Godel's Proof of God

Godel only engaged in this sort of theme because of Leibniz (proving the existence of God).  

Leibniz calls this a proof of a necessary being, not a proof of God, but everyone else calls this a proof of God. 

http://www.leibniz-translations.com/proof.htm brings Leibniz’s proof. 


It reads:

If a necessary being is possible, it actually exists.

Necessary being?

Who says that this is possible, and why do they say that?

Then how is it that we go from possible to actually exists? 

Perhaps it exists as an idea (like at least or something)?

For let us suppose it does not exist - from that I shall argue like this:
    A necessary being does not exist, by the hypothesis.
    Whatever does not exist can possibly not exist.

If something is true, then it is also possibly true. 

It is falsely said of whatever can possibly not exist that it cannot not-exist.

What?

We can accept the first direction, right? We here talk about the direction if something is true, then it is possibly true.

However, we cannot accept the second: If something is possibly true, then it is true does not look like a correct assumption. 

This is not an acceptable move. 

Therefore it looks correct asserting that this is false, and then it is falsely said of whatever can possibly not exist that it cannot not-exist.

Of whatever it is falsely said that it cannot not-exist, it is falsely said that it is necessary.

Sure. 

If it is false that something cannot not-exist, then it must be because it can not-exist, what makes of the thing something not necessary (even though we are not seeing the purpose it serves, like necessary for what? 

For as long as we do not see the purpose of the thing, we cannot sign under the logic involved). It may be that we need something and we die because the thing does not exist, so that its non-existence is allowed, yet it is necessary, what does not make it false that it is necessary. 

Call the following line (W).

For necessary is that which cannot not-exist.

Not really. We have just proven that it is all context-dependent. 

Therefore it is falsely said that a necessary being is necessary.

(?) Now we do not see any connection between what is said before this sentence and this sentence (because of (W))… . 

This conclusion is either true or false.

This is not a conclusion, therefore it is a false conclusion.

If it is true, it follows that a necessary being implies contradiction, or is impossible, because contradictory things are demonstrated of it, namely that it is not necessary. For a contradictory conclusion can be shown only when a thing implies contradiction.

If a conclusion is false, and we do not see a contradiction, then the argument is not something we can judge based on our logical inferences.

If the conclusion is false, it is necessary that something is wrong with the premises.

No, it is not. We may simply have drawn wrong inferences, as it is clearly the case. 

Yet the hypothesis can only be false because of the premises, namely that a necessary being does not exist.

Once more, this is not really the case.

Therefore we have concluded that a necessary being is either impossible or exists.

No, we have not.

Therefore if we define God as ens a se [being from itself], or as a being from whose essence existence follows, or as a necessary being, it follows that if God is possible he actually exists.

No, nothing like that. 

We do understand, however, that if a necessary being is that whose essence existence follows, then it has to exist when it is necessary.

If words from the lexicon are used to prove our points in Logic, that will confuse people. 

Besides, that is a rule for Logic: we perform extraordinary effort to have words that allow for just one sense being inserted in the mathematical/logical universe, not mattering if we have to create them or not. 

If he defines a necessary being as something that exists, then we do not have any inference there. 

It is all improper language. 

Perhaps we could make Leibniz's argument be a lot shorter following what we are learning now: God is a being whose essence implies existence. Because we think that we know His essence (therefore it does exist), we have to acknowledge His existence. 


Once more, we would have problems here with Leibniz's reasoning, but way fewer problems than before. Why could God not be only essence, like without existence? What is existence and what is essence?


It is quite a shock learning that a mathematician of so much value, creator of our Calculus (http://www.storyofmathematics.com/17th_leibniz.html),  has so many problems with either the figure of God (and that is why he cannot reason well when trying to write about this topic) or Classical Logic when the context is not one that belongs to Pure Mathematics (yet it should not be tried in any other context).


The proof above is not the same we see described by the Stanford Encyclopedia of Philosophy, however.

There (http://plato.stanford.edu/entries/leibniz/), we read:

(1)	God is a being having all perfections. (Definition)
(2)	A perfection is a simple and absolute property. (Definition)
(3)	Existence is a perfection.
(4)	If existence is part of the essence of a thing, then it is a necessary being.
(5)	If it is possible for a necessary being to exist, then a necessary being does exist.
(6)	It is possible for a being to have all perfections.
(7)	Therefore, a necessary being (God) does exist.

