Occam's Razor V. Goddidit

[LNC]

I think the problem with the paradox is that it use finite numbers and infinite sets combined, and paradoxes will always arise from that. The paradox was intended more to show that we can't use common sense when applied to infinite sets, not to prove that actual infinite can't exist. If actual infinite cannot exist, then God cannot exist in actuality.

 

Lets say we have an infinite number of guests, but they each bring an infinite number of extra guests, they can all fit in the same hotel as well. Or lets say we have an infinite number of hotels, and only one guest. We can play with all these things for infinite time, but we'd never get to one answer. 1/0 is still undefined.

 

It is to show that an infinite cannot be instantiated into the physical world. I am not sure how you would apply this to God and show the same sort of contradiction, maybe you could show me how. Also, your first statement does not make sense as far as a defeater argument, maybe you could also give more details and a more detailed example as to why you think so. The one you provided doesn't seem to say enough to make the point.

[Ouroboros]

I think the problem with the paradox is that it use finite numbers and infinite sets combined, and paradoxes will always arise from that. The paradox was intended more to show that we can't use common sense when applied to infinite sets, not to prove that actual infinite can't exist. If actual infinite cannot exist, then God cannot exist in actuality.

 

Lets say we have an infinite number of guests, but they each bring an infinite number of extra guests, they can all fit in the same hotel as well. Or lets say we have an infinite number of hotels, and only one guest. We can play with all these things for infinite time, but we'd never get to one answer. 1/0 is still undefined.

 

It is to show that an infinite cannot be instantiated into the physical world. I am not sure how you would apply this to God and show the same sort of contradiction, maybe you could show me how.

Eh. You're not making sense here, and you're committing the fallacy of special pleading. It doesn't help your case. Basically you're giving God a free-pass from the paradox. God as the necessary exception. Without even giving a reason why God is the only necessary exception from the paradox.

 

A self-caused universe is such a necessary exception too.

 

Maybe you should who me how God is an exception before you start throwing rocks at me? Why should I prove God to not be an exception or to prove the self-caused universe to be the exception, when you yet haven't given any argument why God is the only necessary exception?

 

Also, your first statement does not make sense as far as a defeater argument, maybe you could also give more details and a more detailed example as to why you think so. The one you provided doesn't seem to say enough to make the point.

You don't make sense. And I think your arguments are circular and begging the questions. Besides you are constantly falling into the fallacy of equivocation and jumping on the band-wagon. But here's an example of why infinite and finite can collide if we try to use common sense to them, as in the hotel paradox:

 

I) 1 = 3/3

II) 3/3 = 3 * 1/3

III) 1/3 = 0.333... (infinite)

IV) 3 * 0.333...(inf) = 0.999...(inf)

.: 1 = 0.999...(inf)

 

A paradox when playing around with finite and infinite series. Division by zero is a no-no, so is talking about causes outside of a causal world, and time beyond the beginning of time. To argue an outside cause and being outside time is to divide by zero.

 

Perhaps you should give a concrete example of a non-caused, non-temporal being, with a spirit, to support your argument first, before you use that as an a priori assumption to your premises?

[LNC]

Let us assume, for the sake of argument, that this statement is correct. Occam's Razor tells us to look for the most parsimonious explanation. Yet the "goddidit" explanation is the exact opposite of parsimonious. Here is why:

 

- Positing the existence of an invisible, un-measurable, unfathomable, omnipotent being introduces logical, philosophical, and scientific problems which at the very least are equal to those posed by a godless Universe. I would argue that they are for more problematic than any of the natural explanations proposed, but it is enough to show that they are at least equal. That being the case, the introduction of such a being unnecessarily multiplies entities.

 

- Saying that the Universe cannot be uncaused but an indefinable unprovable "god" can be uncaused is illogical. If it is possible for something to exist which is uncaused, then it is just as possible for the Universe to be uncaused as it is for a "god" to be uncaused.

 

- If it it not possible for anything to exist without a cause, then "god" must also have a cause, which leads us to the infinite regression fallacy.

 

Let me address your points here:

 

- I don't think your explanation is quite accurate for how I or others would describe God, especially being unfathomable. Apparently Jesus said he was God and he was fathomable (at least somewhat so). Anyway, I really don't see what these adjectives have to do with whether God is necessary for the existence of the universe, or why it necessarily poses logical or philosophical problems. You also are assuming that positing God poses problems equal to or greater than a godless universe, yet you haven't shown evidence for that. I believe that is question-begging as that is what we are here to discuss, you cannot just assume the answer within your argument.

