On 2021-09-19 09:46, olcott wrote:
On 9/19/2021 10:40 AM, André G. Isaak wrote:
On 2021-09-19 08:34, olcott wrote:
On 9/18/2021 11:19 PM, André G. Isaak wrote:
On 2021-09-18 22:10, André G. Isaak wrote:
And note that Rice is talking about properties of Turing Machines
(or, more properly, of the language accepted by a TM), not
computations.
I realized immediately after hitting 'send' that the above will no
doubt confuse you since people have been telling you that Turing
Machines can only express computations whereas C/x86 aren't thus
constrained.
A computation is a Turing Machine description PLUS an input string.
Rice's theorem is concerned with the Turing Machine's themselves.
The Linz proof shows that you cannot construct a halting decider,
i.e. a decider which correctly determines for any given TM + input
string pair, whether that pair represents a halting computation.
Rice's theorem, on the other hand, would rule out the construction
of something like a Decider Decider, i.e. a TM which takes as its
input a TM description and determines whether that TM qualifies as
a decider, i.e. is guaranteed to halt on *any* possible input.
André
Here is where I referred to my code defining a
a decidability decider nine days before you did:
Where did I define or even mention a 'decidability decider'? Above I
discussed (but did not define) a DECIDER decider, i.e. a TM which
determines whether another TM qualifies as a decider.
On 9/9/2021 10:25 AM, olcott wrote:
It is the case that H(P,P)==0 is correct
It is the case that H1((P,P)==1 is correct
It is the case the this is inconsistent.
It is the case that this inconsistency
defines a decidability decider that correctly
defines a decidability decider that correctly
defines a decidability decider that correctly
rejects P on the basis that P has the
pathological self-reference(Olcott 2004) error.
So what exactly is it that the above is deciding? And how does this
relate to Rice? If you want to claim this is somehow related to rice,
you need to identify some semantic property that you claim to be able
to decide.
André
It is deciding that either H/P or H1/P form the pathological
self-reference error(Olcott 2004). As I said in 2004 this is the same
error as the Liar Paradox. This means that either H/P or H1/P are not
correctly decidable.
The post in which I mentioned a 'decider decider' which you somehow
misread as 'decidability decider' was intended to clarify a single
sentence from an earlier post which you entirely ignored. Why don't you
go back and actually read that earlier post and address the points made therein.
Your ill-defined notion of a 'pathological self-reference error' doesn't appear to be a property of a Turing Machine, which is what Rice's
theorem is concerned with. To the extent that it is a property at all,
it appears to be a property of specific computations, so this has
absolutely no relevance to Rice.
André
On 2021-09-19 10:39, olcott wrote:
On 9/19/2021 11:11 AM, André G. Isaak wrote:
On 2021-09-19 09:46, olcott wrote:
On 9/19/2021 10:40 AM, André G. Isaak wrote:
On 2021-09-19 08:34, olcott wrote:
On 9/18/2021 11:19 PM, André G. Isaak wrote:
On 2021-09-18 22:10, André G. Isaak wrote:
And note that Rice is talking about properties of Turing
Machines (or, more properly, of the language accepted by a TM), >>>>>>>> not computations.
I realized immediately after hitting 'send' that the above will
no doubt confuse you since people have been telling you that
Turing Machines can only express computations whereas C/x86
aren't thus constrained.
A computation is a Turing Machine description PLUS an input string. >>>>>>>
Rice's theorem is concerned with the Turing Machine's themselves. >>>>>>>
The Linz proof shows that you cannot construct a halting decider, >>>>>>> i.e. a decider which correctly determines for any given TM +
input string pair, whether that pair represents a halting
computation.
Rice's theorem, on the other hand, would rule out the
construction of something like a Decider Decider, i.e. a TM which >>>>>>> takes as its input a TM description and determines whether that
TM qualifies as a decider, i.e. is guaranteed to halt on *any*
possible input.
André
Here is where I referred to my code defining a
a decidability decider nine days before you did:
Where did I define or even mention a 'decidability decider'? Above
I discussed (but did not define) a DECIDER decider, i.e. a TM which
determines whether another TM qualifies as a decider.
On 9/9/2021 10:25 AM, olcott wrote:
It is the case that H(P,P)==0 is correct
It is the case that H1((P,P)==1 is correct
It is the case the this is inconsistent.
It is the case that this inconsistency
defines a decidability decider that correctly
defines a decidability decider that correctly
defines a decidability decider that correctly
rejects P on the basis that P has the
pathological self-reference(Olcott 2004) error.
So what exactly is it that the above is deciding? And how does this
relate to Rice? If you want to claim this is somehow related to
rice, you need to identify some semantic property that you claim to
be able to decide.
