Re: This makes all Analytic(Olcott) truth computable

On 8/19/24 8:40 AM, olcott wrote:

On 8/18/2024 1:17 PM, Richard Damon wrote:

On 8/18/24 7:51 AM, olcott wrote:

On 8/18/2024 5:28 AM, Mikko wrote:

On 2024-08-16 22:16:59 +0000, olcott said:
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On 8/16/2024 5:03 PM, Richard Damon wrote:

On 8/16/24 5:35 PM, olcott wrote:

On 8/16/2024 4:05 PM, Richard Damon wrote:

On 8/16/24 4:39 PM, olcott wrote:

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ZFC didn't need to do that. All they had to do is
redefine the notion of a set so that it was no longer
incoherent.
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I guess you haven't read the papers of Zermelo and Fraenkel. They created a new definition of what a set was, and then showed what that implies, since by changing the definitions, all the old work of set theory has to be thrown out, and then we see what can be established.
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None of this is changing any more rules. All
of these are the effects of the change of the
definition of a set.
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No, they defined not only what WAS a set, but what you could do as basic operations ON a set.
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Axiom of extensibility: the definition of sets being equal, that ZFC is built on first-order logic.

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Axion of regularity/Foundation: This is the rule that a set can not be a member of itself, and that we can count the members of a set.
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This one is the key that conquered Russell's Paradox.
If anything else changed it changed on the basis of this change
or was not required to defeat RP.

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That is not sufficient. They also had to Comprehension.
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Axiom Schema of Specification: We can build a sub-set from another set and a set of conditions. (Which implies the existance of the empty set)

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This is added to keep most of Comprenesion but not Russell's set.
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All they did was (as I already said) was redefine the notion of a set.
That this can still be called set theory seems redundant.
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Nope, the redefined the notion of a set, AN THEN WORKED OUT WHAT THAT MEANS TO SET THEORY.
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You don't seem to understand the work involved in that, which is why you don't understand what you need to do to make your change.
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Note the generic term "Set Theory" doesn't define a particular set of rules except by common agreement. Prior to Russel, that generic term refered to what is now called "Naive Set Theory". Russel showed that system was broken.
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Z/F worked out a new set of axioms (using SOME of the old ones, some slightly modified, and some new ones). Then they worked out many of the properties of that system so it was actually usable. Thus ZF-Set Theory, and ZFC-Set Theory were born. (and later some other variants). Because it was decided by the general community to be so useful, the default meaning of "Set Theory" changed (as words in Natural Lanugages, i.e. outside Formal System tend to do).
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If you want to propose a new logic system with different definitions, you need to do the same thing. You need to first formally define what your axioms of your basic system are, then show what you can do with those.
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Then you need to show why your system is better than the existing one. You don't have the breaking inconsistancy that Russel showed in Naive Set Theory, so you need to make a good demonstration showing that your system has some advantage, being able to do something that conventional logic can't do, and that at least most of the things we do with conventional logic still apply.
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My guess is this last point is going to be a problem, as Proofs like those of Godel and Tarski show that with very basic operations, system that support the full properties of Natual Numbers experience the issues you claim your definition solves, so either it doesn't remove them (and thus doesn't get any advantages) or it can't support the properties of the Natural Numbers, which makes it a very limited logic system.

 Before anyone can work out the details of the effects of
what my proposed change to the definition of a formal
system involves it cannot be rejected out-of-hand as incorrect
without review.
 

No, it CAN be rejected out of hand when you try to IMPROPERLY apply it to a system that doesn't use them.
Write up your system and prove what it does as a foundation, then we can talk about what it does.
Trying to just graft it into the existing system is just a LIE and proves your ignorance of what you should be doing.
It makes one wonder if you are even capable of building the system you claim to be talking about.