I have focused on analytic truth-makers where an expression of language
x is shown to be true in language L by a sequence of truth preserving operations from the semantic meaning of x in L to x in L.
In rare cases such as the Goldbach conjecture this may require an
infinite sequence of truth preserving operations thus making analytic knowledge a subset of analytic truth. https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
There are cases where there is no finite or infinite sequence of
truth preserving operations to x or ~x in L because x is self-
contradictory in L. In this case x is not a truth-bearer in L.
On 7/22/2024 7:01 PM, Richard Damon wrote:
On 7/22/24 12:42 PM, olcott wrote:
I have focused on analytic truth-makers where an expression of
language x is shown to be true in language L by a sequence of truth
preserving operations from the semantic meaning of x in L to x in L.
In rare cases such as the Goldbach conjecture this may require an
infinite sequence of truth preserving operations thus making analytic
knowledge a subset of analytic truth.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
There are cases where there is no finite or infinite sequence of
truth preserving operations to x or ~x in L because x is self-
contradictory in L. In this case x is not a truth-bearer in L.
So, now you ADMIT that Formal Logical systems can be "incomplete"
because there exist analytic truths in them that can not be proven
with an actual formal proof (which, by definition, must be finite).
*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.
On 7/22/2024 7:17 PM, Richard Damon wrote:
On 7/22/24 8:11 PM, olcott wrote:
On 7/22/2024 7:01 PM, Richard Damon wrote:
On 7/22/24 12:42 PM, olcott wrote:
I have focused on analytic truth-makers where an expression
of language x is shown to be true in language L by a sequence
of truth preserving operations from the semantic meaning of x
in L to x in L.
In rare cases such as the Goldbach conjecture this may
require an infinite sequence of truth preserving operations
thus making analytic knowledge a subset of analytic truth.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
There are cases where there is no finite or infinite sequence
of truth preserving operations to x or ~x in L because x is
self- contradictory in L. In this case x is not a
truth-bearer in L.
So, now you ADMIT that Formal Logical systems can be
"incomplete" because there exist analytic truths in them that
can not be proven with an actual formal proof (which, by
definition, must be finite).
*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?
You are just caught in your own lies.
YOU ADMITTED that statements, like Goldbach's conjecture, might be
true based on being only established by an infinite series of
truth preserving operations.
You seem to be too stupid about this too. You are too stupid to grasp
the idea of true and unknowable.
In any case you are not too stupid to know that every expression that requires an infinite sequence of truth preserving operations would
not be true in any formal system.
In PA, G (not g, that is the variable) is shown to be TRUE, but
only estblished by an infinite series of truth preserving
operations, that we can show exist by a proof in MM.
No stupid that is not it. A finite sequence of truth preserving
operations in MM proves that G is true in MM. Some people use lower
case g.
Here is the convoluted mess that Gödel uses https://www.liarparadox.org/G%C3%B6del_Sentence(1931).pdf
The truth of G transfers, because it uses nothing of MM, the Proof
does not, as it depends on factors in MM, so can't be expressed in
PA.
No stupid that is not how it actually works. Haskell Curry is the
only one that I know that is not too stupid to understand this. https://www.liarparadox.org/Haskell_Curry_45.pdf
On 7/22/2024 8:42 PM, Richard Damon wrote:
On 7/22/24 8:44 PM, olcott wrote:
On 7/22/2024 7:17 PM, Richard Damon wrote:
On 7/22/24 8:11 PM, olcott wrote:
On 7/22/2024 7:01 PM, Richard Damon wrote:
On 7/22/24 12:42 PM, olcott wrote:
I have focused on analytic truth-makers where an expression
of language x is shown to be true in language L by a sequence
of truth preserving operations from the semantic meaning of x
in L to x in L.
In rare cases such as the Goldbach conjecture this may
require an infinite sequence of truth preserving operations
thus making analytic knowledge a subset of analytic truth.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
There are cases where there is no finite or infinite sequence
of truth preserving operations to x or ~x in L because x is
self- contradictory in L. In this case x is not a
truth-bearer in L.
