Re: Truthmaker Maximalism and undecidable decision problems

On 6/9/24 2:13 PM, olcott wrote:

On 6/9/2024 1:08 PM, Richard Damon wrote:

On 6/9/24 1:18 PM, olcott wrote:

On 6/9/2024 10:36 AM, olcott wrote:

*This has direct application to undecidable decision problems*
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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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Now that truthmaker and truthbearer are fully anchored it is easy to see
that self-contradictory expressions are simply not truthbearers.
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“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.
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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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Unless the system is inconsistent, in which case they can be.
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Note,

 When I specify the ultimate foundation of all truth then this
does apply to truth in logic, truth in math and truth in science.

Nope. Not for Formal system, which have a specific definition of its truth-makers, unless you let your definition become trivial for Formal logic where a "truth-makers" is what has been defined to be the "truth-makers" for the system.

 *Three laws of logic apply to all propositions*
¬(p ∧ ¬p) Law of non-contradiction
  (p ∨ ¬p) Law of excluded middle
   p = p   Law of identity

Nope, only for systems that accept those requirements.
There are (typically non-binary) systems that do not include one or both of the first two "laws".
I am not sure about the third, while I can't think of a system that doesn't have the law of identity, I am not sure it is absoultely required.
(after a bit of research)
In Schrödinger logic https://en.wikipedia.org/wiki/Schrödinger_logic
the law of identity is greatly restricted, because the statement x = y is not a well-formed formula in many cases, so it might not be true that x = x

 Inconsistent systems cannot be truthmakers
in those cases where they derive inconsistency.
 

Illogical.
"inconsistent SYSTEMS" are not the same sort of thing as a "truth-maker" as the first is a system of logic, and the second is a statement expressed in such a system.