Re: Truthmaker Maximalism and undecidable decision problems

On 2024-06-10 14:52:50 +0000, olcott said:

On 6/10/2024 2:19 AM, Mikko wrote:

On 2024-06-10 02:47:07 +0000, olcott said:
 

On 6/9/2024 2:36 PM, Richard Damon wrote:

On 6/9/24 3:08 PM, olcott wrote:

On 6/9/2024 1:54 PM, Richard Damon wrote:

On 6/9/24 2:40 PM, olcott wrote:

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.

 So, you admit that your definition is just inconsistant, as it says FOR ALL and then you admit it isn't FOR ALL
 And a formal system proven inconsistant isn't necessarily incorrect, just inconsistent.
 

 To the extent that they define inconsistency they
are not truth-makers.

  YOU hae a TYPE ERROR in your statement.
 That just proves that YOUR logic is incorrect.
 How can a SYSTEM be a propsition?
 

 *Stopping at your first big mistake*
 When we ask the question: What is a truthmaker? The generic answer is whatever makes an expression of language true <is> its truthmaker.
 A cat in your living room is not a proposition yet makes the
sentence: "there is a cat in my living room" true, thus <is> its
truthmaker.

 With that interpretation an inconsistent system is a truthmaker as it
makes the sentence "the system is inconsistent" true. And so is everything
else that one can mention so the word "truthmaker" does not really mean
anything.
 

 "the system is inconsistent" TWO ISOMORPHIC EXAMPLES ARE PROVIDED
 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.
 “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 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.
 "the system is inconsistent" is too vague, what system?

That expression is rarely used except in a context were "the system" is not
ambiguous. What I said above is equally applicable to every such context
although just one is suffient for the point. If you want a specific example
you may choose any inconsistent system.

Truthmakers simultaneously refer the entire universe of
all true statements. I already handled the key most important
counter-example in all of the literature on Truthmaker Maximalism:
“this sentence has no truthmaker”

--
Mikko