Does Omniscience Negate Free Will?

[DaveC426913]

What is this 'you' thing you speak of, if not the brain/mind.

Unless you believe in some sort of supernatural soul, I'd say separating the two doesn't make much sense. Neuroscience, although it is in its infancy, shows quite a correlation between brain and mind.
The mind is what the brain does.

My keyboard affects my computer processor. My computer processor does not affect my keyboard. While there is a strong correlation, they are distinct.

And the processor does not need to have a "supernatural" processor to acknowledge that keyboard and processor are different (there are no memory registers dedicated to - or output paths to - the keyboard, for example. It is an input-only device.)

 

[JoeDawg]

My keyboard affects my computer processor. My computer processor does not affect my keyboard. While there is a strong correlation, they are distinct.

Actually, your keyboard needs to 'recognized' as an input device; without some kind of processing, your keyboard won't receive any power, and certainly won't be useful as an input device.

On top of that, both processor and keyboard, are hardware. Neither represents a good comparison to any idea of 'mind as distinct from brain'. If anything, in a computer, the running operating system is a good example of mind... and it can both affect hardware and disappears when power is cut off.

 

[FayeKane]

Of course not.

The question is another example of people taking the names of things as more important than the things themselves.

Look, this question is identical to:
Look back in time and observe what someone did. It's fixed. It can't change. Their world-line is frozen in time.

So did the person have free will?

Yes. Not only that, but most of what happened was chaotic or completely random. Certainly all quantum events that day were.

Just as acceleration in three dimensions is rotation in four, there is no difference between "free will" and "predestination"; they are just names of two places to look at the same action from: inside the system and outside of it.

-- faye

 

[Mattara]

Of course the existence of an omniscient being would disprove free will. It will also prove it. It will even prove that all cheese on the moon is blue or that Obama is part of an elaborate alien conspiracy. Perhaps we are presupposing that omniscience is a coherent concept?

 

[DaveC426913]

Of course the existence of an omniscient being would disprove free will. It will also prove it. It will even prove that all cheese on the moon is blue or that Obama is part of an elaborate alien conspiracy. Perhaps we are presupposing that omniscience is a coherent concept?

It would do none of these things. Why do you say this?

 

[Sorry!]

Of course not.

The question is another example of people taking the names of things as more important than the things themselves.

Look, this question is identical to:
Look back in time and observe what someone did. It's fixed. It can't change. Their world-line is frozen in time.

So did the person have free will?

Yes. Not only that, but most of what happened was chaotic or completely random. Certainly all quantum events that day were.

Just as acceleration in three dimensions is rotation in four, there is no difference between "free will" and "predestination"; they are just names of two places to look at the same action from: inside the system and outside of it.

-- faye

Hmmm... this leads me to question if in the Quantum world there is such a 'history' timeline...

I'm actually going to go look that up.

 

[DaveC426913]

Look back in time and observe what someone did. It's fixed. It can't change. Their world-line is frozen in time.

So did the person have free will?

Yes.

That is a very illuminating way of looking at the problem.

 

[Zantra]

"you've already made the choice, you just have to understand it"

Omniscence does not negate free will- here's why. You've seen all possible futures- many worlds theory, etc, so you know the outcome of every choice, and based on that, you chose a path. The key word here is "choose" Assuming many worlds there's always an opporunity to choose a different path, even knowing all of your outcomes- emotion could come into play-aka the choice of NEO to save his girlfriend instead of Zion. You know saving many lives is the best move, but you make the "emotional choice" anyhow.
It's the human paradox. Of course if you make every choice based solely on unemotional criteria, you're following "rules". You know which of the paths you'll choose, and why, and as a omniscent being, you choose not to make a decision based on anything other than those rules. However, since you are omniscent, you've made these rules and if you choose to break them based on emotion, it brings free will back into play.

If many worlds is untrue, then you see a straight line back and forth- you see one possible future, and the path you've chosen, regardless of any changes you make between here and there, you know that is where you end up. all roads lead to one future. In this case free will is not possible because there is only one outcome- THE future.

 

[DaveC426913]

And the whole 'emotional choice' argument is a total red herring. Why you choose a different outcome is irrelevant to whether you can choose a different outcome. You're starting to talk about which choice is right or wrong. You've sort of gotten lost in your own argument on that one.

