dart200 <user7160@newsgrouper.org.invalid> writes:
we should then consider a working thesis: no paradoxical machine is the
simplest of their class of functionally equivalent machines.
You don't define what a "paradoxical machine" is. Can you do so?
I could take a guess, as it is a phrase commonly used by Usenet cranks
to refer to a machine they think exists but does not. But I don't want
to assume you've made the same mistake. Have you ever seen one? Can
you show one? Can you define the term in a way that is close to being
clear and unambiguous?
consider the basic paradox form:
deciderP(input) - decides if input has property P or !P
machineP() - machine that has property P
machine!P() - machine that has property !P
// undecidable by deciderP for property P
undP = () -> {
if ( deciderP(undP) == TRUE )
machine!P()
else
machineP()
}
This does not help. For example, let's assume decider37t(input)
correctly decides (returns true) if the input machine executes more than
37 state transitions (and false otherwise). What is paradoxical about und37t?
Again, I could guess that you only want people to use this "basic
paradox form" when deciderP does not exist, and so neither does undP;
i.e. only when the conditions of Rice's theorem are satisfied. But you haven't said that, so I should let you clarify your definition.
On 2/8/2026 6:48 PM, Ben Bacarisse wrote:
dart200 <user7160@newsgrouper.org.invalid> writes:
we should then consider a working thesis: no paradoxical machine is the
simplest of their class of functionally equivalent machines.
You don't define what a "paradoxical machine" is.-a Can you do so?
I could take a guess, as it is a phrase commonly used by Usenet cranks
to refer to a machine they think exists but does not.-a But I don't want
to assume you've made the same mistake.-a Have you ever seen one?-a Can
you show one?-a Can you define the term in a way that is close to being
clear and unambiguous?
consider the basic paradox form:
-a-a deciderP(input) - decides if input has property P or !P
-a-a machineP()-a-a-a-a-a - machine that has property P
-a-a machine!P()-a-a-a-a - machine that has property !P
-a-a // undecidable by deciderP for property P
-a-a undP = () -> {
-a-a-a-a if ( deciderP(undP) == TRUE )
-a-a-a-a-a-a machine!P()
-a-a-a-a else
-a-a-a-a-a-a machineP()
-a-a }
This does not help.-a For example, let's assume decider37t(input)
correctly decides (returns true) if the input machine executes more than
37 state transitions (and false otherwise).-a What is paradoxical about
und37t?
Again, I could guess that you only want people to use this "basic
paradox form" when deciderP does not exist, and so neither does undP;
i.e. only when the conditions of Rice's theorem are satisfied.-a But you
haven't said that, so I should let you clarify your definition.
I proved that the Halting Problem is
merely the Liar Paradox disguised 22 years ago https://groups.google.com/g/sci.logic/c/Hs78nMN6QZE/m/ID2rxwo__yQJ
On 2/8/26 8:06 PM, olcott wrote:
On 2/8/2026 6:48 PM, Ben Bacarisse wrote:
dart200 <user7160@newsgrouper.org.invalid> writes:
we should then consider a working thesis: no paradoxical machine is the >>>> simplest of their class of functionally equivalent machines.
You don't define what a "paradoxical machine" is.-a Can you do so?
I could take a guess, as it is a phrase commonly used by Usenet cranks
to refer to a machine they think exists but does not.-a But I don't want >>> to assume you've made the same mistake.-a Have you ever seen one?-a Can
you show one?-a Can you define the term in a way that is close to being
clear and unambiguous?
consider the basic paradox form:
-a-a deciderP(input) - decides if input has property P or !P
-a-a machineP()-a-a-a-a-a - machine that has property P
-a-a machine!P()-a-a-a-a - machine that has property !P
-a-a // undecidable by deciderP for property P
-a-a undP = () -> {
-a-a-a-a if ( deciderP(undP) == TRUE )
-a-a-a-a-a-a machine!P()
-a-a-a-a else
-a-a-a-a-a-a machineP()
-a-a }
This does not help.-a For example, let's assume decider37t(input)
correctly decides (returns true) if the input machine executes more than >>> 37 state transitions (and false otherwise).-a What is paradoxical about
und37t?
Again, I could guess that you only want people to use this "basic
paradox form" when deciderP does not exist, and so neither does undP;
i.e. only when the conditions of Rice's theorem are satisfied.-a But you >>> haven't said that, so I should let you clarify your definition.
I proved that the Halting Problem is
merely the Liar Paradox disguised 22 years ago
https://groups.google.com/g/sci.logic/c/Hs78nMN6QZE/m/ID2rxwo__yQJ
No, you proved you don't understand what the Halting Problem *IS*
The decider doesn't give its answer as an input the to machine under
test, it returns that answer to its caller.
Thus, all you do is prove your ignorance.
On 2/9/2026 6:51 AM, Richard Damon wrote:
On 2/8/26 8:06 PM, olcott wrote:
On 2/8/2026 6:48 PM, Ben Bacarisse wrote:
dart200 <user7160@newsgrouper.org.invalid> writes:
we should then consider a working thesis: no paradoxical machine is >>>>> the
simplest of their class of functionally equivalent machines.
You don't define what a "paradoxical machine" is.-a Can you do so?
I could take a guess, as it is a phrase commonly used by Usenet cranks >>>> to refer to a machine they think exists but does not.-a But I don't want >>>> to assume you've made the same mistake.-a Have you ever seen one?-a Can >>>> you show one?-a Can you define the term in a way that is close to being >>>> clear and unambiguous?
consider the basic paradox form:
-a-a deciderP(input) - decides if input has property P or !P
-a-a machineP()-a-a-a-a-a - machine that has property P
-a-a machine!P()-a-a-a-a - machine that has property !P
-a-a // undecidable by deciderP for property P
-a-a undP = () -> {
-a-a-a-a if ( deciderP(undP) == TRUE )
-a-a-a-a-a-a machine!P()
-a-a-a-a else
-a-a-a-a-a-a machineP()
-a-a }
This does not help.-a For example, let's assume decider37t(input)
correctly decides (returns true) if the input machine executes more
than
37 state transitions (and false otherwise).-a What is paradoxical about >>>> und37t?
Again, I could guess that you only want people to use this "basic
paradox form" when deciderP does not exist, and so neither does undP;
i.e. only when the conditions of Rice's theorem are satisfied.-a But you >>>> haven't said that, so I should let you clarify your definition.
I proved that the Halting Problem is
merely the Liar Paradox disguised 22 years ago
https://groups.google.com/g/sci.logic/c/Hs78nMN6QZE/m/ID2rxwo__yQJ
No, you proved you don't understand what the Halting Problem *IS*
The decider doesn't give its answer as an input the to machine under
test, it returns that answer to its caller.
Thus, all you do is prove your ignorance.
22 years ago I made you the decider and you
could not decide because the HP <is> the LP.
On 11/02/2026 21:53, Alan Mackenzie wrote:
Mathematicians have proven that many decision problems can not be
answered, all the nonsense about "idiosyncrasies of self-referential
logic" notwithstanding.
