Re: HHH(DD) --- COMPUTE ACTUAL MAPPING FROM INPUT TO OUTPUT --- Using Finite String Transformations

Op 22.apr.2025 om 18:38 schreef olcott:

On 4/22/2025 10:27 AM, Alan Mackenzie wrote:

olcott <polcott333@gmail.com> wrote:

On 4/21/2025 4:33 PM, Alan Mackenzie wrote:

olcott <polcott333@gmail.com> wrote:

On 4/21/2025 3:57 AM, Mikko wrote:

On 2025-04-20 05:18:56 +0000, olcott said:

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On 4/19/2025 2:48 AM, Mikko wrote:

On 2025-04-17 19:57:30 +0000, olcott said:

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On 4/17/2025 2:19 PM, Alan Mackenzie wrote:

olcott <polcott333@gmail.com> wrote:

On 4/17/2025 6:49 AM, Alan Mackenzie wrote:

olcott <polcott333@gmail.com> wrote:

On 4/16/2025 1:09 PM, Alan Mackenzie wrote:

Mr Flibble <flibble@red-dwarf.jmc.corp> wrote:

On Wed, 16 Apr 2025 13:29:18 +0100, Richard Heathfield wrote:

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[ .... ]

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All of logic, reasoning and computation boils down to finite
string transformations on inputs deriving outputs.

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That's a big assertion, one you have not proved.  It is one you
can't prove, even were it true, since you don't understand the
concept of proof.

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When a categorically exhaustive search is made it is self- evident
that all computation, logic, and human reasoning has as its
barest possible essence transforming input finite strings into
outputs via finite string transformations.

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It is not at all self-evident.

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It is self-evident that there are no exceptions to the rule
the all truth that is entirely anchored in fully formalized
semantics an be expressed as finite string transformations
from input finite strings.

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It seems that there is an error above as I can't parse it. But it is
not clear how that should be corrected.

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All mental, computational or logical reasoning
boils down to finite string transformation rules
applied to finite strings deriving finite string
outputs.

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That no counter-example to this rule exists is its proof.

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Unproven non-existence of counter-examples is not a proof. In particular
mental reasoning is too poorly understood to be sure about anything.

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In other words you cannot find a counter-example.
I claim that the entire category of counter-example
to the above statement is the empty set.

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You're being stupid.  Just because you can't think up a counterexample
doesn't mean other more intelligent people can't.

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When you try and find any computation that is not
essentially finite string transformations to finite
strings it is self-evident that none can possibly exist.

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It's self evident only to the arrogantly stupid.

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All computation is isomorphic to:
Finite string transformations to finite strings.

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Is that really the best you can manage?  Simply repeat discredited
falsehood, ignoring the argument which discredits it?
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 All computation is defined to be represented as finite
string transformations to finite strings.
 a function is computable if there exists an algorithm
that can do the job of the function, i.e. given an input
of the function domain it can return the corresponding output.
https://en.wikipedia.org/wiki/Computable_function
 On Turing Machines inputs <are> finite strings, and
finite string transformation rules <are> applied to
these finite strings to derive corresponding outputs.
 

And it has been proven that no finite string transformations are possible that report the halting behaviour for all inputs that specify a correct program.
There is no algorithm that can determine for all possible inputs whether the input specifies a program that (according to the semantics of the machine language) halts when directly executed.
Agreed?