If many worlds is untrue, then you see a straight line back and forth- you see one possible future, and the path you've chosen, regardless of any changes you make between here and there, you know that is where you end up. all roads lead to one future. In this case free will is not possible because there is only one outcome- THE future.

Your conclusion does not follow.

The fact that the only possible future will show which face of the penny DID land face-up does not mean I have no free-will over which face I DECIDE to place face-up.

I wonder if you are making an implicit assumption that the person whose free-will is in question is the same person who has the omniscience. That is not a given.

If there is a single entity anywhere that is omniscient, then the paradox begins to rear its head for anyone and everyone everywhere.

 

[Zantra]

And the whole 'emotional choice' argument is a total red herring. Why you choose a different outcome is irrelevant to whether you can choose a different outcome. You're starting to talk about which choice is right or wrong.

I went off on a tangent there... but I was making the point that:

1.Knowing the future impacts your choice, so the choice you make based on knowing the future is possibly not the same one you would have made not knowing the future.

2. Being omniscient doesn't negate free will- you have much more information about the choices you make and how your decision will impact events, BUT it is still a choice. It's still a decision to be made, and all your changing with omniscience are the circumstances.

You like chocolate ice cream. If given a choice between vanilla and chocolate you will invariably choose chocolate. If you're omniscient and you see that down the line choosing chocolate leads to a tragic event, choosing vanilla does not- you will choose vanilla. Does that change the fact that you like chocolate? No. Let's say you see all permutations of the ice cream choice, and it has zero impact on your existence- it's a completely neutral event. you're going to CHOOSE chocolate, not based on your omniscience, but based on a preference you have. you've just made a choice.

Or let's take a step further. You're omniscient, but you get bored, and you decide to discontinue seeing into the future. You now have to make decisions based on a blind choice. Does that mean as a omniscient being you're turning free will on or off? no it means you're making a "choice" based on less information. It's possibly a different choice than you'd make if you turned it off. What if you decide to turn it off and you doing percieve the ice cream choice-then you choose chocolate because it's tasty. tragedy occurs. Would this have happened if you weren't bored?

Your conclusion does not follow.

The fact that the only possible future will show which face of the penny DID land face-up does not mean I have no free-will over which face I DECIDE to place face-up.

I wonder if you are making an implicit assumption that the person whose free-will is in question is the same person who has the omniscience. That is not a given.

If there is a single entity anywhere that is omniscient, then the paradox begins to rear its head for anyone and everyone everywhere.

One possible future means you learned about your future, you reacted based on that knowledge, and so your choices inevitably led to that future. You made choices base on knowing the future, but if you are seeing it, that future is one based on the inclusion of your foresight of the events. hence you see that the penny is heads. You try to "choose" to make it tails, but it doesn't matter, because whatever choices you make DO eventually lead to heads- that is the inescapable fact of a single time line- no deviation because it is a single, unchanging timeline that only gives you the illusion of choice.

Now, if you're omniscient, you understand this anyway, and don't try to fight the flow of events, because it's unchangable. If you're suggesting they can change it, then it defies the laws of a single universe- So we accept that omniscient beings can only exist in a multiverse with infinite deviations.

As far as omniscient beings implying a paradox, it implies a multiverse by virtue of the nature of the omniscience. Or are we talking about a being who can observe but not change the future? The assumtion is that omniscence=ability to change the future.

But define the rules of this being- I for instance, assume he is unique- you sound like you're inferring that this being is an eventuality that can be achieved by all- I assume a unique set of circumstances that created him, cannot be duplicated, and thus, no one else be like this singular individual. he/she is the only one to ever exist wit this ability.

 

[DaveC426913]

Or are we talking about a being who can observe but not change the future?

That is the definition of omniscient.

You may be confusing omniscient with omnipotent.

The assumtion is that omniscence=ability to change the future.

That is an assumption and it is not granted.

But define the rules of this being- I for instance, assume he is unique- you sound like you're inferring that this being is an eventuality that can be achieved by all- I assume a unique set of circumstances that created him, cannot be duplicated, and thus, no one else be like this singular individual. he/she is the only one to ever exist wit this ability.

