Re: This makes all Analytic(Olcott) truth computable

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.

>
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.
>

 No, they defined not only what WAS a set, but what you could do as basic operations ON a set.
 Axiom of extensibility: the definition of sets being equal, that ZFC is built on first-order logic.

 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.
 

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.

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)
 Axiom of Pairing: Given two sets, we can make a set that contains the two sets.
 Axiom of Union: Given two (or more) sets, we can make a set of the elements that exist in any of the sets.
 Axiom schema of Replacement: We can build a set from another set and a mapping function
 Axiom of Infiity: We can make a set with a countable infinite number of members.
 Axiom of Power Set: There exist a set that contains every subset of another set.
 To move from ZF to ZFC we add:
Axiom of Choice/Well Ordering:
  So, they did more that just "Define what a set is"
 

--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer