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.