It's not at all clear to me that those unanswerables are properly
classified as "decision problem" unless one uses an auto-explication (my
term for when a term is both an explicatum and explicandum of an explication). Carnap's definition of explication excludes such an act
(though I don't know if he'd picked up the bad habit of using "decision problem" as an explicatum).
I think Carnap would have admitted "L-decision problem" as an explicatum
of the explicandum "decision problem". The nonsense act of calling pathologically self-referential problems as "L-decision problems" would
be obvious because one does not have a problem of choosing between only classifications "true" and "false" when one has merely been fooled into thinking those are candidates without a whole heap of others beside.
I hereby indulge myself with some old-timey assertive logistic
philosophy, you might call it a strawman, something to ponder and burn down:
We can understand the fallacy by making explicit the implicit false assumption: "the sentence after the conjunctive connector following can
be assigned no valuation but 'true' or 'false' AND blah-blah". That is
the cultural synergy covertly induced in the ponderer by a poetic form
of expression ("proposition" the explicatum, not the explicandum, it's another auto-explication) but it's not /well/ formalised in that it's a
mess of massive description and wonderment. I think usage of AND gives
us falsity for pathologically self-referential 'blah-blah' if we have
the right type-system but other connectives give us other, non-truth, classifications. A connective that means the implication of neither
truth nor falsity is also available. Of course, the ponderer has the inducement in the form of a volition to be disobedient and choose to
react in a variety of unassertive ways.
A proof is a proof.
Tautology.
On 12/02/2026 20:02, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory Tristan Wibberley
<tristan.wibberley+netnews2@alumni.manchester.ac.uk> wrote:
On 11/02/2026 21:53, Alan Mackenzie wrote:
Mathematicians have proven that many decision problems can not be
answered, all the nonsense about "idiosyncrasies of self-referential
logic" notwithstanding.
It's not at all clear to me that those unanswerables are properly
classified as "decision problem" unless one uses an auto-explication (my >>> term for when a term is both an explicatum and explicandum of an
explication). Carnap's definition of explication excludes such an act
(though I don't know if he'd picked up the bad habit of using "decision
problem" as an explicatum).
My understanding of a "decision problem" is one whose solution is a
machine which, in finite time, can correctly classify any machine into
one of two categories.
Then a problem without a solution is not a decision problem; I think
that's the right way to think about it. I think Olcott thinks about it
that way too, at least for days at a time. Conversations here manage to
make me slip between modes sometimes.
In this sense there is no solution to the halting problem.
And by your partial explication above, the halting problem is therefore
not a decision problem. I don't think your explication will stick still
for more than half a sentence, though; at any moment I think you or
someone else studious will say that there /is/ a solution to the halting problem, the solution they will moot is that there is no universal halt-decider.
The Church-Turing thesis is clearly not the kind of thing that is
provable. That's why it's not called a conjecture.
--
Ben.
Ben Bacarisse <ben@bsb.me.uk> wrote:
[ .... ]
The Church-Turing thesis is clearly not the kind of thing that is
provable. That's why it's not called a conjecture.
I don't understand that bit. What is unprovable about the Church-Turing thesis? I think it hypothesises that there is no computing machine more powerful than a turing machine.
What would prevent a proof along the lines of supposing the existence of
such a more powerful machine, then proving it was actually equivalent to
some turing machine?
Alan Mackenzie <acm@muc.de> writes:
Ben Bacarisse <ben@bsb.me.uk> wrote:
[ .... ]
The Church-Turing thesis is clearly not the kind of thing that is
provable. That's why it's not called a conjecture.
I don't understand that bit. What is unprovable about the Church-Turing
thesis? I think it hypothesises that there is no computing machine more
powerful than a turing machine.
There are, purely theoretical, models of computation (my preferred
phrase) that are more powerful than Turing machines but they are not considered "effective". The thesis is about what effectively computable means and this is where the problem lies. It's not a well-defined
concept, though almost everyone just /assumes/ it means "what TMs (and so
on) can do".
What would prevent a proof along the lines of supposing the existence of
such a more powerful machine, then proving it was actually equivalent to
some turing machine?
Perhaps it would have been better to say that one can't imagine what
such a proof could look like. Can you?
The "more powerful" bit is easy. One would assume that the more
powerful model can compute at least one function that is not TM
computable.
But how would the notion that it is none-the less "effective" be
specified?
And what form could the equivalence proof take, given that we can
assume nothing about model other that the fact that is it more
powerful and yet effective?
It's not something I've given much thought to so I'd be interested if
you can go further with the notion.
----
Ben.
Ben Bacarisse <ben@bsb.me.uk> wrote:
Alan Mackenzie <acm@muc.de> writes:
Ben Bacarisse <ben@bsb.me.uk> wrote:
[ .... ]
The Church-Turing thesis is clearly not the kind of thing that is
provable. That's why it's not called a conjecture.
I don't understand that bit. What is unprovable about the Church-Turing >>> thesis? I think it hypothesises that there is no computing machine more >>> powerful than a turing machine.
There are, purely theoretical, models of computation (my preferred
phrase) that are more powerful than Turing machines but they are not
considered "effective". The thesis is about what effectively computable
means and this is where the problem lies. It's not a well-defined
concept, though almost everyone just /assumes/ it means "what TMs (and so
on) can do".
I think I'm beginning to see the problem. These more powerful models of computation presumably lack the "finite structure" of a turing machine -
the finite number of states, of possible symbols on the tape, and the discreteness of the tape movements.
Maybe analogue devices (slide rules, differential analysers, etc.) come
into this category. Though these could not duplicate the effect of a
turing machine, they do something altogether different.
What would prevent a proof along the lines of supposing the existence of >>> such a more powerful machine, then proving it was actually equivalent to >>> some turing machine?
Perhaps it would have been better to say that one can't imagine what
such a proof could look like. Can you?
No. I'm pretty confused about the whole question.
The "more powerful" bit is easy. One would assume that the more
powerful model can compute at least one function that is not TM
computable.
There are only a countable number of turing machines, but an uncountable number of functions. So that "at least one" would probably be an
uncountably infinite number.
But how would the notion that it is none-the less "effective" be
specified?
I think it needs to be a machine of some sort, in the sense of being a
finite collection of rods, gears, states, tapes, whatever ... But I
can't picture any such device which wouldn't be equivalent to a turing machine.
And what form could the equivalence proof take, given that we can
assume nothing about model other that the fact that is it more
powerful and yet effective?
Maybe there could be a proof that any machine worthy of the description
would be equivalent to a turing machine. This would need to formalise exactly what a "machine" is. Maybe this has been done already.
--It's not something I've given much thought to so I'd be interested if
you can go further with the notion.
I'll see if I can come up with something more coherent after some more thought.
--
Ben.
Alan Mackenzie <acm@muc.de> writes:
Ben Bacarisse <ben@bsb.me.uk> wrote:
[ .... ]
The Church-Turing thesis is clearly not the kind of thing that is
provable. That's why it's not called a conjecture.
I don't understand that bit. What is unprovable about the Church-Turing
thesis? I think it hypothesises that there is no computing machine more
powerful than a turing machine.
There are, purely theoretical, models of computation (my preferred
phrase) that are more powerful than Turing machines but they are not considered "effective".