I do not see any of this as relevant. One omniscient being or many, you get the same result.

The issue I see is that you seem to assume the omniscient entity and the subject in question about free will are the same entity (i.e. it is his own future he is seeing). That is not a given.

 

[Mattara]

It would do none of these things. Why do you say this?

If omniscience exists, then surely the set of all true propositions must exist. If it could be shown that this set has contradictory properties, then it follows that omniscience cannot exist.

Let T be the set of all true propositions so that T = {x(1), x(2), x(3), ..., x(n)}, where x(1), x(2), ..., x(n) are true propositions. From this set, we can form the power set U that consists of all combinations of the elements in T. Thus, U contains more elements than T, since U both contains all elements of T plus additional elements that are the combinations of elements in T. Naturally, if X and Y are both true, then then the statement X AND Y (and so on through all combinations) is also true. So all elements in U are also true propositions. However, since T is the set of all true propositions, U must contain the same or less number of elements than U.

Thus assuming that the set of all true propositions exist, we get the result that U is both a subset of T and not a subset of T. This is an absurd result, so the initial premise of the possibility of omniscience has to be rejected.

Perhaps you have noticed a mistake in this line of reasoning? If so, please share it with me.

 

[w3390]

I know of one good argument that says that a supreme being cannot be omnipotent, omniscient, and omnibenevolent because of the problem of evil. However, this argument can be resolved by saying that evil is caused by free will, which would have to be present from a supreme being which must create the best possible universe.

 

[DaveC426913]

If omniscience exists, then surely the set of all true propositions must exist.
If it could be shown that this set has contradictory properties, then it follows that omniscience cannot exist.

Let T be the set of all true propositions so that T = {x(1), x(2), x(3), ..., x(n)}, where x(1), x(2), ..., x(n) are true propositions. From this set, we can form the power set U that consists of all combinations of the elements in T. Thus, U contains more elements than T, since U both contains all elements of T plus additional elements that are the combinations of elements in T. Naturally, if X and Y are both true, then then the statement X AND Y (and so on through all combinations) is also true. So all elements in U are also true propositions. However, since T is the set of all true propositions, U must contain the same or less number of elements than U.

Thus assuming that the set of all true propositions exist, we get the result that U is both a subset of T and not a subset of T. This is an absurd result, so the initial premise of the possibility of omniscience has to be rejected.

Perhaps you have noticed a mistake in this line of reasoning? If so, please share it with me.

I don't suppose you would translate this into layperson's language for those of us who did not study logic in post-sec...

 

[Zantra]

I know of one good argument that says that a supreme being cannot be omnipotent, omniscient, and omnibenevolent because of the problem of evil. However, this argument can be resolved by saying that evil is caused by free will, which would have to be present from a supreme being which must create the best possible universe.

good and evil are human concepts. You're presupposing that this being is bound by a code, or rules, which is unlikely. You're projecting a human concept onto a being that doesn't know any punishment, consequences or restrictions. It assumes emotions like empathy, regret, compassion, and fear, which this type of being probably wouldn't posess.
It's far more likely that "the best possible universe" is whatever this being sees fit to do.

Or is that not the argument?

 

[DaveC426913]

good and evil are human concepts. You're presupposing that this being is bound by a code, or rules, which is unlikely. You're projecting a human concept onto a being that doesn't know any punishment, consequences or restrictions. It assumes emotions like empathy, regret, compassion, and fear, which this type of being probably wouldn't posess.
It's far more likely that "the best possible universe" is whatever this being sees fit to do.

Or is that not the argument?

Well, he did stipulate 'omnibenevolent', which means, yes, a moral code.

 

[Zantra]

Well, he did stipulate 'omnibenevolent', which means, yes, a moral code.

I missed that part..loophole... nice

 

[Zantra]

OK I confess I didn't read the whole thread, so I missed X-ray's post here:

1. An infallible, omniscient, being exists. [Assumption]
2. This being has foreknowledge that event 'A' will occur. [Definition of omniscience]
3. 'A' must occur. [Definition of infallible]
4. I cannot choose to do any action which would make it so that 'A' does not occur. [Points, 1, 2, 3]
5. I lack free will. [Point 4]

This is just a variation on the God and an immovable boulder fallacy.