So, now you ADMIT that Formal Logical systems can be
"incomplete" because there exist analytic truths in them that
can not be proven with an actual formal proof (which, by
definition, must be finite).
*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?
You are just caught in your own lies.
YOU ADMITTED that statements, like Goldbach's conjecture, might be
true based on being only established by an infinite series of
truth preserving operations.
You seem to be too stupid about this too. You are too stupid to grasp
the idea of true and unknowable.
In any case you are not too stupid to know that every expression that
requires an infinite sequence of truth preserving operations would
not be true in any formal system.
So, is Goldbach'c conjecture possibly true in the formal system of
Mathematics, even if it can't be proven?
No. If it requires an infinite sequence of truth preserving
operations it is not true in any system requiring a finite
sequence.
In rare cases such as the Goldbach conjecture this may require an infinite sequence of truth preserving operations thus making analytic knowledge a subset of analytic truth.
If so, why can't Godel's G be?
Gödel's G is true in MM.
In PA, G (not g, that is the variable) is shown to be TRUE, but
only estblished by an infinite series of truth preserving
operations, that we can show exist by a proof in MM.
No stupid that is not it. A finite sequence of truth preserving
operations in MM proves that G is true in MM. Some people use lower
case g.
But the rules of construction of MM prove that statements matching
certain conditions that are proven in MM are also true in PA.
That is merely a false assumption.
And G meets that requirements. (note g is the number, not the statement)
We can show in MM, that no natural number g CAN satisfy that
relationship, because we know of some additional properties of that
relationship from our knowledge in MM that still apply in PA.
Thus, Godel PROVED that G is true in PA as well as in MM.
That is merely a false assumption. Truth-makers cannot cross system boundaries.
He also PROVED that there can't be a proof in PA for it.
Here is the convoluted mess that Gödel uses
https://www.liarparadox.org/G%C3%B6del_Sentence(1931).pdf
And your inability to understand it doesn't make it wrong.
It is only his false conclusion that makes him wrong.
His false conclusion is anchored in an incorrect
foundation of expressions that are true on the basis
of their meaning.
It makes YOU wrong.
The truth of G transfers, because it uses nothing of MM, the Proof
does not, as it depends on factors in MM, so can't be expressed in
PA.
No stupid that is not how it actually works. Haskell Curry is the
only one that I know that is not too stupid to understand this.
https://www.liarparadox.org/Haskell_Curry_45.pdf
Really, then show what number g could possibly sattisfy the relationship.
Incorrect foundation of truth-makers.
I don't think you even undertstand what Curry is talking about, in
fact, from some of your past comments, I am sure of that. (Note, not
all "true" statements in L are "elementary statements" for the theory
L as I believe you have stated in the past.
Mere stupidly empty rhetoric entirely bereft of any supporting
reasoning probably used to try to hide your own ignorance.
A theory is thus a way of picking out from the statements of F
a certain subclass of true statements.
Curry, Harkell B. 1977. Foundations of Mathematical Logic. Page:45
The statements of F are called elementary statements to distinguish
them from other statements which we may form from them … A theory (over
F is defined as a conceptual class of these elementary statements. Let T
be such a theory. Then the elementary statements which belong to T we
shall call the elementary theorems of T; we also say that these
elementary statements are true for T. Thus, given T, an elementary
theorem is an elementary statement which is true. A theory is thus a way
of picking out from the statements of F a certain subclass of true statements.
https://www.liarparadox.org/Haskell_Curry_45.pdf
On 7/22/2024 9:56 PM, Richard Damon wrote:
On 7/22/24 10:12 PM, olcott wrote:
On 7/22/2024 8:42 PM, Richard Damon wrote:
On 7/22/24 8:44 PM, olcott wrote:
On 7/22/2024 7:17 PM, Richard Damon wrote:
On 7/22/24 8:11 PM, olcott wrote:
On 7/22/2024 7:01 PM, Richard Damon wrote:
On 7/22/24 12:42 PM, olcott wrote:
I have focused on analytic truth-makers where an expression
of language x is shown to be true in language L by a sequence >>>>>>>>> of truth preserving operations from the semantic meaning of x >>>>>>>>> in L to x in L.
