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On 5/19/24 4:12 PM, olcott wrote:Truthbearer(L,x) ≡ (True(L,x) ∨ True(L,~x))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:>>>
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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p = ~True(L,p) // p is not a truth bearer because its refers to itself
Just like (with context) YOU can be refered to a PO, Peter, Peter Olcott or Olcott, and all the reference get to the exact same entity, so any "name" for the expressp = ~True(L,p)
True(L,p) is falseSo since True(L, p) is false, then ~True(L, p) is true.
True(L,~p) is false
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~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.
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*ONE LEVEL OF INDIRECT REFERENCE MAKES ALL THE DIFFERENCE*
Is the definition of an English word one level LESS of indirection than the word itself?This sentence is not true("This sentence is not true") is true.
I don't think you understand what it means to define something.x := y means x is defined to be another name for y
"Definition by example" is worse than "Proof by example", at least proof by example can be correct if the assertion is that there exists, and not for all.A simpler isomorphism of the same thing is proof by analogy.
A level of indirection:p := True(L,p)
p: "This sentence is true", which is exactly the same as "p is true" since "this sentence" IS p
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