The Relationship Between Math and Physics

Science
Philosophy

(Antoine Suarez) #41

Thanks Dan for raising this interesting objection.

“Defining ‘the mind of Dan Eastwood’ in a symbolic system” isn’t any more possible than “defining ‘the mind of God’ in a symbolic system.

How do you prove the existence of Dan Eastwood’s mind? On the basis of the existence of speech or written text we identify as contents of such a mind, like for instance the comments you have posted in this thread.

The existence of a ‘yes’ or ‘no’ answer to the question of whether there is or not a largest perfect number implies the existence of a mind that contains such an answer. However, at present no human mind contains it. Therefore, there is a non-human mind containing this answer.

On the other hand, to solve a problem human mind has to discover the fitting algorithm (a finite set of symbolic operations). This way of working implies Turing’s and Gödel’s theorem: At any time T of history there will be unsolved problems in arithmetic’s whose solution exists and has to be contained in a mind. This omniscient non-human mind is what I define as God.

To this extent this reasoning does not invoke any content of religious faith or revelation, but only the principle that certain achievements require intelligent authors.

It’s one thing to say that the existence of any mind is “an un-provable proposition in ANY symbolic system”, it’s another thing to say that the existence of any mind is not provable at all.

In summary: If you deny the existence of a mind containing the answers to all unsolved solvable problems in arithmetic you can as well deny the existence of Dan Eastwood’s mind.


(John Harshman) #42

A fine syllogism. The problem with it would seem to lie in the major premise, which is clearly false. You have given no reason why a question that has a yes or no answer implies that someone knows the answer. I’m looking out my window right now, and I ask whether there is a squirrel on the other side of that wall. The answer to that question is clearly yes or no, but I don’t know which, and neither does anyone else. Does that in fact imply the existence of God? Perhaps, but you would have a hard time convincing anyone. Perhaps the argument just looks more impressive when you add mathematics.


(Dan Eastwood) #43

Easy, you query for a response, as you have just demonstrated.

Non-Sequitur. It does not follow that such a non-human mind exists. This criticism has been made several times now, and you have not attempted to address it. I suggest the only possible answer is such a non-human mind can only be a human assumption, never demonstrated. Again, logical proof of the mind of God implies that humans can understand such a thing. That ought not to be possible by logical and theological standards.

There could easily be questions (many, no doubt) for which you or I do not know the answer, but some other human does and we simply remain unaware of it. Does the non-human mind simultaneously exist and not-exist?

Similarly there could be a question with no answer today, which is answered tomorrow. Does this non-human mind suddenly poof out of existence because someone figured it out? That other unanswered questions still remain is simply moving the goalpost with each answered question.

There must also be UNKNOWN questions which will forever remain unanswered, implying that no such non-human mind exists. This argument self-contradictory.

* edit: those last two sentences might be affirming the consequent. We could speculate about a non-human mind that doesn’t give a fizzle about what we do or do not know.


(Antoine Suarez) #44

You got it right John!

In the case of the squirrel you are in possession of the method for answering the question you ask: You go out of your house, get to “the other side of that wall” and then you observe whether or not there is a squirrel there. You possess the method to answer the question, and this leads to you to think the answer to the “squirrel question” does exist in your mind, and there is no need of invoking God’s mind.

In his celebrated speech at the Second International Mathematicians Congress (Paris, August 8, 1900), David Hilbert shared the conviction that there is a universal method or algorithm which allows us to answer every question in arithmetics through pure calculation by a finite number of purely logical steps: “We hear within us the perpetual call: There is the problem. Seek its solution. You can find it by pure reason, for in mathematics there is no ignorabimus ", Hilbert emphatically said.

If such a universal algorithm exists, then you could believe that all the mathematical truth is contained in your mind. The same way as you believe that you actually possess the answer to the “squirrel question”.

Nonetheless, we know today that there cannot be such a universal algorithm: This is the amazing result of Gödel’s and Turing’s theorems.

Consequently, there must be a non-human mind that contains the answers to all arithmetic questions. This omniscient mind is what I define as God’s mind.