 

- Here again, you are engaging in question-begging by saying that God is unprovable. God by philosophical definition is an uncaused or necessary being. The question is whether he exists, which is what we are here to discuss. You are also engaged in a category error here in that physical stuff, by scientific, as well as philosophical reasoning is not eternal. First, the 2nd Law of Thermodynamics (2LOT) would indicate that matter moves toward entropy and therefore is not eternal. Second, we have the problem of actually instantiating a physical infinite to overcome. These are not limitations to which God succumbs as he is not physical and existed timelessly causally prior to the existence of the universe. I don't find philosophers who consider this a logical contradiction, but if you know of some and can point to their arguments, I would be happy to consider them. You also have yet to address the issue of an uncaused universe.

 

- Again, the limitation is that physical things don't exist without a cause. However, this issue is addressed by Leibniz in his cosmological argument. The argument rests on the idea that everything is either a necessary entity or a contingent entity. Contingent entities owe their existence to another prior entity, whereas, necessary entities do not. Another characteristic of a contingent entity is that we could imagine a world in which it could not exist, whereas, a necessary entity must exist in every possible world. The universe is clearly contingent in that there are possible worlds in which it fails to attain; whereas, God is a necessary being. There are a few different arguments that we could discuss to make this case, I would recommend that you read Alvin Plantinga's Ontological Argument. Now, I know that a lot of skeptics dismiss the ontological argument; however, Plantinga and others have made a solid case for it and it logically carries.

 

- You have not made a positive argument for your case up to this point, so I will read on and see whether you do so.

 

We most certainly do. The Universe exists. There is no empirical evidence of a causative agency for the Universe. Therefore, the data presented by the mere existence of the Universe suggests that things come into existence uncaused. The "out of nothing" part of your argument is a straw man, however - nobody is suggesting that the Universe came into existence "out of nothing." Rather, it is suggested that the Universe has always existed in some form or another, and that the current state of the Universe - with matter, time, and all the attendant laws of physics - had a discernible point of origin called the Big Bang.

 

- That is question begging. You also have no empirical data to suggest that the universe is eternal, you are merely making a metaphysical assumption here, not a scientific assertion. You cannot say that the universe exists, therefore it is eternal as that is assuming the conclusion within your argument, the classic definition of a circular argument. Unless you have data to show that the universe always existed, your statement is a faith statement.

 

This problem looms far larger for the "goddidit" hypothesis than it does for any natural explanation of the origin of the Universe. The "god" answer is purely metaphysical, not merely "suggestive" of the metaphysical. It therefore fails much more dramatically on the same grounds.

 

Both answers are purely metaphysical as you have no data to suggest that the universe is past-eternal. The question is which explanation best explains all of reality and the naturalistic one, I think, falls short in many more areas than to posit an intelligent agent. I have listed some of those before so I won't repeat myself. So far, you haven't given any reason to suggest a naturalistic explanation other than the universe exists, and that is not an explanation, it is merely an observation.

 

This illustrates a common misperception related to the idea that time "began" with the Big Bang. It appears to be logically contradictory only because of the position from which you are viewing it: you are inside a post-Big Bang Universe, in which the laws of physics cannot allow for self-causation. Yet the first instants of the Universe appear to have operated under a set of laws which violate everything we consider to be a "law of physics."

 

However, since you seem to lean more towards philosophy rather than science, I will refer you to Quentin Smith's excellent article, A Cosmological Argument for a Self-caused Universe.

 

How can you prove your assertion since we cannot measure before the Big Bang? Since you pointed me to an article by Quentin Smith rather than making the argument yourself, let me simply point you to a rebuttal of his argument rather than arguing it myself, you can find it here.

 

Again, if the introduction of hypotheses which cannot be falsified or tested is a legitimate argument, then Occam's Razor suggests that we should accept a natural explanation rather than multiplying entities by introducing a supernatural being.

 

What's more, there is no concrete answer yet agreed upon by the scientific community as to whether the Universe is past eternal. If such an answer is arrived at, it will be through observation and logic, not through the frivolous introduction of an unnecessary entity.

 

I don't see how you can argue your case since it also cannot be falsified. It seems that we would be at a stalemate in regard to applying OR by your view. I don't see in OR that one should default to a naturalistic explanation as that would not be a necessary fall back position. It is also question-begging again on your part to do so. Can you actually show me where OR would allow for this, rather than just asserting it? I would like to see you make argument evidence rather than make assertions with assumptions.

 

Hilbert's Hotel serves merely to illustrate that a subset of an infinite set can itself be infinite. It is a mathematical explanation, not a negation of the concept of infinity. Mathematics is full of paradox.

