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On 5/19/2024 12:17 PM, Richard Damon wrote:Then ~True(L,p) can't be a truth beared as they are the SAME STATEMENT, just using different "names".On 5/19/24 9:41 AM, olcott wrote:p = ~True(L,p) // p is not a truth bearer because its refers to itself>>
True(L,x) is always a truth bearer.
when x is defined as True(L,x) then x is not a truth bearer.
So, x being DEFINED to be a certain sentence doesn't make x to have the same meaning as the sentence itself?
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What does it mean to define a name to a given sentence, if not that such a name referes to exactly that sentence?
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True(L,p) is falseSo since True(L, p) is false, then ~True(L, p) is true.
True(L,~p) is false
~True(True(L,p)) is true and is referring to the p that refersWhy add the indirection? p is the NAME of the statement, which means exactly the same thing as the statement itself.
to itself it is not referring to its own self.
*ONE LEVEL OF INDIRECT REFERENCE MAKES ALL THE DIFFERENCE*
So, p := ~True(L, p) means p is just another name, and thus another way to referencex := y means x is defined to be another name for y>>
~True(L,x) is always a truth bearer.
when x is defined as ~True(L,x) then x is not a truth bearer.
Again, what does "Defined as" mean to you?
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https://en.wikipedia.org/wiki/List_of_logic_symbols
LP := ~True(L,LP)No, it to be what you are meaning, it would be:
means ~True(~True(~True(~True(~True(...)))))
It is the common convention to encode self-reference incorrectly.
LP ↔ ~True(L, LP)
ϕ(x) there is a sentence ψ such that S ⊢ ψ ↔ ϕ⟨ψ⟩.
The sentence ψ is of course not self-referential in a
strict sense, but mathematically it behaves like one.
https://plato.stanford.edu/entries/self-reference/
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