Re: A different perspective on undecidability --- incorrect question

On 10/25/24 10:37 AM, olcott wrote:

On 10/25/2024 3:14 AM, Mikko wrote:

On 2024-10-24 16:07:03 +0000, olcott said:
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On 10/24/2024 9:06 AM, Mikko wrote:

On 2024-10-22 15:04:37 +0000, olcott said:
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On 10/22/2024 2:39 AM, Mikko wrote:

On 2024-10-22 02:04:14 +0000, olcott said:
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On 10/16/2024 11:37 AM, Mikko wrote:

On 2024-10-16 14:27:09 +0000, olcott said:
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The whole notion of undecidability is anchored in ignoring the fact that
some expressions of language are simply not truth bearers.

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A formal theory is undecidable if there is no Turing machine that
determines whether a formula of that theory is a theorem of that
theory or not. Whether an expression is a truth bearer is not
relevant. Either there is a valid proof of that formula or there
is not. No third possibility.
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After being continually interrupted by emergencies
interrupting other emergencies...
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If the answer to the question: Is X a formula of theory Y
cannot be determined to be yes or no then the question
itself is somehow incorrect.

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There are several possibilities.
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A theory may be intentionally incomplete. For example, group theory
leaves several important question unanswered. There are infinitely
may different groups and group axioms must be true in every group.
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Another possibility is that a theory is poorly constructed: the
author just failed to include an important postulate.
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Then there is the possibility that the purpose of the theory is
incompatible with decidability, for example arithmetic.
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An incorrect question is an expression of language that
is not a truth bearer translated into question form.
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When "X a formula of theory Y" is neither true nor false
then "X a formula of theory Y" is not a truth bearer.

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Whether AB = BA is not answered by group theory but is alwasy
true or false about specific A and B and universally true in
some groups but not all.

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See my most recent reply to Richard it sums up
my position most succinctly.

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We already know that your position is uninteresting.
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Don't want to bother to look at it (AKA uninteresting) is not at
all the same thing as the corrected foundation to computability
does not eliminate undecidability.

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No, but we already know that you don't offer anything interesting
about foundations to computability or undecidabilty.

 In the same way that ZFC eliminated RP True_Olcott(L,x)
eliminates undecidability. Not bothering to pay attention
is less than no rebuttal what-so-ever.
 

Then you plan to do the work to show this?
Or do you think ZF only wrote down there rules and said to everyone, just believe us, this fixes everything.
Of course, my guess is you have on idea how to do that, as you don't understand how the logic works.
I am not sure if you understand what is needed to even properly define your initial set of axioms to build your logic on.
And by changing the rules of logic, you need to rederive the rules of logic under your system, and then show that they are at least as useful as the classical one.
ZF had the advantage that it was well known that "Naive" set theory was broken, and so people were looking for something to replace it.
Until you can actually demonstrate that something logictians want is broken, you have a major uphill battle.
The fact that many systems are incomplete, and many problems turn out to be uncomputable isn't a problem in logic, as it has been shown to be a pretty natural proerty following from the power of the logic system to express more than can be actually known.
All I can see is your logic system tries to work by limiting what can be talked about, to keep things under that threshold where capability to express grows faster than the capability to know does, which leads to those properties.
I am also not sure if your ideas are really knew, as there are a number of theories of restricted logic, and you haven't been about to define yours well enough to compare them. I am not sure YOU even undertstand what you want well enough to actually definie it to do so.

 

Ae also know
that a good foundation to computability does not eliminate
undecidablility but proves it, and also proves uncomputablility
of various functions.
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Whether some foundation can be correct or what it would mean to
call it so is a different problem.
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It does eliminate undecidability
and not bothering to look at it is no actual rebuttal.

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You may say so but you don't offer any good argument to support
that claim. Instead you offer various indications that you will
never present a good argument about anything.
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