First order logic, set theory and God

[I_am_not_mafia]

" ... to explain how the universe was created by something external to it."


That's an ill-founded claim. I, neither Hatcher, have stated that the cause was external to V(universe or reality), if you had read carefully, you'd see that G is either a component or a subsystem of V and hence internal (part of) to V, while being different from V itself; G ≠ V. On that basis, your idea of a "larger external universe" containing another universe - is bogus, nonsensical and to be categorically dismissed.

Ah right that makes a lot more sense.

The universe was created by something inside the universe before the universe existed.

Got it!

The reason why casaulity is used in hatcher's proof is because it attempts to articulate the ultimate origin of existence. Thermodynamics doesn't. All it does is it explains the entropy of thermal energy and its conservation within the universe, and for that reason it falls flat at demonstrating the existence of a metaphysical reality.

There is no evidence for a metaphysical reality. Nor is there any reason to suggest that one exists.

Thermodynamics on the other hand explains why everything within the universe has formed the way it has.

So if you are going to cherry pick any thing from inside the universe to explain what was happening before its existence, why pick a ' logical and relational principle' rather than a universal physical law?

[polymath257]

Once again, what allows you to construct the system V in this 'proof'? What set theory are you using?

The problem is that sets of the type of V are *known* to not be constrictible in most standard set theories: they lead to inconsistencies like Russell's paradox or Cantor's paradox. They are 'too big' to be sets.

So, unless you give *first order* axioms allowing for the construction of your system V, you have no proof.

Good luck.

Next, your axiom of sufficiency is way, way too strong. In all likelihood, the *most* that we can say is that all *finite* phenomena have causes (whether themselves or another). But, if this is the case, then there is no guarantee your system V (even if you can construct it) will have a cause since it is likely that V is an infinite system.

Also, remember that constructing infinite systems is not a first order process in general.

The way the proof avoids Russell's paradox boils down to how concepts are defined and classified.


It is crucial to understand that with respect to composition, we have a hierarchy of complexity.

Let us define the words - componential as the attribute of being a component and composite as the attribute of having components.

1- At the lowest level is the componential non-composite entity A which is a component but does not have any component, such that x∉A∈B, for some B.

2- Next, are componential composite entity A which both have components and are components, such that E∈A∈B, for some E and B,

3- Finally, you have the non-componential composite entity A which have components but is never a component of anything, such that B∈A∉x, for some B.


Now according to the above definitions, V can be defined as the whole of reality which is that non-componential composite entity whose components are precisely all existing entities who are necessarily componential and can either be composite or non-composite.

Now according to Russell's paradox, the pertinent question to ask ourselves is if V as the set of all existing componential entities, a componential entity itself and therefore a member of that set?

Well no, since by the very definition of V, it has already been established that it is non-componential. But then one might ask " how can we know that V is non-componential and hence not a component of anything ? " Well because if we assumed V to be componential, then by definition it cannot be the set of all existing componential entities as one will commit the error of Russell's paradox where V becomes a member of the set of all componential entities. Therefore V∈V.

Alternatively we ask, can V as an non-componential entity be the set of all componential entities ? Yes, because non-componential and componential are two distinct categories and thus V can become the set of all existing componential entitities without becoming a member of that set. On that basis, we have completely disqualified V as a universal sets of all sets(and therefore Russell's paradox is not an issue anymore) by restricting V as a set of all sets that satisfies the property that every entity A  of a set is componential.  


As for your argument about the principle of suffiency - your notion V being an infinite system requiring no cause is a baseless assumption, and I would even further argue, that such an assumption can be nullified by the very fact that V is composite. Since we can admit that V does not even exist until all its components exist, then it begs the question as to when will V ever be formed if it would take an infinite amount of time for it components to come into existence ? Never. Thus to entertain V as an infinite system is tantamount to the denial of it's very existence.

Well, V is an abstract set, so is not something that needs to come into existence (you haven't included time in your formal system). And, once again, you have not given an axiom that allows for the construction of V.
Now, your argument fails in the case of an infinite regress: it always exists as an infinite regress, so does not have to 'come into existence'. In fact, if we have an infinite regress, let S be the system of all entities in that infinite regress. Then S cannot be caused because any cause would have to come before that regress, which is impossible.

So, once again, your P1 is brought into question in the case of infinite collections.

This doesn't show that ALL infinite collections have no cause, but it does show that all infinite collections that contain an infinite regress are without causes.

Again, a much more reasonable version of P1 is to assume that all finite systems are caused, but leave open the issue of infinite systems. This is a minimal extension of what we can hope to know or verify and so is a more reasonable assumption to make than the stronger version you choose.

