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Anyone for Kurt Godel's ontological proof?

Smithereens
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1/24/2015 7:29:57 AM
Posted: 1 year ago
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.
Music composition contest: http://www.debate.org...
Amoranemix
Posts: 521
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1/24/2015 11:50:49 AM
Posted: 1 year ago
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.
The earth does not belong to man; man belongs to the earth.
Wocambs
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1/24/2015 8:26:06 PM
Posted: 1 year ago
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.
Smithereens
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1/24/2015 10:12:28 PM
Posted: 1 year ago
At 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 normally

A 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.
Music composition contest: http://www.debate.org...
Smithereens
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1/24/2015 10:23:04 PM
Posted: 1 year ago
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.
Music composition contest: http://www.debate.org...
johnlubba
Posts: 2,892
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1/25/2015 1:20:28 AM
Posted: 1 year ago
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'll get right back to you on this in about 15 years or so.
Amoranemix
Posts: 521
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1/25/2015 2:54:25 AM
Posted: 1 year ago
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.
The earth does not belong to man; man belongs to the earth.
Smithereens
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1/25/2015 3:33:28 AM
Posted: 1 year ago
At 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.
Music composition contest: http://www.debate.org...
sadolite
Posts: 8,838
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1/25/2015 9:09:14 AM
Posted: 1 year ago
OR some people say there isn't a barn because they stand too close to the door and can't see the barn.
It's not your views that divide us, it's what you think my views should be that divides us.

If you think I will give up my rights and forsake social etiquette to make you "FEEL" better you are sadly mistaken

If liberal democrats would just stop shooting people gun violence would drop by 90%
Wocambs
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1/25/2015 8:12:31 PM
Posted: 1 year ago
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.
Smithereens
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1/26/2015 4:18:36 AM
Posted: 1 year ago
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.
Music composition contest: http://www.debate.org...
Amoranemix
Posts: 521
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1/26/2015 11:30:42 AM
Posted: 1 year ago
Smithereens 8
Debates 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.
Wocambs
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1/26/2015 7:57:18 PM
Posted: 1 year ago
At 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.
chui
Posts: 507
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1/27/2015 7:06:54 AM
Posted: 1 year ago
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?
SirCrona
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1/28/2015 10:20:57 AM
Posted: 1 year ago
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.

Silly Godal, everyone knows that math was invented by Satan.
seriously though, those math proofs are incoherent.
Smithereens
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1/30/2015 9:51:44 PM
Posted: 1 year ago
At 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.
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Smithereens
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1/30/2015 9:52:52 PM
Posted: 1 year ago
At 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?
Music composition contest: http://www.debate.org...
Smithereens
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1/31/2015 5:01:31 AM
Posted: 1 year ago
At 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.
Music composition contest: http://www.debate.org...
Wocambs
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1/31/2015 11:44:07 AM
Posted: 1 year ago
At 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'.
Smithereens
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1/31/2015 10:15:44 PM
Posted: 1 year ago
At 1/31/2015 11:44:07 AM, Wocambs wrote:
At 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.

It is in fact perfectly possible that an apple does not exist. Just because it does exist in reality doesn't mean that it has to. Modal logic doesn't make assumptions like that. We can't prove an apple exists, if an apple must exist, it has necessary existence. If it isn't logically necessary for an apple to exist, then it possibly exists. An apple in reality is not logically required to exist, even though it does. Therefore, its property is possible. All things can be categorised into necessary and possible and their negations (though there are other categories). You don't seem to understand how the possible and necessary operators are used in modal logic, forget about the use of them in common English language, they actually mean different things in modal logic. Again, something possibly exists if it's non existence is logically incoherent. This means that it must be possible for it to exist in reality, even if it doesn't exist in reality. Unicorns are an example. They, like apples, can exist in reality, and there is nothing logically unfeasible about positing their existence. Hence, it is logically incoherent to categorically state that unicorns don't exist, as nothing logically prohibits it. A 4 sided triangle however cannot exist, as it's existence is logically incoherent, whereas its non existence is perfectly ok. Therefore, a unicorn and an apple possibly exist, a 4 sided triangle necessarily does not exist. A 3 sided triangle has contingent existence, which is another branch altogether, and basically means 'if X, then necessarily Y.' So if a triangle exists, it will necessarily have 3 sides.


