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.

>>>> 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.
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.

--
Copyright 2021 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre
minds." Einstein