Turing invented TMs to capture the notion of what is computable
On 20/02/2026 18:11, Ben Bacarisse wrote:
Turing invented TMs to capture the notion of what is computable
I'm curious to know how his motives are known. He worked in defence
research so I expected he was studying the maximum possible capability
of enemy computing infrastructure to help direct research resources.
On 20/02/2026 18:11, Ben Bacarisse wrote:
Turing invented TMs to capture the notion of what is computable
I'm curious to know how his motives are known.
He worked in defence research
so I expected he was studying the maximum possible capability--
of enemy computing infrastructure to help direct research resources.
Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> writes:
On 20/02/2026 18:11, Ben Bacarisse wrote:
Turing invented TMs to capture the notion of what is computable
I'm curious to know how his motives are known.
At one level there are very clear. In 1928, Hilbert and Ackermann posed
the question of whether first-order logic was decidable -- was there an
algorithm that can determine if a given statement is universally valid. (Given other results this is equivalent to deciding, algorithmically, if
a given statement is provable.)
At the time of his now famous paper he was working with Church who had
turned his attention to this as yet unsolved problem. At the time, most mathematicians thought the answer would be "yes". Of course the first
step is to capture the notion of an algorithm or process. Church came
up with the lambda calculus, and Turing the abstract machine that not
bears his name.
However, the idea that mathematics and specifically proofs, might be automated goes way back to at least Leibniz.
He worked in defence research
Not at the time, no. He was just a PhD student interested in formal
logic and the intriguing unsolved problems of the time, one of which was about what can be determined by finite "mechanical" means.
so I expected he was studying the maximum possible capability
of enemy computing infrastructure to help direct research resources.
On 2/24/26 4:09 PM, Ben Bacarisse wrote:
Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk>
writes:
On 20/02/2026 18:11, Ben Bacarisse wrote:
Turing invented TMs to capture the notion of what is computable
I'm curious to know how his motives are known.
At one level there are very clear.-a In 1928, Hilbert and Ackermann posed
the question of whether first-order logic was decidable -- was there an
and they all gave up on essentially meaninglessly garbage like
und = () -> halts(und) && loop()
it's kinda funny actually, all these greats getting their panties all twisted up /in the same way/ because of failure to appropriately handle
a lil' self-referential contradiction
even funnier are all the reactions from chucklefucks resolutely
defending that century long failure as MuH uNQuEsTioNAbLe tRuTH
actually it's not that funny, or funny at all. makes me want to kill
myself for being a such a fking EfniEfiA
algorithm that can determine if a given statement is universally valid.
(Given other results this is equivalent to deciding, algorithmically, if
a given statement is provable.)
At the time of his now famous paper he was working with Church who had
turned his attention to this as yet unsolved problem.-a At the time, most
mathematicians thought the answer would be "yes".-a Of course the first
step is to capture the notion of an algorithm or process.-a Church came
up with the lambda calculus, and Turing the abstract machine that not
bears his name.
However, the idea that mathematics and specifically proofs, might be
automated goes way back to at least Leibniz.
He worked in defence research
Not at the time, no.-a He was just a PhD student interested in formal
logic and the intriguing unsolved problems of the time, one of which was
about what can be determined by finite "mechanical" means.
so I expected he was studying the maximum possible capability
of enemy computing infrastructure to help direct research resources.
On 2/24/26 7:39 PM, dart200 wrote:
On 2/24/26 4:09 PM, Ben Bacarisse wrote:
Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk>
writes:
On 20/02/2026 18:11, Ben Bacarisse wrote:
Turing invented TMs to capture the notion of what is computable
I'm curious to know how his motives are known.
At one level there are very clear.-a In 1928, Hilbert and Ackermann posed >>> the question of whether first-order logic was decidable -- was there an
and they all gave up on essentially meaninglessly garbage like
Only meaningless to the stupid.
und = () -> halts(und) && loop()
it's kinda funny actually, all these greats getting their panties all
twisted up /in the same way/ because of failure to appropriately
handle a lil' self-referential contradiction
But the "self-reference" isn't actually there in the Turing Formulation.
even funnier are all the reactions from chucklefucks resolutely
defending that century long failure as MuH uNQuEsTioNAbLe tRuTH
actually it's not that funny, or funny at all. makes me want to kill
myself for being a such a fking EfniEfiA
Mqybe you should if you are that dumb.
(Not really, but if you want to keep bringing it up, actually think what
it would do).
algorithm that can determine if a given statement is universally valid.
(Given other results this is equivalent to deciding, algorithmically, if >>> a given statement is provable.)
At the time of his now famous paper he was working with Church who had
turned his attention to this as yet unsolved problem.-a At the time, most >>> mathematicians thought the answer would be "yes".-a Of course the first
step is to capture the notion of an algorithm or process.-a Church came
up with the lambda calculus, and Turing the abstract machine that not
bears his name.
However, the idea that mathematics and specifically proofs, might be
automated goes way back to at least Leibniz.
He worked in defence research
Not at the time, no.-a He was just a PhD student interested in formal
logic and the intriguing unsolved problems of the time, one of which was >>> about what can be determined by finite "mechanical" means.
so I expected he was studying the maximum possible capability
of enemy computing infrastructure to help direct research resources.
On 2/24/26 7:39 PM, dart200 wrote:
On 2/24/26 4:09 PM, Ben Bacarisse wrote:
Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk>
writes:
On 20/02/2026 18:11, Ben Bacarisse wrote:
Turing invented TMs to capture the notion of what is computable
I'm curious to know how his motives are known.
At one level there are very clear.-a In 1928, Hilbert and Ackermann posed >>> the question of whether first-order logic was decidable -- was there an
and they all gave up on essentially meaninglessly garbage like
Only meaningless to the stupid.
und = () -> halts(und) && loop()
it's kinda funny actually, all these greats getting their panties all
twisted up /in the same way/ because of failure to appropriately
handle a lil' self-referential contradiction
But the "self-reference" isn't actually there in the Turing Formulation.
even funnier are all the reactions from chucklefucks resolutely
defending that century long failure as MuH uNQuEsTioNAbLe tRuTH
actually it's not that funny, or funny at all. makes me want to kill
myself for being a such a fking EfniEfiA
Mqybe you should if you are that dumb.
(Not really, but if you want to keep bringing it up, actually think what
it would do).
algorithm that can determine if a given statement is universally valid.
(Given other results this is equivalent to deciding, algorithmically, if >>> a given statement is provable.)
At the time of his now famous paper he was working with Church who had
turned his attention to this as yet unsolved problem.-a At the time, most >>> mathematicians thought the answer would be "yes".-a Of course the first
step is to capture the notion of an algorithm or process.-a Church came
up with the lambda calculus, and Turing the abstract machine that not
bears his name.
However, the idea that mathematics and specifically proofs, might be
automated goes way back to at least Leibniz.
He worked in defence research
Not at the time, no.-a He was just a PhD student interested in formal
logic and the intriguing unsolved problems of the time, one of which was >>> about what can be determined by finite "mechanical" means.
so I expected he was studying the maximum possible capability
of enemy computing infrastructure to help direct research resources.