 

You have made an assertion, but not really given an explanation here. You haven't actually addressed the logical paradoxes posed by Hilbert, therefore, you haven't defeated it as a defeater. I am not talking about mathematical paradoxes, I am talking about instantiating these principles to find out if they can attain in the real world, and in this case, it seems that they cannot. I see no reason to see that they can based upon what you have said.

 

"I believe" is not a rational basis on which to base such an assertion. You have failed to demonstrate any way in which the introduction of "god" does not violate Occam's Razor.

 

You believe that just because the universe exists that it has a natural cause to explain it, without a bit of evidence to support your assertion. I don't know that you have even attempted to make a positive case for your assertion, simply attempted to defeat the argument for God as the explanation. However, it still does not mean that a natural explanation is the default fall back, there are plenty of other explanations that you would also have to knock down. It seems that you might have an easier time to make a positive case for your side rather than to try to defeat every other possible explanation out there.

[Deva]

In the hotel example, the number of guests must exceed infinity if there are not enough rooms in the hotel, and the number of rooms is infinite.

 

Help this non-math person. Am I just dense? How can the number of anything exceed infinity?

 

That's part of the contradiction of instantiating an actual infinite, infinity cannot be exceeded.

 

It says a lot that your explanation is so obscure and hard to understand. Your God can't just come out and reveal himself plainly but you must resort to a bunch of mathematical paradoxes that most people even with a college education can't get...

 

Yet if we don't believe, we all go to hell. Nice..

[Shyone]

In the hotel example, the number of guests must exceed infinity if there are not enough rooms in the hotel, and the number of rooms is infinite.

 

Help this non-math person. Am I just dense? How can the number of anything exceed infinity?

 

That's part of the contradiction of instantiating an actual infinite, infinity cannot be exceeded.

 

It says a lot that your explanation is so obscure and hard to understand. Your God can't just come out and reveal himself plainly but you must resort to a bunch of mathematical paradoxes that most people even with a college education can't get...

 

Yet if we don't believe, we all go to hell. Nice..

This whole exchange, from beginning to end, is about things that no one knows. No one. What caused the singularity? Itself or God? What's a god? The causer of the singularity. If the singularity requires a cause, why not god. Because.... BULLSHIT!

 

Everything we know, everything we have experience of, everything in the universe has a natural explanation. The universe is, by definition, "all there is." If some puny accidental energetic cosmic burp is god, so the fuck what?

 

Is this obtuse, distant, unknown and unknowable, "possibility" supposed to mean something? This is supposed to mean that Jesus died on a stick for some cosmic purpose? People, for thousands of years, have been killing each other and their children for this?

[Ouroboros]

It says a lot that your explanation is so obscure and hard to understand. Your God can't just come out and reveal himself plainly but you must resort to a bunch of mathematical paradoxes that most people even with a college education can't get...

You got it.

 

Many years ago, I believed in the First Cause/Kalaam and all these different arguments too, but I actually let go of them just because of what you said above. Why should have to resort to prove God through some intricate explanation on which the dedicated philosophers in that particular niche can't even agree? It left me with faith based on feeling the "presence" of God instead, praying, and waiting for some clear, physical evidence that God existed.

 

Yet if we don't believe, we all go to hell. Nice..

What's nice is that Kalaam was (is) a Muslim philosophical school, not a Christian. In other words, Craig borrowed from a heretic, false, and devilish religion to prove his own. Hmm...

[Deva]

Sometimes it strikes me with total force how absurd it is for an educated adult to buy any Christian doctrine as true. Supposedly the same God who created all the galaxies, black holes, stars, the incredible destructive power of nature in a supernova, volcano or hurricane, etc, etc.. We are actually supposed to believe this God is so "holy" he can't be with "sinners".

 

Oh,wait a minute, that's right, God screwed up and let the devil ruin his creation so now we have this other God (Satan) in charge, who has more power than God. Therefore what we see is no longer God's big plan or expression.

 

Since nature has been ruined by the Fall and is no longer a true expression of God, take your mathematical paradoxes elsewhere LNC. They are twisted and ruined by sin like the whole of nature [major sarcasm, folks].

[Abiyoyo]

..........snip

 

These and other reasons lead me to negate these three naturalistic explanations. Can you think of any that I have missed? Or, do you have a counter to my negation of any of these points?

 

I believe that God is necessary to explain the universe and therefore, does not violate Occam's Razor. Your thoughts?

 

Well, with this lengthy explanation and the added debating; I will say that Occam's Razor rules itself out as a possible solution, as it can be a complicated process.

 

Occam's Razor loses. Goddidit wins. Next.

