1 (halting), DD() doesn't halt, Halting Problem
undecidable.
3) HHH(DD) doesn't report, Halting Problem undecidable.
Olcott's smoke and mirrors cannot obscure this reality.
/Flibble
It is probably worht point out that the version of the proof that
Olcott is looking at is NOT a "Diagonalization" proof, but a proof by
contradiction.
There *IS* a verision of the proof based on diagonalization but it is
more complicated and harder to understand, but does avoid the proof by >>>> contradiction. It does require accepting the proof of the construction >>>> of the target machine.
Diagonalization is a specific method used to achieve the contradiction
in the most common presentations of the proof.
/Flibble
proof by contradiction of showing that the decider can exist as it
creates a direct logical contradiction.
The diagonalization method isn't as dependent on the contradiction, but
typically starts with an enumeration of all possible deciders on one
axis, and the enumerated equivalent pathological programs, in the same
order, on the other, with its answer, and then shows that no where on
the diagonal is a correct answer (since the behavior of the pathological
program will be the opposite of what is on that diagonal).
While it shows "a contradiction", that contradiction is an immediate
result of the question, and to as is typical of a proof by
contradiction, beginning with an assumption that is much later proved to
not possible to have been made.
Olcott's logic doesn't seem to be able to support a proof by
contradiction, as he doesn't allow the reversing of the implication.
Of course, it also just allows starting with lies and proving false
statements from lies, but he tries to hide that part.
What do you hope to achieve by continuing to write verbose responses to
his posts given that he seems to be ignoring you now?
/Flibble
On 8/17/25 4:51 PM, Mr Flibble wrote:
On Sun, 17 Aug 2025 16:45:45 -0400, Richard Damon wrote:
On 8/17/25 4:11 PM, Mr Flibble wrote:
On Sun, 17 Aug 2025 15:28:42 -0400, Richard Damon wrote:The Linz method that Peter quotes is not a diagonalization proof, but
On 8/17/25 2:13 PM, Mr Flibble wrote:
For a simulating halt decider, HHH, simulating the program from the >>>>>> classic diagonalization proof, DD, using a description of DD, a
finite string, there are only three possibilities:
1) HHH(DD) == 0 (non-halting), DD() halts, Halting Problem
undecidable.
2) HHH(DD) == 1 (halting), DD() doesn't halt, Halting Problem
undecidable.
3) HHH(DD) doesn't report, Halting Problem undecidable.
Olcott's smoke and mirrors cannot obscure this reality.
/Flibble
It is probably worht point out that the version of the proof that
Olcott is looking at is NOT a "Diagonalization" proof, but a proof
by contradiction.
There *IS* a verision of the proof based on diagonalization but it
is more complicated and harder to understand, but does avoid the
proof by contradiction. It does require accepting the proof of the
construction of the target machine.
Diagonalization is a specific method used to achieve the
contradiction in the most common presentations of the proof.
/Flibble
a proof by contradiction of showing that the decider can exist as it
creates a direct logical contradiction.
The diagonalization method isn't as dependent on the contradiction,
but typically starts with an enumeration of all possible deciders on
one axis, and the enumerated equivalent pathological programs, in the
same order, on the other, with its answer, and then shows that no
where on the diagonal is a correct answer (since the behavior of the
pathological program will be the opposite of what is on that
diagonal).
While it shows "a contradiction", that contradiction is an immediate
result of the question, and to as is typical of a proof by
contradiction, beginning with an assumption that is much later proved
to not possible to have been made.
Olcott's logic doesn't seem to be able to support a proof by
contradiction, as he doesn't allow the reversing of the implication.
Of course, it also just allows starting with lies and proving false
statements from lies, but he tries to hide that part.
What do you hope to achieve by continuing to write verbose responses to
his posts given that he seems to be ignoring you now?
/Flibble
Education of the other readers that might otherwise be persuded.
Perhaps I influnced you away from his errors that seemed to have a sway
on you for awhile
On Sun, 17 Aug 2025 17:01:23 -0400, Richard Damon wrote:
On 8/17/25 4:51 PM, Mr Flibble wrote:
On Sun, 17 Aug 2025 16:45:45 -0400, Richard Damon wrote:
On 8/17/25 4:11 PM, Mr Flibble wrote:
On Sun, 17 Aug 2025 15:28:42 -0400, Richard Damon wrote:The Linz method that Peter quotes is not a diagonalization proof, but
On 8/17/25 2:13 PM, Mr Flibble wrote:
For a simulating halt decider, HHH, simulating the program from the >>>>>>> classic diagonalization proof, DD, using a description of DD, a
finite string, there are only three possibilities:
1) HHH(DD) == 0 (non-halting), DD() halts, Halting Problem
undecidable.
2) HHH(DD) == 1 (halting), DD() doesn't halt, Halting Problem
undecidable.
3) HHH(DD) doesn't report, Halting Problem undecidable.
Olcott's smoke and mirrors cannot obscure this reality.
/Flibble
It is probably worht point out that the version of the proof that
Olcott is looking at is NOT a "Diagonalization" proof, but a proof >>>>>> by contradiction.
There *IS* a verision of the proof based on diagonalization but it >>>>>> is more complicated and harder to understand, but does avoid the
proof by contradiction. It does require accepting the proof of the >>>>>> construction of the target machine.
Diagonalization is a specific method used to achieve the
contradiction in the most common presentations of the proof.
/Flibble
a proof by contradiction of showing that the decider can exist as it
creates a direct logical contradiction.
The diagonalization method isn't as dependent on the contradiction,
but typically starts with an enumeration of all possible deciders on
one axis, and the enumerated equivalent pathological programs, in the
same order, on the other, with its answer, and then shows that no
where on the diagonal is a correct answer (since the behavior of the
pathological program will be the opposite of what is on that
diagonal).
While it shows "a contradiction", that contradiction is an immediate
result of the question, and to as is typical of a proof by
contradiction, beginning with an assumption that is much later proved
to not possible to have been made.
Olcott's logic doesn't seem to be able to support a proof by
contradiction, as he doesn't allow the reversing of the implication.
Of course, it also just allows starting with lies and proving false
statements from lies, but he tries to hide that part.
What do you hope to achieve by continuing to write verbose responses to
his posts given that he seems to be ignoring you now?
/Flibble
Education of the other readers that might otherwise be persuded.
Perhaps I influnced you away from his errors that seemed to have a sway
on you for awhile
The only idea of Olcott's that I didn't dismiss out of hand was the
general idea of a Simulating Halt Decider; I never agreed with Olcott on
the central premise his approach relies upon: that aborting the simulation and reporting non-halting is valid.
/Flibble
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