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?
Clearly you don't have a clue about the logic you are attempting to argue against. But even in this paragraph, you still assume too much. Please go ahead and be the first human ever to be able to describe the nature of reality in terms of necessary existence. Typical Gnostic...

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'.
Your argument is virtually identical to a philosophy that became outdated last century. Logical positivism is basically this paragraph in a nutshell, and you must be the only person left who still believes it. Defining God as something that exists is not the same as defining the christian God into existence. The ontological argument holds that the greatest possible thing must exist, since because it can exist, its non existence would mean that it cannot exist, which contradicts the fact that it can exist. If the greatest possible anything is argued to exist, then the argument doesn't work as there is still something greater than it, that being something not limited to the concept of what it is. Guanillos island for example, is the greatest possible island, and he argued that it must exist under the logic of the ontological argument. What he neglected to consider was that there is still something greater than the greatest possible island, that being something which doesn't have to be an island (limitless form), which is not restricted to exist in a single position in space/time (omnipresense), and which has no epistemic boundary of scope (omniscience). Such an island we would call a 'being' since it is merely something that is, and that being would fit a pantheistic definition of God. Your thoughts were first discussed and dismissed hundreds of years ago. A more modern approach would be to claim subjectivity in the definition of greatest possible being, however it seems you have some catching up to do.
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Wocambs
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2/1/2015 12:09:34 AM
Posted: 1 year ago
At 1/31/2015 10:15:44 PM, Smithereens wrote:
It is in fact perfectly possible that an apple does not exist. Just because it does exist in reality doesn't mean that it has to
If it isn't logically necessary for an apple to exist, then it possibly exists
Please go ahead and be the first human ever to be able to describe the nature of reality in terms of necessary existence

It does mean that it 'has to'. There are no real alternatives to reality, and so reality, and every part of it, 'must exist'. If it possibly exists, then there are other possibilities - but there are none. It is impossible for something different from reality to exist, it is, as you say, logically incoherent. Therefore, there are no other logical possibilities, and the apple 'necessarily' exists. That, however, is bullsh*t, because we are never in a position to say that the apple exists with certainty. That's where 'possible' comes in. It is possible that reality is such that this apple is a necessary feature of it, or perhaps that apple is necessarily not a feature of it.

The ontological argument holds that the greatest possible thing must exist, since because it can exist, its non existence would mean that it cannot exist, which contradicts the fact that it can exist

'Greatest' isn't a meaningful word here. It means whatever you think it does. Satisfied?

My actual response is that if I imagine the greatest thing, and I imagine that it actually exists, then none of its properties are changed when I stop imagining it to actually exist and start believing that it does. The argument is just a trick. When I think of God, I do imagine him as something that actually exists in this world, and I could not think of him as any greater if I actually started believing in him. I'm being too generous even in this.

The wording of your argument makes no sense to me. He can exist, which means that he can't not exist, which means that he must exist? As I said, if something can exist, then its possibly what must exist.

Clearly you don't have a clue about the logic you are attempting to argue against
Your argument is virtually identical to a philosophy that became outdated last century. Logical positivism is basically this paragraph in a nutshell, and you must be the only person left who still believes it
Your thoughts were first discussed and dismissed hundreds of years ago. A more modern approach would be to claim subjectivity in the definition of greatest possible being, however it seems you have some catching up to do.

Well, if you want to be a b*tch about it.

Your apparent dyslexia annoys me. Belittling me and proceeding to spell 'Gaunilo' incorrectly just proves you to be the worst kind of idiot - an arrogant one. The fact that you worship modal logic and criticise my views for being 'old' and 'dismissed' makes you appear like a dogmatic snide who jumps on whatever philosophical trend is around, apart from, apparently, atheism, because you can't accept what has been an obvious fact to everyone born after 1500, that God doesn't exist, and you can't imagine him into existence.