André
It is deciding that either H/P or H1/P form the pathological
self-reference error(Olcott 2004). As I said in 2004 this is the
same error as the Liar Paradox. This means that either H/P or H1/P
are not correctly decidable.
The post in which I mentioned a 'decider decider' which you somehow
misread as 'decidability decider' was intended to clarify a single
sentence from an earlier post which you entirely ignored. Why don't
you go back and actually read that earlier post and address the
points made therein.
Your ill-defined notion of a 'pathological self-reference error'
doesn't appear to be a property of a Turing Machine, which is what
Rice's theorem is concerned with. To the extent that it is a property
at all, it appears to be a property of specific computations, so this
has absolutely no relevance to Rice.
André
It is the property of H(P,P).
Right, which means this is entirely irrelevant to Rice's theorem.
u32 PSR_Olcott_2004(u32 P)
{
return H1(P,P) != H(P,P);
}
Decides that H(P,P) cannot correctly decide the halt status of its input,
No, it does not. It decides that the results of H1(P, P) doesn't match
the results of H(P, P). It 'decides' that one of these is correct and
the other is not but it cannot tell you which one, which means it can't decide whether H(P, P) can correctly decide the halt status of its input.
thus a semantic property of H relative to P.
That's not a property (semantic or otherwise) of *either* P or H.
The Liar Paradox works this same way.
The liar's paradox is completely irrelevant to Linz.
André
The pathological self-reference error (Olcott 2004) is specifically
relevant to:
(a) The Halting Theorem
(b) The 1931 Incompleteness Theorem
(c) The Tarski undefinability theorem
(d) The Liar Paradox (upon which (c) is based).
On 2021-09-19 11:07, olcott wrote:
On 9/19/2021 11:56 AM, André G. Isaak wrote:
On 2021-09-19 10:39, olcott wrote:
On 9/19/2021 11:11 AM, André G. Isaak wrote:
On 2021-09-19 09:46, olcott wrote:
On 9/19/2021 10:40 AM, André G. Isaak wrote:
On 2021-09-19 08:34, olcott wrote:
On 9/18/2021 11:19 PM, André G. Isaak wrote:
On 2021-09-18 22:10, André G. Isaak wrote:
And note that Rice is talking about properties of Turing
Machines (or, more properly, of the language accepted by a >>>>>>>>>> TM), not computations.
I realized immediately after hitting 'send' that the above will >>>>>>>>> no doubt confuse you since people have been telling you that >>>>>>>>> Turing Machines can only express computations whereas C/x86
aren't thus constrained.
A computation is a Turing Machine description PLUS an input
string.
Rice's theorem is concerned with the Turing Machine's themselves. >>>>>>>>>
The Linz proof shows that you cannot construct a halting
decider, i.e. a decider which correctly determines for any
given TM + input string pair, whether that pair represents a >>>>>>>>> halting computation.
Rice's theorem, on the other hand, would rule out the
construction of something like a Decider Decider, i.e. a TM
which takes as its input a TM description and determines
whether that TM qualifies as a decider, i.e. is guaranteed to >>>>>>>>> halt on *any* possible input.
André
Here is where I referred to my code defining a
a decidability decider nine days before you did:
Where did I define or even mention a 'decidability decider'?
Above I discussed (but did not define) a DECIDER decider, i.e. a >>>>>>> TM which determines whether another TM qualifies as a decider.
On 9/9/2021 10:25 AM, olcott wrote:
It is the case that H(P,P)==0 is correct
It is the case that H1((P,P)==1 is correct
It is the case the this is inconsistent.
It is the case that this inconsistency
defines a decidability decider that correctly
defines a decidability decider that correctly
defines a decidability decider that correctly
rejects P on the basis that P has the
pathological self-reference(Olcott 2004) error.
So what exactly is it that the above is deciding? And how does
this relate to Rice? If you want to claim this is somehow related >>>>>>> to rice, you need to identify some semantic property that you
claim to be able to decide.
André
It is deciding that either H/P or H1/P form the pathological
self-reference error(Olcott 2004). As I said in 2004 this is the
same error as the Liar Paradox. This means that either H/P or H1/P >>>>>> are not correctly decidable.
The post in which I mentioned a 'decider decider' which you somehow
misread as 'decidability decider' was intended to clarify a single
sentence from an earlier post which you entirely ignored. Why don't
you go back and actually read that earlier post and address the
points made therein.
Your ill-defined notion of a 'pathological self-reference error'
doesn't appear to be a property of a Turing Machine, which is what
Rice's theorem is concerned with. To the extent that it is a
property at all, it appears to be a property of specific
computations, so this has absolutely no relevance to Rice.
