Re: This makes all Analytic(Olcott) truth computable

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.

 but they couldn't just "add" it to set theory, they needed to define the full set.
 I think you problem is you just don't understand how formal logic works.
 

I think at a higher level of abstraction.
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.
My redefinition of formal system does this exact same
sort of thing in the same way. I do change the term
{logical operation} to {truth preserving operation}.
Other than that the only thing that is changed is
the notion of {formal system}. I don't even change
this very much.
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer