Featured Weakness of God's proofs, and incompleteness theorem

Discussion in 'Science and Religion' started by questfortruth, Oct 25, 2020.

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1. questfortruth Well-Known Member

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INTRODUCTION

Colin McLarty, What does it take to prove Fermat's last theorem?
Grothendieck and the logic of number theory,''
Bulletin of Symbolic Logic 16(3), 359-377 (2010).

MY CONTRIBUTION

\begin{abstract}
I argue, that a good paper with good proof can contain weak spots.
So the proofs for God do. And so even the proof of Fermat's theorem does.
Therefore, if you demand the strong proof for Fermat -- you will fail,
just like demanding the strong proof for God. Valid proof is allowed to be weak,
but it is better to be rather short weak proof, than over 100 pages long weak proof.

Remaining over 300 years an unsolved problem, the recently
proven Fermat's Last Theorem has stimulated the
development of algebraic number theory in the 19th century
and the proof of the modularity theorem in the 20th century.
I am presenting new insights on the numbers and on the Theorem.
\end{abstract}

\section{Is Wiles's proof weak or strong one?}

Fermat's Last Theorem is one of
the most popular theorems in mathematics. Its condition is
formulated simply, at the school'' arithmetic level, but many
mathematicians have been looking for the proof of the theorem
for more than three hundred years. Proved 1994 by Andrew Wiles
(proof published 1995).

But some parts of the work contain stronger arguments than
other parts. And this means that there are the weakest points
and the strongest points. And this is a normal phenomenon in a
research work.

Humankind is not yet done with Fermat's Last Theorem. The
Dr.~McLarty's paper~\cite{Mc} explores the set-theoretic assumptions
used in the currently published proof of Fermat's Last Theorem,
how these assumptions figure in the methods Wiles uses, and the
currently known prospects for a proof using weaker assumptions.
Fermat's Last Theorem is just about numbers, so it seems like
we ought to be able to prove it by just talking about numbers,''
McLarty said. I believe that can be done, but it will require
many new insights into numbers. It will be very hard.'' I am
presenting several new insights here.

Can a research paper that has weaknesses be logically correct?
Does a weak spot in the paper asks from a reader a tiny bit of
trust, faith, hope, and love, a
bit of scientific courage and determination? A bit of risk?
A bit of real life.

\section{G\"odel}

INTRODUCTION

MY CONTRIBUTION

Due to the Incompleteness Theorems of G\"odel~\cite{Godel} one
can say, that some true conjectures do not have valid proofs.
One could think it also about the attempts to prove the
Fermat's Last Theorem outside of the set theory methods, but I was
lucky.

At school task-books, all problems have a solution. On the other hand,
the universities are teaching problems without found solutions, [but
with an unknown, hidden answer, e.g.\ we do not know is the Twin
Prime Conjecture trueor false, but there is definite answer to it].
While joyful discovering solutions
to the Riemann, Goldbach, ABC Hypotheses, Fermat's Last Theorem,
I cannot find a solution to the Twin Prime Conjecture. Maybe the
twin primes don't have a solution: they have an answer that cannot
be reached by a logical path.

This fact was first discovered by G\"odel.
My demonstration of G\"odel's incompleteness theorem:
Some hypotheses have a limited number of solutions, for example, two.
But we don't know that. Then, having found these two solutions, we
will look for the third. Then the probability of finding the third
solution is less than 100 \% even using unlimited resources and
research time. The probability of finding solutions is
not dictated by the order of finding solutions, therefore the
probability of finding the very first solution is also less than 100 \%.
Since there are problems where the probability of finding a solution
is less than 100 \%, then there are also problems where the number of
possible solutions is zero [because of definition of probability].

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3. questfortruth Well-Known Member

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Perhaps it is strong proof of Fermat's Last Theorem, in just 5 pages. Weak or strong - depends on the opinion of a reader. I am trying to publish it in a top journal, therefore, I am not sharing it for now.

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4. Altfish Veteran Member

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What is wrong with Andrew Wiles 1994/5 proof?

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5. ratiocinator Lightly Seared on the Reality Grill

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This does not demonstrate Gödel's theorem.

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6. questfortruth Well-Known Member

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I is logical but has weak spots (according to Dr. McLarty).

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7. questfortruth Well-Known Member

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You are wrong here. It does perfectly demonstrate Gödel's result.

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8. ratiocinator Lightly Seared on the Reality Grill

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It doesn't even make any sense. If you're just basing the probability on the number of solution there are, then it attaches to the number you'll find, not to each individual proof.

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9. questfortruth Well-Known Member

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And indeed, we have faced problems, which had no solution during the year 2020AD. They are n out of N problems. Thus, we can estimate the number of the problems (the x), which have no solution within 2020AD up to 30 000 AD (and beyond): 0<x/N<n/N. By the definition of probability, the chance [seen from the end of 2019 AD], that a blindly picked problem has no solution is p=x/N. I argue, that the p can not be zero if the N is large enough.
Here the set N contains the problems
at the start of 2020 AD only, thus, it is a fundamental constant
throughout all future. The x and n are sub-sets in N.

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10. Altfish Veteran Member

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Who is Dr McLarty?

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11. questfortruth Well-Known Member

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A scientist, PhD.

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12. Altfish Veteran Member

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Can you give me a link? I've tried googling but many Dr. McLarty's come up. Do you have a first name.

