On 1/28/2023 11:35 AM, Richard Damon wrote:
> On 1/28/23 11:45 AM, olcott wrote:
>> On 1/28/2023 10:08 AM, Richard Damon wrote:
>>> On 1/28/23 10:49 AM, olcott wrote:
>>>> On 1/28/2023 7:00 AM, Richard Damon wrote:
>>>>> On 1/28/23 12:19 AM, olcott wrote:
>>>>>> On 1/27/2023 10:54 PM, Richard Damon wrote:
>>>>>>> On 1/27/23 11:47 PM, olcott wrote:
>>>>>>>> On 1/27/2023 10:05 PM, Richard Damon wrote:
>>>>>>>>> On 1/27/23 10:59 PM, olcott wrote:
>>>>>>>>>> On 1/27/2023 9:47 PM, Richard Damon wrote:
>>>>>>>>>>> On 1/27/23 10:34 PM, olcott wrote:
>>>>>>>>>>>> On 1/27/2023 9:19 PM, Richard Damon wrote:
>>>>>>>>>>>>> On 1/27/23 8:56 PM, olcott wrote:
>>>>>>>>>>>>>> On 1/26/2023 10:16 PM, Richard Damon wrote:
>>>>>>>>>>>>>>> On 1/26/23 10:46 PM, olcott wrote:
>>>>>>>>>>>>>>>> To be correct the TM need not calculate the sum of every
>>>>>>>>>>>>>>>> finite
>>>>>>>>>>>>>>>> set of finite strings of ASCII digits, it merely has to
>>>>>>>>>>>>>>>> always
>>>>>>>>>>>>>>>> compute this sum correctly for any arbitrary element of the
>>>>>>>>>>>>>>>> finite set of finite strings.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> NBot talking about "Sums"
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> I just proved that there are no countability issues with the
>>>>>>>>>>>>>> computability of halting on the basis that there are no
>>>>>>>>>>>>>> countability
>>>>>>>>>>>>>> issues with the computation of sums.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> Nope. Falllicy of proof byt example.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> None-the-less if sum has no countability issue with any
>>>>>>>>>>>> finite set of
>>>>>>>>>>>> finite strings then H cannot have any countability issue
>>>>>>>>>>>> with any
>>>>>>>>>>>> finite pair of finite strings.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> How do you make a countable infinite number of machine make
>>>>>>>>>>> an uncountable number of maps.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> I ask you again can you count to one?
>>>>>>>>>
>>>>>>>>> YTes, SO WHAT.
>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> There is only one machine that always has a finite number of
>>>>>>>>>> inputs.
>>>>>>>>>> We don't need any maps we only need one set of inputs deriving
>>>>>>>>>> a single
>>>>>>>>>> output for any arbitrary set of inputs. When we think of this
>>>>>>>>>> as sums
>>>>>>>>>> then it is obvious that countability is not an issue.
>>>>>>>>>
>>>>>>>>> So you are saying that the machine that computes the prime
>>>>>>>>> factors of its input it the same machine that computes its
>>>>>>>>> inputs factorial?
>>>>>>>>>
>>>>>>>>> You DO understand that a Turing Machine can be treated as a
>>>>>>>>> computation that computes a specific mapping of inputs to outputs?
>>>>>>>>>
>>>>>>>>
>>>>>>>> A TM must only compute the mapping from any arbitrary finite set of
>>>>>>>> inputs to its finite set of outputs.
>>>>>>>>
>>>>>>>>> Maybe not, as you are too stupid.
>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Is there any finite set of finite strings of ASCII digits that
>>>>>>>>>> cannot be
>>>>>>>>>> summed by a TM? No, therefore computability is proven.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> But summing isn't the only operation that a TM can do.
>>>>>>>>
>>>>>>>> That there is never any countability issue in the computing
>>>>>>>> mapping of
>>>>>>>> one arbitrary finite set of inputs to its corresponding finite
>>>>>>>> set of
>>>>>>>> outputs with any computation at all proves that there is no such
>>>>>>>> issue
>>>>>>>> for summing or halt status detection.
>>>>>>>
>>>>>>> So you are claiming that proof by example is true, that if one
>>>>>>> example out of a set is true, the statement is true for all?
>>>>>>>
>>>>>>> The fact that ONE machine can be counted, doesn't mean that all
>>>>>>> can be.
>>>>>>>
>>>>>>>>
>>>>>>>> If X always works then X always works with Y or Z.
>>>>>>>
>>>>>>> So if this statement is true, you are a Hypocritical Pathological
>>>>>>> Lying Idiot.
>>>>>>>
>>>>>>
>>>>>> As always when you run out of reasoning you resort to ad hominem
>>>>>> because
>>>>>> gullible fools will take ad hominem as rebuttal. Ad hominem makes
>>>>>> you look quite foolish to anyone accustomed to academic decorum.
>>>>>
>>>>> No, I am showing you are using invalid logic.
>>>>>
>>>>> Your statement is only true if you assume it to be true, and use it
>>>>> as one of your truth makers that can make it true.  This is not an
>>>>> allowed operation, as if you do, then you get that exact same
>>>>> arguement I was using.
>>>>>
>>>>> So, *IF* you want to say your argument is valid, you *MUST& accept
>>>>> that mine is too, and thus you are what I said.
>>>>>
>>>>> The fact that you don't get it, might say my results are valid
>>>>> anyway independent of validity of the statement.
>>>>>
>>>>> In looking at your connection to truth makers view, X reaches back
>>>>> to some base truth makers, but also links back to itself. This
>>>>> leads to an infinite loop in the connection logic, where there is
>>>>> always a piece of the connection not connected to things alreayd
>>>>> known to be truth makers, so the statement has never been
>>>>> established as True, which requires that ALL neccessary premises
>>>>> for the statement be connected to know truth makers.
>>>>>
>>>>> This is the flaw of you thinking you work backwards from the