On 2/24/26 6:13 PM, Richard Damon wrote:
On 2/24/26 7:39 PM, dart200 wrote:
On 2/24/26 4:09 PM, Ben Bacarisse wrote:
Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> >>>> writes:and they all gave up on essentially meaninglessly garbage like
On 20/02/2026 18:11, Ben Bacarisse wrote:
Turing invented TMs to capture the notion of what is computable
I'm curious to know how his motives are known.
At one level there are very clear.-a In 1928, Hilbert and Ackermann
posed
the question of whether first-order logic was decidable -- was there an >>>
Only meaningless to the stupid.
und = () -> halts(und) && loop()
it's kinda funny actually, all these greats getting their panties all
twisted up /in the same way/ because of failure to appropriately
handle a lil' self-referential contradiction
But the "self-reference" isn't actually there in the Turing Formulation.
i've already quoted this at you
/Now let K be the D.N of H. What does H do in the K-th section of
its motion? It must test whether K is satisfactory/
H is literally testing it's own D.N...
even funnier are all the reactions from chucklefucks resolutely
defending that century long failure as MuH uNQuEsTioNAbLe tRuTH
actually it's not that funny, or funny at all. makes me want to kill
myself for being a such a fking EfniEfiA
Mqybe you should if you are that dumb.
(Not really, but if you want to keep bringing it up, actually think
what it would do).
algorithm that can determine if a given statement is universally valid. >>>> (Given other results this is equivalent to deciding,
algorithmically, if
a given statement is provable.)
At the time of his now famous paper he was working with Church who had >>>> turned his attention to this as yet unsolved problem.-a At the time,
most
mathematicians thought the answer would be "yes".-a Of course the first >>>> step is to capture the notion of an algorithm or process.-a Church came >>>> up with the lambda calculus, and Turing the abstract machine that not
bears his name.
However, the idea that mathematics and specifically proofs, might be
automated goes way back to at least Leibniz.
He worked in defence research
Not at the time, no.-a He was just a PhD student interested in formal
logic and the intriguing unsolved problems of the time, one of which
was
about what can be determined by finite "mechanical" means.
so I expected he was studying the maximum possible capability
of enemy computing infrastructure to help direct research resources.
On 2/24/26 9:47 PM, dart200 wrote:
On 2/24/26 6:13 PM, Richard Damon wrote:
On 2/24/26 7:39 PM, dart200 wrote:
On 2/24/26 4:09 PM, Ben Bacarisse wrote:
Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> >>>>> writes:
On 20/02/2026 18:11, Ben Bacarisse wrote:
Turing invented TMs to capture the notion of what is computable
I'm curious to know how his motives are known.
At one level there are very clear.-a In 1928, Hilbert and Ackermann >>>>> posed
the question of whether first-order logic was decidable -- was
there an
and they all gave up on essentially meaninglessly garbage like
Only meaningless to the stupid.
und = () -> halts(und) && loop()
it's kinda funny actually, all these greats getting their panties
all twisted up /in the same way/ because of failure to appropriately
handle a lil' self-referential contradiction
But the "self-reference" isn't actually there in the Turing Formulation.
i've already quoted this at you
/Now let K be the D.N of H. What does H do in the K-th section of
its motion? It must test whether K is satisfactory/
H is literally testing it's own D.N...
But it doesn't have a reference to that. it computed that.
You don't seem to understand what a "reference" is.
Do you think that a compiler can't compile the code for itself?
Yes, a decider that decides on all inputs (as the decision problem
requires) needs to be able to decide about the "value" that it
represents itself.
In part, the undecidability comes out of the fact that the machinery of
the system IS powerful enough that we can convert the machines into
values that can be their inputs.
Since "Turing Complete" machines can do this, any system that can't must
be less powerful than "Turing Complete".
even funnier are all the reactions from chucklefucks resolutely
defending that century long failure as MuH uNQuEsTioNAbLe tRuTH
actually it's not that funny, or funny at all. makes me want to kill
myself for being a such a fking EfniEfiA
Mqybe you should if you are that dumb.
(Not really, but if you want to keep bringing it up, actually think
what it would do).
algorithm that can determine if a given statement is universally
valid.
(Given other results this is equivalent to deciding,
algorithmically, if
a given statement is provable.)
At the time of his now famous paper he was working with Church who had >>>>> turned his attention to this as yet unsolved problem.-a At the time, >>>>> most
mathematicians thought the answer would be "yes".-a Of course the first >>>>> step is to capture the notion of an algorithm or process.-a Church came >>>>> up with the lambda calculus, and Turing the abstract machine that not >>>>> bears his name.
However, the idea that mathematics and specifically proofs, might be >>>>> automated goes way back to at least Leibniz.
He worked in defence research
Not at the time, no.-a He was just a PhD student interested in formal >>>>> logic and the intriguing unsolved problems of the time, one of
which was
about what can be determined by finite "mechanical" means.
so I expected he was studying the maximum possible capability
of enemy computing infrastructure to help direct research resources. >>>>>
On 2/24/26 7:52 PM, Richard Damon wrote:
On 2/24/26 9:47 PM, dart200 wrote:
On 2/24/26 6:13 PM, Richard Damon wrote:
On 2/24/26 7:39 PM, dart200 wrote:
On 2/24/26 4:09 PM, Ben Bacarisse wrote:
Tristan Wibberley
<tristan.wibberley+netnews2@alumni.manchester.ac.uk>
writes:
On 20/02/2026 18:11, Ben Bacarisse wrote:
Turing invented TMs to capture the notion of what is computable >>>>>>>I'm curious to know how his motives are known.
At one level there are very clear.-a In 1928, Hilbert and Ackermann >>>>>> posed
the question of whether first-order logic was decidable -- was
there an
and they all gave up on essentially meaninglessly garbage like
Only meaningless to the stupid.
und = () -> halts(und) && loop()
it's kinda funny actually, all these greats getting their panties
all twisted up /in the same way/ because of failure to
appropriately handle a lil' self-referential contradiction
But the "self-reference" isn't actually there in the Turing
Formulation.
i've already quoted this at you
/Now let K be the D.N of H. What does H do in the K-th section of
its motion? It must test whether K is satisfactory/
H is literally testing it's own D.N...
But it doesn't have a reference to that. it computed that.
You don't seem to understand what a "reference" is.
it has an addressable copy of it's source code on the tape, encoded into
a description number, that it tests
that's the only kind of self-reference that exists in turing machines,
and it always involves some steps in the computation to setup, unless
it's directly set as the input ... but either way it's a reference to itself, and the reference to itself is keystone in undecidability proofs
Do you think that a compiler can't compile the code for itself?
Yes, a decider that decides on all inputs (as the decision problem
requires) needs to be able to decide about the "value" that it
represents itself.
In part, the undecidability comes out of the fact that the machinery
of the system IS powerful enough that we can convert the machines into
values that can be their inputs.
Since "Turing Complete" machines can do this, any system that can't
must be less powerful than "Turing Complete".
even funnier are all the reactions from chucklefucks resolutely
defending that century long failure as MuH uNQuEsTioNAbLe tRuTH
actually it's not that funny, or funny at all. makes me want to
kill myself for being a such a fking EfniEfiA
Mqybe you should if you are that dumb.