[Ouroboros]

What's nice is that Kalaam was (is) a Muslim philosophical school, not a Christian. In other words, Craig borrowed from a heretic, false, and devilish religion to prove his own. Hmm...

Oh! I think...this means Craig is not committing the genetic fallacy. Yes?

I'm not sure if it's that fallacy or not, but you could be right. I think it at least points to that Kalaam doesn't prove Jesus, God, YHWH, Allah, or any of the Greek gods; even deists could use it. So lets say someone got convinced through the Kalaam argument and then converted to Islam. Would LNC see this as a victory for his argument? I think the apologists should be a little careful for what they wish for.

[Guest Davka]

Let us assume, for the sake of argument, that this statement is correct. Occam's Razor tells us to look for the most parsimonious explanation. Yet the "goddidit" explanation is the exact opposite of parsimonious. Here is why:

 

- Positing the existence of an invisible, un-measurable, unfathomable, omnipotent being introduces logical, philosophical, and scientific problems which at the very least are equal to those posed by a godless Universe. I would argue that they are for more problematic than any of the natural explanations proposed, but it is enough to show that they are at least equal. That being the case, the introduction of such a being unnecessarily multiplies entities.

 

- Saying that the Universe cannot be uncaused but an indefinable unprovable "god" can be uncaused is illogical. If it is possible for something to exist which is uncaused, then it is just as possible for the Universe to be uncaused as it is for a "god" to be uncaused.

 

- If it it not possible for anything to exist without a cause, then "god" must also have a cause, which leads us to the infinite regression fallacy.

 

Let me address your points here:

 

- I don't think your explanation is quite accurate for how I or others would describe God, especially being unfathomable. Apparently Jesus said he was God and he was fathomable (at least somewhat so). Anyway, I really don't see what these adjectives have to do with whether God is necessary for the existence of the universe, or why it necessarily poses logical or philosophical problems.

 

Well, at least you're consistent. Once again, you leap triumphantly on irrelevant semantic arguments, while completely ignoring the irrefutable core argument. You don't like the adjectives "unfathomable" and "omnipotent?" Fine, deal with the ones that actually affect the conversation: INVISIBLE and UNMEASURABLE. Do you deny that these are near-universally accepted descriptions of the Bible God?

 

You also are assuming that positing God poses problems equal to or greater than a godless universe, yet you haven't shown evidence for that. I believe that is question-begging as that is what we are here to discuss, you cannot just assume the answer within your argument.

 

Positing, Hell. I'm pointing out to you the irrefutable truth of the matter. To deny that claiming the existence of an invisible, immeasurable being is anything other than introducing a completely unnecessary entity is to deny reality. That you would even argue this point shows an incredible amount of arrogance and/or intellectual dishonesty on your part.

 

You are also engaged in a category error here in that physical stuff, by scientific, as well as philosophical reasoning is not eternal. First, the 2nd Law of Thermodynamics (2LOT) would indicate that matter moves toward entropy and therefore is not eternal.

 

Once again your ignorance is staggering. The 1st law of thermodynamics states that energy/matter/light (all the same thing according to Einstein) cannot be destroyed. It can only change form. Think about that: ENERGY = MASSC². And it cannot be destroyed. That's another way of saying that it's eternal. It will always be around. Entropy has nothing to do with that. "Lasts forever" = "is eternal." Get it?

 

Second, we have the problem of actually instantiating a physical infinite to overcome.

 

And once again I am gobsmacked by your abysmal inability to comprehend the basics of what you are talking about. Let me give you an example of this kind of mathematical paradox in the real world, and how it is overcome:

 

Let's say you wish to walk across a street. Before you can cross the street, you must first reach the halfway point. But before you reach the halfway point, you must first reach the point halfway between where you begin and the halfway point. In fact, before you reach that point, you must first reach the point halfway between where you are and it.

 

Since it will always be possible to divide the space you must first cross in half, there are an infinite number of "halfway points" between where you start out and the other side of the street. And since it is clearly impossible to ever pass through an infinite number of points, it is also clearly impossible to ever cross the street.

 

This is the same absurd logic you use to demonstrate that we cannot have passed through an infinite amount of time to reach the present. It is a variant on the Hilbert's Hotel paradox. It is a way of demonstrating mathematically that something which clearly can be accomplished is "impossible."

 

 

Again, the limitation is that physical things don't exist without a cause.

 

Unfounded assertion.

 

 

You also have no empirical data to suggest that the universe is eternal, you are merely making a metaphysical assumption here, not a scientific assertion.

 

Do you deny that assuming the existence of God is anything other than a metaphysical assumption?

