Case Against Truth + Omniscience

Pikachu
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Case Against Truth + Omniscience

I am realy not sure if this argument is logicaly valid but here is my 2 years old objection against onmiscience without using the rocky thingy.

Basically, we can show that absolute omniscience is impossible from set theory but I think we can go a lot further than this. A common theist modification is that to adopt a God that knows "everything that it is logically possible to know" - however - I believe that even this is impossible.

Justification:

There are two steps to my justification. The first assumes the set every truth that is logically possible to know, T, is finite. We then show that this can't be the case.

The second step is to show no T of infinite magnitude that has this property.

Finite case:

1. T is the set of all truths that are logically possible to know and T is finite.
2. Take the power set of T and call it PT.
3. For each element e in PT ask the question, Q: is e a member of T.
4. In step 3, there must be at least one truth yielded by Q that is not in T.
5. T is meant to be the set of truths that are logically possible to know but we've just found a truth that is not in T.
6. Contradiction.

Infinite case:

1. T is the set of all truths that are logically possible to know.
2. take the power set of T and call it PT.
3. For each element in e in PT ask the question, Q: is e a member of T.
4. For each element in PT we can construct a trivial truth that is not in T. i.e. If truth is in T or not.
5. The size of PT is greater than that of T.
6. Contradiction since T is meant to be the set of all truths that are logically possible to know, but the set of derived truths PT is large than T itself!

Okay.. assuming my proofs are sound we've got a really strong argument against omniscience but I'm not done yet.. we can go even further.

How many truths are there?

1. There are at least as many truths as there are real numbers.
2. To record a truth we have to use words.
3. There are only a countably infinite number of sentences.

Conclusion: There are more truths than there are sentences to express them. In fact, it goes further than this. There are more true statements in mathematics than there are proofs to prove them.

God had no time to create time.


todangst
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Pikachu wrote:I am realy not

Pikachu wrote:
I am realy not sure if this argument is logicaly valid but here is my 2 years old objection against onmiscience without using the rocky thingy.

Basically, we can show that absolute omniscience is impossible from set theory but I think we can go a lot further than this. A common theist modification is that to adopt a God that knows "everything that it is logically possible to know" - however - I believe that even this is impossible.

Setting a limit on omnipotence is a contradiction anyway (This god is also omnipotent). Setting a limit of 'logical possibility' only leads us to the question: 'what decides logical possibility if not omnipotence?!"

Quote:

Justification:

There are two steps to my justification. The first assumes the set every truth that is logically possible to know, T, is finite. We then show that this can't be the case.

The second step is to show no T of infinite magnitude that has this property.

Finite case:

1. T is the set of all truths that are logically possible to know and T is finite.
2. Take the power set of T and call it PT.
3. For each element e in PT ask the question, Q: is e a member of T.
4. In step 3, there must be at least one truth yielded by Q that is not in T.
5. T is meant to be the set of truths that are logically possible to know but we've just found a truth that is not in T.
6. Contradiction.

Infinite case:

1. T is the set of all truths that are logically possible to know.
2. take the power set of T and call it PT.
3. For each element in e in PT ask the question, Q: is e a member of T.
4. For each element in PT we can construct a trivial truth that is not in T. i.e. If truth is in T or not.
5. The size of PT is greater than that of T.
6. Contradiction since T is meant to be the set of all truths that are logically possible to know, but the set of derived truths PT is large than T itself!

Okay.. assuming my proofs are sound we've got a really strong argument against omniscience but I'm not done yet.. we can go even further.

How many truths are there?

1. There are at least as many truths as there are real numbers.
2. To record a truth we have to use words.
3. There are only a countably infinite number of sentences.

Conclusion: There are more truths than there are sentences to express them. In fact, it goes further than this. There are more true statements in mathematics than there are proofs to prove them.

Nice work.

Those who know the good, do the good. - Socrates

Books on atheism.


Pikachu
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- Sets are natural things to

Quote:
Setting a limit on omnipotence is a contradiction anyway (This god is also omnipotent). Setting a limit of 'logical possibility' only leads us to the question: 'what decides logical possibility if not omnipotence?!"

Yeah because T can't include PT. PT is always larger than T. From any given T I can construct at least Card(PT) truths that aren't in T. There is no way T can map in a one to one fashion to PT so T isn't the same size as PT - hence we show that T can't exist.

What i'm doing is assuming that T can exist, and showing that by assuming it's existance it leads to a contradiction, i.e. it would require a powerset to map to the original set which is impossible.

God had no time to create time.