The premise number (2) is already a bit controversial: perfection is an absolute property.


Perfection is a personal concept, ultra personal, instead.

In the end of 2001, we thought that Tom Cruise was absolutely perfect (just like ourselves, by the way). Would we not find people on earth to say that his nose is too big, or that he is too short, or that he is promiscuous, or that he is homosexual, or that he is a drug addict, or a coward, or a criminal, and others, like all depending on their personal experience with Tom Cruise, and their own concept of perfection?

How come this is an absolute property then? It is a super relative one instead.

Simple property? Joking! Perfection is a complex property.


What sort of definition of simple are we considering? 


If we ourselves think that someone is perfect, we are thinking of morality, physicality, partnership, virility, and things like that. 

Is that simple? 

A person must have almost all qualities that we can think of, if not all of them, for us to think that they are perfect. 

That has to be super complex, not simple.

Existence is a perfection? It just gets worse!

If we are suffering violation of human rights, especially of the most serious type, such as slavery, brainwashing, or torture, how come we would not think, probably for the entire amount of time in which we are in that situation, that human existence is absolutely imperfect, like it is something absolutely undesirable. 

If we have spiritual beliefs, then we would think that we are losing because of being alive, and we would not have lost had we not been born, so that this is an absolute imperfection, rather than just an imperfection.

Since we cannot really believe that (2) is a rational move (one step is enough), this is not a proof of anything (therefore this is not a proof of the existence of God, and this is also not a proof of the existence of a necessary being).

(Poor Leibniz?)

A Proof of God

How it all started is an impossible-to-solve puzzle because there is always an unanswered question, and there is always at least one unanswered question whilst we are limited to the human shape.

All is knowledge, and all is achievable through it.

If all is knowledge, but our existence is not enough to cope with certain pieces of knowledge, and one piece is enough, say the never-answered question, then there is something or someone who has the knowledge, and that someone or that something is not part of human kind.

Knowledge must belong to someone or something because otherwise it would not be knowledge; it would be another thing. 

Knowledge has to belong. Knowledge cannot exist per se.

Who has it then?

Nobody who is alive, and is a human being has it.

Therefore, the dead or the about-to-be-born might have it if it belongs to humanity somehow.

Not mattering to whom it belongs, it is something beyond the living creatures.


It could not be that the living creatures who are not human beings have it because they clearly know less than us.

It belongs to a non-human entity in our sense of non-human, for the body on its own cannot have knowledge, like perhaps devices inside of it can have knowledge, but not the dead body.


There is also a chance that knowledge belong to the about-to-be-born. Now we have a blurred area: are the about-to-be-born human beings?  


If they are, and knowledge belongs to them, then perhaps knowledge belongs to human beings.


However, if we can never access what they know through them, would it not be better excluding them from human kind in terms of mental maps?


Their knowledge cannot belong to human kind anyway. 

The body can have knowledge if the person is in it, if the human being is alive...

We do not call the corpse human being. 

We call the corpse dead human being, therefore non-human being.

We do not call the about-to-be-born human being, we call them human being in formation, therefore non-human being.


Now call this non-human entity, who has the knowledge, God and we then have a proof of the existence of God based on epistemic beliefs that are universally seen as beliefs of human kind.

Obs.: We have called our article with Semiotica A Solution to The Sorites to copy the name of our talk at the Newcastle University in 2000. However, we never wanted to call it either of them A Solution for we are the only ones who have the solution instead. Our research supervisor insisted that we called our work that way. This little piece, however, we call A Proof of God for willing to call it this way. 


There must be zillions of proofs of the existence of God. This is just one more.

Godel's Proof of God I

A batch of discussions from LinkedIn.


All belongs to the American Mathematical Society.


The name Godel appears in one of the discussions.

The page that appears in the link, http://www.linkedin.com/groupAnswers?viewQuestionAndAnswers=&discussionID=5799804668464873475&gid=158723&trk=eml-anet_dig-b_nd-pst_ttle-cn&fromEmail=&ut=1I5h5SzSJxYlY1, makes us see that several researchers, and members of the mainstream media have texts on the topic.

Giacinto Genco asks us to visit http://math.stackexchange.com/questions/248548/godels-ontological-proof-how-does-it-work#!, and the comments area brings someone's sigmatoids. Those imply that what is on the site may be a proof of the existence of God.