 

 

So far, you haven't given any reason to suggest a naturalistic explanation other than the universe exists, and that is not an explanation, it is merely an observation.

 

Gee - the Universe is observable. "God" isn't. And yet you claim that "goddidit" is somehow a more reasonable assumption than "it was always thus"?

 

Did you even bother to read Quentin Smith's article? Or did you simple google for a refutation and post it? You claimed that nobody has made an argument for a self-caused Universe. I linked to precisely such an argument. YOU WERE WRONG.

 

The thing is, LNC, you are not willing to actually chew on, ponder, or honestly examine any argument presented here. You won't wrestle with the concepts personally - you merely spout blather and dodge questions with semantic drivel. You are not here to learn, you are here only to offer kneejerk refutations.

 

I have demonstrated a number of times that you don't know what the fuck you are talking about. You idiotically assert that 2LOT somehow negates 1LOT, a line of reasoning which would get you an F in a real school. But because you attend a school which teaches moonbeams and fairy wings, your professors will never point out the fallacy in your pathetic excuses for arguments.

 

If you were willing to really struggle with these very complex and very difficult issues, you would be worth talking to. Abiyoyo manages to do that and remain a Christian, as does end3. But your compartmentalized thinking seems to be too threatened by reality. You are a waste of time.

 

You just got pwned, smacked down, and teabagged. And you're too thick to even realize it. I'm done with you.

 

You will be added to my "ignore" list as soon as I click "Add Reply." It's been enlightening - the last time I dealt with such a severe case of obtuse ineffectual resistance to reality it was in conversation with a Jehovah's Witness. Congratulations, you win the "brainwashed cultist of the year" award.

 

Drink your kool-aid in good health.

[LNC]

I know it can be a bit to grasp, but philosophers have thought through all of these ideas and they do cohere. I don't think that it is only belief in God that requires this level of cognition; I am in a discussion group now that is wrestling with these questions in relation to the universe, man, time, morality, the mind, and other issues.

So... if philosophers have thought about this, and some of them have solid arguments for a self-caused universe... then they are wrong because they don't agree with your favorite philosopher? How does that hang together? We should believe the Craig-an philosophy to be correct, and Quentin Smith's to be wrong, on your say so? Okay. Yes, God LNC! The almighty LNC has spoken! Hark and obey. You are telling the truth, because you are the truth teller and anything you say is the truth so when you tell us the truth it must be the truth so help me LNC...

 

I am surprised that you wouldn't demand supporting empirical evidence for something being self-caused. Are we to assume that just because someone says that the universe is self-caused merely because it exists and they have a prior eliminated all other possible explanations that it has therefore happened? I don't consider that to be a strong enough argument, especially since it lacks explanatory power and scope to account for other factors such as fine tuning, existence of the mind, existence of objective morality and others. Where is the evidence for self-causation?

[Ouroboros]

I am surprised that you wouldn't demand supporting empirical evidence for something being self-caused.

Quantum events are considered by some (or many?) scientists to be self-caused. Of course we can't be sure if that's true, but at least that's more evidence than God.

 

And I'm equally surprised that you wouldn't demand supporting empirical evidence for something like a non-temporal super-being.

 

Are we to assume that just because someone says that the universe is self-caused merely because it exists and they have a prior eliminated all other possible explanations that it has therefore happened?

Back at you. Are we to assume that just because Craig says that the universe is caused by an outside non-temporal being (infinite nonetheless), and a priori eliminated all other possible explanations for causation or time, therefore he is right?

 

I don't consider that to be a strong enough argument, especially since it lacks explanatory power and scope to account for other factors such as fine tuning, existence of the mind, existence of objective morality and others.

And I don't consider a First Cause explanation based on a post hoc fallacy to be good enough argument, since it lacks explanatory paower and doesn't account for other factors or other possibilities.

 

 

Where is the evidence for self-causation?

Quantum Mechanics, but you don't believe it does.

 

Where is the evidence for a non-temporal being?

 

---edit---

 

Just an addition here, what is Free Will? Is it self-caused or is it caused by an outside force? When you use your Free Will to decided something, is God the First Cause to that particular decision, or did You cause that decision? If you caused it, isn't that a self-caused event to "will that decision into existence"?

 

To me it sounds like you are describing a complete deterministic world. Are you? If not, then what is your Free Will, if not a self-causing instrument?

[Caretaker]

Second, to instantiate an infinite would also lead to logical problemsas illustrated by David Hilbert in his Hilbert's hotel example. He setsup an illustration of a hotel with an infinite amount of rooms andevery room full...

