Re: This makes all Analytic(Olcott) truth computable

On 8/17/24 12:51 PM, olcott wrote:

On 8/17/2024 11:46 AM, Richard Damon wrote:

On 8/17/24 12:35 PM, olcott wrote:

On 8/17/2024 11:28 AM, Richard Damon wrote:

On 8/17/24 11:47 AM, olcott wrote:

On 8/17/2024 10:33 AM, Richard Damon wrote:

On 8/17/24 11:12 AM, olcott wrote:

On 8/17/2024 9:53 AM, Richard Damon wrote:

On 8/17/24 10:45 AM, olcott wrote:

On 8/17/2024 9:40 AM, Richard Damon wrote:

On 8/17/24 12:05 AM, olcott wrote:

On 8/16/2024 5:57 PM, Richard Damon wrote:

On 8/16/24 6:40 PM, olcott wrote:

On 8/16/2024 5:19 PM, Richard Damon wrote:

On 8/16/24 6:16 PM, olcott wrote:

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:

On 8/16/2024 2:42 PM, Richard Damon wrote:

On 8/16/24 2:11 PM, olcott wrote:

On 8/16/2024 11:32 AM, Richard Damon wrote:

On 8/16/24 7:02 AM, olcott wrote:

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*This abolishes the notion of undecidability*
As with all math and logic we have expressions of language
that are true on the basis of their meaning expressed
in this same language. Unless expression x has a connection
(through a sequence of true preserving operations) in system
F to its semantic meanings expressed in language L of F
x is simply untrue in F.

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But you clearly don't understand the meaning of "undecidability"

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Not at all. I am doing the same sort thing that ZFC
did to conquer Russell's Paradox.
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If you want to do that, you need to start at the basics are totally reformulate logic.
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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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but they couldn't just "add" it to set theory, they needed to define the full set.
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I think you problem is you just don't understand how formal logic works.
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I think at a higher level of abstraction.

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No, you don't, unless you mean by that not bothering to make sure the details work.
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You can't do fundamental logic in the abstract.
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That is just called fluff and bluster.
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All that they did is just like I said they redefined
what a set is. You provided a whole bunch of details of
how they redefined a set as a rebuttal to my statement
saying that all they did is redefine a set.

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Showing the sort of thing YOU need to do to redefine logic
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I said that ZFC redefined the notion of a set to get rid of RP.
You show the steps of how ZFC redefined a set as your rebuttal.

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No, you said that "ALL THEY DID" was that, and that is just a LIE.
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They developed a full formal system.
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They did nothing besides change the definition of
a set and the result of this was a new formal system.
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I guess you consider all the papers they wrote describing the effects of their definitions "nothing"
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Not at all and you know this.
One change had many effects yet was still one change.
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But would mean nothing without showing the affects of that change.
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Yet again with your imprecise use of words.
When any tiniest portion of the meaning of an expression
has been defined this teeny tiny piece of the definition
makes this expression not pure random gibberish.
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Meaningless does not mean has less meaning, it is
an idiom for having zero meaning.
https://www.britannica.com/dictionary/meaningless
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And your statements have NO Meaning because they are based on LIE.
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We can not use the "ZFC" set theory from *JUST* the definition, but need all the other rules derived from it.

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The root cause of all of the changes is the redefinition
of what a set is. Likewise with my own redefinition of a
formal system by simply defining the details of True(L,x).
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Once I specify the architecture others can fill in the details.
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Yes, the ROOT was that change, but you don't understand that if they JUST did that root, and not the other work, Set theory would not have been "fixed", as it still wouldn't have been usable.
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 Defining that no set can be a member of itself would seem
to do the trick.
 

But usable, until integrated into a Formal Logic system.
After all, logic rules don't "interrupt" other logic and say you can't do this step that other rules allow you to do. ALL logic rules are just permissive steps saying what you can do when you use them. In fact, if one set of rules allow you to do something, and another rule tries to say you can't, all that has done is make you system inconsistant.
THe fact that Naive Set Theory had a number of rules that allowed you to construct such a set, means you need to remove those, and trace back to what used them and what caused them.
This is why you need to create a brand new Formal System, so you can start with the needed clean state.
Now, any results proven from just axioms you kept from the previous system will still be true and are thus quickly shown. But you can't just take an "random" theory from Naive Set Theory and use it until you can show that its proof path still holds, and wasn't based on something you changed in a way that makes it no longer true.
But, as I have pointed out, your lack of understanding about what a Formal Proof is in a Formal Logic System seems to mean you just don't understand any of this, and you just keep on demonstrating how ignorant you are of that fact.