(Not really, but if you want to keep bringing it up, actually think
what it would do).
algorithm that can determine if a given statement is universally
valid.
(Given other results this is equivalent to deciding,
algorithmically, if
a given statement is provable.)
At the time of his now famous paper he was working with Church who >>>>>> had
turned his attention to this as yet unsolved problem.-a At the
time, most
mathematicians thought the answer would be "yes".-a Of course the >>>>>> first
step is to capture the notion of an algorithm or process.-a Church >>>>>> came
up with the lambda calculus, and Turing the abstract machine that not >>>>>> bears his name.
However, the idea that mathematics and specifically proofs, might be >>>>>> automated goes way back to at least Leibniz.
He worked in defence research
Not at the time, no.-a He was just a PhD student interested in formal >>>>>> logic and the intriguing unsolved problems of the time, one of
which was
about what can be determined by finite "mechanical" means.
so I expected he was studying the maximum possible capability
of enemy computing infrastructure to help direct research resources. >>>>>>
On 2/24/26 11:02 PM, dart200 wrote:
On 2/24/26 7:52 PM, Richard Damon wrote:
On 2/24/26 9:47 PM, dart200 wrote:
On 2/24/26 6:13 PM, Richard Damon wrote:
On 2/24/26 7:39 PM, dart200 wrote:
On 2/24/26 4:09 PM, Ben Bacarisse wrote:
Tristan Wibberley
<tristan.wibberley+netnews2@alumni.manchester.ac.uk>
writes:
On 20/02/2026 18:11, Ben Bacarisse wrote:
Turing invented TMs to capture the notion of what is computable >>>>>>>>I'm curious to know how his motives are known.
At one level there are very clear.-a In 1928, Hilbert and
Ackermann posed
the question of whether first-order logic was decidable -- was
there an
and they all gave up on essentially meaninglessly garbage like
Only meaningless to the stupid.
und = () -> halts(und) && loop()
it's kinda funny actually, all these greats getting their panties >>>>>> all twisted up /in the same way/ because of failure to
appropriately handle a lil' self-referential contradiction
But the "self-reference" isn't actually there in the Turing
Formulation.
i've already quoted this at you
/Now let K be the D.N of H. What does H do in the K-th section of
its motion? It must test whether K is satisfactory/
H is literally testing it's own D.N...
But it doesn't have a reference to that. it computed that.
You don't seem to understand what a "reference" is.
it has an addressable copy of it's source code on the tape, encoded
into a description number, that it tests
that's the only kind of self-reference that exists in turing machines,
and it always involves some steps in the computation to setup, unless
it's directly set as the input ... but either way it's a reference to
itself, and the reference to itself is keystone in undecidability proofs
Which isn't a "Reference" in the meaning of the word.
Just shows that Turing Machines CAN'T have "self-references" as defined
in logic.
It is processing an input that just happens to match a description of itself.
Since that is a legal input, no foul.
In other words, to try to prohibit this input, means you can't be as powerful in computing as a Turing Machine.
Thus, this "problem" is ESSENTIAL to the nature of the machines, and
can't be just "fixed".
Do you think that a compiler can't compile the code for itself?
Yes, a decider that decides on all inputs (as the decision problem
requires) needs to be able to decide about the "value" that it
represents itself.
In part, the undecidability comes out of the fact that the machinery
of the system IS powerful enough that we can convert the machines
into values that can be their inputs.
Since "Turing Complete" machines can do this, any system that can't
must be less powerful than "Turing Complete".
even funnier are all the reactions from chucklefucks resolutely
defending that century long failure as MuH uNQuEsTioNAbLe tRuTH
actually it's not that funny, or funny at all. makes me want to
kill myself for being a such a fking EfniEfiA
Mqybe you should if you are that dumb.
(Not really, but if you want to keep bringing it up, actually think >>>>> what it would do).
algorithm that can determine if a given statement is universally >>>>>>> valid.
(Given other results this is equivalent to deciding,
algorithmically, if
a given statement is provable.)
At the time of his now famous paper he was working with Church
who had
turned his attention to this as yet unsolved problem.-a At the
time, most
mathematicians thought the answer would be "yes".-a Of course the >>>>>>> first
step is to capture the notion of an algorithm or process.-a Church >>>>>>> came
up with the lambda calculus, and Turing the abstract machine that >>>>>>> not
bears his name.
However, the idea that mathematics and specifically proofs, might be >>>>>>> automated goes way back to at least Leibniz.
He worked in defence research
Not at the time, no.-a He was just a PhD student interested in formal >>>>>>> logic and the intriguing unsolved problems of the time, one of
which was
about what can be determined by finite "mechanical" means.
so I expected he was studying the maximum possible capability
of enemy computing infrastructure to help direct research
resources.
On 2/24/26 11:02 PM, dart200 wrote:
On 2/24/26 7:52 PM, Richard Damon wrote:
On 2/24/26 9:47 PM, dart200 wrote:
On 2/24/26 6:13 PM, Richard Damon wrote:
On 2/24/26 7:39 PM, dart200 wrote:
On 2/24/26 4:09 PM, Ben Bacarisse wrote:
Tristan Wibberley
<tristan.wibberley+netnews2@alumni.manchester.ac.uk>
writes:
On 20/02/2026 18:11, Ben Bacarisse wrote:
Turing invented TMs to capture the notion of what is computable >>>>>>>>I'm curious to know how his motives are known.
At one level there are very clear.-a In 1928, Hilbert and
Ackermann posed
the question of whether first-order logic was decidable -- was
there an
and they all gave up on essentially meaninglessly garbage like
Only meaningless to the stupid.
und = () -> halts(und) && loop()
it's kinda funny actually, all these greats getting their panties >>>>>> all twisted up /in the same way/ because of failure to
appropriately handle a lil' self-referential contradiction
But the "self-reference" isn't actually there in the Turing
Formulation.
i've already quoted this at you
/Now let K be the D.N of H. What does H do in the K-th section of
its motion? It must test whether K is satisfactory/
H is literally testing it's own D.N...
But it doesn't have a reference to that. it computed that.
You don't seem to understand what a "reference" is.
it has an addressable copy of it's source code on the tape, encoded
into a description number, that it tests
that's the only kind of self-reference that exists in turing machines,
and it always involves some steps in the computation to setup, unless
it's directly set as the input ... but either way it's a reference to
itself, and the reference to itself is keystone in undecidability proofs
Which isn't a "Reference" in the meaning of the word.
Just shows that Turing Machines CAN'T have "self-references" as defined
in logic.
It is processing an input that just happens to match a description of itself.
Since that is a legal input, no foul.
In other words, to try to prohibit this input, means you can't be as powerful in computing as a Turing Machine.
Thus, this "problem" is ESSENTIAL to the nature of the machines, and
can't be just "fixed".
Do you think that a compiler can't compile the code for itself?
Yes, a decider that decides on all inputs (as the decision problem
requires) needs to be able to decide about the "value" that it
represents itself.
In part, the undecidability comes out of the fact that the machinery
of the system IS powerful enough that we can convert the machines
into values that can be their inputs.
