Prove that God doesn't exist.

[Dr.Who]

Russell's paradox is resolved by axiomatic set theory.

Sorry, I thought you werw saying that Russell's paradox was a result of set theory.

 

[numinus]

Are all paradoxes a result of the self-referencing fallacy?

Not all. Paradoxes also arise from circular reasoning and infinite regress.

Russell's paradox comes to mind because it is considered as set-theoretic -- meaning it arises from some fundamental defect in the theory itself. The omnipotence paradox is, in my opinion, a variant of this. It ensues from a naive interpretation of the set predicate.

 

[numinus]

Sorry, I thought you werw saying that Russell's paradox was a result of set theory.

Yes.

Prior to axiomatic set theory, there was naive set theory (cantor). The system is naive because it pre-supposes that any conceivable predicate may be used to govern sets.

 

[Dr.Who]

Not all. Paradoxes also arise from circular reasoning and infinite regress.

Russell's paradox comes to mind because it is considered as set-theoretic -- meaning it arises from some fundamental defect in the theory itself. The omnipotence paradox is, in my opinion, a variant of this. It ensues from a naive interpretation of the set predicate.

The question was if there are any unresolved paradoxes.

If paradoxes can be the result of self-referencing, circular reasoning, infinite regress, and who know what else then it is'nt very productive to only answer that some are resolved through set theory as an explanation of self-referencing.

What we really need to know still remiains. Are there any unresolved paradoxes?

 

[clarkatticus]

I read the first posts of this thread and fast-forewarded to the last. Quite a jump in logic.Religion and faith as a paradox and now the scientific argument over paradoxs'. I am an athiest, there are many things I do not understand completely nor has science explained all. This does not bother me, I refuse still to appoint a diety to explain that which I currenty do not fully comprehend. And as for the other question in the thread, why should religion be excluded from government? It is the basic premis of all religions and faiths that "theirs" is the true faith, exclusive of all other. So which faith would you have in gov? Christian? Fair enough, perhaps Baptist so all dancing in public schools can be banned. Perhaps Mormon, and Mormon prayers can be recited in all public schools. Perhaps Catholic, we can add the Pope to the presidents advisors, or, my personal fav, Jehova Witness, now they can come to your door and sell the presidents agenda along with watchtower. I don't think you guys have really thought this through-

 

[numinus]

The question was if there are any unresolved paradoxes.

If paradoxes can be the result of self-referencing, circular reasoning, infinite regress, and who know what else then it is'nt very productive to only answer that some are resolved through set theory as an explanation of self-referencing.

What we really need to know still remiains. Are there any unresolved paradoxes?

Resolved in what sense?

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

Antinomy (Greek αντι-, for or instead of, plus νομος, law) literally means the mutual incompatibility, real or apparent, of two laws. It is a term used in logic and epistemology.

The term acquired a special significance in the philosophy of Immanuel Kant (1724–1804), who used it to describe the equally rational but contradictory results of applying to the universe of pure thought the categories or criteria of reason proper to the universe of sensible perception or experience (phenomena). Empirical reason cannot here play the role of establishing rational truths because it goes beyond possible experience and is applied to the sphere of that which transcends it.

For Kant there are four antinomies connected with:

1. the limitation of the universe in respect of space and time,

2. the theory that the whole consists of indivisible atoms (whereas, in fact, none such exist),

3. the problem of free will in relation to universal causality

4. the existence of a necessary being

There is no resolution. One only accepts the limitations of physical phenomena in relation to 'the universe of pure thought'.