Furthermore, because of the question of infinite regresses (which are certainly a possibility), the version of P1 you adopt is likely to be false.

With this modification, you have the issue of determining whether your collection V is finite or infinite. Only in the former case are you guaranteed a cause.

[Amarok]

The way the proof avoids Russell's paradox boils down to how concepts are defined and classified.


It is crucial to understand that with respect to composition, we have a hierarchy of complexity.

Let us define the words - componential as the attribute of being a component and composite as the attribute of having components.

1- At the lowest level is the componential non-composite entity A which is a component but does not have any component, such that x∉A∈B, for some B.

2- Next, are componential composite entity A which both have components and are components, such that E∈A∈B, for some E and B,

3- Finally, you have the non-componential composite entity A which have components but is never a component of anything, such that B∈A∉x, for some B.


Now according to the above definitions, V can be defined as the whole of reality which is that non-componential composite entity whose components are precisely all existing entities who are necessarily componential and can either be composite or non-composite.

Now according to Russell's paradox, the pertinent question to ask ourselves is if V as the set of all existing componential entities, a componential entity itself and therefore a member of that set?

Well no, since by the very definition of V, it has already been established that it is non-componential. But then one might ask " how can we know that V is non-componential and hence not a component of anything ? " Well because if we assumed V to be componential, then by definition it cannot be the set of all existing componential entities as one will commit the error of Russell's paradox where V becomes a member of the set of all componential entities. Therefore V∈V.

Alternatively we ask, can V as an non-componential entity be the set of all componential entities ? Yes, because non-componential and componential are two distinct categories and thus V can become the set of all existing componential entitities without becoming a member of that set. On that basis, we have completely disqualified V as a universal sets of all sets(and therefore Russell's paradox is not an issue anymore) by restricting V as a set of all sets that satisfies the property that every entity A  of a set is componential.  


As for your argument about the principle of suffiency - your notion V being an infinite system requiring no cause is a baseless assumption, and I would even further argue, that such an assumption can be nullified by the very fact that V is composite. Since we can admit that V does not even exist until all its components exist, then it begs the question as to when will V ever be formed if it would take an infinite amount of time for it components to come into existence ? Never. Thus to entertain V as an infinite system is tantamount to the denial of it's very existence.

Well, V is an abstract set, so is not something that needs to come into existence (you haven't included time in your formal system). And, once again, you have not given an axiom that allows for the construction of V.
Now, your argument fails in the case of an infinite regress: it always exists as an infinite regress, so does not have to 'come into existence'. In fact, if we have an infinite regress, let S be the system of all entities in that infinite regress. Then S cannot be caused because any cause would have to come before that regress, which is impossible.

So, once again, your P1 is brought into question in the case of infinite collections.

This doesn't show that ALL infinite collections have no cause, but it does show that all infinite collections that contain an infinite regress are without causes.

Again, a much more reasonable version of P1 is to assume that all finite systems are caused, but leave open the issue of infinite systems. This is a minimal extension of what we can hope to know or verify and so is a more reasonable assumption to make than the stronger version you choose.

Furthermore, because of the question of infinite regresses (which are certainly a possibility), the version of P1 you adopt is likely to be false.

With this modification, you have the issue of determining whether your collection V is finite or infinite. Only in the former case are you guaranteed a cause.

And again poly you lay down the law against people who repeat the oft unsupported nonsense apologists trot out about an infinite regress . It's almost as bad as their unsupported assertions about nothing .

[DeistPaladin]

Likely he's moved on to another skeptic forum to do his cut-and-paste dump.

I think I should move on as well.

Good luck to all.

Theists need to understand a certain fatigue with debating the same rehashed arguments over and over. "Oh, here we go with this bullshit again". Sometimes it's easier to laugh and be dismissive about the same PRATTs ("Previously Refuted A Thousand Times") than to engage them as you might like, especially when delivered in the obnoxious manner that "The Pompous Apologist" archetype is fond of using.

[T0 Th3 M4X]

I think I should move on as well.

Good luck to all.

Theists need to understand a certain fatigue with debating the same rehashed arguments over and over. "Oh, here we go with this bullshit again". Sometimes it's easier to laugh and be dismissive about the same PRATTs ("Previously Refuted A Thousand Times") than to engage them as you might like, especially when delivered in the obnoxious manner that "The Pompous Apologist" archetype is fond of using.

I don't think it's a "theistic problem", but rather a "people problem."  When I was in college, there were probably about 2 pages of logical fallacies that were considered to be of importance and to be wary of when public speaking.  Now there are literally books loaded with new fallacies people have come up with to push or parry arguments.  Part of me says it's out of necessity, and the other half of me says it's because people have forgotten what it means to be civil.  When I go to the grocery store, I can't tell who the Christians, Muslims, or atheists are, but we're all there for the same purpose.  Nobody gets mad at anybody unless you give someone a reason to.  If people would apply that same type of courtesy to discussions, then there would be more understanding of different views.

[Pat Mustard]

Sorry, but I don't apply circular logic to my thinking, so I can't agree with your statement.

Not knowing (for me) means I can't declare. 

And if you can't decide you are then best off provisionally accepting the null hypothesis, which is in this case is "there is no god". Claiming that god exists is a positive claim, it is making a prediction about reality which must both agree with what we currently know and also be predictive of future or future discovered phenomena existing in reality.

No one single person has been able to show any evidence for the god assertion*.

*Generally in science you have hypotheses and theories. Personally I think there should be four 1) assertions, which are just personal prejudices, 2) conjectures, which have some basis in reality but have not been examined for factuality, 3) hypotheses, which generally agree with what we do know but haven't been tested for predictiveness and finally 4) theories which have gone through the whole gamut of falsification methods and are still standing. You'll notice that 3 and 4 are (as I describe them) pretty close to what the scientific community treat them as, whereas 1 & 2 are not generally mentioned.

PS the rest of your post is pure unadulterated bullshit. We both know that you want the situation to be "if there is anything we don't know about the universe then god must be the answer", we both know you're not looking for evidence, because you already have the answer and are afraid that you'll lose it.

[T0 Th3 M4X]

Sorry, but I don't apply circular logic to my thinking, so I can't agree with your statement.

Not knowing (for me) means I can't declare. 

And if you can't decide you are then best off provisionally accepting the null hypothesis, which is in this case is "there is no god".  Claiming that god exists is a positive claim, it is making a prediction about reality which must both agree with what we currently know and also be predictive of future or future discovered phenomena existing in reality.

No one single person has been able to show any evidence for the god assertion*.

*Generally in science you have hypotheses and theories.  Personally I think there should be four 1) assertions, which are just personal prejudices, 2) conjectures, which have some basis in reality but have not been examined for factuality, 3) hypotheses, which generally agree with what we do know but haven't been tested for predictiveness and finally 4) theories which have gone through the whole gamut of falsification methods and are still standing. You'll notice that 3 and 4 are (as I describe them) pretty close to what the scientific community treat them as, whereas 1 & 2 are not generally mentioned.

I don't have to claim either.  If I do, I have to substantiate a value of 0 (atheism) or 1+ (theism)

There are already 4 (or more) Hypotheses, Theories, Laws, Facts.

Your statement that, "No one single person has been able to show any evidence for the god assertion." isn't a scientific statement.  Here are some obvious flaws with it...

-It's redundant (although probably the least significant flaw.  One single person?  Isn't it assumed it's a value of 1?  Unless you mean it's a single person that isn't in a romantic relationship, but I'm assuming that's not what you're talking about.  "Any evidence" is also redundant. If you just need a value of 1 "any" doesn't need to be there.  You should just say, "show evidence for the god assertion.

-You can't substantiate your claim.  How do you know?  You haven't shown how you know this.  Is everybody is supposed to assume that you've searched and exhausted every possibility counter to your own belief?

- Accepting a null hypothesis isn't necessarily conclusive, although it can be assumed if you make the same observation enough times.  In scientific study, you're attempting to determine "relationship", then assign a value to that relationship.  Maybe if you're accepting the null hypothesis your research parameters were poor.  Regardless, you haven't shown any study that does any of this.

-Additionally your statement is inclusive of all people past and present.  Are we supposed to assume you created a time machine and observed all of them?

[unfogged]

There are already 4 (or more) Hypotheses, Theories, Laws, Facts.

Are those in order? Are you implying that a theory becomes a law and that facts are somehow more definite than either?

If so, that's not how scientists would use those terms. Hypotheses are proposed to explain facts and laws and develop into theories when the evidence is strong enough.

[T0 Th3 M4X]

There are already 4 (or more) Hypotheses, Theories, Laws, Facts.

Are those in order?  Are you implying that a theory becomes a law and that facts are somehow more definite than either?

If so, that's not how scientists would use those terms.  Hypotheses are proposed to explain facts and laws and develop into theories when the evidence is strong enough.

No particular order. I was just typing them up as fast as I could for the sake of responding.

[brewer]

Still no god yet, damn.