Since "Turing Complete" machines can do this, any system that can't
must be less powerful than "Turing Complete".
even funnier are all the reactions from chucklefucks resolutely
defending that century long failure as MuH uNQuEsTioNAbLe tRuTH
actually it's not that funny, or funny at all. makes me want to
kill myself for being a such a fking EfniEfiA
Mqybe you should if you are that dumb.
(Not really, but if you want to keep bringing it up, actually think >>>>> what it would do).
algorithm that can determine if a given statement is universally >>>>>>> valid.
(Given other results this is equivalent to deciding,
algorithmically, if
a given statement is provable.)
At the time of his now famous paper he was working with Church
who had
turned his attention to this as yet unsolved problem.-a At the
time, most
mathematicians thought the answer would be "yes".-a Of course the >>>>>>> first
step is to capture the notion of an algorithm or process.-a Church >>>>>>> came
up with the lambda calculus, and Turing the abstract machine that >>>>>>> not
bears his name.
However, the idea that mathematics and specifically proofs, might be >>>>>>> automated goes way back to at least Leibniz.
He worked in defence research
Not at the time, no.-a He was just a PhD student interested in formal >>>>>>> logic and the intriguing unsolved problems of the time, one of
which was
about what can be determined by finite "mechanical" means.
so I expected he was studying the maximum possible capability
of enemy computing infrastructure to help direct research
resources.
On 2/24/26 8:29 PM, Richard Damon wrote:
On 2/24/26 11:02 PM, dart200 wrote:
On 2/24/26 7:52 PM, Richard Damon wrote:
On 2/24/26 9:47 PM, dart200 wrote:
On 2/24/26 6:13 PM, Richard Damon wrote:
On 2/24/26 7:39 PM, dart200 wrote:
On 2/24/26 4:09 PM, Ben Bacarisse wrote:
Tristan Wibberley
<tristan.wibberley+netnews2@alumni.manchester.ac.uk>
writes:
On 20/02/2026 18:11, Ben Bacarisse wrote:
Turing invented TMs to capture the notion of what is computable >>>>>>>>>I'm curious to know how his motives are known.
At one level there are very clear.-a In 1928, Hilbert and
Ackermann posed
the question of whether first-order logic was decidable -- was >>>>>>>> there an
and they all gave up on essentially meaninglessly garbage like
Only meaningless to the stupid.
und = () -> halts(und) && loop()
it's kinda funny actually, all these greats getting their panties >>>>>>> all twisted up /in the same way/ because of failure to
appropriately handle a lil' self-referential contradiction
But the "self-reference" isn't actually there in the Turing
Formulation.
i've already quoted this at you
/Now let K be the D.N of H. What does H do in the K-th section of
its motion? It must test whether K is satisfactory/
H is literally testing it's own D.N...
But it doesn't have a reference to that. it computed that.
You don't seem to understand what a "reference" is.
it has an addressable copy of it's source code on the tape, encoded
into a description number, that it tests
that's the only kind of self-reference that exists in turing
machines, and it always involves some steps in the computation to
setup, unless it's directly set as the input ... but either way it's
a reference to itself, and the reference to itself is keystone in
undecidability proofs
Which isn't a "Reference" in the meaning of the word.
not worthy of my time to debate semantics over something making up
conflicts that need not exist
it's a self-reference for anyone but someone bent on being contrarian
for the sake of it, and i will keep referring to it like regardless of
ur objections
Just shows that Turing Machines CAN'T have "self-references" as
defined in logic.
It is processing an input that just happens to match a description of
itself.
Since that is a legal input, no foul.
In other words, to try to prohibit this input, means you can't be as
powerful in computing as a Turing Machine.
Thus, this "problem" is ESSENTIAL to the nature of the machines, and
can't be just "fixed".
Do you think that a compiler can't compile the code for itself?
Yes, a decider that decides on all inputs (as the decision problem
requires) needs to be able to decide about the "value" that it
represents itself.
In part, the undecidability comes out of the fact that the machinery
of the system IS powerful enough that we can convert the machines
into values that can be their inputs.
Since "Turing Complete" machines can do this, any system that can't
must be less powerful than "Turing Complete".
even funnier are all the reactions from chucklefucks resolutely >>>>>>> defending that century long failure as MuH uNQuEsTioNAbLe tRuTH
actually it's not that funny, or funny at all. makes me want to >>>>>>> kill myself for being a such a fking EfniEfiA
Mqybe you should if you are that dumb.
(Not really, but if you want to keep bringing it up, actually
think what it would do).
algorithm that can determine if a given statement is universally >>>>>>>> valid.
(Given other results this is equivalent to deciding,
algorithmically, if
a given statement is provable.)
At the time of his now famous paper he was working with Church >>>>>>>> who had
turned his attention to this as yet unsolved problem.-a At the >>>>>>>> time, most
mathematicians thought the answer would be "yes".-a Of course the >>>>>>>> first
step is to capture the notion of an algorithm or process.
Church came
up with the lambda calculus, and Turing the abstract machine
that not
bears his name.
However, the idea that mathematics and specifically proofs,
might be
automated goes way back to at least Leibniz.
He worked in defence research
Not at the time, no.-a He was just a PhD student interested in >>>>>>>> formal
logic and the intriguing unsolved problems of the time, one of >>>>>>>> which was
about what can be determined by finite "mechanical" means.
so I expected he was studying the maximum possible capability >>>>>>>>> of enemy computing infrastructure to help direct research
resources.
On 2/24/26 7:39 PM, dart200 wrote:
On 2/24/26 4:09 PM, Ben Bacarisse wrote:
Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk>
writes:
On 20/02/2026 18:11, Ben Bacarisse wrote:
Turing invented TMs to capture the notion of what is computable
I'm curious to know how his motives are known.
At one level there are very clear.-a In 1928, Hilbert and Ackermann posed >>> the question of whether first-order logic was decidable -- was there an
and they all gave up on essentially meaninglessly garbage like
Only meaningless to the stupid.
und = () -> halts(und) && loop()
it's kinda funny actually, all these greats getting their panties all
twisted up /in the same way/ because of failure to appropriately
handle a lil' self-referential contradiction
But the "self-reference" isn't actually there in the Turing Formulation.
even funnier are all the reactions from chucklefucks resolutely
defending that century long failure as MuH uNQuEsTioNAbLe tRuTH
actually it's not that funny, or funny at all. makes me want to kill
myself for being a such a fking EfniEfiA
Mqybe you should if you are that dumb.
(Not really, but if you want to keep bringing it up, actually think what
it would do).
On 2/24/2026 6:13 PM, Richard Damon wrote:
On 2/24/26 7:39 PM, dart200 wrote:
On 2/24/26 4:09 PM, Ben Bacarisse wrote:
Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> >>>> writes:and they all gave up on essentially meaninglessly garbage like
On 20/02/2026 18:11, Ben Bacarisse wrote:
Turing invented TMs to capture the notion of what is computable
I'm curious to know how his motives are known.