 

In the hotel example, the number of guests must exceed infinity if there are not enough rooms in the hotel, and the number of rooms is infinite.

 

Help this non-math person. Am I just dense? How can the number of anything exceed infinity?

 

 

Math Graduate student speaking here~

 

Oh Infinity, what would math be without you?

 

Okay, keep in mind that Infinity is NOT a number, although we mathematicians are sometimes lazy and treat it as such.

 

There are some weird things that happen with infinite sets that do not happen with finite sets.

 

So when you count the number of eggs in a carton, what you are really doing is identifying some one-to-one correspondence between the following set:

 

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

 

With the set of all eggs in the carton.

 

By one-to-one correspondence, I mean, every number is associated with an egg, each egg is associated with some number, no two distinct numbers are associated with the same egg, and no two distinct eggs are associated with the same number.

 

The nature of finite sets is that if you were to add or remove at least one egg from the carton, it is impossible to find a one-to-one correspondence between the above set of numbers and the new set. It can't happen.

 

-----------------

 

We say a set is infinite if we can find some sort of correspondence (not necessarily one-to-one) from ALL natural numbers:

 

{0, 1, 2, 3, 4, 5, 6, ... }

 

To the set such that every number is associated with some element in the set, and no two distinct numbers are associated with the same element. But we do not require that every element in that set be associated with some number. In fact, if we can find some one-to-one correspondence between the natural numbers and a set, we call that set "countably infinite." Believe it or not, there is a set of numbers that is infinite, but not countable.

 

Now, let's look at a *proper* subset of the natural numbers, the even natural numbers:

 

{0, 2, 4, 6, 8, 10, ... }

 

Intuition might tell you that there are "fewer" even natural numbers than natural numbers since every even natural number is a natural number, but not every natural number is an even natural number, but in math, we consider these sets to have the same "number" of elements. They are of the same size. In math, the only question we ask when we concern when two sets have the same "number" of elements (even infinite sets) is "Can we find a one-to-one correspondence between the sets?"

 

Yes we can here:

 

0 ⟷ 0

1 ⟷ 2

2 ⟷ 4

3 ⟷ 6

4 ⟷ 8

5 ⟷ 10

...

...

...

 

Notice that in the example of Hilbert's Hotel, you have three sets:

 

The set of rooms: {R1, R2, R3, R4, R5, R6, ....}

The set of occupants: {O1, O2, O3, O4, O5, O6, ....}

The new arrival: {N}

 

When the new arrival arrives, the room assignments were as follows:

 

O1 ⟷ R1

O2 ⟷ R2

O3 ⟷ R3

O4 ⟷ R4

...

O(n) ⟷ R(n)

...

...

 

To accommodate this new person, all that needs to be done is to find a new one-to-one correspondence:

 

N ⟷ R1

O1 ⟷ R2

O2 ⟷ R3

O3 ⟷ R4

O4 ⟷ R5

...

O(n) ⟷ R(n+1)

...

...

 

Now believe this! You can even drive up with a bus with countably infinite number of passengers:

 

{P1, P2, P3, P4, ... }

 

And you can STILL accommodate these newcomers:

 

P1 ⟷ R1

O1 ⟷ R2

P2 ⟷ R3

O2 ⟷ R4

P3 ⟷ R5

O3 ⟷ R6

P4 ⟷ R7

O4 ⟷ R8

...

P(n) ⟷ R(2n-1)

O(n) ⟷ O(2n-1)

...

...

 

 

It gets even better. You can have a convoy of a countably infinite number of buses, each with a countably infinite number of passengers:

 

{B1, B2, B3, B4, B5, ....}

 

B1 contains {P1,1; P1,2; P1,3; P1,4; .... }

B2 contains {P2,1; P2,2; P2,3; P2,4; .... }

B3 contains {P3,1; P3,2; P3,3; P3,4; .... }

...

...

...

 

 

And yet, The Hilbert Hotel can still find a place for all of these people:

 

P1,1 ⟷ R1

 

P1,2 ⟷ R2

P2,1 ⟷ R3

 

P3,1 ⟷ R4

P2,2 ⟷ R5

P1,3 ⟷ R6

 

P4,1 ⟷ R7

P3,2 ⟷ R8

P2,3 ⟷ R9

P1,4 ⟷ R10

 

...

...

...

 

 

However, it is VERY POSSIBLE to have an infinite set that cannot fit inside another infinity. The lowest level of infinity is countable, that which you can assign a one-to-one correspondence with the natural numbers.

 

The Real Numbers. You know, those dreaded decimal numbers with never ending decimals that we can only approximate (pi, for instance).

