On 3/18/25 11:02 AM, olcott wrote:
On 3/18/2025 8:39 AM, Mikko wrote:
On 2025-03-17 14:08:49 +0000, olcott said:
On 3/16/2025 11:36 PM, Mr Flibble wrote:
On Sun, 16 Mar 2025 22:52:13 -0400, Richard Damon wrote:
On 3/16/25 7:33 PM, olcott wrote:
On 3/16/2025 3:20 PM, joes wrote:
Am Sun, 16 Mar 2025 14:32:38 -0500 schrieb olcott:
Only when the problem is defined to require H to return a correct >>>>>>>> halt status value for an input that is actually able to do the >>>>>>>> opposite of whatever value that H returns.
And since it *is* a possible input...
A finite string is a possible input.
An executing process IS NOT A POSSIBLE INPUT.
So, I guess you don't understand what a program is, or how a compiler >>>>> can generate a program.
The "finite string" that defines the program, defines all the details >>>>> need to generate the behavior of that program, so the RESULTS of
executiong that program is a valid question.
Every polar (yes/no) question that lacks a correct yes or no answer >>>>>>>> is an incorrect polar question.
Disproving the assumption that a decider exists in the first place. >>>>>>>
In the same way that no one can "decide" whether this sentence is
true
or false: "What time is it?"
Sure it can, it can reject it as an incorrect statement, and thus not >>>>> true. (It doesn't need to say it is false, just not true).
One can argue that asking whether that question is true or false is a
category error (so cannot be answered at all) but you seem to think
there
is a third result that is neither true or false which suggests my tri- >>>> result signalling simulating halt decider has legs afterall - i.e.
signalling not a program (i.e. pathological input) is akin to the
category
error of that question.
/Flibble
Yes you are correct it is a category error
in the same way that the Liar Paradox is a category error.
Neither questions nor self-contradictions has a truth value.
When we only allow truth preserving operations to connect
a sequence of inference steps then the principle of
explosion says that contradictions are true.
Not necessarily. If you require that every step is connected by a truth
preserving operation to an earlier step you can have no first step and
therefore no proof of anyting. In order to prove anything you need some
primitive theorems.
We begin with a finite set of basic facts of the world
organized in an inheritance hierarchy knowledge ontology
encoded in Rudolf Carnap meaning postulates using something
like an extended form of Montague Grammar.
Which means you are including the basic definitions of the foundations
for the Natural Numbers, and thus the Proof of Godel and Tarski apply to
your system.
Sorry, you are just showing you don't understand what you are talking about.
If your theory is consistent or paraconsistent there is a sentnece that
cannot be proven.
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