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On 6/9/2024 10:36 AM, olcott wrote:Unless the system is inconsistent, in which case they can be.*This has direct application to undecidable decision problems*Now that truthmaker and truthbearer are fully anchored it is easy to see
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When we ask the question: What is a truthmaker? The generic answer is
whatever makes an expression of language true <is> its truthmaker. This
entails that if there is nothing in the universe that makes expression X
true then X lacks a truthmaker and is untrue.
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X may be untrue because X is false. In that case ~X has a truthmaker.
Now we have the means to unequivocally define truth-bearer. X is a
truth-bearer iff (if and only if) X or ~X has a truthmaker.
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I have been working in this same area as a non-academician for a few
years. I have only focused on expressions of language that are {true on
the basis of their meaning}.
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that self-contradictory expressions are simply not truthbearers.
“This sentence is not true” can't be true because that would make it
untrue and it can't be false because that would make it true.
Within the the definition of truthmaker specified above: “this sentence
has no truthmaker” is simply not a truthbearer. It can't be true within
the above specified definition of truthmaker because this would make it
false. It can't be false because that makes
it true.
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