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| From | Richard Damon <richard@damon-family.org> |
|---|---|
| Newsgroups | comp.theory, sci.logic |
| Subject | Re: Analytic Truth-makers |
| Date | 2024-07-24 19:57 -0400 |
| Organization | i2pn2 (i2pn.org) |
| Message-ID | <4b85633014d21d53e9494bc7dcfbdb15afc24edf@i2pn2.org> (permalink) |
| References | (9 earlier) <v7prni$1j3e7$1@dont-email.me> <b969998e09a55fb3ab05b2a19fd28a36ca56ecc7@i2pn2.org> <v7pup8$1ji5b$1@dont-email.me> <994febb86b9367c19b35fc184522efc3f562ab04@i2pn2.org> <v7r2k1$1pa7u$1@dont-email.me> |
Cross-posted to 2 groups.
On 7/24/24 10:20 AM, olcott wrote:
> On 7/24/2024 6:28 AM, Richard Damon wrote:
>> On 7/24/24 12:09 AM, olcott wrote:
>>> On 7/23/2024 10:27 PM, Richard Damon wrote:
>>>> On 7/23/24 11:17 PM, olcott wrote:
>>>>> On 7/23/2024 10:03 PM, Richard Damon wrote:
>>>>>> 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
>>>>>
>>>>> You ONLY construe it to be true in PA because that is
>>>>> the answer that you memorized.
>>>>
>>>> No, it is True in PA, because it is LITERALLY True by the words it
>>>> uses.
>>>>
>>>>>
>>>>> When you understand that true requires a sequence of
>>>>> truth preserving operations and they do not exist in
>>>>> PA then it is not true in PA.
>>>>
>>>> But they DO exist in PA, I guess you just don't understand how math
>>>> works.
>>>>
>>>> The sequence of steps is:
>>>>
>>>> Check the number 0 to see if it satisfies the PRR. Answer = No.
>>>> Check the number 1 to see if it satisfies the PRR. Answer = No.
>>>> Check the number 2 to see if it satisfies the PRR. Answer = No.
>>>>
>>>> keep repeating counting up through all the Natural Numbers.
>>>> From the trick in MM, we can see that the math in PA will say no to
>>>> all of them.
>>>>
>>>> Thus, after an infinite number of steps of truth preserving
>>>> operations, we reach the conclusion that NO natural numbers actually
>>>> exist that meet that PRR, just like G claimed, so it is correct.
>>>>
>>>
>>> The lack of a proof means untruth.
>>
>> Nope, lack of a proof means unknown, as you have agreed.
>
> If an infinite number of steps fail to show that G is
> provable in PA then G is untrue in PA.
But the infinte number of steps DO show that G is true in PA, because is
shows that EVERY Natural Number fails to meet the requirment.
YOu don't seem to be understanding the English, I think your brainwashed
filter is just clogged.
>
>> After all, you admitted that if the Goldbach conjecture would be an
>> Analytic TRUTH if it was only established by an infinite sequence of
>> truth preserving operations.
>>
>
> If an infinite number of steps do show that Goldbach is
> provable in PA then Goldbach is true in PA.
Right, Just like they showed that G is true.
>
>> Since you don't know the meaning of the words, you just prove yourself
>> unqualified to talk about such things.
>>
>
> Any proof requiring an infinite number of steps never resolved
> to a truth value thus its truth value remains unknown.
No, "Proofs" can not have an infinite number of steps, proofs are ALWAYS
finite in conventional logic.
>
> An alternative finite proof in MM only shows that the expression
> is true in MM.
Nope, since the rules of math are the same, it must also be true in PA.
I guess you think that just because 2+3 = 5 in one system with normal
mathematics, in another system with the exact same rules for mathematics
then 2 + 3 might be 6.
>
> Truthmakers cannot cross system boundaries. --
> Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
> hits a target no one else can see." Arthur Schopenhauer
>
But the base truthmakers for G in MM and PA are the same items, there is
just a short cut in MM to let us colapse the infinte chain to a finite
chain.
Those based truthmakers are that when we access every number, none of
them will satisfy the PRR. It is just that in MM, we know something new
about those models.
