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Anyone for Kurt Godel's ontological proof?

 Posts: 8,346 Add as FriendChallenge to a DebateSend a Message 1/24/2015 7:29:57 AMPosted: 3 years agoKurt Godel for those who are unfamiliar, was a brilliant mathematician who devised a proof for god using higher order logic. Recently, computer scientists interested in developing tools for higher-order theorem provers found that Godel's proof was mathematically valid.Their basic conclusions were as follows, as is provided in the link to their research submission:> The modal system K is sufficient for proving Theorem 1, 2 and 4> Modal logic S5 is not needed for proving T3; the logic KB is sufficient.> For proving theorem T1, only the left to right direction of axiom A1 is needed. However, the backward direction of A1 is required for proving T2.(another conclusion I left out due to source-formatting issues on DDO)If you're not familiar with the argument, here it is: http://www.debate.org...If you're not familiar with the modal/predicate jargon, just google it.Article at http://arxiv.org...I'm interested in doing a debate with someone using predicate/higher order logic. PM if interested."Your signature should not have the name of other players in the game, nor should it have the words VTL, Vote, or Unvote." ~Yraelz, 2017 Debate challenge 'Solipsism is false:' http://www.debate.org... If God were real... http://www.debate.org...
 Posts: 564 Add as FriendChallenge to a DebateSend a Message 1/24/2015 11:50:49 AMPosted: 3 years agoI am game as con provided I can figure out how to use those fancy symbols and don't have to do the WW II debate simultaneously.I'll PM you this if that is a requirement.The earth does not belong to man; man belongs to the earth.
 Posts: 1,505 Add as FriendChallenge to a DebateSend a Message 1/24/2015 8:26:06 PMPosted: 3 years agoAt 1/24/2015 7:29:57 AM, Smithereens wrote:Kurt Godel for those who are unfamiliar, was a brilliant mathematician who devised a proof for god using higher order logic. Recently, computer scientists interested in developing tools for higher-order theorem provers found that Godel's proof was mathematically valid.Their basic conclusions were as follows, as is provided in the link to their research submission:> The modal system K is sufficient for proving Theorem 1, 2 and 4> Modal logic S5 is not needed for proving T3; the logic KB is sufficient.> For proving theorem T1, only the left to right direction of axiom A1 is needed. However, the backward direction of A1 is required for proving T2.(another conclusion I left out due to source-formatting issues on DDO)If you're not familiar with the argument, here it is: http://www.debate.org...If you're not familiar with the modal/predicate jargon, just google it.Article at http://arxiv.org...I'm interested in doing a debate with someone using predicate/higher order logic. PM if interested.Like all such arguments it fails because it is 'metaphysical'. 'Necessary existence' is not a property; 'X necessarily exists' means that the proposition 'X exists' is necessarily true. It signifies a conclusion, not a definition. To define something as necessarily existent is thus pure sophistry.
 Posts: 8,346 Add as FriendChallenge to a DebateSend a Message 1/24/2015 10:12:28 PMPosted: 3 years agoAt 1/24/2015 11:50:49 AM, Amoranemix wrote:I am game as con provided I can figure out how to use those fancy symbols and don't have to do the WW II debate simultaneously.I'll PM you this if that is a requirement.For the argument, you'll only need to know that:> All Greek letters are instance variables> P means positive> Backwards 'E' is the existential quantifier.> Inverted 'A' is the universal quantifier.> The subject is lowercase, the predicate, uppercase. (usually)> All symbols commonly used in propositional calculus apply normallyA basic knowledge of other logic systems should suffice. I'm ideally after a debate on the argument, its premises, its conclusion and its logic, not a thematic rebuttal of anything that claims to be an ontological argument for God."Your signature should not have the name of other players in the game, nor should it have the words VTL, Vote, or Unvote." ~Yraelz, 2017 Debate challenge 'Solipsism is false:' http://www.debate.org... If God were real... http://www.debate.org...