 

If you suppose that you had some one-to-one correspondence between the natural numbers and real numbers between 0 and 1:

 

1 ⟷ 0.(D1,1)(D1,2)(D1,3)...

2 ⟷ 0.(D2,1)(D2,2)(D2,3)...

3 ⟷ 0.(D3,1)(D3,2)(D3,3)...

4 ⟷ 0.(D4,1)(D4,2)(D4,3)...

...

...

...

 

Where each (Dn,k) represents a decimal place, I can always find a real number that cannot possibly show up in that list:

 

0.(R1)(R2)(R3)(R4)....

 

Where R1 is not equal to D1,1, R2 is not equal to D2,2, R3 is not equal to D3,3, and so on.

 

http://www.math.utep.edu/Faculty/lesser/hotelinfinity.html

[NotBlinded]

The principal of causality itself is a metaphysical discussion LNC. Now what are you going to argue?

 

Yes it is, and it is a first principle that under girds science. I am not sure what question you are asking. Maybe you could give me more detail.

LNC, you are hopeless.

 

Here is what you said that led to me posting that:

 

I would submit that each of these explanations has logical and philosophical, as well as, scientific problems. First, we have no empirical data suggesting that things can come into existence uncaused out of nothing. It seems to suggest such an explanation would be a metaphysical suggestion rather than a scientific suggestion and it fails on the grounds of violating the principal of causality which is one of the foundational principles that under girds the whole scientific enterprise. To suggest such a thing would bring the whole enterprise into question.

You continually use metaphysical ideas in your posts and at the same time, slam others for using metaphysical ideas. You again did this to your post to Davka (#29).

 

I could say what you said above back at you and it would stand it's ground just as well if not better from a self-caused universe point of view addressing the Goddidit view. They are both metaphysical discussions, so stop with the apparent attempt to confuse others.

[Guest Davka]

Pure curiosity: I totally get the fact that you can have a countably infinite subset of an infinite set. What I was wondering, while reading through your post, is whether there could be an infinite number of countably infinite subsets?

 

For example, it seems to me that the set of real numbers would have an infinite number of countably infinite subsets. Is this accurate?

[NotBlinded]

Second, to instantiate an infinite would also lead to logical problemsas illustrated by David Hilbert in his Hilbert's hotel example. He setsup an illustration of a hotel with an infinite amount of rooms andevery room full...

 

In the hotel example, the number of guests must exceed infinity if there are not enough rooms in the hotel, and the number of rooms is infinite.

 

Help this non-math person. Am I just dense? How can the number of anything exceed infinity?

 

 

Math Graduate student speaking here~

 

What?

[Skankboy]

The key is if time is past infinite it means that an infinite amount of time would be required to reach today as a terminus; yet, an infinite amount of time cannot be crossed, so therefore, we should not be at today.

Yes but by this reasoning there's an infinite amount of space between me and the fridge (as I could take 6 feet from me to the frige and then cut it in half an infinite number of times) so I can never reach it.

 

That argument also assumes today as a terminus instead of as a point along and infinitely long line (time stretching in both directions). When seen this way, no contradiction.

 

The best answer I can give is that nothing is truly infinite. Infinite is a concept that works in some applications but that I don't believe has any parallels in actual existence.

[LNC]

Eh. You're not making sense here, and you're committing the fallacy of special pleading. It doesn't help your case. Basically you're giving God a free-pass from the paradox. God as the necessary exception. Without even giving a reason why God is the only necessary exception from the paradox.

 

A self-caused universe is such a necessary exception too.

 

Maybe you should who me how God is an exception before you start throwing rocks at me? Why should I prove God to not be an exception or to prove the self-caused universe to be the exception, when you yet haven't given any argument why God is the only necessary exception?

 

No, I don't believe that I am special pleading as we are discussing two different kinds of entities, a physical universe and a non-physical God. It is the physicality of the universe that presents the paradoxical problem. I have not argued that God is infinite in the number of parts that he contains - he has no parts. Nor have I said that God is past eternal as he existed timelessly causally prior to the existence of the universe. So, unless you can show that I have committed some sort of special pleading in relationship to God and infinites, then I don't think that your objection is valid. God is not, by definition self-caused as God is not caused at all, but then again, God is not a material being and matter does require a cause and, according to what we know of physics, cannot be past eternal as that would violate the 2nd law of thermodynamics.

 

BTW, I don't engage in rock-throwing, I am simply pointing out problems with a self-caused or past eternal universe. There is nothing intended to be personal about these arguments. The problem is that something has to be necessary, either God, the universe, or something else. The universe appears, according to all we know about it scientifically, to be contingent, so there needs to be another explanation as to what is necessary for its existence and God seems to be a valid possibility.