André
It is the property of H(P,P).
Right, which means this is entirely irrelevant to Rice's theorem.
Many historical posts in comp.theory say otherwise.
If a function can be provided that correctly decides that a specific
TM cannot correctly decide a specific input pair (according to many
historical posts on comp.theory) this does refute Rice's theorem.
So what is the semantic property *of P* that you claim your
PSR_Olcott_2004 is capable of identifying?
You can't claim that there is anything 'erroneous' about P. There isn't.
The fact that you run into a problem when you pass a description of P to
some *other* TM is not an indicator that there is something wrong with
P. That's like saying that the expression 40 + 50 is 'erroneous' because
I can't pass it as an argument to tangent().
u32 PSR_Olcott_2004(u32 P)
{
return H1(P,P) != H(P,P);
}
Decides that H(P,P) cannot correctly decide the halt status of its
input,
No, it does not. It decides that the results of H1(P, P) doesn't
match the results of H(P, P). It 'decides' that one of these is
correct and the other is not but it cannot tell you which one, which
means it can't decide whether H(P, P) can correctly decide the halt
status of its input.
I simply have not gotten to that part yet.
And yet you claimed to be able to 'decide' that H(P, P) cannot correctly decide the halt status of its input. Until you actually 'get to that
part' you have no business making such a claim.
thus a semantic property of H relative to P.
That's not a property (semantic or otherwise) of *either* P or H.
The Liar Paradox works this same way.
The liar's paradox is completely irrelevant to Linz.
André
The pathological self-reference error (Olcott 2004) is specifically
relevant to:
(a) The Halting Theorem
(b) The 1931 Incompleteness Theorem
(c) The Tarski undefinability theorem
(d) The Liar Paradox (upon which (c) is based).
So why don't you:
(a) provide a proper definition of "pathological self-reference error"
That means a definition which will allow one to unambiguosly determine whether an arbitrary expression/entity has this error.
(b) explain in what sense an "error" is a property.
(c) demonstrate that whatever property you are referring to is a
*semantic* property.
André
On 2021-09-19 11:54, olcott wrote:
On 9/19/2021 12:25 PM, André G. Isaak wrote:
On 2021-09-19 11:07, olcott wrote:
On 9/19/2021 11:56 AM, André G. Isaak wrote:
On 2021-09-19 10:39, olcott wrote:
On 9/19/2021 11:11 AM, André G. Isaak wrote:
On 2021-09-19 09:46, olcott wrote:
On 9/19/2021 10:40 AM, André G. Isaak wrote:
On 2021-09-19 08:34, olcott wrote:
On 9/18/2021 11:19 PM, André G. Isaak wrote:
On 2021-09-18 22:10, André G. Isaak wrote:
And note that Rice is talking about properties of Turing >>>>>>>>>>>> Machines (or, more properly, of the language accepted by a >>>>>>>>>>>> TM), not computations.
I realized immediately after hitting 'send' that the above >>>>>>>>>>> will no doubt confuse you since people have been telling you >>>>>>>>>>> that Turing Machines can only express computations whereas >>>>>>>>>>> C/x86 aren't thus constrained.
A computation is a Turing Machine description PLUS an input >>>>>>>>>>> string.
Rice's theorem is concerned with the Turing Machine's
themselves.
The Linz proof shows that you cannot construct a halting >>>>>>>>>>> decider, i.e. a decider which correctly determines for any >>>>>>>>>>> given TM + input string pair, whether that pair represents a >>>>>>>>>>> halting computation.
Rice's theorem, on the other hand, would rule out the
construction of something like a Decider Decider, i.e. a TM >>>>>>>>>>> which takes as its input a TM description and determines >>>>>>>>>>> whether that TM qualifies as a decider, i.e. is guaranteed to >>>>>>>>>>> halt on *any* possible input.
André
Here is where I referred to my code defining a
a decidability decider nine days before you did:
Where did I define or even mention a 'decidability decider'? >>>>>>>>> Above I discussed (but did not define) a DECIDER decider, i.e. >>>>>>>>> a TM which determines whether another TM qualifies as a decider. >>>>>>>>>
On 9/9/2021 10:25 AM, olcott wrote:
It is the case that H(P,P)==0 is correct
It is the case that H1((P,P)==1 is correct
It is the case the this is inconsistent.
It is the case that this inconsistency
defines a decidability decider that correctly
defines a decidability decider that correctly
defines a decidability decider that correctly
rejects P on the basis that P has the
pathological self-reference(Olcott 2004) error.