 Posts: 8,346 Add as FriendChallenge to a DebateSend a Message 1/24/2015 10:23:04 PMPosted: 3 years agoAt 1/24/2015 8:26:06 PM, Wocambs wrote:At 1/24/2015 7:29:57 AM, Smithereens wrote:Kurt Godel for those who are unfamiliar, was a brilliant mathematician who devised a proof for god using higher order logic. Recently, computer scientists interested in developing tools for higher-order theorem provers found that Godel's proof was mathematically valid.Their basic conclusions were as follows, as is provided in the link to their research submission:> The modal system K is sufficient for proving Theorem 1, 2 and 4> Modal logic S5 is not needed for proving T3; the logic KB is sufficient.> For proving theorem T1, only the left to right direction of axiom A1 is needed. However, the backward direction of A1 is required for proving T2.(another conclusion I left out due to source-formatting issues on DDO)If you're not familiar with the argument, here it is: http://www.debate.org...If you're not familiar with the modal/predicate jargon, just google it.Article at http://arxiv.org...I'm interested in doing a debate with someone using predicate/higher order logic. PM if interested.Like all such arguments it fails because it is 'metaphysical'. 'Necessary existence' is not a property; 'X necessarily exists' means that the proposition 'X exists' is necessarily true. It signifies a conclusion, not a definition. To define something as necessarily existent is thus pure sophistry.Absolutely ridiculous to claim that something fails merely because it is 'metaphysical.' The statement: 'Statements can be true' is a metaphysical statement. It is also the conclusion from a set of implied premises. The argument that statements can be true does not 'fail' simply because it happens to be metaphysical. In fact, a metaphysical statement is more likely to be true than a statement about physical reality.If necessary existence is not a property, what is it? A property merely describes attributes of a concept, using other concepts. Necessary existence is such a concept, attributed to other concepts. Hence a property."Your signature should not have the name of other players in the game, nor should it have the words VTL, Vote, or Unvote." ~Yraelz, 2017 Debate challenge 'Solipsism is false:' http://www.debate.org... If God were real... http://www.debate.org...
 Posts: 2,919 Add as FriendChallenge to a DebateSend a Message 1/25/2015 1:20:28 AMPosted: 3 years agoAt 1/24/2015 7:29:57 AM, Smithereens wrote:Kurt Godel for those who are unfamiliar, was a brilliant mathematician who devised a proof for god using higher order logic. Recently, computer scientists interested in developing tools for higher-order theorem provers found that Godel's proof was mathematically valid.Their basic conclusions were as follows, as is provided in the link to their research submission:> The modal system K is sufficient for proving Theorem 1, 2 and 4> Modal logic S5 is not needed for proving T3; the logic KB is sufficient.> For proving theorem T1, only the left to right direction of axiom A1 is needed. However, the backward direction of A1 is required for proving T2.(another conclusion I left out due to source-formatting issues on DDO)If you're not familiar with the argument, here it is: http://www.debate.org...If you're not familiar with the modal/predicate jargon, just google it.Article at http://arxiv.org...I'm interested in doing a debate with someone using predicate/higher order logic. PM if interested.I'll get right back to you on this in about 15 years or so.
 Posts: 564 Add as FriendChallenge to a DebateSend a Message 1/25/2015 2:54:25 AMPosted: 3 years agoI was not referring to the symbols' meaning, but to using them in a formal debate, as apparently this site is not equipped to handle them and I have only one formal debate under my belt. It would be unfair if you could use math symbols and I couldn't.I plan to question the soundness or validity of this particular argument, but may also use more general objections.The earth does not belong to man; man belongs to the earth.
 Posts: 8,346 Add as FriendChallenge to a DebateSend a Message 1/25/2015 3:33:28 AMPosted: 3 years agoAt 1/25/2015 2:54:25 AM, Amoranemix wrote:I was not referring to the symbols' meaning, but to using them in a formal debate, as apparently this site is not equipped to handle them and I have only one formal debate under my belt. It would be unfair if you could use math symbols and I couldn't.I plan to question the soundness or validity of this particular argument, but may also use more general objections.Debates allow any symbols. Forums don't, if that's what you mean."Your signature should not have the name of other players in the game, nor should it have the words VTL, Vote, or Unvote." ~Yraelz, 2017 Debate challenge 'Solipsism is false:' http://www.debate.org... If God were real... http://www.debate.org...
 Posts: 10,078 Add as FriendChallenge to a DebateSend a Message 1/25/2015 9:09:14 AMPosted: 3 years agoOR some people say there isn't a barn because they stand too close to the door and can't see the barn.Beware of the people who are in your circle but are not in your corner. And with the stroke of a pen people 18 to 21 who own a gun became criminals and public enemy #1 having committed no crime and having said nothing. Just like the Jews in Germany during WW2. Must be a weird feeling. When I hear people crying and whining about their first world problems I think about the universe with everything in it and people in wheelchairs and all of their problems go away.