The mentioned proof also appears in http://thinkingaboutphilosophy.blogspot.com.au/2012/10/mathematical-proof-of-existence-of-god.html and http://www.religiousforums.com/forum/general-religious-debates/155882-mathematicians-claim-have-proof-god-exists.html.

The problem with this proof is evident. 


One can tell there is a fallacy by analysing its first line.

See:

Axiom 1 can only translate into:

1. Assume that some property P can be given to any property of the type phi.
2. Assume that, for each, and every, object you pick in the universe of objects available, it is  necessarily the case that if they have the property phi, then they have the property psi.
3. We therefore may infer that all objects with a property of the type psi have the property P. 

Changing that into words, the whole lot, tells us that this is not a logical proof.

Call phi having a unique model of steering wheel, like a model that is manufactured to match a specific model of car, which may be manufactured by at least two different companies. 


In the universe of companies that manufacture this model, only company X makes use of our particular model of steering wheel.

Call x car.

Call psi belonging to the specific model of car.

Call P belonging to the only company that manufactures that sort of car, with that sort of steering wheel (company X).

We then have:

1. It is necessarily the case that every car that has that model of steering wheel (therefore property phi) is a car of that specific model (therefore has the property psi).
2. It is a fact that every car with that model of steering wheel is a car that belongs to the only company that manufactures that sort of car (with that particular wheel. That is company X).
3. Therefore, every car that is of that specific model is manufactured by that only company that manufactures that sort of car (company X).

The fallacy is that the model may be manufactured by at least two companies. 



The conclusion does not follow from the premises.

We do not have a proof if any of the premises is wrong.

If our starting point is a wrong premise, we should reach a contradiction to get a proof of the opposite to our premise in the case of Classical Logic.

There is no point in analysing this any further because this proof is not equivalent to http://hroman.com/kurt-godels-mathematical-proof-of-the-existence-of-god/, or http://www.decodedscience.com/modal-logic-proved-godel-right-god-exists/38801, or http://www.reddit.com/r/explainlikeimfive/comments/1g006w/eli5_kurt_godels_ontological_proof_for_the/, or http://www.infidels.org/library/modern/graham_oppy/godel.html.

On page 6 of http://arxiv.org/pdf/0904.3921v2.pdf, definition III.2 is Axiom 1 here.



Therefore the proof in this paper is also not a proof.

We may come back to this proposal later on, since the other sources bring a different proof under the name Godel’s Ontological Proof or Godel’s Proof of God.

Strength of Belief

Today, at LinkedIn (www.linkedin.com), which is a social networking system that we respect this far, we got this discussion, which looked pretty much uninspiring, on strength of belief (History and Philosophy of Science, Is there a way of measuring how strongly one believes in something? - started by Don Wade on the 02/10/13), finally bringing some ideas that we could be interested in.

We think that these thoughts, of strength of belief, started arriving at our minds because of Fuzzy Logic, which is a logical system started by Prof. Dr. Zadeh (http://www.cs.berkeley.edu/~zadeh/)  long time ago (yet recently, if we consider the history of Science, or even the history of Logic).

Dr. Prof. Graham Priest cared a lot about this thing when we were studying with him (2000, University of Queensland).

He cared so much that he coerced us to include Fuzzy Logic (http://plato.stanford.edu/entries/logic-fuzzy/) in our talk at the Newcastle University (http://www.newcastle.edu.au/, 2000, A Solution to The Sorites Paradox, http://www.degruyter.com/abstract/j/semi.2006.2006.issue-160/sem.2006.053/sem.2006.053.xml?rskey=Tl3tg8&result=2. We do apologize for the poor revision of this article in terms of the English language. Please compare it with the last articles, published with E-Logos, and share our sadness regarding that, but also rejoice on the findings). This talk was about a solution that we had judged definite. Actually, Prof.  Dr. Hyde also believed that we had solved The Sorites in that 2000 (http://www.uq.edu.au/hprc/dr-dominic-hyde), and he is regarded as an expert on this problem.

We then did that, but our oppositions to mathematizing language are never ending… .

Basically, we must understand that language is there to try to make the other person, that with whom we communicate, see, in their own head, what we see in ours when we make efforts to communicate with them. 

We say that because we do not believe we ever truly communicate.

