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On 5/19/2024 6:30 PM, Richard Damon wrote:Irrelvent.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:>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
Then ~True(L,p) can't be a truth beared as they are the SAME STATEMENT, just using different "names".
p = ~True(L,p) Truthbearer(L,p) is false
q = ~True(L,p) Truthbearer(L,q) is true
Right, that is a sentence about another sentence (that is part of itself)>p = ~True(L,p)
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 express
>True(L,p) is false>
True(L,~p) is false
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So since True(L, p) is false, then ~True(L, p) is true.
>~True(True(L,p)) is true and is referring to the p that refers>
to itself it is not referring to its own self.
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*ONE LEVEL OF INDIRECT REFERENCE MAKES ALL THE DIFFERENCE*
Why add the indirection? p is the NAME of the statement, which means exactly the same thing as the statement itself.
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does not mean that same thing as True(L, ~True(L,p))
The above ~True(L, p) has another ~True(L,p) embedded in p.
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.
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Nope.I don't think you understand what it means to define something.x := y means x is defined to be another name for y
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https://en.wikipedia.org/wiki/List_of_logic_symbols
LP := ~True(L, LP)
specifies ~True(~True(~True(~True(~True(...)))))
Which isn't a valid proof in a formal system. You seem to think Formal System are a loosy goosy with proofs as Philosophy."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.
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Nope, it is equivelent to that, but doesn't SPECIFY that.A level of indirection:p := True(L,p)
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p: "This sentence is true", which is exactly the same as "p is true" since "this sentence" IS p
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specifies True(True(True(True(True(...)))))
*Prolog sees the same infinite recursion and rejects it*Right, because prolog can't handle any levels of self referencing, and thus is not suitable for logic that can do that.
?- TT = true(TT).
TT = true(TT).
?- unify_with_occurs_check(TT, true(TT)).
false.
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