As a corollary from this it follows that the answers to every answerable question we can ask, do exist in God’s mind before we become capable of answering it. This was the “new proof” of God’s existence Moses Mendelssohn provided in his Morgenstunden 1785, who concluded that everything that is thinkable must be actually thought by some thinking being.

However, as you very well remark:

Indeed, if you do not add mathematics you can easily delude yourself: You can belief that you possess the answer, because you possess the method to find it. Or you can say the answer is “outside there” in the material world. When you add mathematics it becomes clear that the answer is in a mind and that this mind cannot be a human mind.


(John Harshman) #45

Interesting. You say I got it right and then go on to claim to show that I’m wrong.

No it doesn’t. Perhaps it would lead you to think that, but the connection is not apparent. Having the method to answer the question does not imply that the answer exists in my mind. Further, even if it did, I could ask other simple questions that I have no method to answer, for example “How many helium atoms are in this room right now?”, and yet that still doesn’t imply God.

You could believe anything you liked, but I don’t see a rational connection between the premise and the conclusion. Invoking Hilbert seems nothing more than name-dropping.

Corollaries of non sequiturs are not valid. And that wasn’t even a corollary.

That is no more clear than the idea that the answer to the squirrel question is also in my mind. Less so, in fact. No, what mathematics does is merely to make your conclusion seem more sciencey and thus more attractive. The squirrel question is useful because it exposes the bare bones of your faulty reasoning more clearly.


(Antoine Suarez) #46

No. According to the logical standards of “non-contradiction” it simply means that:

  • the non-human mind (God’s mind) exists;

  • some humans by reading God’s mind become aware of some contents in it;

  • other humans have not yet developed fitting skills to read God’s mind and get the same contents, although they may have got other contents.

Again. You are disregarding logical standards:

What does it mean “the question is answered tomorrow”?

Simply means that “tomorrow” the answer is both in God’s mind and in our minds. The same way as your comment, once posted it is in my mind without being removed from your mind.

I sincerely thank you Dan, for this remark: It strengthens my argument in a way I haven’t thought before of.

There are certainly many UNKNOWN questions to us humans, as you rightly claim. This means that these questions actually exist: What does not exist cannot be “unknown”. And the answers to them do exist as well.

On the other hand, “questions” are not entities existing on its own: they do exist in some mind. Since they are “unknown” to us, they must exist in some non-human mind, in which the answers to them co-exist as well. This is a magnificent characterization of the omniscient mind: It is a mind in which there is no separation between question and answer.

By contrast our human minds are limited because in them there is separation in time between question and answer. Accordingly, the “unknown questions” you refer to do not “remain forever unanswered” in God’s mind but only in our limited human minds. And this is also an argument in favor of eternal life after dead: It is noting other as a continuation of earthly life, where we will directly read into God’s mind, endlessly becoming aware of questions we did never asked before, and gazing in awe to the answers.

In fact, we are completing here the profound Moses Mendelssohn’s proof of God’s existence. This proof remained sadly unconsidered and undiscussed because Mendelssohn’s philosophy was “euthanized” by Immanuel Kant’s criticism. Fortunately, today in the light of Gödel’s and Turing’s theorem Mendelssohn’s proof can be discussed more in depth. It amounts to state: Every sound question a human asks proves by itself the existence of God!

This claim is contradicted by the simple fact that we humans exist.

If the omniscient-mind “doesn’t give a fizzle about what we do or do not know”, we would know nothing at all, that is would not exist. So if we do exist is because the omniscient mind loves us and makes the world so that we can calculate it and live comfortably in it. Once again: “the appropriateness of mathematics for describing the world is a wonderful gift of God and we should be thankful for it”.


(Dan Eastwood) #47

I’m sorry @AntoineSuarez, but I see nothing but non-sequitur statements and begging the question of the mind of God. If this makes you happy I cannot object, but I think you are selectively ignoring the flaws in your own argument. Since you are not addressing the criticisms, there isn’t much more to say.


(Bill Cole) #48

Can you be more specific?


(Bill Cole) #49

I find this an interesting claim. Is it supported by Godel’s incompleteness theorem. If so, how?