You also make stupid mistakes:

Again, something possibly exists if it's non existence is logically incoherent

That would make it necessarily exist.

You've kept me up late, and you've put me in a bad mood, so I can now lie in bed thinking about the bullsh*t arguments of someone who wants their daddy. Does this make you happy? Instead of talking about the greatest possible thing we should talk about the greatest possible you. That concept does not contain the property 'annoying to Wocambs when he wants to sleep'.
Smithereens
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2/1/2015 12:47:19 AM
Posted: 1 year ago
At 2/1/2015 12:09:34 AM, Wocambs wrote:
At 1/31/2015 10:15:44 PM, Smithereens wrote:
It is in fact perfectly possible that an apple does not exist. Just because it does exist in reality doesn't mean that it has to
If it isn't logically necessary for an apple to exist, then it possibly exists
Please go ahead and be the first human ever to be able to describe the nature of reality in terms of necessary existence

It does mean that it 'has to'. There are no real alternatives to reality, and so reality, and every part of it, 'must exist'. If it possibly exists, then there are other possibilities - but there are none. It is impossible for something different from reality to exist, it is, as you say, logically incoherent. Therefore, there are no other logical possibilities, and the apple 'necessarily' exists. That, however, is bullsh*t, because we are never in a position to say that the apple exists with certainty. That's where 'possible' comes in. It is possible that reality is such that this apple is a necessary feature of it, or perhaps that apple is necessarily not a feature of it.
Again, under the logic, there isn't a requirement for anything in reality to exist. It matters not if something exists, if it doesn't have to exist, it exists possibly. You are using possible and necessary as if this were a discussion about epistemology instead. You seem to think that because no other reality is possible, an apple necessarily exists. This is not possible world semantics. This is a simplified literal take on the English definitions of the words. Alternatives to reality is not a consideration, its irrelevant to the discussion whether or not an alternative reality can exist.

The ontological argument holds that the greatest possible thing must exist, since because it can exist, its non existence would mean that it cannot exist, which contradicts the fact that it can exist

'Greatest' isn't a meaningful word here. It means whatever you think it does. Satisfied?
I pointed out earlier that this response was the more modern one than the dead rebuttal you were attempting to argue. Godel's argument doesn't use Maximally great being however, though your argument that the word can mean whatever you think it does can also apply to every word you have thus far spoken. For coherent language to exist, we assume objectivity, and maximal greatness is a term just like any other. For the purposes of debate, it would refer to something that is not limited by anything, hence has maximal potential. The argument builds on that by saying that if such a thing can exist, it will exist.

My actual response is that if I imagine the greatest thing, and I imagine that it actually exists, then none of its properties are changed when I stop imagining it to actually exist and start believing that it does. The argument is just a trick. When I think of God, I do imagine him as something that actually exists in this world, and I could not think of him as any greater if I actually started believing in him. I'm being too generous even in this.
Kant's argument that existence is not a predicate I don't buy at all. Since the argument is positing something with maximal potential, non-existence would be the greatest possible restriction to that cause. However, in this paragraph you seem to contradict what you were arguing for earlier about possible world semantics. Here you are perfectly ok with it, saying that you can imagine the greatest thing, that's a blatant use of the logic.

The wording of your argument makes no sense to me. He can exist, which means that he can't not exist, which means that he must exist? As I said, if something can exist, then its possibly what must exist.
If something can exist, then it must be impossible that they necessarily can't exist. If they couldn't exist, then it wouldn't be true that they can exist. It's fairly easy to follow.


Clearly you don't have a clue about the logic you are attempting to argue against
Your argument is virtually identical to a philosophy that became outdated last century. Logical positivism is basically this paragraph in a nutshell, and you must be the only person left who still believes it
Your thoughts were first discussed and dismissed hundreds of years ago. A more modern approach would be to claim subjectivity in the definition of greatest possible being, however it seems you have some catching up to do.

Well, if you want to be a b*tch about it.

Your apparent dyslexia annoys me. Belittling me and proceeding to spell 'Gaunilo' incorrectly just proves you to be the worst kind of idiot - an arrogant one. The fact that you worship modal logic and criticise my views for being 'old' and 'dismissed' makes you appear like a dogmatic snide who jumps on whatever philosophical trend is around, apart from, apparently, atheism, because you can't accept what has been an obvious fact to everyone born after 1500, that God doesn't exist, and you can't imagine him into existence.
My, so easy to stir up. I hope that's not affecting your ability to convey your ideas fluently. If the fact that I switched two letters in a non-English name upsets you so much, at least try to hold in a discussion without breaking the ToS. It's perfectly normal the practice of upsetting an opponent for the advantage, just don't make it so easy for me. I'm not a theist nor an atheist, I simply here to argue.

You also make stupid mistakes:
none made so far:

Again, something possibly exists if it's non existence is logically incoherent

That would make it necessarily exist.
No, necessary existence adds an additional qualifier, that there is no possible world where it's non-existence is coherent. Possible means that it must exist in at least one possible world, hence it's total non existence is logically incoherent. Nothing more, nothing less.

You've kept me up late, and you've put me in a bad mood, so I can now lie in bed thinking about the bullsh*t arguments of someone who wants their daddy. Does this make you happy? Instead of talking about the greatest possible thing we should talk about the greatest possible you. That concept does not contain the property 'annoying to Wocambs when he wants to sleep'.
I don't have a dad, I'm the immaculate conception. And of course this makes me happy, I rarely meet people who rise to the bait so easily. Way too easy. Just a typical response to would be bigots who enter the discussion with an agenda to push. I'm glad you mistook it for arrogance, that was funny.

You were trolled by the way, I think I need to actually point it out.
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chui
Posts: 507
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2/1/2015 2:27:51 AM
Posted: 1 year ago
At 1/31/2015 5:01:31 AM, Smithereens wrote:
At 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.

So I can make any assumption I like without worrying?

How do you respond to this example:

I assume everything I say is objective truth.
I say you are wrong.
By my unprovable assumption this is an irrefutable valid argument.

I think my argument above is idiotic. Surely assumptions must be acknowledged and challenged or we can create an infinite number of ever more ridiculous arguments.
Smithereens
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2/1/2015 2:36:49 AM
Posted: 1 year ago
At 2/1/2015 2:27:51 AM, chui wrote:
At 1/31/2015 5:01:31 AM, Smithereens wrote:
At 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.

So I can make any assumption I like without worrying?
No, how did you draw that conclusion from what I said?

How do you respond to this example:

I assume everything I say is objective truth.
I say you are wrong.
By my unprovable assumption this is an irrefutable valid argument.

I think my argument above is idiotic. Surely assumptions must be acknowledged and challenged or we can create an infinite number of ever more ridiculous arguments.
Assumptions =/= axioms. An axiom is a statement that must be true regardless of anything. Assumptions are not. Refer back to our conversation earlier. Statements which must be true are statements such as 1+1=2, because logic requires some statements to be true. The ontological argument uses axioms to prove theorems.
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Graincruncher
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2/2/2015 7:40:30 AM
Posted: 1 year ago
At 1/30/2015 9:51:44 PM, Smithereens wrote:
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.

Incorrect due to incompleteness, although not the theorem. It is an axiom that is possibly necessary within the framework of mathematics. A necessary being is only necessary in a world that axiomatically necessitates one. It is not necessarily the case that we are in such a world.

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.

No it isn't, it's absolute twaddle of the highest order. That there are necessary elements to an axiomatic system? Sure. That we necessarily exist in a world which itself necessarily consists of axioms that would require there to be a god? Not even close. We know far too little about the universe to even have a vague shot at saying so and it is the height of self-delusion to tell yourself otherwise.