First, #3 is not necessarly granted if the implication is that omniscience means infallibility. Infallibility implies mistakes. Mistakes require rules. I submit that an omniscient being isn't necessarily subjected to "rules" to guide them. They just do what they do. I think people are thinking of God, and omniscience doesn't necessarily mean God. If we are talking about God,which goes back to benevolence, then the above 5 statements can hold up- otherwise no.

So the assumption is that an omniscient being cannot exist because it cannot fully know itsself.

The problem with that is that this is an assumption. why can't an omniscient being know itsself? It's not necessarily an infinite loop. You know everything, including how you exist, and how you function, the sum of your knowledge, and how you came to posess it.

If you're omniscient, you can IMPLY that this being's mind is infinite- this doesn't necessarily imply that he's omnipotent, just that his mind is infite, which is another human concept. Maybe it's just of a capacity that's incomprehensible to us. We make assumptions about boundaries that we can't see beyond, because it helps us convince ourselves that we're on top.

Again, everything above is only proven IF you make certain assumptions.

 

[Mattara]

I don't suppose you would translate this into layperson's language for those of us who did not study logic in post-sec...

It would perhaps loose some of its precision, but I will give it a try. If omniscience is possible, then it seems reasonable to conclude that there exists a collection of all truths (T). This would exist in the mind of the omniscient entity. By combining all of the truths in this collection, you could make a collection (U) that has all of the same truths as the original (T), plus all of the combinations of all the truths in the original collection. Thus U is larger (contains more truths) than T. However, since T is defined as containing all truths, U must contain the same number or fewer truths than T. This is a logical contradiction, so the assumption of the possibility of the existence of T, and thus the possibility of omniscience has to be rejected.

 

[DaveC426913]

It would perhaps loose some of its precision, but I will give it a try. If omniscience is possible, then it seems reasonable to conclude that there exists a collection of all truths (T). This would exist in the mind of the omniscient entity. By combining all of the truths in this collection, you could make a collection (U) that has all of the same truths as the original (T), plus all of the combinations of all the truths in the original collection. Thus U is larger (contains more truths) than T. However, since T is defined as containing all truths, U must contain the same number or fewer truths than T. This is a logical contradiction, so the assumption of the possibility of the existence of T, and thus the possibility of omniscience has to be rejected.

Yeah, that's what I gathered after reading it through. It wasn't as cryptic as I thought it was (or I'm better than I thought I was).

It seems to me, your logic is self-contradictory, having nothing to do with omniscience.

"it seems reasonable to conclude that there exists a collection of all X"
"By combining all X in this collection, you could make a collection (U) that has all of the same X, plus all of the combinations of all X in the original collection."
etc. etc.

You see, the contradiction occurs on your logic, not in its application to omniscience. The contradiction is that you start with a premise which you then immediately prove false.

 

[Mattara]

Yeah, that's what I gathered after reading it through. It wasn't as cryptic as I thought it was (or I'm better than I thought I was).

It seems to me, your logic is self-contradictory, having nothing to do with omniscience.

"it seems reasonable to conclude that there exists a collection of all X"
"By combining all X in this collection, you could make a collection (U) that has all of the same X, plus all of the combinations of all X in the original collection."
etc. etc.

You see, the contradiction occurs on your logic, not in its application to omniscience. The contradiction is that you start with a premise which you then immediately prove false.

Yes, the contradiction occurs in the logical deduction if you assume that omniscience is possible, which leads us to reject the initial premise.

http://en.wikipedia.org/wiki/Proof_by_contradiction

Similarly, if you wish to prove that the square root of 2 is irrational, you assume that it is rational and then derive a logical contradiction. This contradiction forces you to abandon your assumption that the square root of 2 is irrational and conclude that it has to be rational.

The key steps in my argument is (1) omniscience implies the existence of a set of all true propositions and (2) assuming that a set of all true propositions exists leads to a logical contradiction and (3) to avoid this contradiction, the initial premise of the possibility of omniscience has to be rejected. I suspect that (1) is the weakest point in the argument.

Or did you mean something else entirely?