In rare cases such as the Goldbach conjecture this may
require an infinite sequence of truth preserving operations
thus making analytic knowledge a subset of analytic truth.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
There are cases where there is no finite or infinite sequence >>>>>>>>> of truth preserving operations to x or ~x in L because x is
self- contradictory in L. In this case x is not a
truth-bearer in L.
So, now you ADMIT that Formal Logical systems can be
"incomplete" because there exist analytic truths in them that
can not be proven with an actual formal proof (which, by
definition, must be finite).
*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?
You are just caught in your own lies.
YOU ADMITTED that statements, like Goldbach's conjecture, might be >>>>>> true based on being only established by an infinite series of
truth preserving operations.
You seem to be too stupid about this too. You are too stupid to grasp >>>>> the idea of true and unknowable.
In any case you are not too stupid to know that every expression that >>>>> requires an infinite sequence of truth preserving operations would
not be true in any formal system.
So, is Goldbach'c conjecture possibly true in the formal system of
Mathematics, even if it can't be proven?
No. If it requires an infinite sequence of truth preserving
operations it is not true in any system requiring a finite
sequence.
So you LIED when you said Goldbach's conjuecture could bve actually
TRUE even if it could only be established to be true by an infinite
sequence of truth preserving operations.
That you stupidly screw up the meaning of what I said in your own head
is your stupidity and not my dishonesty.
Remember, you said:
In rare cases such as the Goldbach conjecture this may require an
infinite sequence of truth preserving operations thus making analytic
knowledge a subset of analytic truth.
Or are statements that are analytic truth not always true statements?
You never did have a clue of what I meant by that. I still
mean the same thing. Some analytic truth is unknown.
If so, why can't Godel's G be?
Gödel's G is true in MM.
And in PA, as proven,
That is not the way it works. Truth-makers cannot
cross system boundaries.
YOu are just showing your ignorance.
In PA, G (not g, that is the variable) is shown to be TRUE, but
only estblished by an infinite series of truth preserving
operations, that we can show exist by a proof in MM.
No stupid that is not it. A finite sequence of truth preserving
operations in MM proves that G is true in MM. Some people use lower
case g.
But the rules of construction of MM prove that statements matching
certain conditions that are proven in MM are also true in PA.
That is merely a false assumption.
So, how can the fact that it is shown that no number CAN satisfy the
relationship not make it true that no number does satisfy the
relationship?
When what-ever xyz and ~xyz cannot be proved in abc then
xyz is not a truth-bearer in abc.
You seem to have an error in your logic?
You seem to be a sheep mindlessly accepting the incoherent
received view.
And G meets that requirements. (note g is the number, not the
statement)
We can show in MM, that no natural number g CAN satisfy that
relationship, because we know of some additional properties of that
relationship from our knowledge in MM that still apply in PA.
Thus, Godel PROVED that G is true in PA as well as in MM.
That is merely a false assumption. Truth-makers cannot cross system
boundaries.
It didn't need to. The truth-makers are the fact that no number will
satisfy that relationship. That is just an established fact.
We just got a short cut to allow us to do it faster in MM
There must be a contiguous sequence of truth preserving
operations in the same language in the same system from the
meaning of the expression in the language to the expression
in the language of the system else the expression is untrue
in the system.
All knowledge is computable on the basis of axioms.
or, do you thing that two system that share the same rules of
arithmetic could have x+y = 5 in one systen but = 6 in the other?
One system of arithmetic and another system of sorting eggs
have no common communication basis.
He also PROVED that there can't be a proof in PA for it.
Here is the convoluted mess that Gödel uses
https://www.liarparadox.org/G%C3%B6del_Sentence(1931).pdf
And your inability to understand it doesn't make it wrong.
It is only his false conclusion that makes him wrong.
His false conclusion is anchored in an incorrect
foundation of expressions that are true on the basis
of their meaning.
And what is the error?
Claiming the answer is wrong, but not being able to show an error just
says that YOUR logic is wrong.
True(L,x) means a sequence of truth preserving operations
from the meaning of x expressed in L to x in L.
Sorry, but that is how logic works, at least that is how working logic
works.
It makes YOU wrong.