The fact that you say he/she is a scientist worries me, we need a mathematician not a scientist.

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13. questfortruth Well-Known Member

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It is because the wife of Mr. Nobel was taken by a mathematician (as many suggest). Thus: math is not a discipline for Nobel Prize, and even not a science.

Please read the thread more carefully. There is the first name of the doctor and the title of his paper, etc.

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14. ratiocinator Lightly Seared on the Reality Grill

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You really are all over the place. Either the "2020AD up to 30 000 AD (and beyond)" is supposed to assume that we will find the solutions to all problems that have solutions, in which case x is the number of unsolvable problems and you've assumed your conclusion (that x is not zero), or it's just the number that we'll find in a given time, in which case you've said nothing at all about unsolvable problems.

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15. questfortruth Well-Known Member

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You are making too peer peer-review. Try doing a review with less peer. Try to see something good, not all bad things that are out there.

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Very confusing response.

The problem with your argument is your comparing 'apples and oranges,' and the arguments for math theorem logic are not remotely related to the apologetic logical arguments for the existence of God.

It is best to simplify the problem of proof for math axioms, and not play mystical blue smoke and mirrors and confusion.

Gödel’s Incompleteness Theorems

For a particular set of axioms, there are different “models” implementing those axioms. A model is an example of something that satisfies those axioms.

As a non-mathematical example of a model, let’s say the axioms that define being a “car” are that you have at least 3 wheels, along with at least one engine that rotates at least one of the wheels. A standard car clearly follows those axioms, and is therefore a model for the “car axioms.” A bus would also be a model for the car axioms.

Of course, there are models that are very non-standard…

Mathematical axioms work the same way. There are axioms for the natural numbers, and their addition and multiplication, called “Peano arithmetic” (pay-AH-no). The normal natural numbers, $[​IMG]$ follow these axioms, so are the standard model for them. But there are non-standard models that still follow the Peano arithmetic axioms.

Each model is a bit different. There may be some statements (theorems) that are true in some of the models, but not true in another model.

Even if a statement is true, though, you want to be able to prove it true, using only the axioms that your model satisfies.2

Gödel’s completeness theorem answers the question, “Using the axioms, is it always possible to prove true statements are true?”

His completeness theorem says you can prove a statement is true using your chosen axioms if and only if that statement is true in all possible models of those axioms.3

On the other hand the for apologetic logical arguments it is not a matter of incompleteness as in math. The math logic is universally accepted by mathematicians, and problem of incompleteness is without controversy, but it is accepted that incompleteness can be resolved as in Andrew Wiles 1994/5 proof.

Apologetics on the other hand relies of structured logical arguments based on premises that are claimed to lead to the conclusions for the existence of God. The problem is only those that believe in the conclusions accept the premises.

Example: Kalam cosmological argument - Wikipedia

The most prominent form of the argument, as defended by William Lane Craig, states the Kalam cosmological argument as the following brief syllogism:[4]

1. Whatever begins to exist has a cause.
2. The universe began to exist.
3. Therefore, the universe has a cause.
Given the conclusion, Craig appends a further premise and conclusion based upon a conceptual analysis of the properties of the cause:[5]

1. The universe has a cause.
2. If the universe has a cause, then an uncaused, personal Creator of the universe exists who sans (without) the universe is beginningless, changeless, immaterial, timeless, spaceless and enormously powerful.
3. Therefore, an uncaused, personal Creator of the universe exists, who sans the universe is beginningless, changeless, immaterial, timeless, spaceless and infinitely powerful.
Referring to the implications of Classical Theism that follow from this argument, Craig writes:[6]

"... transcending the entire universe there exists a cause which brought the universe into being ex nihilo ... our whole universe was caused to exist by something beyond it and greater than it. For it is no secret that one of the most important conceptions of what theists mean by 'God' is Creator of heaven and earth."

The problem is that the premises are not accepted by those that do not believe.

1) Whatever begins to exist has a cause. - Whatever begins to exist can have a natural cause.

2) The universe began to exist - Unknown, Fallacy of 'arguing from ignorance.' It is possible based on the evidence that our universe can have a natural cause in a multiverse with a natural cause. Infinity? Turtles all the way down.

3) Therefore the universe has a cause - By the evidence the universe can have a natural cause.

Since these premises are not accepted by those that do not 'believe' only those that believe in a God accept the conclusion that a (personal?) Creator exists or is necessary.

I believe in God, and fully realize that the traditional apologetic arguments fail due to circular reasoning where the premises are deliberately constructed to justify the conclusion.

Hint: The 20202 Nobel Prize in Physics involved research research on the origins of the universe as a singularity, black hole research, and how singularities naturally form based on Quantum Mechanics.

The bottom line is that the premises for the Cosmological argument are not accepted, because of premises are unacceptable based on the fallacy of 'argument from ignorance' and hypothetical unknowns.

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17. Altfish Veteran Member

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What has the (a) Nobel Prize got to do with Fermat?
Fermat postulated a mathematical question; it was solved by a mathematician.

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18. questfortruth Well-Known Member

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Colin McLarty, What does it take to prove Fermat's last theorem?
Grothendieck and the logic of number theory,''
Bulletin of Symbolic Logic 16(3), 359-377 (2010).

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19. questfortruth Well-Known Member

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Do we have evidence in favor of the Multiverse?!

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Thank you

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