 

[octelcogopod]

I think your logic is kind of flawed to begin with.
First off how do you define a truth in terms of consciousness?
We don't know how a truth manifests itself in consciousness.
Our minds allow us to "think" and sometime we can predict future events, and understand past events, but the actual process is still not understood.
To be omniscient you can't just remember all the universes information like humans do, and even if you do that memory can be flawed or incomplete (it always is for humans anyway) so I find it hard to apply humans consciousness to a godlike entity.

Furthermore there are numerous technical issues with gods memory, like for instance the way humans remember. We can't remember all our memories at once, we have to go through them in sequence, if god has to do the same, how can we be certain he will remember it the same way every time? And how can we be certain his brain is perfect? Gods brain must by definition be immensely huge to be able to contain every truth in the universe, and as such there must be lots of room for errors. God must be the perfect machine built on physical principles ?

And finally how can god (or we) be sure something is true? God would be in a solipsistic world and could never actually prove everything. Just like we can't now. Consciousness automatically leads to solipsism, and also the errors of conscious experience.

I'm bringing this up because I think your premise is false. I do not think there can be a god with consciousness that is omniscient, and if there was, he would work on a completely different level than us.
The concepts of truth and knowledge are estimations, they never contain ALL the information about the events. If god had a complete overview of the physical reality, along with all the emergent properties like consciousness, and he could understand 100% all the implications of everything, then I don't believe he's anything remotely like human consciousness, in fact he would be completely out of our reach, even conceptually.

The ops problem is actually just another determinism vs free will debate, and I'd rather tackle it grassroot style; namely that if all physical reality is determinstic, how can we have free will? It's exactly the same as asking if god can see everything, how can we have free will.

 

[Mattara]

I do not think there can be a god with consciousness that is omniscient, and if there was, he would work on a completely different level than us.

I also think that consciousness without life is contradictory. I just assumed that omniscient was defined as or implied knowing all true propositions, but you are absolutely right that there are contradictions in assuming that consciousness can exist without life or matter in the first place.

namely that if all physical reality is determinstic, how can we have free will? It's exactly the same as asking if god can see everything, how can we have free will.

I concur. I agree that libertarian or acausal freedom cannot exist given determinism. But then again, it could be argued that "acausal freedom" is itself a contradiction, for if no part of your being, not your moral character, your knowledge, your thoughts, your emotions and so (which there are scientific grounds for thinking that these are properties of a material brain) on can determine how you act (this surely follows from the definition of libertarian freedom), then it is difficult to see how you could be free in any morally important sense of the word.

 

[DaveC426913]

Yes, the contradiction occurs in the logical deduction if you assume that omniscience is possible, which leads us to reject the initial premise.

No. You completely ignored what I said.

The contradiction occurs internal to your logic, regardless of any application to omniscience.
I'll show you again:

"it seems reasonable to conclude that there exists a collection of all X"
"By combining all X in this collection, you could make a collection (U) that has all of the same X, plus all of the combinations of all X in the original collection."
etc. etc.

You have just proven that X cannot exist. X could be anything. Note there is no reference to omniscience. We get a contradiction before we even finish writing out the logic. Therefore, the logic is flawed.

 

[Mattara]

No. You completely ignored what I said.

The contradiction occurs internal to your logic, regardless of any application to omniscience.
I'll show you again:

"it seems reasonable to conclude that there exists a collection of all X"
"By combining all X in this collection, you could make a collection (U) that has all of the same X, plus all of the combinations of all X in the original collection."
etc. etc.

You have just proven that X cannot exist. X could be anything. Note there is no reference to omniscience. We get a contradiction before we even finish writing out the logic. Therefore, the logic is flawed.

No, that argument only works if X is all true propositions, since those are the only elements that can be joined together and still be true.

Let's assume that X is the collection of all customer payments of a day, where each element is a customer payment. If you combine two customer payments, there is nothing that would suggest that the result would also be a customer payment.

Or assume that X is the collection of all prime numbers below ten.

X = {1,2,3,5,7,9}

Joining these together does not necessarily form another prime number below then, for instance, 5 and 3, 9 and 7, 9 and 5, are not prime numbers below 10. There are many other examples, these are just the ones I could come up with on the top of my head.