At one level there are very clear.-a In 1928, Hilbert and Ackermann
posed
the question of whether first-order logic was decidable -- was there an >>>
Only meaningless to the stupid.
und = () -> halts(und) && loop()
it's kinda funny actually, all these greats getting their panties all
twisted up /in the same way/ because of failure to appropriately
handle a lil' self-referential contradiction
But the "self-reference" isn't actually there in the Turing Formulation.
even funnier are all the reactions from chucklefucks resolutely
defending that century long failure as MuH uNQuEsTioNAbLe tRuTH
actually it's not that funny, or funny at all. makes me want to kill
myself for being a such a fking EfniEfiA
Mqybe you should if you are that dumb.
(Not really, but if you want to keep bringing it up, actually think
what it would do).
dart is a low life that likes to tell others to snuff themselves out.
Laughs about it. Sigh. I suggest plonking that garbage.
[...]
On 2/28/26 6:24 PM, Richard Damon wrote:
On 2/28/26 8:24 PM, dart200 wrote:
On 2/28/26 2:08 PM, Richard Damon wrote:
On 2/28/26 12:38 PM, dart200 wrote:
On 2/28/26 5:21 AM, Richard Damon wrote:
On 2/27/26 6:09 AM, dart200 wrote:
On 2/27/26 2:51 AM, Tristan Wibberley wrote:
On 24/02/2026 21:30, dart200 wrote:
On 2/24/26 11:38 AM, Tristan Wibberley wrote:
On 22/02/2026 21:08, dart200 wrote:
On 2/22/26 12:49 PM, Chris M. Thomasson wrote:...
On 2/22/2026 9:04 AM, dart200 wrote:
an effective enumeration of all turing machines was proven on >>>>>>>>>>>>> turing's original paper and can be reused anywhere... >>>>>>>>>>>>You think you can test all of them one by one? Don't tell me >>>>>>>>>>>> you think
yes that's what diagonal proofs do...
Eh?!
A test is a procedure! You can't test /all/ of an infinitude >>>>>>>>>> one by one.
that exactly what turing does in his proof: he defines a
comptuation
that enumerates out all the numbers, testing each one of they >>>>>>>>> represent
a "satisfactory"/"circle-free" machine, and adding that to
diagonal
across defined across computable numbers
it really would be a great exercise to carefully read p247 of >>>>>>>>> turing's
proof and produce the psuedo-code for the machine H, assuming that >>>>>>>>> machine D exists
I'll get to it sooner then, because it's mad. Are you sure he >>>>>>>> didn't
reason quantified over all but phrase it like a procedure for >>>>>>>> what he
the theory of computation is the theory of such procedures, and >>>>>>> understanding the diagonal procedure is critical to understanding >>>>>>> the *base* contradiction/paradox that the rest of his support for >>>>>>> godel's result is then built on
And focusing on what is said to be impossible and not changing the >>>>>> problem is also important.
The problem with the diagonal generation isn't the generation of
the diagonal itself, but effectively enumerating the enumeration
in the first place.
i don't see any indication that turing realized a difference there
Then you zre just showing your stupidity, because YOU can't tell the
difference.
After all, on page 246 he says:
The computable sequences are therefore not enumerable.
Here is is SPECIFICALLY talking about the effective enumeration of
the computable sequences.
He then points out that he can directly show that the "anti-
diagonal" of the (non-effectively computed) enumeration can't be
computed but that "This proof, although perfectly sound, has the
disadvantage that it may leave the reader with a feeling that 'there
must be something wrong'".
it is wrong,
No, YOU are wrong, as you don't understand what is being done.
I think he is refering he to the standard anti-diagonal arguement,
which shows that since for all n, position n differs from the value in
number n, there can not be any element that matches the anti-diagonal.
It is just a natural fact of countable infinity, something it seems
you just don't understand.
Show how that is actually wrong.
wow, u know up until now, i thot i fully agreed with turing's short
diagonal proof, but in writing this post i now find myself in a subtle,
yet entirely critical disagreement:
/let an be the n-th computable sequence, and let -an(m) be the m-th
figure in an. Let +# be the sequence with 1--an(m) as its n-th. figure. Since +# is computable, there exists a number K [== +#] such that 1--an(n)
= -aK(n) for all n. Putting n = K, we have 1 = 2-aK(K), i.e. 1 is even.
This is impossible/
the fallacy here is assuming that because the direct diagonal is
computable, that one can therefore compute the anti-diagonal using the direct diagonal. the abstract definition makes it look simple, but this ignores the complexities of self-referential analysis (like what turing details on the next page)
in both methods i have for rectifying the paradox found in the direct diagonal (either (1) filtering TMs or (2) using RTMs), neither can be
used to then compute the anti-diagonal
in (1) the algo to compute an inverse diagonal is filtered out like
turing's paradoxical variation of the direct diagonal would be, and
there is no analogous non-paradoxical variation that has a hard coded
value that is inverse to what it does return ... such a concept is
entirely nonsensical. a function can only return what it does, it can't
also return the inverse to what it returns eh???
in (2) the attempt to compute an inverse diagonal with RTMs just fails
for reasons u'd only understand by working thru the algo urself (p7 of
re: turing's diagonals)
the premise:
/Let +# be the sequence with 1--an(m) as its n-th/
= -aK(n) for all n/
\_(paa)_/->
is just not sufficient evidence that such +# is actually computable given the direct diagonal -an()
one cannot just assume that because the diagonal across computable
numbers is computable, therefore the anti-diagonal across computable
numbers is computable...
He doesn't. You are just showing your stupidity,
He is proving the enumeration is uncomputable, and without the
enumeration, you can't compute either of them.
neither method i have for fixing the diagonal computation across the
computable numbers can be used to compute the inverse diagonal
But your method still doesn't let you compute the enumeration, and
thus you can't actually compute the diagonal.
Remember, the problem definitions requires that the listing be a
COMPLETE listing of the computable numbers / machine that compute
computable numbers, in some definite order.
If your enumeration isn't complete, your diagonal isn't correct.
so while i agree with turing that the anti-diagonal is not
computable, i don't agree that the normal diagonal is not computable
Why?
How does D decide on the original H?
Your modified H still needs a correct D to decide on all the other
machines, including his original H that doesn't use your "trick"
But instead, he can prove with a more obvious process, that the
Decider "D" that could be used to effectively enumerate the sequence
of machine that produce computable numbers can not esit.
Thus, he clearly knows the difference, but is pointing out that the
attempt to compute the diagonal clearly reveals the issue with
effectively enumerating the sequences.
well, he didn't consider that perhaps the proper algo for computing
the diagonal can avoid the paradox on itself ...
But it doesn't.
Your just don't understand that D just can't correctly decide on his
given H.
no idea why ur claiming that
i clearly understand that D cannot decide correctly on turing's H,
because my response to this is that D does not need to decide correctly
on H to compute a diagonal
It doesn't matter that your new H doesn't get stuck on itself, it will
still error on Turing's H.
turing's H, as it stands, doesn't even exist my dude. he doesn't specify what D (or H) needs to do when encountering the /undecidable input/ of
H, so therefore both D and H are an incomplete specifications of a machine
IF D is wrong by deciding it is not circle free, then your H will
compute the wrong diagonal, as the resulting version of his H WILL be
circle free (since it never tries to simulate itself) and thus DOES
produce an computable number that your computation misses.
Or, if that D is wrong by decing it IS circle free, then when you H
tries to process it, it will get stuck in the infinite loop.