The truth of G transfers, because it uses nothing of MM, the Proof >>>>>> does not, as it depends on factors in MM, so can't be expressed in >>>>>> PA.
No stupid that is not how it actually works. Haskell Curry is the
only one that I know that is not too stupid to understand this.
https://www.liarparadox.org/Haskell_Curry_45.pdf
Really, then show what number g could possibly sattisfy the
relationship.
Incorrect foundation of truth-makers.
Nope, stupidity of Olcott.
The insight of Olcott seeing that only Haskell Curry
has similar ideas.
I don't think you even undertstand what Curry is talking about, in
fact, from some of your past comments, I am sure of that. (Note, not
all "true" statements in L are "elementary statements" for the
theory L as I believe you have stated in the past.
Mere stupidly empty rhetoric entirely bereft of any supporting
reasoning probably used to try to hide your own ignorance.
Good discription of your argument.
A theory is thus a way of picking out from the statements of F
a certain subclass of true statements.
Curry, Harkell B. 1977. Foundations of Mathematical Logic. Page:45
The statements of F are called elementary statements to distinguish
them from other statements which we may form from them … A theory
(over F is defined as a conceptual class of these elementary
statements. Let T be such a theory. Then the elementary statements
which belong to T we shall call the elementary theorems of T; we also
say that these elementary statements are true for T. Thus, given T,
an elementary theorem is an elementary statement which is true. A
theory is thus a way of picking out from the statements of F a
certain subclass of true statements.
https://www.liarparadox.org/Haskell_Curry_45.pdf
Yep, you just don't understand what he is saying.
I guess you are just too dumb to reason with, and you have proven that
your logic of "correct reasoning" is justs a method you use to come up
with wrong answers.
Only people as stupid as you would try to point out errors
by only using insults. You can't point of how my understanding
of Curry is incorrect because my understanding is correct.
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?
~True(L,x) ∧ ~True(L,~x)
means that x is not a truth-bearer in L.
It does not mean that L is incomplete
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.
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.
~True(L,x) ∧ ~True(L,~x)
means that x is not a truth-bearer in L.
It does not mean that L is incomplete
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.
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
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.
Except you just defined that this isn't true, as you admit that the
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. >>>>
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.
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.
Memorizing a view and insisting that this view must
be correct because that is what you memorized is what
mindless robots would do.
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.
Memorizing a view and insisting that this view must
be correct because that is what you memorized is what
mindless robots would do.
And making up an idea and refusing to test it or compare it to facts,
like you do just shows that you are just an ingorant pathological
lying idiot who recklessly disregards the truth because you only
beleive your own lies.
Sorry, you are just proving you are unfit for logic. My guess is you
are going to be working out that infinite proof in Gehenna.
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 >>>>>>>>>>>> andWhat makes it different fron Goldbach's conjecture?
~g is not provable in PA then g is not a truth-bearer in PA. >>>>>>>>>>>
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.
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.
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.
An alternative finite proof in MM only shows that the expression
is true in MM.
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
On 7/24/2024 6:57 PM, Richard Damon wrote:
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 andWhat makes it different fron Goldbach's conjecture?
~g is not provable in PA then g is not a truth-bearer in PA. >>>>>>>>>>>>>
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.
No stupid it does not shown this.
An infinite number of steps fail to meet the requirement
of showing that G is true.
"This sentence is not true" is indeed not true and that
*does not make it true* even though its assertion is satisfied.
On 7/24/2024 8:05 PM, Richard Damon wrote:
On 7/24/24 8:44 PM, olcott wrote:
On 7/24/2024 6:57 PM, Richard Damon wrote:
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:
[...]
I think a better example might be Goodstein's theorem [1]. >>>>>>>>>>>>>>*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? >>>>>>>>>>>>>>
* 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.
No stupid it does not shown this.
An infinite number of steps fail to meet the requirement
of showing that G is true.
Then how does that same sort of infinite sequence make Goldbach's
conjecture true.
"This sentence is not true" is indeed not true and that
*does not make it true* even though its assertion is satisfied.
So? That isn't the chain that G uses.
You already admitted that after an infinite sequence of operations
G is not satisfied in PA.
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