Godel's Incompleteness theorem and god
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05-01-2017, 12:17 PM
RE: Godel's Incompleteness theorem and god
(05-01-2017 11:26 AM)Chas Wrote:  
(04-01-2017 08:02 PM)Paleophyte Wrote:  It's more than a little ironic on several levels that theists should be using Godel's proof that absolute knowledge is unobtainable to demonstrate the existence of their god.

It doesn't say that. It says that any system of knowledge of the complexity of arithmetic cannot be complete within that system, that is using only the rules of that system.

It is complete knowledge that is denied, not absolute knowledge. And this only applies to formal systems.

And not all formal systems. First order logic is complete and consistent.

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05-01-2017, 02:37 PM
RE: Godel's Incompleteness theorem and god
(05-01-2017 12:17 PM)GirlyMan Wrote:  
(05-01-2017 11:26 AM)Chas Wrote:  It doesn't say that. It says that any system of knowledge of the complexity of arithmetic cannot be complete within that system, that is using only the rules of that system.

It is complete knowledge that is denied, not absolute knowledge. And this only applies to formal systems.

And not all formal systems. First order logic is complete and consistent.

"any system of knowledge of the complexity of arithmetic cannot be complete" q.v.

Skepticism is not a position; it is an approach to claims.
Science is not a subject, but a method.
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05-01-2017, 02:40 PM
RE: Godel's Incompleteness theorem and god
(05-01-2017 02:37 PM)Chas Wrote:  
(05-01-2017 12:17 PM)GirlyMan Wrote:  And not all formal systems. First order logic is complete and consistent.

"any system of knowledge of the complexity of arithmetic cannot be complete" q.v.

Okay. But first order logic does not require the Peano postulates and Godel's completeness theorem ensures it is complete. Am I missing your point?

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05-01-2017, 02:45 PM
RE: Godel's Incompleteness theorem and god
(05-01-2017 02:40 PM)GirlyMan Wrote:  
(05-01-2017 02:37 PM)Chas Wrote:  "any system of knowledge of the complexity of arithmetic cannot be complete" q.v.

Okay. But first order logic does not require the Peano postulates and Godel's completeness theorem ensures it is complete. Am I missing your point?

Talking past each other? I did specify the system's complexity. Consider

Were you just pointing out that first order predicate logic is simple enough to be complete and consistent?

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Science is not a subject, but a method.
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05-01-2017, 02:49 PM
RE: Godel's Incompleteness theorem and god
(05-01-2017 02:45 PM)Chas Wrote:  
(05-01-2017 02:40 PM)GirlyMan Wrote:  Okay. But first order logic does not require the Peano postulates and Godel's completeness theorem ensures it is complete. Am I missing your point?

Talking past each other? I did specify the system's complexity. Consider

Were you just pointing out that first order predicate logic is simple enough to be complete and consistent?

and the fact that first order logic is a formal system.

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