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On 8/23/2024 3:34 AM, Mikko wrote:No, it defined a NEW form of set theory, and new formal systems adopted it, it didn't even try to change anything that was based on any other form of set theory.On 2024-08-22 13:23:39 +0000, olcott said:Then According to your reasoning ZFC is wrong because
>On 8/22/2024 7:06 AM, Mikko wrote:>On 2024-08-21 12:47:37 +0000, olcott said:>
>>>
Formal systems kind of sort of has some vague idea of what True
means. Tarski "proved" that there is no True(L,x) that can be
consistently defined.
https://en.wikipedia.org/wiki/ Tarski%27s_undefinability_theorem#General_form
>
*The defined predicate True(L,x) fixed that*
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 then x is simply
untrue in F.
>
Whenever there is no sequence of truth preserving from
x or ~x to its meaning in L of F then x has no truth-maker
in F and x not a truth-bearer in F. We never get to x is
undecidable in F.
Tarski proved that True is undefineable in certain formal systems.
Your definition is not expressible in F, at least not as a definition.
>
Like ZFC redefined the foundation of all sets I redefine
the foundation of all formal systems.
You cannot redefine the foundation of all formal systems. Every formal
system has the foundation it has and that cannot be changed. Formal
systems are eternal and immutable.
>
it is not allowed to redefine the foundation of set
theory.
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