>>>>> premise to the truth makers, you can decieve yourself with such a
>>>>> loop, thinking it has been established, when it is just a floating
>>>>> island of unsupported logic. If you start at the Truth Makers, you
>>>>> can't run into this problem, as you never had the presumptive
>>>>> statement available to incorrectly use.
>>>>>
>>>>
>>>> A counter-example to my reasoning does not exist.
>>>>
>>>
>>> Nope, I have given it.
>>>
>>>> “Analytic” sentences, such as “Pediatricians are doctors,” have
>>>> historically been characterized as ones that are true by virtue of the
>>>> meanings of their words alone and/or can be known to be so solely by
>>>> knowing those meanings.
>>>> https://plato.stanford.edu/entries/analytic-synthetic/
>>>
>>> Right, and a sentence that depends on its own truth value (like if H
>>> returns the right value ...) are proved to be able to lead to
>>> cotradictipons.
>>>
>>>>
>>>> This is correctly paraphrased as
>>>>
>>>> Analytical truth is the connection from an expression X of formal or
>>>> natural language L using truth preserving operations to expressions
>>>> of L
>>>> that have been stipulated to be true.
>>>
>>> Right, and you can not create such a chain to the statement you are
>>> making.
>>>
>>>>
>>>> We know that cat are animals is true entirely on the basis of the
>>>> meaning of the words. The meaning of words are expressions of L that
>>>> have been stipulated to be true.
>>>
>>> So. Red Herring. Means nothing about the error of using a statement
>>> that references its own truth.
>>>
>>> Your statement that H can do xxx if H correctly decides yyy is a
>>> statement of the class that has been proven to lead to logical
>>> paradoxes.
>>>
>>> Such a statement can never be actually connected to previously
>>> accepted truth makers unless you can prove INDEPENDENTLY of that
>>> statement that H does give a correct decision.
>>>
>>> The fact that we know, by definition, that H(D,D) must be 1 to be
>>> correct if D(D) halts,
>>
>> *Changing the subject away from the following is a dishonest dodge*
>>
>> When the first seven instructions of D are correctly simulated by H it
>> can be seen that the simulated D would never stop running unless
>> aborted by H.
>>
>> H: Begin Simulation   Execution Trace Stored at:112ae5
>> Address_of_H:1383
>>   machine   stack     stack     machine    assembly
>>   address   address   data      code       language
>>   ========  ========  ========  =========  =============
>> [000019b3][00112ad1][00112ad5] 55         push ebp       // begin D
>> [000019b4][00112ad1][00112ad5] 8bec       mov ebp,esp
>> [000019b6][00112acd][00102aa1] 51         push ecx
>> [000019b7][00112acd][00102aa1] 8b4508     mov eax,[ebp+08]
>> [000019ba][00112ac9][000019b3] 50         push eax       // push D
>> [000019bb][00112ac9][000019b3] 8b4d08     mov ecx,[ebp+08]
>> [000019be][00112ac5][000019b3] 51         push ecx       // push D
>> [000019bf][00112ac1][000019c4] e8bff9ffff call 00001383  // call H
>> H: Infinitely Recursive Simulation Detected Simulation Stopped
>>
>> *D only stops running when H aborts its simulation of D*
>>
>>>> If there is a countability issue with calculating the sum of arbitrary
>>>> finite sets of finite strings of ASCII digits that prevented a correct
>>>> sum from being calculated then there would be an element of this set
>>>> that cannot be summed.
>>>
>>> No, you don't understand countability, and are trying to apply it to
>>> a Red Herring. You seem to think that "Computation" == "Sum", which
>>> is just a proof of your ignorance.
>>>
>>>>
>>>> Not being able to count all of the sets of finite strings to be summed
>>>> in no way prevents any element of the sets of finite strings from being
>>>> correctly summed, thus has no impact on computability.
>>>>
>>>
>>> It isn't the set of finite strings that is uncountable, it is the set
>>> of mappings every finite string individualy to 0 or 1 that is
>>> uncountable.
>>>
>>
>> You are restricting the set of natural number sums to 1 and 0?
>
> No, I am restricting the output of a decider to accept or reject.
>
> The set of mappings (functions) of N -> N is also an uncountable set,
> but that just shows that not all functions on the Natural Numbers are
> computable. Showing that not a decision functions are computable is a
> stronger statement.
>
>>
>> Sum does not map every set of finite strings of ASCII digits to the
>> sum of these ASCII digit finite strings. It need not do that.
>
> Why do you keep talking about Sum" That is just Herring with Red sauce.
>

We can transform sum into a simple decider.
A TM decider takes a space delimited finite list of finite strings of
ASCII digits: [0123456789]+ such that the first string is the sum of the
remaining elements. Each element of the list is delimited by a
single space. The last element is marked by four trailing spaces.

IS_SUM computes the sum and compares this computed sum to the first
element on this list. IS_SUM accepts or rejects its input on the basis
that the computed == the first element of its finite list of finite
strings.

IS_SUM need not compute the mapping from every set of finite strings to
its accept or reject state, it only needs to compute the mapping from
any arbitrary element of the finite sets of finite strings of ASCII
digits.

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