 Posts: 1,505 Add as FriendChallenge to a DebateSend a Message 1/25/2015 8:12:31 PMPosted: 3 years agoAt 1/24/2015 10:23:04 PM, Smithereens wrote:At 1/24/2015 8:26:06 PM, Wocambs wrote:At 1/24/2015 7:29:57 AM, Smithereens wrote:Kurt Godel for those who are unfamiliar, was a brilliant mathematician who devised a proof for god using higher order logic. Recently, computer scientists interested in developing tools for higher-order theorem provers found that Godel's proof was mathematically valid.Their basic conclusions were as follows, as is provided in the link to their research submission:> The modal system K is sufficient for proving Theorem 1, 2 and 4> Modal logic S5 is not needed for proving T3; the logic KB is sufficient.> For proving theorem T1, only the left to right direction of axiom A1 is needed. However, the backward direction of A1 is required for proving T2.(another conclusion I left out due to source-formatting issues on DDO)If you're not familiar with the argument, here it is: http://www.debate.org...If you're not familiar with the modal/predicate jargon, just google it.Article at http://arxiv.org...I'm interested in doing a debate with someone using predicate/higher order logic. PM if interested.Like all such arguments it fails because it is 'metaphysical'. 'Necessary existence' is not a property; 'X necessarily exists' means that the proposition 'X exists' is necessarily true. It signifies a conclusion, not a definition. To define something as necessarily existent is thus pure sophistry.Absolutely ridiculous to claim that something fails merely because it is 'metaphysical.' The statement: 'Statements can be true' is a metaphysical statement. It is also the conclusion from a set of implied premises. The argument that statements can be true does not 'fail' simply because it happens to be metaphysical. In fact, a metaphysical statement is more likely to be true than a statement about physical reality.If necessary existence is not a property, what is it? A property merely describes attributes of a concept, using other concepts. Necessary existence is such a concept, attributed to other concepts. Hence a property.'Necessary' doesn't make any sense in that context. Whether it exists or not is a question to which an answer must be found. Asking 'Does something that must exist actually exist?' doesn't seem to be a very reasonable question.
 Posts: 8,346 Add as FriendChallenge to a DebateSend a Message 1/26/2015 4:18:36 AMPosted: 3 years agoAt 1/25/2015 8:12:31 PM, Wocambs wrote:At 1/24/2015 10:23:04 PM, Smithereens wrote:At 1/24/2015 8:26:06 PM, Wocambs wrote:At 1/24/2015 7:29:57 AM, Smithereens wrote:Kurt Godel for those who are unfamiliar, was a brilliant mathematician who devised a proof for god using higher order logic. Recently, computer scientists interested in developing tools for higher-order theorem provers found that Godel's proof was mathematically valid.Their basic conclusions were as follows, as is provided in the link to their research submission:> The modal system K is sufficient for proving Theorem 1, 2 and 4> Modal logic S5 is not needed for proving T3; the logic KB is sufficient.> For proving theorem T1, only the left to right direction of axiom A1 is needed. However, the backward direction of A1 is required for proving T2.(another conclusion I left out due to source-formatting issues on DDO)If you're not familiar with the argument, here it is: http://www.debate.org...If you're not familiar with the modal/predicate jargon, just google it.Article at http://arxiv.org...I'm interested in doing a debate with someone using predicate/higher order logic. PM if interested.Like all such arguments it fails because it is 'metaphysical'. 'Necessary existence' is not a property; 'X necessarily exists' means that the proposition 'X exists' is necessarily true. It signifies a conclusion, not a definition. To define something as necessarily existent is thus pure sophistry.Absolutely ridiculous to claim that something fails merely because it is 'metaphysical.' The statement: 'Statements can be true' is a metaphysical statement. It is also the conclusion from a set of implied premises. The argument that statements can be true does not 'fail' simply because it happens to be metaphysical. In fact, a metaphysical statement is more likely to be true than a statement about physical reality.If necessary existence is not a property, what is it? A property merely describes attributes of a concept, using other concepts. Necessary existence is such a concept, attributed to other concepts. Hence a property.'Necessary' doesn't make any sense in that context. Whether it exists or not is a question to which an answer must be found. Asking 'Does something that must exist actually exist?' doesn't seem to be a very reasonable question.In fact it is, something which must exist, such as the laws of logic, exists. If God can be shown to be a necessary existent, it follows that he exists."Your signature should not have the name of other players in the game, nor should it have the words VTL, Vote, or Unvote." ~Yraelz, 2017 Debate challenge 'Solipsism is false:' http://www.debate.org... If God were real... http://www.debate.org...