This argument only works if X is the set of all true propositions, since any combinations of true propositions are by definition also true. That's the key feature you need to have for such an argument to work.

 

[tauon]

@Mattara

it does not follow.
you defined T, the set of all true propositions:

T={p| p is true}

then it seems that you "defined" another set, U.
you first defined it as the power set of T (the set of all subsets of T)
U1 has of course a greater cardinality than T- as you mentioned.
however, you then re-defined U as the set of all true conjunctions (by redefining "combination" as "logical conjunction") - I'll call this set U'.
out of the blue, you jumped a gap and transferred properties U to U', you stated that the second U' has a greater cardinality than T. this is false as U'⊆T and the demonstration is trivial:

the conjunction of true propositions is a true proposition. q.e.d.

U' is a subset of T, it is impossible for U' to have a greater cardinality than T.
Then you concluded that if we assume that the set of all true propositions exists, we get the result that U' is both a subset of T and not a subset of T.
How exactly is U' not a subset of T? you didn't demonstrate that part... what you demonstrated is that T is a subset of U not U'. the power set of a set is not identical with the set of the conjunctions of true propositions... you mixed definitions.

 

[Mattara]

@Mattara

it does not follow.
you defined T, the set of all true propositions:

T={p| p is true}

then it seems that you "defined" another set, U.
you first defined it as the power set of T (the set of all subsets of T)
U1 has of course a greater cardinality than T- as you mentioned.
however, you then re-defined U as the set of all true conjunctions (by redefining "combination" as "logical conjunction") - I'll call this set U'.
out of the blue, you jumped a gap and transferred properties U to U', you stated that the second U' has a greater cardinality than T. this is false as U'⊆T and the demonstration is trivial:

the conjunction of true propositions is a true proposition. q.e.d.

U' is a subset of T, it is impossible for U' to have a greater cardinality than T.
Then you concluded that if we assume that the set of all true propositions exists, we get the result that U' is both a subset of T and not a subset of T.
How exactly is U' not a subset of T? you didn't demonstrate that part... what you demonstrated is that T is a subset of U not U'. the power set of a set is not identical with the set of the conjunctions of true propositions... you mixed definitions.

I did no such redefinition. U contains all the elements that T contains in addition to all the combinations of elements in T. Because U contains the exact same elements as T, plus all the combinations of the elements of T. A power set contains by definition more elements than it' set (if there are more than two elements). But since no set can contain more elements than T (since it is the set of all true propositions), we get a contradiction and the initial assumption of omniscience has to be rejected.

Perhaps you need to review the definition of a power set.

http://en.wikipedia.org/wiki/Power_set

 

[cosmo123]

Although you cannot choose to do an action that makes 'A' not occur, I don't see how it follows that you do not choose for 'A' to occur. Perhaps the omniscient being's foreknowledge that 'A' will occur is the result of the being knowing that you will choose to do 'A'. If so, then if you had chosen to do something other than 'A', the omniscient being would have had foreknowledge that this other thing would occur.

I don't know much about philosopht, but this seems correct. You can rearrange it to apply to the past, instead of the future, and it is still essentially the same, although obviously untrue.

1. An infallible, omniscient, being exists. [Assumption]
2. This being has knowledge that event 'A' has occured. [Definition of omniscience]
3. 'A' must have occured. [Definition of infallible]
4. I could not have chosen any other action than A [Points, 1, 2, 3]
5. I lacked free will when I chose A. [Point 4]

It's just all in the wrong order. A chicken will die by getting shot by me, therefore i must shoot the chicken. I didnt shoot the chicken because it died, the chicken died because i shot it.

You going to perform that event in the future caused the supreme being, in the past, to know you were going to do it, in that order.

This idea also has the obvious problem that a supreme being can't affect what you do just by looking at you.

 

[FayeKane]

> Perhaps you have noticed a mistake in this line of reasoning? If so, please share it with me.

Okay Aristotle, but you asked for it. I don't want to get banned for being "rude" again.

> If omniscience exists, then surely the set of all true propositions must exist.

Really? Why? Is this axiomatic?

Either be rigorous or don't use the predicate calculus. It's not a child's toy.

