Re: Truthmaker Maximalism and undecidable decision problems

On 2024-06-10 14:43:34 +0000, olcott said:

On 6/10/2024 2:13 AM, Mikko wrote:

On 2024-06-09 18:40:16 +0000, olcott said:
 

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*
 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.
 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.
 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}.
 

 Now that truthmaker and truthbearer are fully anchored it is easy to see
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.
 

 Unless the system is inconsistent, in which case they can be.
 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.
 

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

 A formal system can be inconsistent without being incorrect.

 *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*

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.

People are free to stipulate the value of PI as exactly
3.0 and they are simply wrong.

But they are free to use the small greek letter pi for other purposes.
--
Mikko