 Posts: 564 Add as FriendChallenge to a DebateSend a Message 1/26/2015 11:30:42 AMPosted: 3 years agoSmithereens 8Debates allow any symbols. Forums don't, if that's what you mean.In this debate you inserted pictures for the logical deductions :http://www.debate.org...Later, however, you placed them in the text. Is there a way to test that ?The earth does not belong to man; man belongs to the earth.
 Posts: 1,505 Add as FriendChallenge to a DebateSend a Message 1/26/2015 7:57:18 PMPosted: 3 years agoAt 1/26/2015 4:18:36 AM, Smithereens wrote:At 1/25/2015 8:12:31 PM, Wocambs wrote:At 1/24/2015 10:23:04 PM, Smithereens wrote:At 1/24/2015 8:26:06 PM, Wocambs wrote:At 1/24/2015 7:29:57 AM, Smithereens wrote:Kurt Godel for those who are unfamiliar, was a brilliant mathematician who devised a proof for god using higher order logic. Recently, computer scientists interested in developing tools for higher-order theorem provers found that Godel's proof was mathematically valid.Their basic conclusions were as follows, as is provided in the link to their research submission:> The modal system K is sufficient for proving Theorem 1, 2 and 4> Modal logic S5 is not needed for proving T3; the logic KB is sufficient.> For proving theorem T1, only the left to right direction of axiom A1 is needed. However, the backward direction of A1 is required for proving T2.(another conclusion I left out due to source-formatting issues on DDO)If you're not familiar with the argument, here it is: http://www.debate.org...If you're not familiar with the modal/predicate jargon, just google it.Article at http://arxiv.org...I'm interested in doing a debate with someone using predicate/higher order logic. PM if interested.Like all such arguments it fails because it is 'metaphysical'. 'Necessary existence' is not a property; 'X necessarily exists' means that the proposition 'X exists' is necessarily true. It signifies a conclusion, not a definition. To define something as necessarily existent is thus pure sophistry.Absolutely ridiculous to claim that something fails merely because it is 'metaphysical.' The statement: 'Statements can be true' is a metaphysical statement. It is also the conclusion from a set of implied premises. The argument that statements can be true does not 'fail' simply because it happens to be metaphysical. In fact, a metaphysical statement is more likely to be true than a statement about physical reality.If necessary existence is not a property, what is it? A property merely describes attributes of a concept, using other concepts. Necessary existence is such a concept, attributed to other concepts. Hence a property.'Necessary' doesn't make any sense in that context. Whether it exists or not is a question to which an answer must be found. Asking 'Does something that must exist actually exist?' doesn't seem to be a very reasonable question.In fact it is, something which must exist, such as the laws of logic, exists. If God can be shown to be a necessary existent, it follows that he exists.Let's think about possible existence. If something possibly exists, that means that it may or may not exist, and you are not in a position to claim that it must exist or that it cannot exist. An apple does not possess the quality of 'possibly existent' - the 'possibly' refers to what kind of conclusion we are making. Clearly if God can be shown to necessarily exist, then we already have the conclusion that he does, but there must be some argument that necessarily entails that he does exist, and not an argument which performs the easy task of proving that something whose non-existence is defined as literally impossible actually exists. To define God as possessing the quality of 'necessary existence' entails that, of course, he must exist, but defining something as existing and then proceeding to make an argument as to how his existence follows from his definition of something-that-exists is valid only in the sense that its conclusion 'follows' from its premises. It still isn't sound.