People who believe in Fuzzy Logic, the pure thing, not the applied concept, used in air-conditioning (http://www.simplecodeworks.com/KSCO/book/chapter7.htm), for instance, and the concept was applied thanks to an Engineer who listened to Zadeh once, believe that we communicate for real all the time instead, basically.

Trivially, were that ever true, we would be able to get some mathematical function describing the processes of human communication to perfection.

The reasons why we do not really communicate are never ending, and are also quite obvious.

First of all, communication is not a process that starts in our mouth or hands: Communication starts inside of us, or even outside, perhaps through spiritual processes, through what some people who some call spiritists have called calls from beyond.

We may be anthropocentric and then believe that all is controlled and generated by human beings.

In this case, we will certainly believe that we can control all more times than we will believe that we cannot control at least part of it.

We may also be geocentric and believe that The Globe commands all through electric discharge processes, for instance.

In this case, we would not strongly believe that we can control the communication process between human beings.

The difference then, in terms of theories, starts with ourselves, like with what we believe inside of ourselves about our own existence: Are we on top of all that happens to us or we are at least sometimes victim or passive agent?

To try to exhaust all the ways that lead to Graham Priest, we will then take his side in the story, as for 2000, personal conversations: We can do it!

Events of our life, in terms of communication, are then all anthropocentric.

Things will fall to land quite easily on this first move, but we will pretend that they do not in order to keep on going.

If we manage all processes of ours of communication, we may assume that at least one other human being also does.

In this case, communication may happen without any noise and the words can transmit perfectly well the original idea, that that we had in our own heads before making efforts to communicate.

Things being this way, we can definitely mathematically measure our discourse, provided we divide it adequately (paragraph, sentence, word or whatever we think will work).

We can measure, for instance, the strength of universal belief that one gives to our utterances, or even of personal belief.

This way, if Hamish, who we are extremely fond of in 2013 and 2014, says I love you, we could have a personal belief of, say, 20% that he does, perhaps based on his decisions regarding our practical life, like based on the why he would not stop crime against us and other practical factors that, in a logical head, would measure how much that could be true.

We believe that we have never been so fond of someone that we could touch physically because, for instance, we have swapped syllables whilst speaking to him face-to-face for the first time in our life, what then gives us a strength of 100% of belief, as for ourselves, in our utterance We are extremely fond of Hamish, from Adelaide.

Now, first of all, in the world of Graham Priest and Lofti Zadeh, obviously amongst plenty of others, we have some Mathematics that can be attached to our discourse.

With Science, we are then after a universal agreement on a factor that describes that strength and, only if that is not possible, do we go for theories, probably on the hope of approaching the truth by either upper or lower bounds, so that through refinement we get there (all extremely mathematical).

Now, let’s come back to our real life example, since communication, not language per se, which may even be cold and scientific, does involve human beings (so far, at least whilst Marcia R. Pinheiro is alive, like this is what we, Marcia R. Pinheiro, know for sure).

Well, does Hamish love us with a rate of 100% of absence of doubts or he loves us with a rate of 99.2% (or even of 20%, our own belief or what we believe to be our belief) instead?

Once more, and we beg the reader of this blog (is there any?) to also read our solution to The Liar, published with the so prestigious vehicle E-Logos, there are several complexities (that are usually unexpected) in the human world (which are obviously not found in the world of the symbols, or the semiotic world, as we will call it from now onwards). For instance, how much can we evaluate ourselves and under what conditions is that to be believed?

It is widely known, for instance, that a depressed human being will underestimate everything that could be positive in their lives, so that there would be (how much per cent?) a reduction that should be considered if we judge that we are depressed, for instance, as we evaluate Hamish’s feelings for us.

On the other hand, how much Hamish himself believed his assertion by the time he said it?

He could be saying that just to keep us going if we are suffering extraordinary crime for long, for instance, and really do not have reasons to keep on trying.

In this case, Hamish would know, internally, that he did not mean it, but we could believe that he meant that with all our soul because he put so much effort into convincing us of that that we took it for granted. In this hypothesis, he would have done that out of generosity, not out of the truth of his heart or soul.

We then start seeing that there is a never-ending universe of mathematicalities that has to be considered, even if we are insane enough to believe that communication is something that we could be mathematizing in what comes to human beings.

We obviously cannot translate human actions, and communication does involve those, into any sort of Cartesian Mathematics. 