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Re: Analytic Truth-makers Richard Damon <richard@damon-family.org> - 2024-07-22 20:01 -0400
Re: Analytic Truth-makers olcott <polcott333@gmail.com> - 2024-07-22 19:11 -0500
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Re: Analytic Truth-makers olcott <polcott333@gmail.com> - 2024-07-22 19:44 -0500
Re: Analytic Truth-makers Richard Damon <richard@damon-family.org> - 2024-07-22 21:42 -0400
Re: Analytic Truth-makers olcott <polcott333@gmail.com> - 2024-07-22 21:12 -0500
Re: Analytic Truth-makers Richard Damon <richard@damon-family.org> - 2024-07-22 22:56 -0400
Re: Analytic Truth-makers olcott <polcott333@gmail.com> - 2024-07-22 23:07 -0500
Re: Analytic Truth-makers Richard Damon <richard@damon-family.org> - 2024-07-23 07:30 -0400
Re: Analytic Truth-makers olcott <polcott333@gmail.com> - 2024-07-23 09:55 -0500
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Re: "undecidable" / "unentscheidbar" (Was Analytic Truth-makers) Mild Shock <janburse@fastmail.fm> - 2024-07-23 23:13 +0200
Re: Analytic Truth-makers olcott <polcott333@gmail.com> - 2024-07-23 19:25 -0500
Re: Analytic Truth-makers Richard Damon <richard@damon-family.org> - 2024-07-23 22:15 -0400
Gödel's Basic Logic Course at Notre Dame (Was: Analytic Truth-makers) Mild Shock <janburse@fastmail.fm> - 2024-07-23 14:02 +0200
Re: Gödel's Basic Logic Course at Notre Dame (Was: Analytic Truth-makers) olcott <polcott333@gmail.com> - 2024-07-23 09:58 -0500
Re: Gödel's Basic Logic Course at Notre Dame (Was: Analytic Truth-makers) Mild Shock <janburse@fastmail.fm> - 2024-07-23 22:36 +0200
Re: Gödel's Basic Logic Course at Notre Dame (Was: Analytic Truth-makers) olcott <polcott333@gmail.com> - 2024-07-23 15:43 -0500
Re: Gödel's Basic Logic Course at Notre Dame (Was: Analytic Truth-makers) Richard Damon <richard@damon-family.org> - 2024-07-23 22:15 -0400
Re: Gödel's Basic Logic Course at Notre Dame (Was: Analytic Truth-makers) Mild Shock <janburse@fastmail.fm> - 2024-07-23 22:44 +0200
Re: Gödel's Basic Logic Course at Notre Dame (Was: Analytic Truth-makers) Mild Shock <janburse@fastmail.fm> - 2024-07-23 22:52 +0200
Re: Gödel's Basic Logic Course at Notre Dame (Was: Analytic Truth-makers) olcott <polcott333@gmail.com> - 2024-07-23 19:18 -0500
Re: Gödel's Basic Logic Course at Notre Dame (Was: Analytic Truth-makers) Richard Damon <richard@damon-family.org> - 2024-07-23 22:15 -0400
Re: Gödel's Basic Logic Course at Notre Dame (Was: Analytic Truth-makers) Mild Shock <janburse@fastmail.fm> - 2024-07-24 22:33 +0200
Re: Gödel's Basic Logic Course at Notre Dame (Was: Analytic Truth-makers) olcott <polcott333@gmail.com> - 2024-07-24 15:45 -0500
Re: Gödel's Basic Logic Course at Notre Dame (Was: Analytic Truth-makers) Mild Shock <janburse@fastmail.fm> - 2024-07-24 23:54 +0200
Re: Gödel's Basic Logic Course at Notre Dame (Was: Analytic Truth-makers) Mild Shock <janburse@fastmail.fm> - 2024-07-24 23:54 +0200
Re: Gödel's Basic Logic Course at Notre Dame (Was: Analytic Truth-makers) Richard Damon <richard@damon-family.org> - 2024-07-24 19:57 -0400
Re: Analytic Truth-makers Wasell <wasell@example.com> - 2024-07-23 16:51 +0200
Re: Analytic Truth-makers olcott <polcott333@gmail.com> - 2024-07-23 11:26 -0500
Re: Analytic Truth-makers Richard Damon <richard@damon-family.org> - 2024-07-23 22:15 -0400
Re: Analytic Truth-makers olcott <polcott333@gmail.com> - 2024-07-23 21:45 -0500
Re: Analytic Truth-makers Richard Damon <richard@damon-family.org> - 2024-07-23 23:03 -0400
Re: Analytic Truth-makers olcott <polcott333@gmail.com> - 2024-07-23 22:17 -0500
Re: Analytic Truth-makers Richard Damon <richard@damon-family.org> - 2024-07-23 23:27 -0400
Re: Analytic Truth-makers olcott <polcott333@gmail.com> - 2024-07-23 23:09 -0500
Re: Analytic Truth-makers Richard Damon <richard@damon-family.org> - 2024-07-24 07:28 -0400
Re: Analytic Truth-makers olcott <polcott333@gmail.com> - 2024-07-24 09:20 -0500
Re: Analytic Truth-makers Richard Damon <richard@damon-family.org> - 2024-07-24 19:57 -0400
Re: Analytic Truth-makers olcott <polcott333@gmail.com> - 2024-07-24 19:44 -0500
Re: Analytic Truth-makers Richard Damon <richard@damon-family.org> - 2024-07-24 21:05 -0400
Re: Analytic Truth-makers olcott <polcott333@gmail.com> - 2024-07-25 09:12 -0500
Re: Analytic Truth-makers Richard Damon <richard@damon-family.org> - 2024-07-25 19:35 -0400
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