 Posts: 561 Add as FriendChallenge to a DebateSend a Message 1/27/2015 7:06:54 AMPosted: 3 years agoAt 1/24/2015 7:29:57 AM, Smithereens wrote:Kurt Godel for those who are unfamiliar, was a brilliant mathematician who devised a proof for god using higher order logic. Recently, computer scientists interested in developing tools for higher-order theorem provers found that Godel's proof was mathematically valid.Their basic conclusions were as follows, as is provided in the link to their research submission:> The modal system K is sufficient for proving Theorem 1, 2 and 4> Modal logic S5 is not needed for proving T3; the logic KB is sufficient.> For proving theorem T1, only the left to right direction of axiom A1 is needed. However, the backward direction of A1 is required for proving T2.(another conclusion I left out due to source-formatting issues on DDO)If you're not familiar with the argument, here it is: http://www.debate.org...If you're not familiar with the modal/predicate jargon, just google it.Article at http://arxiv.org...I'm interested in doing a debate with someone using predicate/higher order logic. PM if interested.I find ontological arguments both fascinating and at the same time maddening. Fascinating because I love logical puzzles but maddening because in the end they don't actually tell us anything because they have to rest on axioms and definitions which are basically un-provable assumptions.For example the paper you reference claims rightly that Godel's argument is logically valid in that it has internal consistency. But it does not mean it is a sound argument because it is based on 5 separate axioms and 3 definitions which themselves cannot be proven.Even if we accept this argument it does not really tell us anything useful. What is a positive property? What is a being that possess's all positive properties like? Is Godel's god the same as the god described in ones preferred holy book?Let's hope "the truth is out there" cos there is bugger all round here.
 Posts: 139 Add as FriendChallenge to a DebateSend a Message 1/28/2015 10:20:57 AMPosted: 3 years agoAt 1/24/2015 7:29:57 AM, Smithereens wrote:Kurt Godel for those who are unfamiliar, was a brilliant mathematician who devised a proof for god using higher order logic. Recently, computer scientists interested in developing tools for higher-order theorem provers found that Godel's proof was mathematically valid.Their basic conclusions were as follows, as is provided in the link to their research submission:> The modal system K is sufficient for proving Theorem 1, 2 and 4> Modal logic S5 is not needed for proving T3; the logic KB is sufficient.> For proving theorem T1, only the left to right direction of axiom A1 is needed. However, the backward direction of A1 is required for proving T2.(another conclusion I left out due to source-formatting issues on DDO)If you're not familiar with the argument, here it is: http://www.debate.org...If you're not familiar with the modal/predicate jargon, just google it.Article at http://arxiv.org...I'm interested in doing a debate with someone using predicate/higher order logic. PM if interested.Silly Godal, everyone knows that math was invented by Satan.seriously though, those math proofs are incoherent.
 Posts: 564 Add as FriendChallenge to a DebateSend a Message 1/30/2015 2:00:16 PMPosted: 3 years agoI understand there will be no testing. So be it.When do we start ?The earth does not belong to man; man belongs to the earth.
 Posts: 8,346 Add as FriendChallenge to a DebateSend a Message 1/30/2015 9:51:44 PMPosted: 3 years agoAt 1/26/2015 7:57:18 PM, Wocambs wrote:Let's think about possible existence. If something possibly exists, that means that it may or may not exist, and you are not in a position to claim that it must exist or that it cannot exist. An apple does not possess the quality of 'possibly existent' - the 'possibly' refers to what kind of conclusion we are making.This is largely misguided due to an incorrect use of possible world semantics. Possible existence entails that there is nothing logically contradictory about the concept of its existence, hence it can possibly exist. An apple can possibly exist, therefore the modal operator assigned to describe the existence of an apple is 'possible.' 1+1=2 is an axiom that is possibly necessary, as the negation of this principle is not logically coherent. S4 and S5 equates possibly necessary and necessarily necessary to necessary. Hence, an apple possibly exists, and 1+1=2 is necessarily true.Clearly if God can be shown to necessarily exist, then we already have the conclusion that he does, but there must be some argument that necessarily entails that he does exist, and not an argument which performs the easy task of proving that something whose non-existence is defined as literally impossible actually exists.The argument that necessary existence infers actual existence coupled with Godel's argument that God is a necessary existent is perfectly acceptable. It's allowed, and it's valid.To define God as possessing the quality of 'necessary existence' entails that, of course, he must exist, but defining something as existing and then proceeding to make an argument as to how his existence follows from his definition of something-that-exists is valid only in the sense that its conclusion 'follows' from its premises. It still isn't sound.You generalize one form of the ontological argument universally, and unjustly. However, in defense of ontological arguments which do simple follow the 3 premise version, it is still a logical supposition. If something can be defined to exist, it is because it has been defined for a reason. In modal ontological arguments, this is because of a reductio ad absurdum which concludes that it is possible to conceptualize a being greater than the greatest possible being. Since contradictions can't exist, the negation is by principle, true. In this case, it's the necessary existence of God."Your signature should not have the name of other players in the game, nor should it have the words VTL, Vote, or Unvote." ~Yraelz, 2017 Debate challenge 'Solipsism is false:' http://www.debate.org... If God were real... http://www.debate.org...