 

[numinus]

I read the first posts of this thread and fast-forewarded to the last. Quite a jump in logic.Religion and faith as a paradox and now the scientific argument over paradoxs'. I am an athiest, there are many things I do not understand completely nor has science explained all. This does not bother me, I refuse still to appoint a diety to explain that which I currenty do not fully comprehend. And as for the other question in the thread, why should religion be excluded from government? It is the basic premis of all religions and faiths that "theirs" is the true faith, exclusive of all other. So which faith would you have in gov? Christian? Fair enough, perhaps Baptist so all dancing in public schools can be banned. Perhaps Mormon, and Mormon prayers can be recited in all public schools. Perhaps Catholic, we can add the Pope to the presidents advisors, or, my personal fav, Jehova Witness, now they can come to your door and sell the presidents agenda along with watchtower. I don't think you guys have really thought this through-

Hmmmm.

Religion is a right of thought. It is inseparable from the human person in much the same way that thought is inseparable from action. Your president brings to the oval office his entire thoughts. Who is to say that the actions of a sitting president is or isn't prompted by religious thoughts?

What you probably meant is the principle of separation of church and state. What it means is that the church may not wield the coercive powers of the state (civilian and military) nor can the state deprive the members of any church their right of thought.

In fact, it is the only way by which the essence of both the church and the state could rationally be separated.

And being an atheist (hence the absence of religion) doesn't excuse you since your thoughts on atheism can just as easily be imposed on other people (through the coercive powers of the state) as any church. What this all amounts to is a fundamental freedom of conscience.

 

[Dr.Who]

Hmmmm.

Religion is a right of thought. It is inseparable from the human person in much the same way that thought is inseparable from action. Your president brings to the oval office his entire thoughts. Who is to say that the actions of a sitting president is or isn't prompted by religious thoughts?

What you probably meant is the principle of separation of church and state. What it means is that the church may not wield the coercive powers of the state (civilian and military) nor can the state deprive the members of any church their right of thought.

In fact, it is the only way by which the essence of both the church and the state could rationally be separated.

And being an atheist (hence the absence of religion) doesn't excuse you since your thoughts on atheism can just as easily be imposed on other people (through the coercive powers of the state) as any church. What this all amounts to is a fundamental freedom of conscience.

Of course the president has religious thoughts. One cannot think and not have religious thoughts. Even the atheist has religious thoughts. In fact a lot of atheist think about religious thougts a lot more than your run of the mill man on the street. e.g. "Is there a God" = religious thought. "I think there is not a God'" = religious thought. "I think there is a God." = religious thought.

 

[clarkatticus]

whether or not you have faith means nothing to me. I would not spend an ounce of energy to defend Jesus, Buddha, Mohammad or Satan. I would however, fight to my last breath for your right to believe. Athiesm is more common than you think, prevalent even in our nations birth. I have no need to preach, I believe athiesm is a result of very personal reflection, not the direction of others.

 

[Dr.Who]

Resolved in what sense?

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

Antinomy (Greek αντι-, for or instead of, plus νομος, law) literally means the mutual incompatibility, real or apparent, of two laws. It is a term used in logic and epistemology.

I have been thinking of sylogisms.

Supose that one set out a sylogism:

If: A
And: B
Then: C

And another:

If: D
And: E
Then: F

We know that A, B, D, and E are all true.

But what happens when C contradicts F?

Lets analyze a paradox with that:

"This sentence is false."

A: The sentence is either true or false.
B: it is false.
C: Then it is true

That logic is faulty since it cannot be both true and false. Therefore we must change one of the assumptions. Lets try again:


A`: The sentence is either true or false.
B`: it is true.
C`: Then it is false.

That logic is faulty since it cannot be both true and false. Therefore we must change one of the assumptions.


Can we change assumption A or A`?

Can the sentence be both false and true? No.
Can it be neither false nor true? I don't know but that would solve the dillemma. Lets set that up and ask?


D: The first sylogism is not logical
E: The second sylogism is not logical
F: at least one sentence that is either true or false cannot be either.

Hmmm? That can't be.

I don't know if there are any paradoxes that we could apply this logic to and come up stumped while not making any mistakes (I can the mistake I made above). But if we do then logic must be ilogical. (kind of in the way that 2 feet +2 feet =4 feet except at light speeds or in the big bang)

I am not particularly interested in knowing if that paradox is solved or not but in knowing if there are any that have not been solved. If any one has not been solved then the door is open to the possibility that the resolution is that logic is not logical.

