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

On 4/22/2025 4:12 AM, Mikko wrote:

On 2025-04-21 20:41:14 +0000, olcott said:
 

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.

>

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.

>

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-exitence 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.

 But you never prove what you claim.
 

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.

 That's not a proof. That is just another claim that you can't prove.
 

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.
People here stupidly assume that the outputs are not
required to correspond to the inputs. That comes from
learn-by-rote with zero depth of understanding.
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer