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Most people posing this question want not only an answer, but an explanation of why that is the answer. That explanation must always include a precise definition of "all-powerful." Many who are pushing for such an answer want not only an explanation, but something worthy of being called a "proof."

Proof is actually a mathematical term, with a very precise definition. There are many classes of formal systems which can admit proofs, but First Order Logic (FOL) and Second Order Logic (SOL) are by far the most common. The individual posing the question will need to declare what sort of proof they accept. Since FOL and SOL are the most common systems people use, it is most likely they will name one of the two.

FOL is the most commonly referenced formal system with regard for proofs (for reasons we will see in a moment). However, defining "all powerful" within the confines of the language FOL supports is tricky. FOL requires everything it will talk about (officially called the "domain of discourse") to be defined as a set. "All powerful" could be defined as "For-all things that can be done, Supreme-Being can do it," however defining a set of "things that can be done" which includes creation and lifting of this particular rock is not possible. You need to go one step further, using categories rather than sets before you can use such a phrase, but FOL simply doesn't do that. (if you want to go further into why this is true, look into the work of Bertrand Russel into paradoxes and set theory)

SOL also works on a domain of discourse defined by sets. However, its semantics allow some clever structures which define categories using sets, construct the category which includes creation and lifting of the rock, and then you can go about your proof. At first glance, this looks like a winner!

As part of building his incompleteness theorems Gödel demonstrated a major limitation of SOL. It turns out that it is impossible to make any proof about a SOL system unless it happens to be reducible to FOL (i.e. you claimed you were using SOL, but you never actually used any of its fancy abilities). We've argued that the set of things that can be done cannot be described in FOL, so Gödel proves that any result regarding creation and lifting of our rock cannot possibly be proven.

The final answer is to allow admission of other formal systems besides FOL and SOL which can handle this particular case. However, in practice, the reason we use FOL and SOL is because it is remarkably hard to come up with a formal system which others can agree with. You can come up with any formal system you want, but unless both parties agree on what a "proof" should behave like, there really can't be any headway.

So, in all, the anti-ontological argument itself is phrased using a language which is tremendously unfriendly to proofs. Anyone seeking a proof will find themselves bound by the language of the problem.

Most people posing this question want not only an answer, but an explanation of why that is the answer. That explanation must always include a precise definition of "all-powerful." Many who are pushing for such an answer want not only an explanation, but something worthy of being called a "proof."

Proof is actually a mathematical term, with a very precise definition. There are many classes of formal systems which can admit proofs, but First Order Logic (FOL) and Second Order Logic (SOL) are by far the most common. The individual posing the question will need to declare what sort of proof they accept. Since FOL and SOL are the most common systems people use, it is most likely they will name one of the two.

FOL is the most commonly referenced formal system with regard for proofs (for reasons we will see in a moment). However, defining "all powerful" within the confines of the language FOL supports is tricky. FOL requires everything it will talk about (officially called the "domain of discourse") to be defined as a set. "All powerful" could be defined as "For-all things that can be done, Supreme-Being can do it," however defining a set of "things that can be done" which includes creation and lifting of this particular rock is not possible. You need to go one step further, using categories rather than sets before you can use such a phrase, but FOL simply doesn't do that.

SOL also works on a domain of discourse defined by sets. However, its semantics allow some clever structures which define categories using sets, construct the category which includes creation and lifting of the rock, and then you can go about your proof. At first glance, this looks like a winner!

As part of building his incompleteness theorems Gödel demonstrated a major limitation of SOL. It turns out that it is impossible to make any proof about a SOL system unless it happens to be reducible to FOL (i.e. you claimed you were using SOL, but you never actually used any of its fancy abilities). We've argued that the set of things that can be done cannot be described in FOL, so Gödel proves that any result regarding creation and lifting of our rock cannot possibly be proven.

The final answer is to allow admission of other formal systems besides FOL and SOL which can handle this particular case. However, in practice, the reason we use FOL and SOL is because it is remarkably hard to come up with a formal system which others can agree with. You can come up with any formal system you want, but unless both parties agree on what a "proof" should behave like, there really can't be any headway.

So, in all, the anti-ontological argument itself is phrased using a language which is tremendously unfriendly to proofs. Anyone seeking a proof will find themselves bound by the language of the problem.

Most people posing this question want not only an answer, but an explanation of why that is the answer. That explanation must always include a precise definition of "all-powerful." Many who are pushing for such an answer want not only an explanation, but something worthy of being called a "proof."

Proof is actually a mathematical term, with a very precise definition. There are many classes of formal systems which can admit proofs, but First Order Logic (FOL) and Second Order Logic (SOL) are by far the most common. The individual posing the question will need to declare what sort of proof they accept. Since FOL and SOL are the most common systems people use, it is most likely they will name one of the two.

FOL is the most commonly referenced formal system with regard for proofs (for reasons we will see in a moment). However, defining "all powerful" within the confines of the language FOL supports is tricky. FOL requires everything it will talk about (officially called the "domain of discourse") to be defined as a set. "All powerful" could be defined as "For-all things that can be done, Supreme-Being can do it," however defining a set of "things that can be done" which includes creation and lifting of this particular rock is not possible. You need to go one step further, using categories rather than sets before you can use such a phrase, but FOL simply doesn't do that. (if you want to go further into why this is true, look into the work of Bertrand Russel into paradoxes and set theory)

SOL also works on a domain of discourse defined by sets. However, its semantics allow some clever structures which define categories using sets, construct the category which includes creation and lifting of the rock, and then you can go about your proof. At first glance, this looks like a winner!

As part of building his incompleteness theorems Gödel demonstrated a major limitation of SOL. It turns out that it is impossible to make any proof about a SOL system unless it happens to be reducible to FOL (i.e. you claimed you were using SOL, but you never actually used any of its fancy abilities). We've argued that the set of things that can be done cannot be described in FOL, so Gödel proves that any result regarding creation and lifting of our rock cannot possibly be proven.

The final answer is to allow admission of other formal systems besides FOL and SOL which can handle this particular case. However, in practice, the reason we use FOL and SOL is because it is remarkably hard to come up with a formal system which others can agree with. You can come up with any formal system you want, but unless both parties agree on what a "proof" should behave like, there really can't be any headway.

So, in all, the anti-ontological argument itself is phrased using a language which is tremendously unfriendly to proofs. Anyone seeking a proof will find themselves bound by the language of the problem.

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Most people posing this question want not only an answer, but an explanation of why that is the answer. That explanation must always include a precise definition of "all-powerful." Many who are pushing for such an answer want not only an explanation, but something worthy of being called a "proof."

Proof is actually a mathematical term, with a very precise definition. There are many classes of formal systems which can admit proofs, but First Order Logic (FOL) and Second Order Logic (SOL) are by far the most common. The individual posing the question will need to declare what sort of proof they accept. Since FOL and SOL are the most common systems people use, it is most likely they will name one of the two.

FOL is the most commonly referenced formal system with regard for proofs (for reasons we will see in a moment). However, defining "all powerful" within the confines of the language FOL supports is tricky. FOL requires everything it will talk about (officially called the "domain of discourse") to be defined as a set. "All powerful" could be defined as "For-all things that can be done, Supreme-Being can do it," however defining a set of "things that can be done" which includes creation and lifting of this particular rock is not possible. You need to go one step further, using categories rather than sets before you can use such a phrase, but FOL simply doesn't do that.

SOL also works on a domain of discourse defined by sets. However, its semantics allow some clever structures which define categories using sets, construct the category which includes creation and lifting of the rock, and then you can go about your proof. At first glance, this looks like a winner!

As part of building his incompleteness theorems Gödel demonstrated a major limitation of SOL. It turns out that it is impossible to make any proof about a SOL system unless it happens to be reducible to FOL (i.e. you claimed you were using SOL, but you never actually used any of its fancy abilities). We've argued that the set of things that can be done cannot be described in FOL, so Gödel proves that any result regarding creation and lifting of our rock cannot possibly be proven.

The final answer is to allow admission of other formal systems besides FOL and SOL which can handle this particular case. However, in practice, the reason we use FOL and SOL is because it is remarkably hard to come up with a formal system which others can agree with. You can come up with any formal system you want, but unless both parties agree on what a "proof" should behave like, there really can't be any headway.

So, in all, the anti-ontological argument itself is phrased using a language which is tremendously unfriendly to proofs. Anyone seeking a proof will find themselves bound by the language of the problem.