The problem is that in stepping through the machines in order, you
WILL hit these actual machines built on your erroneous D (your D must
have this flaw, as no D without exists), and thus you will be wrong on
THAT input. IT doesn't matter if you get a good answer for yourself.
idk what he would have said about it, but prolly something more
substantial than just calling me ignorant repeatedly
I doubt it.
He likely would have gotten frustrated by your idiodic assertion of
bad logic. You would have likely been escorted out of the meeting as
showing you were unqualified and being a distraction.
Something that seems to be beyond your ignorant understanding.
interestingly: one can only fix the direct diagonal computation
H shows that *IF* you can make that enumeration, you can make the >>>>>> diagonal, and thus the anti-diagonal. The problem is you can't
make that enumeration, and assuming you can just shows unsoundness. >>>>>
like this
u can't do an analogous fix for the inverse/anti-diagonal
computation. it's not possible hard code a machine to return an
inverted value, a machine can only return what it does, not the
inverse of what it does...
so if we can filter out paradoxes from the enumeration, that will
leave a direct diagonal computation extant in that filtered (yet
still turing complete list), while any attempt to compute an
inverse diagonal will not be
But the problem is that "paradoxical machines" don't exist in
isolation, but only in relationship to a given machine trying to
decide them.
right. so if ur constructing a diagonal across computable numbers
then u only need to filter out paradoxes in regards to the classifier
that classifies them as a "satisfactory" number
Right, which he shows can not be done.
please do quote where turing shows we can't filter out such paradoxes...
(also why do always just make random assertions???)
any machine which *is not* "satisfactory" OR *is not* classifiable as
satisfactory by said classifier... can just be skipped
No, it can only skip those that are not satisfactory, not those that
are but it can not classify as such, or your enumeration will not be
complete, and thus just in error.
Thus, it needs to be able to correctly classify ALL machines (as it
will be asked about all machines as it counts through all the
descriptions) and thus Turing's H *WILL* be asked about.
similarly if u want to go a step further an filter out computable
numbers already included on this diagonal, any machine which either
*is* computably equivalent OR *is not* classifiable in regards to
*any* machine already the list... can just be skipped
Nope, you can't skip some machines, as you then might lose some of the
computable numbers.
see you can't compute a diagonal across *all* /machines/, with said
machines, but u can compute a diagonal across *all* /computable numbers/
Nope,
Since the enumeration of ALL Computable numbers can't be done, since
ALL classifiers that attempt it will make an error, you can't do what
you want to do.
nah, (a) computing an enumeration of all /computable numbers/ is not the same thing as (b) computing the enumeration of all machines that compute computable numbers. (b) necessarily has duplicates while (a) does not
need them. turing's paper wrongly conflates (a) with (b)
i'm pretty sure (a) can be done with TMs
(b) probably can't be done with TMs
yes, i still do need to prove my thesis that for any paradoxical
machine, there exists a functionally equivalent machine without such
paradox
And the problem is that your "paradoxical" isn't actually a definable
property (let alone computable). Part of the problem is that if you
look at just a machine description, it doesn't (necessarily) tell you
about the use of an "interface" as that use of an interface can be
just inlined, leaving nothing "in the code" to show it exists.
i'm sorry, are you actually saying the machine description does not
describe what the machine does???
lol
His specified H, with an actually (incorrect) implementation of D
(which is all that CAN exist) will either be circle-free and thus
generate a number (but its D said it isn't, and thus omitted a valid
machine from the list) or it isn't circle-free, and fails to computa
a number, and thus should have been omitted from the list but wasn't.
Thus any H that ACTUALLY EXISTS, isn't a "paradox", it is just built
on an assuption in error.
so despite turing's worries, the existence of a diagonal
computation does not actually then imply the existence of an anti-
diagonal computation, due the same particular self-referential
weirdness that stumped turing the first place
But there is no actuall SELF-REFERENCE, so your logic is just based
on ERROR.
Your attempt to REDEFINE self-reference to mean processing a number
that happens to represent yourself means that you you system "ALL"
doesn't actually mean ALL, and thus is just ill-defined.
i'm sorry, you have an issue with me labeling a number that directly
refers to yourself, as a "self-reference" ???
Sure, because it is just a number. The problem is that you still have
it's a *specific* number that has the currently running machine encoded
into it, it's not "just" a number whatever that means
problems with all the "equivalent" machines that have different numbers.
those are references to functionally equivalent machines, not self- references
It may let you filter out the simplest case used in the proofs, but
doesn't solve the actual problem, as the "Machine Number" doesn't
actually fully identify the problematic cases.
that's not actually true. you can't meaningfully paradox the paradox detector while filter *out* paradoxes to point of creating an actual
problem
let halts be a halting classifier that takes an input machines and
returns true/false whether it halts or not
let paradox_free be a paradox filtering classifier that takes an input classifier, and an input machine to search for paradoxes in regards to: paradox_free(classifier, machine)
for example if take our basic halting paradox:
-a und = () -> halts(und) loop()
then:
-a paradox_free(halts, und) -> TRUE
but you might think one still can bamboozle the paradox classifier like such:
-a undp = () -> {
-a-a-a if ( paradox_free(halts, undp) == TRUE )
-a-a-a-a-a if ( halts(undp) ) loop()
-a }
here if paradox_free(halts,undp) -> FALSE, then the if case run a
halting paradox form making it /undecidable input/ to halts().
however, if paradox_free(halts,undp) -> TRUE, then that if case doesn't
run and clearly halts(undp) -> TRUE without issues
BUT THAT'S FINE FOR OUR USE CASE, no paradox found within a machine is necessary for the particular input->output computation being done, so utilizing the return paradox_free(halts,undp) -> FALSE to filter out paradox_free() paradoxes as well as halts() paradoxes will suffice to produce a turing complete subset of machines that can be totally
classified by halts()
i think a major problem with the consensus perspective is an expectation
of a certain cleanliness in the logic as being the only possibility here
to compute what we want. TM's can't achieve that, but something slightly messier can.
dear future: u see this shit i'm trying work with???? sorry i didn't
manage to make progress any faster, but i'm literally dragging
toddlers kicking and screaming at this point jeez...
In other words, in your world "ALL" isn't a word that can actually be
used.
You don't understand that you need to use actual sound logic,
lol, i can only EfOA someone would engage in sound logic with me
This just shows that you real problem is you don't understand what
...which u won't find interesting, but i can't fix a lack of curiosity >>>>>
Efn+
expected was an inexpert audience, supposing that experts will >>>>>>>> recognise
the relevant mapping to universal quantification?
the actual problem is, and your world is just build on things that
are lies.
IT seems that fundamentally, your world doesn't actually have
"computations" as you don't understand the basic requirement that
they need to be fully defined in the actions they do.
| Sysop: | Amessyroom |
|---|---|
| Location: | Fayetteville, NC |
| Users: | 59 |
| Nodes: | 6 (0 / 6) |
| Uptime: | 24:10:58 |
| Calls: | 810 |
| Calls today: | 1 |
| Files: | 1,287 |
| D/L today: |
12 files (21,036K bytes) |
| Messages: | 195,978 |