 

[Dr.Who]

Actually now I am a little interested in that paradox.

The answer must be that A or A` must really be:

"The sentence is not either true or false" Lets set that up:

"This sentence is false"

We analyze it thus:

G: The sentence is not either true or false.
H: The sentence is not true
I: It must be not false

Hmm? Not sure I did that right? Does "not either true or false" = "not true or not false" IF not then have to write it:

G: The sentence is not either true or false
H The sentence is not true
I: It is something other than true or false

What would that be?

 

[numinus]

whether or not you have faith means nothing to me. I would not spend an ounce of energy to defend Jesus, Buddha, Mohammad or Satan. I would however, fight to my last breath for your right to believe. Athiesm is more common than you think, prevalent even in our nations birth. I have no need to preach, I believe athiesm is a result of very personal reflection, not the direction of others.

Correct. Just saying how the separation of church and state ought to be understood. You may not impose your belief in atheism on others using the coercive force the state.

If yours courts think it is unconstitutional to teach religion in public schools, is it similarly unconstitutional for a teacher to teach atheism? That is the dilemma that arose when your judiciary over-stepped its bounds and started ruling on what can or cannot be taught in public schools.

 

[PLC1]

Correct. Just saying how the separation of church and state ought to be understood. You may not impose your belief in atheism on others using the coercive force the state.

If yours courts think it is unconstitutional to teach religion in public schools, is it similarly unconstitutional for a teacher to teach atheism? That is the dilemma that arose when your judiciary over-stepped its bounds and started ruling on what can or cannot be taught in public schools.

Public schools can not teach atheism. That would be just as unconstitutional as teaching Catholicism, or Islam, or anything else.

 

[numinus]

I have been thinking of sylogisms.

Supose that one set out a sylogism:

If: A
And: B
Then: C

And another:

If: D
And: E
Then: F

We know that A, B, D, and E are all true.

But what happens when C contradicts F?

Lets analyze a paradox with that:

"This sentence is false."

A: The sentence is either true or false.
B: it is false.
C: Then it is true

That logic is faulty since it cannot be both true and false. Therefore we must change one of the assumptions. Lets try again:


A`: The sentence is either true or false.
B`: it is true.
C`: Then it is false.

That logic is faulty since it cannot be both true and false. Therefore we must change one of the assumptions.


Can we change assumption A or A`?

Can the sentence be both false and true? No.
Can it be neither false nor true? I don't know but that would solve the dillemma. Lets set that up and ask?


D: The first sylogism is not logical
E: The second sylogism is not logical
F: at least one sentence that is either true or false cannot be either.

Hmmm? That can't be.

I don't know if there are any paradoxes that we could apply this logic to and come up stumped while not making any mistakes (I can the mistake I made above). But if we do then logic must be ilogical. (kind of in the way that 2 feet +2 feet =4 feet except at light speeds or in the big bang)

I am not particularly interested in knowing if that paradox is solved or not but in knowing if there are any that have not been solved. If any one has not been solved then the door is open to the possibility that the resolution is that logic is not logical.

That is the liar's paradox.

There are many solutions. The most practical being the limitations of language in assigning truth values.

Another solution is that one merely assumes the principle of bivalence to the statement -- the excluded middle. The more popular alternative to binary logic is involves three possible truth values -- true, false and unknown. there are also finite-valued and infinite-valued logical systems.

This is essentially what godel proved in his incompleteness theorem.

 

[numinus]

Public schools can not teach atheism. That would be just as unconstitutional as teaching Catholicism, or Islam, or anything else.

Or they can teach all philosophical schools of thought.

Teaching something does not necessarily amount to practicing it, now, does it? We are talking about institutions of LEARNING. There really is no other way to learn except through a free-for-all dialectics of ideas.