# Would the existance of an omniscient being prove that free will is non-existant?

@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

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

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 dont 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 cant affect what you do just by looking at you.

> 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

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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.

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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.

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.

> 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.

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

> Yes, omniscience entrails

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

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

-- faye kane, smartmouth smartass

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DaveC426913
Gold Member
Guys. Attack the argument, not the arguer (even in self-defense). It is possible to navigate a debate with a minimum of ad hominems.

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.

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.

...

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.