Re: Truthmaker Maximalism and undecidable decision problems --- the way truth really works

On 6/12/2024 2:13 AM, Mikko wrote:

On 2024-06-11 16:06:02 +0000, olcott said:
 

On 6/11/2024 2:45 AM, Mikko wrote:

On 2024-06-10 14:43:34 +0000, olcott said:
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On 6/10/2024 2:13 AM, Mikko wrote:

On 2024-06-09 18:40:16 +0000, olcott said:
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On 6/9/2024 1:29 PM, Richard Damon wrote:

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,

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

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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.
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Formal systems are free to define their own truthmakers.
When these definitions result in inconsistency they are
proved to be incorrect.

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A formal system can be inconsistent without being incorrect.

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*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
*No it cannot*

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Those laws do not constrain formal systems. Each formal system specifies
its own laws, which include all or some or none of those. Besides, a the
word "proposition" need not be and often is not used in the specification
of a formal system.
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*This is the way that truth actually works*

 As far as is empirially known. But a formal system is not limited by
the limitations of our empirical knowledge.
 

If there really is nothing anywhere that makes expression
of language X true then X is untrue.
This covers every truth that can possibly exist, true by
definition, true by entailment, true by observation, true
by an infinite sequence of truth preserving operations.
If nothing makes X true then X is untrue.
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer