Prove that God doesn't exist.

[numinus]

Your own links support what I have said.

The are assumed, taken for granted, taken to be true, assumption. All words from your links.

They are not 'assumptions' in the common meaning of the word because they cannot be otherwise.

 

[Dr.Who]

They are not 'assumptions' in the common meaning of the word because they cannot be otherwise.

I doubt many people are going to buy into that.

Axioms are assumed to be true without proof. That's that.

 

[numinus]

The link indicates that set theory was created to be a theory without paradox. Though it does not say that it succeeded.

For example, set theory is said to not contain a universal set. It has no way to describe everything.

I surmise then that the sentence "the sum of all the parts equals the whole" would be nonsense in set theory. I bet we could build a paradox from that.

Nevertheless, just because set theory MIGHT not contain contain paradoxes does not mean that paradoxes do not exist. It also does not mean that unsolved paradoxes don't exist.

You mean transfinite heirarchy?

What axiomatization does is restrict predicates to set membership -- thereby eliminating self-referencing fallacies. That's all.

 

[numinus]

I doubt many people are going to buy into that.

Axioms are assumed to be true without proof. That's that.

You are playing word games. It is 'without proof' simply because there isn't anything prior to it with which you can fashion a formal proof. And it is 'assumed' precisely because there is no formal proof.

Being 'assumed' or 'without proof' doesn't diminish its truth value. It is self-evidently true. You simply cannot assume otherwise.

 

[Dr.Who]

You mean transfinite heirarchy?

What axiomatization does is restrict predicates to set membership -- thereby eliminating self-referencing fallacies. That's all.

Without going to a math dictionary I don't understand that. Would you mind using layman's terms?

 

[Dr.Who]

You are playing word games. It is 'without proof' simply because there isn't anything prior to it with which you can fashion a formal proof. And it is 'assumed' precisely because there is no formal proof.

Being 'assumed' or 'without proof' doesn't diminish its truth value. It is self-evidently true. You simply cannot assume otherwise.

Being without proof it very well may be true. But it just might be wrong too. So yes you can assume otherwise.

You can build a lot of " if then " statements assuming that the prepositions are true. But at the end of the day you could just as easily have built a whole other set of prepositions where you assumed the opposite. When you are done you can even compare the two sets to see which is more useful. But you still wont know that your assumptions are true.

 

[dogtowner]

You are playing word games.

now that's really funny !

 

[numinus]

Being without proof it very well may be true. But it just might be wrong too. So yes you can assume otherwise.

You can build a lot of " if then " statements assuming that the prepositions are true. But at the end of the day you could just as easily have built a whole other set of prepositions where you assumed the opposite. When you are done you can even compare the two sets to see which is more useful. But you still wont know that your assumptions are true.

One cannot merely assume some premise and build an entire logical system from it because sooner or later, a wrong premise will lead to a logical fallacy -- a conclusion that contradicts its premise.

I have already given set theory as an example. In naive set theory, it was supposed that one may invoke any predicate to govern any set (unrestricted comprehension). At first, the question whether any set is the subset of itself is fairly self-evident -- it is. Unfortunately, such a naive assertion leads to russell's paradox.

 

[numinus]

now that's really funny !

I try to be as accurate and concise as possible in my posts. I'm sorry you don't see that.

 

[numinus]

Without going to a math dictionary I don't understand that. Would you mind using layman's terms?

Hmmm...

You define a particular set by saying 'the set of all x such that x is so and so', do you not?

'....such that x is so and so...' is the predicate -- the rules that say whether a particular thing is or isn't a member of that set.

In naive set theory, it was supposed that one can apply any conceivable predicate to govern any set. The problem arose when one merely assumed that any set is a subset of itself.

The barber's paradox (a variant of russell's paradox after the mathematician bertrand russell) states that a particular barber only shaves those who do not shave themselves. The question is who shaves the barber? If he doesn't shave himself, then he is compelled to shave himself. If he shaves himself, then he ought not to shave himself. It is a self-referencing paradox.

 

[Dr.Who]

Hmmm...

You define a particular set by saying 'the set of all x such that x is so and so', do you not?

'....such that x is so and so...' is the predicate -- the rules that say whether a particular thing is or isn't a member of that set.

In naive set theory, it was supposed that one can apply any conceivable predicate to govern any set. The problem arose when one merely assumed that any set is a subset of itself.

The barber's paradox (a variant of russell's paradox after the mathematician bertrand russell) states that a particular barber only shaves those who do not shave themselves. The question is who shaves the barber? If he doesn't shave himself, then he is compelled to shave himself. If he shaves himself, then he ought not to shave himself. It is a self-referencing paradox.

So are you saying that set theory has a paradox. i.e. an apparent logical fallacy?

 

[Dr.Who]

One cannot merely assume some premise and build an entire logical system from it because sooner or later, a wrong premise will lead to a logical fallacy -- a conclusion that contradicts its premise.

That is exactly what science and philosophy do and paradoxes are apparently those logical fallacies.

I have already given set theory as an example. In naive set theory, it was supposed that one may invoke any predicate to govern any set (unrestricted comprehension). At first, the question whether any set is the subset of itself is fairly self-evident -- it is. Unfortunately, such a naive assertion leads to russell's paradox.

If it has a paradox then until said paradox is resolved it might just mean that the logic falls apart at some point.

 

[numinus]

So are you saying that set theory has a paradox. i.e. an apparent logical fallacy?

The problem, as I have already mentioned, is unrestricted comprehension. The paradox arises from a self-referencing fallacy -- hence the need to formally state axioms.

 

[numinus]

That is exactly what science and philosophy do and paradoxes are apparently those logical fallacies.



If it has a paradox then until said paradox is resolved it might just mean that the logic falls apart at some point.

Russell's paradox is resolved by axiomatic set theory.

 

[Dr.Who]

The problem, as I have already mentioned, is unrestricted comprehension. The paradox arises from a self-referencing fallacy -- hence the need to formally state axioms.

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