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

On 6/12/2024 11:45 AM, Mikko wrote:

On 2024-06-12 14:08:43 +0000, olcott said:
 

On 6/12/2024 8:41 AM, Mikko wrote:

On 2024-06-12 12:44:55 +0000, olcott said:
 

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:
 

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.
 

 *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.

 That does not restrict what a formal system can say.

 If a formal system says:
"cats <are> fifteen story office buildings"
this formal system is wrong.

 No, it is not. If you inteprete a sentence of that language

 *Correct interpretation is hardwired into the formal language*
{cats} and {office buildings} are specified by 128-bit GUIDs.