Re: Analytic Truth-makers

On 7/23/24 10:45 PM, olcott wrote:

On 7/23/2024 9:15 PM, Richard Damon wrote:

On 7/23/24 12:26 PM, olcott wrote:

On 7/23/2024 9:51 AM, Wasell wrote:

On Mon, 22 Jul 2024 20:17:15 -0400, in article
<3fb77583036a3c8b0db4b77610fb4bf4214c9c23@i2pn2.org>, Richard Damon wrote:

>
On 7/22/24 8:11 PM, olcott wrote:

>
[...]
>

*No stupid I have never been saying anything like that* If g and
~g is not provable in PA then g is not a truth-bearer in PA.

>
What makes it different fron Goldbach's conjecture?

>
I think a better example might be Goodstein's theorem [1].
>
* It is expressible in the same language as PA.
>
* It is neither provable, nor disprovable, in PA.
>
* We know that it is true in the standard model of arithmetic.
>
* We know that it is false in some (necessarily non-standard) models
   of arithmetic.
>
* It was discovered and proved long before it was shown to be
   undecidable in PA.
>
The only drawback is that the theorem is somewhat more complicated
than Goldbach's conjecture -- not a lot, but a bit.
>
>
[1] <https://en.wikipedia.org/wiki/Goodstein%27s_theorem>

>
>
I am establishing a new meaning for
{true on the basis of meaning expressed in language}
Formerly known as {analytic truth}.
This makes True(L,x) computable and definable.

>
You may say that, but you then refuse to do the work to actually do that.
>
The problem is that if you try to redefine the foundation, you need to build the whole building all over again, but you just don't understand what you need to do that.
>

>
L is the language of a formal mathematical system.
x is an expression of that language.
>
When we understand that True(L,x) means that there is a finite
sequence of truth preserving operations in L from the semantic
meaning of x to x in L, then mathematical incompleteness is abolished.

>
Except you just defined that this isn't true, as you admit that the Goldbach conjecgture COULD be an analytic truth even if it doesn't have a finte sequence of truth perserving operations,

 I redefined analytic truth to account for that. Things
like the Goldbach conjecture are in the different class
of currently unknowable.

In other words, NOTHING you are talking about apply to the logic that anyone else is using.
Note, Godel's G can't be put into that category, as it is KNOWN to be true in PA, because of a proof in MM that shows that no Natural Number (as both PA and MM have the same mathematics) can satisfy the relationship that was developed in MM using operations that exist in PA, so the relationship moves into PA.
So, PA has a statement that is known to be true in PA (but the knowledge come from outside PA, but in a way that IS transferable). This truth we can see can be established in PA by an infinite sequence of steps, that of checking each of the infinite set of Natural Numbers, and by doing a finite number of steps on each of them, show that that number does ot satisfy the relationship. From the proof in MM, we know that even in PA, no number can satisfy the relationship (remember, MM was defined to have the same mathematics as PA, so the math results transfer) due to the proof in MM.
So, if you really want to create your own logic, you will either need to prevent that sort of math from existing, or have some totally different form of logic, which you will need to fully define.
When you get your paper written FULLY EXPLAINING how it works, and what you can prove from it, you might have something.
Of course, considering you record for working out problems, it seems like it will have a snowflakes chance in hell to actually be written, so I won't hold my breath.
Of course, until you do create such a system and show what it can do, any comments you make about it are just baseless, and any attempt to apply it to other peoples work is just a LIE.
Since they didn't use your logic and your definition (how could they, you haven't actually fully formulated them) you can't hold them to it.
Of course, it seems you don't understand how that works, so good luck trying to create you own system.

 

but only an infinite sequence. But a Analytic Truth MUST be a "truth-bearer", so you just blew up your whole logic system with your lies.
>

>
~True(L,x) ∧ ~True(L,~x)
means that x is not a truth-bearer in L.
It does not mean that L is incomplete
>

>