> If it could be shown that this set has contradictory properties, then it follows that omniscience cannot exist.

No, that doesn't follow either. One of several reasons is that you're assuming that the statements "the set exists" and "the set has contradictory properties" are inconsistent. Not only have you not shown that, but it's not true--Bertrand Russell's barber notwithstanding.

In fact, it's semiotic silliness. You're lost in definitions. Basically, what you're saying is equivalent to: "There can be no god because god can do anything, however he can't make a stone too heavy for him to lift."

While it is true that there is no god, that's not the reason why.

-- faye kane homeless brain

 

[tauon]

I did no such redefinition. U contains all the elements that T contains in addition to all the combinations of elements in T. Because U contains the exact same elements as T, plus all the combinations of the elements of T. A power set contains by definition more elements than it' set (if there are more than two elements). But since no set can contain more elements than T (since it is the set of all true propositions), we get a contradiction and the initial assumption of omniscience has to be rejected.

Perhaps you need to review the definition of a power set.

http://en.wikipedia.org/wiki/Power_set

I don't want to be rude but sorry, you should follow your example and review the definitions of power set, combination and logical conjunction- you're definitely confused.

look, for the sake of brevity let's assume that T is a finite set of just 1 proposition T={p}

then the power set of T (the set of all subsets of T) is:

P(T) = {{}, {p}}

but P(T) ≠ {p, p AND p} = U = T
so indeed P(T) has more elements than T. but P(T) is not the set of conjunctions ("combinations" in the way you're using the term), U.

you mixed 2 definitions of 2 different sets in your argumentation. there is no contradiction, the only mistake here is in your incorrect definitions and use of mathematical notions.

the general case for T={p| p is true} is U ⊆ T ⊆ P(T) , there is no contradiction.

 

[Mattara]

Okay Aristotle, but you asked for it. I don't want to get banned for being "rude" again.


Really? Why? Is this axiomatic?

Either be rigorous or don't use the predicate calculus. It's not a child's toy.



No, that doesn't follow either. One of several reasons is that you're assuming that the statements "the set exists" and "the set has contradictory properties" are inconsistent. Not only have you not shown that, but it's not true--Bertrand Russell's barber notwithstanding.

In fact, it's semiotic silliness. You're lost in definitions. Basically, what you're saying is equivalent to: "There can be no god because god can do anything, however he can't make a stone too heavy for him to lift."

While it is true that there is no god, that's not the reason why.

-- faye kane homeless brain

You obviously do not understand basic logic. Yes, omniscience entrails that a set of all true propositions exists. This would exist in the mind of the omniscient being. Yes, something with contradictory properties cannot exist in reality.

What was your question?

 

[Mattara]

I don't want to be rude but sorry, you should follow your example and review the definitions of power set, combination and logical conjunction- you're definitely confused.

look, for the sake of brevity let's assume that T is a finite set of just 1 proposition T={p}

then the power set of T (the set of all subsets of T) is:

P(T) = {{}, {p}}

but P(T) ≠ {p, p AND p} = U = T
so indeed P(T) has more elements than T. but P(T) is not the set of conjunctions ("combinations" in the way you're using the term), U.

you mixed 2 definitions of 2 different sets in your argumentation. there is no contradiction, the only mistake here is in your incorrect definitions and use of mathematical notions.

the general case for T={p| p is true} is U ⊆ T ⊆ P(T) , there is no contradiction.

No, you can't make that assumption, since T contains more than 1 (and more than 2) elements, or are you suggesting that there only exists one true proposition?

T is the set of all true propositions.
U is the power set of T, which means it contains the exact same elements as T, plus an additional large amount of elements that are the subsets of T (it contains more copies of the elements in T. However, from assuming omniscience, T was defined as the set of all true propositions, which has to be larger than T. Thus T has contradictory properties and cannot exist, and therefore omniscience cannot exist.

I don't know why this is so hard to grasp.

(1) Do you agree that I have defined T as the set of all true propositions?
(2) Do you agree that a power set of T contains more elements than T?
(3) Do you agree that there can be no larger set of true propositions than the set of all true propositions, since a conjunction of two true propositions is also true?

Since both (2) and (3) becomes true if you assume omniscience and 2 AND 3 is a contradiction, the assumption of omniscience is invalid.