(Dan Eastwood) #50

Antoine’s claim, and I’ll try to state this fairly; logical propositions imply an answer to those propositions, which must exist in a mind. Since we do not know the answer to all propositions, the answers must exist in the mind of God. Therefore, God exists.


(Antoine Suarez) #51

Dan, I am afraid: You are not “fairly” reproducing what I claim.

My statement is as follows:

Premise A:

The answer to arithmetic questions like whether or not there is a largest perfect number is either YES or NO.

This answer exists, and therefore also exists the method (algorithm) to access it.

Premise B:

Answers to arithmetic questions like those referred to under Premise A do not exist in any material realm but are contents of some mind.

Premise C:

From Gödel’s and Turing’s theorems it follows that:

At any time T in history there will be arithmetic questions like those referred to under Premise A that can be answered by NO method available at time T to any human mind.

Conclusion :

At time T the answers to all unanswered answerable arithmetic questions, and the methods to answer them, are contained in a non-human mind.

Corollary 1:

If at time later than T, a human mind discovers an algorithm to answer one of the questions that at time T was unanswered, then both the answer and the algorithm become contents of the mind of the human discoverer, but still remain contained in the non-human mind as well.

Corollary 2:

The non-human mind who at time T contains the answers to all unanswered answerable arithmetic questions is an omniscient mind, in which there is no separation between question and answer, by contrast to the limited human mind.

Definition:

God is the omniscient non-human mind referred to in Corollary 2.

Please tell us which precise step in this reasoning you think to be a “non-sequitur” statement.


(Neil Rickert) #52

This part seems absurd to me.

When we say that the answer exists, that is merely a manner of speaking that is common among mathematicians. “Exists” to a mathematician is not at all like the ordinary meaning of “exists”. A mathematical Platonist will say that it exists in the world of Platonic forms. A mathematical fictionalist, such as myself, will say that it exists only as a useful fiction.

That’s not my take on Gödel. Rather, I see Gödel as implying that the answer does not actually exist at all, but that we can adopt additional axioms that specify a preferred answer if we so wish – and without thereby introducing any new contradictions into our axiom system.


(Dr. Patrick Trischitta) #53

Nonsense.


(Dr. Patrick Trischitta) #54

More nonsense.


(Dan Eastwood) #55

@AntoineSuarez thank you for stating that explicitly, I really did not want to misrepresent your claim to Bill.

This does not follow.

Not necessarily. It could be an unprovable proposition, per Gōdel’s Incompleteness theorem.

Agreed. Borrowing from Wiki …

The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an effective procedure (i.e., an algorithm) is capable of proving all truths about the arithmetic of the natural numbers. For any such consistent formal system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that the system cannot demonstrate its own consistency.

Is a natural number a mind? Is God a natural number??
For that matter, is God a consistent system???


(John Harshman) #56

You have just abandoned Gödel’s proof that there are true statements that can’t be “accessed”. Why?

Premise B assumes what you intend to prove.

All that follows these problematic premises is therefore pointless.


(Bill Cole) #57

I would agree with Dan that this part of the argument needs development. Why do the answers have to be contents of some mind?

Perhaps the connection is that the question itself would not exist without a mind. There is supporting evidence here that may help build your premise.


#58

Quoted in Arc Magazine


(Antoine Suarez) #59

Thanks Bruce for this Reference.

Other interesting quotations in the Essay:

Meaning is personal. For there to be any meaning beyond the merely private, the merely subjective, existence-as-such must be personal. There must exist an irreducible unity between mind and being.

Louise intuits the universe as fundamentally personal. “The physical universe,” she muses, “was a language with a perfectly ambiguous grammar. Every physical event was an utterance that could be parsed in two entirely different ways, one causal and the other teleological, both valid, neither one disqualifiable no matter how much context was available.” It should go without saying that there can be no language apart from consciousness, no “utterance” without a speaker.


#60

I should admit that my post was not meant to be taken as a serious argument for your position; frankly, I agree with Neil’s position and with the others who question your premises,.

Borges is a fiction writer known for his philosophical fantasies. So I thought it would interesting to see his take on this type of argument. I don’t think the fact the he makes this type of argument is a positive indication of its soundness.