Then, the most skeptical of the humans would say that we should go for the non-Cartesian Mathematics, and that is definitely what our friend, Prof. Dr. Graham Priest, has done: He said that we should actually change Mathematics, and that is obviously the reason why he joined the non-classicists (those who want to pervert Classical Logic, the logical system that forms the foundations of Mathematics).

Would that not be the same Graham Priest that defied Combinatorics in public when presenting the 3-door puzzle we talked about in our other post?

Surely it was!

Prof. Dr. Graham Priest should understand however that any logical system is a computer model, therefore cannot translate purely human actions, such as communication, to perfection. In fact, not even to imperfection: It cannot deal with them at all.

Even if we decided for an alternative system of measurement, and a person in LinkedIn has inspired us on this one (someone who identified themselves through the name DhanshDhai Misra and a picture but actually does not appear in LinkedIn officially and Master Eric Wasilek), say things we all believe for sure, such as it being impossible that we see stronger beliefs in humans than those of the suicide-bombers, and we used those as a reference (say we created a new ruler, a virtual one, where suicide-bomber's strength would be read, say on the last smallest piece that can be used to measure things in that ruler), we would still have problems on how to rank everything else, and that is just obvious.

This way, even when using a more human-friendly system, made of pictures, which should form our most primitive thought processes (but we ourselves believe in what we call divine inspiration, so that the most basic processes would actually be those appearing before the image), like the one we have just mentioned, the one involving the suicide-bomber, we would have to reach the conclusion that it is impossible to measure human discourse when it is found attached to human perception.

Each one of us, just for starters, would rate the strength of Hamish’s assertions differently.

It really does not matter what processes of decision we choose, say voting, as we would end up getting to in democracy: It is all deemed to be inaccurate and ultra personal, quite trivially, like it all will depend always on the nature of the group under consideration (who judges), for instance, to the least.

If we keep on going in the skeptical line and then say that it is possible to reach a universal consensus about Hamish’s assertions because, for instance, whenever we have democracy, and we put to the vote, everyone agrees that human rights are the most important thing on earth, we will unavoidably reach a limiting line that will form a gap between whatever we write and reality.

That is all obvious.

Even if we were inside of Hamish, say Hamish were bugged in his head, to the top of his spinal cord (from where we believe/know we can access things to best in what regards our bodies), we could absolutely never measure this type of thing accurately.

Why?

Well, not even Hamish can do that, and Hamish is only Hamish, like with certainty, one hundred per cent, if he is not bugged, so that bugging Hamish is creating Hamish’ and analyzing a situation that is not the situation that has been originally proposed to us, therefore is not analyzing or solving the original problem.

Also, with Hamish bugged, we are still not sure, even if we believed that Hamish=Hamish’, and we are sure that Priest would push us to accept this move, that what we see is what we get. Hamish, to the least, might have been influenced, assuming the materialistic position (all we are is matter), by images that he receives his entire life before that moment, so that he actually does not love us, but he loves, for instance, his best friend from childhood, who, by accidental processes, resembles us, say because of our voice, touch or whatever else.

In this case, so assuming that the love for the childhood friend is the actual truth, if we all watch Hamish from inside, believe that Hamish = Hamish’,  and then measure - this believing that we can do that - mathematically the strength of his assertion, finally ranking it as maximum, 100%, or equal to that of the suicide-bomber's, we are obviously committing a horrible scientific mistake.

Basically, Hamish had spent his entire childhood with that female who happened to have something in common with our figure, and his subliminal processes made him associate nurturing, care, and love with us, what then made him come back to the feelings that he used to have for that female ages ago.

In this scenario, Hamish's assertion is not to be believed at all (0%). 

Yet, all in all, why does this matter, like why would any of this ever bring progress to Science? This is about beliefs, not facts. 

It could be useful to us in decision-making if we knew that everything that Hamish says has, for instance, a strength of 20% in terms of universal belief because we have studied the facts of Hamish's life and we have determined that all he says relates to the facts of his life this way. 

Notice, however, that this is a percentage, not an absolute thing, so that we actually have nothing to help us decide. We could go Statistics, however, and use their tools to make a better decision in case that were possible.

We know that this is not possible. Hopefully, the readers of our blog agree with us by now.

All that means is that not mattering what Dr. Prof. Graham Priest comes up with, nothing that has a chance of being purely human, therefore nothing that escapes the computer world by any evaluation of lambda, may be perfectly dealt with by Mathematics, or Logic, per se.