Re: Mathematical incompleteness has always been a misconception --- Ultimate Foundation of Truth

On 3/2/2025 2:21 PM, olcott wrote:

On 3/2/2025 1:13 PM, dbush wrote:

On 3/2/2025 2:11 PM, olcott wrote:

On 3/2/2025 1:04 PM, dbush wrote:

On 3/2/2025 1:57 PM, olcott wrote:

On 3/2/2025 12:22 PM, dbush wrote:

On 3/2/2025 1:10 PM, olcott wrote:

On 3/2/2025 11:19 AM, dbush wrote:

On 3/2/2025 12:14 PM, olcott wrote:

On 3/2/2025 11:11 AM, dbush wrote:

On 3/2/2025 12:08 PM, olcott wrote:

On 3/2/2025 11:00 AM, dbush wrote:

On 3/2/2025 11:53 AM, olcott wrote:

On 3/2/2025 10:28 AM, dbush wrote:>>> So how does changing the definition of truth prevent systems from

existing that contain true statements that have *only* an infinite connection to their truthmaker?

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*This <is> how actual truth has always worked*
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If expression X has a connection to a truth-maker then
X is true otherwise X is untrue, yet possibly not false.
It does not matter what kind of connection this is.
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You didn't answer the question.
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Sure I did
 >> It does not matter what kind of connection this is.
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It does not matter whether the connection is infinite
or not so STFU about it.
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Dishonest dodge.
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You stated that your definition of truth prevents systems from existing that contain true statements that have *only* an infinite connection to their truthmaker.
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So how does that happen?

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I never said anything like that.
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Yes you did:
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On 3/1/2025 11:46 PM, olcott wrote:
 > Incompleteness cannot possibly exist when true means
 > has a truth-maker and untrue means has no truth-maker
 > and false mean ~X has a truth-maker.

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Your paraphrase of that was terribly incorrect.
Has a truth-maker has always been the only correct
way to determine True(x) superseding and replacing
the ill-formed notion of provability.
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I merely substituted the term "incompleteness" with it's official definition.  That you don't understand that definition is not a rebuttal.
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That you attempted to change the idea of "provability" doesn't change the fact that "incompleteness" still refers to the original idea of "provability".
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A system is incomplete if it contains one or more true statements that contain *only* an infinite connection to their truthmakers.
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That doesn't change despite your idea of "truth", so incompleteness still exists.

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One can define a system of arithmetic that does not allow
summing the integers 5 and 3. Such a system would be
incomplete as an artificial contrivance.
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The notions of undecidability and incompleteness are this
same sort of artificial contrivance.
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That's not what incompleteness means.
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For example, Robinson arithmetic is incomplete because the true statement "no number is equal to its successor" has *only* an infinite connection to its truthmaker.
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That is a ridiculously stupid thing to say and you know it.
I may not be alive in a month. Quit f-cking around with
my life's work.
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That you don't know the definition of the terms you're using is not a rebuttal.

 When formal systems can be defined in such a way that they are not
incomplete and undecidability cannot occur it is stupid to define
them differently.
 

That doesn't change the fact that Robinson arithmetic contains the true statement "no number is equal to its successor" that has *only* an infinite connection to the axioms (i.e. the truthmakers) of the system.
It doesn't matter if it's called "incomplete" or something else.  That concept will still exist regardless of its name.
It's also the case that the more axioms that are added to a system that has or more more true statement with *only* an infinite connection to their truthmakers, the more such statements that will exist.