 

[FayeKane]

> something with contradictory properties cannot exist in reality.

What does reality have to do with it? Does your set U, the power set of the set of all true propositions, exist in reality? If so, point to it. If not, feel humiliated.

You obviously do not understand basic logic.

[edit]

I minored in logic. I was also the valedictorian of the UM computer science department (rated 3 in the country).

[edit]

> Yes, omniscience entrails

Does that have something to do with Nietzsche's statement "God is Dead"?

> What was your question?

If a high school kid tries to fool everyone, does he fool himself?


-- faye kane, smartmouth smartass

 

[DaveC426913]

Guys. Attack the argument, not the arguer (even in self-defense). It is possible to navigate a debate with a minimum of ad hominems.

 

[Mattara]

What does reality have to do with it? Does your set U, the power set of the set of all true propositions, exist in reality? If so, point to it. If not, feel humiliated.

Of course U does not exist in reality, that's the whole point of my argument. Omniscience entails that this set exists, but since it cannot (it has contradictory properties), omniscience cannot exist either, and the existence of an omniscient being disproves (or proves) free will per the principle of explosion.

 

[tauon]

No, you can't make that assumption, since T contains more than 1 (and more than 2) elements, or are you suggesting that there only exists one true proposition?

eh, no...of course there is more than one true proposition
that was merely a simple example I used to illustrate the difference between 2 concepts that you are confusing to be identical or similar- it was just an (unsuccessful it seems) attempt to show you how you unjustifiably transfer properties from one set to another.

T is the set of all true propositions.
U is the power set of T, which means it contains the exact same elements as T, plus an additional large amount of elements that are the subsets of T (it contains more copies of the elements in T.

this is partially correct and wrong in the rest.

P(T) is a set that contains sets of "elements", it is a family of sets. T on the other hand, contains true propositions... that P(T) has a greater cardinality than T is indeed correct, but P(T) contains no additional true propositions that are not in T: all elements of P(T) -with the exception of the empty set- are formed as sets of true propositions from T.

also, that P(T) contains more "copies" of the same true proposition is true, but indeed has no relevance whatsoever to the frame of your (incorrect) argument.

However, from assuming omniscience, T was defined as the set of all true propositions, which has to be larger than T.

T={p| p is true} until here, I agree but... what do you mean by T has to be larger than T?

Thus T has contradictory properties and cannot exist, and therefore omniscience cannot exist.

that's very nice except T has no contradictory properties. :)

I don't know why this is so hard to grasp.

oh, ironically: that's exactly what I was thinking...

(1) Do you agree that I have defined T as the set of all true propositions?

of course... I agreed with this part since my first post.

(2) Do you agree that a power set of T contains more elements than T?

why certainly. the power set of a set has a strictly higher cardinality than the set. this is a known mathematical fact.

(3) Do you agree that there can be no larger set of true propositions than the set of all true propositions, since a conjunction of two true propositions is also true?

yes. that there is no "larger" set of true propositions, than the set of all true propositions: that's an a priori truth.

Since both (2) and (3) becomes true if you assume omniscience and 2 AND 3 is a contradiction, the assumption of omniscience is invalid.

2 and 3 are not contradictory!
you fail to understand the notions of power set, and cardinality.
that the power set of T has a higher cardinality than T in no way implies that P(T) contains truths that the set of all truths does not (what it is that you're claiming, and what you state the contradiction to be).

Again, I will type a tiny, trivial example to exemplify this (so we won't go into lengthier text, I'll use a small finite set).

Let S be a an arbitrary finite set: S={x,y},
it's power set is then P(S)={{ },{x},{y},{x, y}}

Evidently, P(S) has no element F where F={z| z ∉ S}.
And this holds for any set (finite or infinite), and it is an a priori truth (from the very definition of the power set) that there is no F ∈ P(S) such that F={z| z ∉ S}, since all the elements of P(S) are defined as subsets of S.

...

 

[sportsstar469]

It's pretty much a moot point since there is no supreme being, but this actually belongs in the Philosophy section.

if there is no supreme being, how do you explain the LARGE presence of atoms on this earth? atoms cannot be created.