Ontological arguments are - universally - semantic nonsenses that try to dictate the nature of reality based on linguistic conventions. Something can only be deemed to be necessary to a system in the context of that system; the meaning of 'necessary' is internal to our linguistic games, which are themselves internal to our universe. So the very concept of necessity is itself contingent on that framework and, unless you suppose grammar is itself infallibly descriptive of the nature of existence (which would be foolish, to say the least), utter bilge when trying to prove something exists.

So you can axiomatically propose a necessary being all you like, but until you show that this world is in accordance with those axioms, all you're doing is saying "well if this is true, so is this". Fine. So prove the first this.
Graincruncher
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2/2/2015 7:43:07 AM
Posted: 1 year ago
At 2/1/2015 2:36:49 AM, Smithereens wrote:
Assumptions =/= axioms. An axiom is a statement that must be true regardless of anything.

Again, incorrect. An axiom is:
noun
noun: axiom; plural noun: axioms

a statement or proposition which is regarded as being established, accepted, or self-evidently true.

It is something you take as a given for a particular argument. It is not something that "must be true regardless of anything" and if you honestly think it is, you need to revise your estimation of how philosophically savvy you are. Downwards. Quite a bit.
Amoranemix
Posts: 521
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2/2/2015 1:42:23 PM
Posted: 1 year ago
Smithereens 18
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?
What is the clause "if there isn't anyone else who wants to" for ?
No, at this time there is no foreseeable part of the year that is inconvenient.

- Smithereens 21
It is in fact perfectly possible that an apple does not exist. Just because it does exist in reality doesn't mean that it has to. Modal logic doesn't make assumptions like that. We can't prove an apple exists, if an apple must exist, it has necessary existence. If it isn't logically necessary for an apple to exist, then it possibly exists.
[ . . . ]
Clearly you don't have a clue about the logic you are attempting to argue against. But even in this paragraph, you still assume too much. Please go ahead and be the first human ever to be able to describe the nature of reality in terms of necessary existence. Typical Gnostic...
- Wocambs 22
It does mean that it 'has to'. There are no real alternatives to reality, and so reality, and every part of it, 'must exist'. If it possibly exists, then there are other possibilities - but there are none. It is impossible for something different from reality to exist, it is, as you say, logically incoherent.
There is nothing logically incoherent about a different reality. In addition, the many worlds hypothesis of quantum mechanics states that an infinite number of realities exist and the multiverse hypothesis postulates many universes.

Wocambs 22 to Smithereens
You've kept me up late, and you've put me in a bad mood, so I can now lie in bed thinking about the bullsh*t arguments of someone who wants their daddy. Does this make you happy? Instead of talking about the greatest possible thing we should talk about the greatest possible you. That concept does not contain the property 'annoying to Wocambs when he wants to sleep'.
I suggest next time you wait for your bad mood to go away before responding, for it makes you look like a jerk.
The earth does not belong to man; man belongs to the earth.
dylancatlow
Posts: 12,245
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2/2/2015 1:58:44 PM
Posted: 1 year ago
At 2/1/2015 12:09:34 AM, Wocambs wrote:
It does mean that it 'has to'. There are no real alternatives to reality, and so reality, and every part of it, 'must exist'.

This is only true insofar as reality has a real explanation according to which alternative definitions of reality are unreal within the context of reality. You cannot point to an uncaused reality as the reason it - and not other realities - exist, since you have not explained why it exists in the first place, so obviously it's insufficient as an explanation. Since the argument "reality exists this way because reality exists this way" is circular, it can only be considered true if reality's structure is circular enough to account for its own existence. I.e., if it's self-explaining.

If it possibly exists, then there are other possibilities - but there are none. It is impossible for something different from reality to exist, it is, as you say, logically incoherent.

There are no other actualized possibilities, but that doesn't mean we cannot come up with definitions of reality which can be ruled out on an a priori basis.