 Posts: 8,346 Add as FriendChallenge to a DebateSend a Message 1/30/2015 9:52:52 PMPosted: 3 years agoAt 1/30/2015 2:00:16 PM, Amoranemix wrote:I understand there will be no testing. So be it.When do we start ?I've taken note of your interest, and will likely spring a challenge when I have the time, if there isn't anyone else who wants to. Is there any part of the year that is inconvenient for you?"Your signature should not have the name of other players in the game, nor should it have the words VTL, Vote, or Unvote." ~Yraelz, 2017 Debate challenge 'Solipsism is false:' http://www.debate.org... If God were real... http://www.debate.org...
 Posts: 8,346 Add as FriendChallenge to a DebateSend a Message 1/31/2015 5:01:31 AMPosted: 3 years agoAt 1/27/2015 7:06:54 AM, chui wrote:At 1/24/2015 7:29:57 AM, Smithereens wrote:Kurt Godel for those who are unfamiliar, was a brilliant mathematician who devised a proof for god using higher order logic. Recently, computer scientists interested in developing tools for higher-order theorem provers found that Godel's proof was mathematically valid.Their basic conclusions were as follows, as is provided in the link to their research submission:> The modal system K is sufficient for proving Theorem 1, 2 and 4> Modal logic S5 is not needed for proving T3; the logic KB is sufficient.> For proving theorem T1, only the left to right direction of axiom A1 is needed. However, the backward direction of A1 is required for proving T2.(another conclusion I left out due to source-formatting issues on DDO)If you're not familiar with the argument, here it is: http://www.debate.org...If you're not familiar with the modal/predicate jargon, just google it.Article at http://arxiv.org...I'm interested in doing a debate with someone using predicate/higher order logic. PM if interested.I find ontological arguments both fascinating and at the same time maddening. Fascinating because I love logical puzzles but maddening because in the end they don't actually tell us anything because they have to rest on axioms and definitions which are basically un-provable assumptions.For example the paper you reference claims rightly that Godel's argument is logically valid in that it has internal consistency. But it does not mean it is a sound argument because it is based on 5 separate axioms and 3 definitions which themselves cannot be proven.Even if we accept this argument it does not really tell us anything useful. What is a positive property? What is a being that possess's all positive properties like? Is Godel's god the same as the god described in ones preferred holy book?Don't worry about 'unprovable assumptions.' Your claim that axioms and definitions cannot be proven assumes that nothing is valid until proven true, which itself cannot be proven true."Your signature should not have the name of other players in the game, nor should it have the words VTL, Vote, or Unvote." ~Yraelz, 2017 Debate challenge 'Solipsism is false:' http://www.debate.org... If God were real... http://www.debate.org...
 Posts: 1,505 Add as FriendChallenge to a DebateSend a Message 1/31/2015 11:44:07 AMPosted: 3 years agoAt 1/30/2015 9:51:44 PM, Smithereens wrote:This is largely misguided due to an incorrect use of possible world semantics. Possible existence entails that there is nothing logically contradictory about the concept of its existence, hence it can possibly exist. An apple can possibly exist, therefore the modal operator assigned to describe the existence of an apple is 'possible.' 1+1=2 is an axiom that is possibly necessary, as the negation of this principle is not logically coherent. S4 and S5 equates possibly necessary and necessarily necessary to necessary. Hence, an apple possibly exists, and 1+1=2 is necessarily true.But an apple doesn't possibly exist. There is no alternative. How can something possibly exist, when there is no possibility of it not existing? A=A, reality is reality; reality at no point was affected by some cause to be one way or another. This is the mistake you make . The 'possibility' refers entirely to our inability to state that the apple definitely exists, and 'necessary' refers entirely to our ability to state that 1+1 is definitely equal to 2.The argument that necessary existence infers actual existence coupled with Godel's argument that God is a necessary existent is perfectly acceptable. It's allowed, and it's valid.The apple balanced on your head, since it is part of reality, and reality necessarily exists, and reality is necessarily the way reality is, must necessarily exist. So where's that apple balanced on your head, Smithers? Wherefore cometh my error?God, being either an element of or identical to some conception of reality, is something to be investigated, not defined as true. He cannot be greater than reality, or cause it. The error used to define God as something that exists can be used to 'prove' the existence of literally anything. I have a conception of reality that does not contain God. If I let myself commit the same error, I could easily argue that my conception of a godless reality, being possible, must exist, because reality 'necessarily exists'.