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On 8/22/2024 7:06 AM, Mikko wrote:THEN DO SO, and show your work,On 2024-08-21 12:47:37 +0000, olcott said:Like ZFC redefined the foundation of all sets I redefine
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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
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*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.
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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.
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the foundation of all formal systems.
Since you haven't defined your whole system, just vaguely expressed the idea for one of its principles, we can't talk about it yet.A problem with your method is that it is ofen not known whether thereTry to show a concrete example of that where self-contradictory
is a sequence of truth-preserving transformations in F and there is
no method to find out.
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expressions are not needed.
So, give a REAL Formal definiton.Your definition also requires truth-preserving is defined withoutBecause it establishes the notion of truth.
reference to truth. Is there any such definiton?
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Truth is what my foundational axiom says that it is.
Truth is the connection from an expression of languageAnd thus you need to list what are, or at least DEFINE what they need to be, but since Truth is defined in terms of these operations, you can't use Truth in the definition of these operatins.
to its stipulative meaning. Many of the conventional
logic operations are truth preserving, some are not.
After the architecture of my system is understood andBut before it can be understood, it needs to be made.
accepted then we do these further elaborations.
This is all aspects of my categorically exhaustively completeSo, DO SO.
system of reasoning. Work on the broadest category first and
then progressively narrow to smaller categories.
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