So what exactly is it that the above is deciding? And how does >>>>>>>>> this relate to Rice? If you want to claim this is somehow
related to rice, you need to identify some semantic property >>>>>>>>> that you claim to be able to decide.
André
It is deciding that either H/P or H1/P form the pathological
self-reference error(Olcott 2004). As I said in 2004 this is the >>>>>>>> same error as the Liar Paradox. This means that either H/P or
H1/P are not correctly decidable.
The post in which I mentioned a 'decider decider' which you
somehow misread as 'decidability decider' was intended to clarify >>>>>>> a single sentence from an earlier post which you entirely
ignored. Why don't you go back and actually read that earlier
post and address the points made therein.
Your ill-defined notion of a 'pathological self-reference error' >>>>>>> doesn't appear to be a property of a Turing Machine, which is
what Rice's theorem is concerned with. To the extent that it is a >>>>>>> property at all, it appears to be a property of specific
computations, so this has absolutely no relevance to Rice.
André
It is the property of H(P,P).
Right, which means this is entirely irrelevant to Rice's theorem.
Many historical posts in comp.theory say otherwise.
If a function can be provided that correctly decides that a specific
TM cannot correctly decide a specific input pair (according to many
historical posts on comp.theory) this does refute Rice's theorem.
So what is the semantic property *of P* that you claim your
PSR_Olcott_2004 is capable of identifying?
You can't claim that there is anything 'erroneous' about P. There isn't. >>>
The fact that you run into a problem when you pass a description of P
to some *other* TM is not an indicator that there is something wrong
with P. That's like saying that the expression 40 + 50 is 'erroneous'
because I can't pass it as an argument to tangent().
u32 PSR_Olcott_2004(u32 P)
{
return H1(P,P) != H(P,P);
}
Decides that H(P,P) cannot correctly decide the halt status of its >>>>>> input,
No, it does not. It decides that the results of H1(P, P) doesn't
match the results of H(P, P). It 'decides' that one of these is
correct and the other is not but it cannot tell you which one,
which means it can't decide whether H(P, P) can correctly decide
the halt status of its input.
I simply have not gotten to that part yet.
And yet you claimed to be able to 'decide' that H(P, P) cannot
correctly decide the halt status of its input. Until you actually
'get to that part' you have no business making such a claim.
Odd man out:
When H1(P,P) != H(P,P) we test
HX(P,P) != H1(P,P)
HX(P,P) != H(P,P)
The one that HX(P,P) agrees with is the correct one.
There are a potentially infinite number of Hns. Your 'decider' only
qualifies as a decider if it works for *every* one of them. Your 'odd
man out strategy' only works if the case you are testing happens to be
among the three which are included in your test function.
thus a semantic property of H relative to P.
That's not a property (semantic or otherwise) of *either* P or H.
The Liar Paradox works this same way.
The liar's paradox is completely irrelevant to Linz.
André
The pathological self-reference error (Olcott 2004) is specifically
relevant to:
(a) The Halting Theorem
(b) The 1931 Incompleteness Theorem
(c) The Tarski undefinability theorem
(d) The Liar Paradox (upon which (c) is based).
So why don't you:
(a) provide a proper definition of "pathological self-reference error"
That means a definition which will allow one to unambiguosly
determine whether an arbitrary expression/entity has this error.
I just provided a reference to function that correctly decide this.
No. You provided an ad hoc function which decides it for a *single*
case. That's not the same thing as a function which correctly decides it.
It is a well-established fact that you cannot trisect an arbitrary angle using only a compass and straightedge. I can show you how to trisect a
90° angle using a compass and straightedge, but this doesn't refute the claim. Only a solution which works for *any* angle would refute the claim.
As long as my "pure function of its inputs" becomes fully validated
I will be able to provide the actual source-code that makes this
decision.
(b) explain in what sense an "error" is a property.
(c) demonstrate that whatever property you are referring to is a
*semantic* property.
André
The pathological self reference error is when an
(a) Input P to a halt decider // halting theorem
has self-reference such that the Boolean value of H(P,P)
cannot be correctly determined by H.
(b) An expression of natural language // liar paradox
has self-reference such that the Boolean value this expression cannot
be correctly determined.
(c) An expression of formal language // incompleteness / undefinability.
has self-reference such that the Boolean value this expression cannot
be correctly determined within the same formal system.
None of those constitute definitions. Nor do they identify properties.
And if you want to claim that PSR is an actual thing, you need a single definition. And, as has been pointed out to you numerous times, neither
the halting problem proofs nor the incompleteness theorem involve self-reference at all. This is just your imaginary bugaboo.
André
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