 

You don't make sense. And I think your arguments are circular and begging the questions. Besides you are constantly falling into the fallacy of equivocation and jumping on the band-wagon. But here's an example of why infinite and finite can collide if we try to use common sense to them, as in the hotel paradox:

 

I) 1 = 3/3

II) 3/3 = 3 * 1/3

III) 1/3 = 0.333... (infinite)

IV) 3 * 0.333...(inf) = 0.999...(inf)

.: 1 = 0.999...(inf)

 

A paradox when playing around with finite and infinite series. Division by zero is a no-no, so is talking about causes outside of a causal world, and time beyond the beginning of time. To argue an outside cause and being outside time is to divide by zero.

 

Perhaps you should give a concrete example of a non-caused, non-temporal being, with a spirit, to support your argument first, before you use that as an a priori assumption to your premises?

 

Either this is merely an apparent paradox or 1 does not really equal 1, which do you think? If 1 does not equal 1, then the law of identity is violated and therefore we have a logical problem. If one does equal one, then we have only an apparent paradox that is worked out somehow. However, your leap from this illustration to the conclusion that talking about causes outside of the causal world seems to be a non-sequitur. I am not sure how you make such a leap logically, you will have to explain that one to me. I also don't argue that time existed before the beginning of time, so that is a straw man. I also don't argue that the cause works outside of time, I argue that the cause and time work simultaneously. The cause exists causally prior to time, yet acts in conjunction with the beginning of time. IOW, his action begins time.

 

God is an example of a non-caused spiritual being who existed atemporally. He created and time began and now, according to some philosophers, exists temporally.

[LNC]

It says a lot that your explanation is so obscure and hard to understand. Your God can't just come out and reveal himself plainly but you must resort to a bunch of mathematical paradoxes that most people even with a college education can't get...

 

Yet if we don't believe, we all go to hell. Nice..

 

To say that my explanation is obscure and hard to understand to you doesn't say anything about the accuracy of the explanation, it merely says that you don't understand it. God has revealed himself many times throughout history. Most recently, he revealed himself in the person of Jesus Christ. The revelation and teachings of Jesus are understandable such that even my young daughters can grasp them. Jesus doesn't expect you to understand college level math to get to heaven, just put simple trust in him and his death and resurrection.

[LNC]

This whole exchange, from beginning to end, is about things that no one knows. No one. What caused the singularity? Itself or God? What's a god? The causer of the singularity. If the singularity requires a cause, why not god. Because.... BULLSHIT!

 

Everything we know, everything we have experience of, everything in the universe has a natural explanation. The universe is, by definition, "all there is." If some puny accidental energetic cosmic burp is god, so the fuck what?

 

Is this obtuse, distant, unknown and unknowable, "possibility" supposed to mean something? This is supposed to mean that Jesus died on a stick for some cosmic purpose? People, for thousands of years, have been killing each other and their children for this?

 

It seems that you have an a priori assumption here that no one can know and I would ask how you know that no one can know? The reason for the need of a cause of the singularity is both philosophical and scientific. The reason that God does not require a cause is philosophical (not scientific as God is not material, the realm to which science is restricted). However, there is no logical contradiction in this idea.

 

Just because everything in the universe may have a natural explanation (a statement for which I don't believe you can provide evidence since there are phenomena within the universe for which we don't currently have a natural explanation), it doesn't follow that the universe must therefore have a natural explanation since that would require either self-causation or a natural source for which we have no empirical evidence. In other words, that would be a metaphysical belief, not a scientific observation. BTW, the universe is not, by definition, all there is, it is all of the material world; however, it does not necessarily follow that the material world is all there is. Again, that would be a metaphysical belief.

 

Your final statement brings up another issue, that of the problem of evil. If this universe is all there is, then evil is just an illusion about which we should not concern ourselves. If we are accidents of nature, then there is no ultimate right or wrong, that "belief" too is just an accident of nature.

[LNC]

Sometimes it strikes me with total force how absurd it is for an educated adult to buy any Christian doctrine as true. Supposedly the same God who created all the galaxies, black holes, stars, the incredible destructive power of nature in a supernova, volcano or hurricane, etc, etc.. We are actually supposed to believe this God is so "holy" he can't be with "sinners".

 

Oh,wait a minute, that's right, God screwed up and let the devil ruin his creation so now we have this other God (Satan) in charge, who has more power than God. Therefore what we see is no longer God's big plan or expression.

 

Since nature has been ruined by the Fall and is no longer a true expression of God, take your mathematical paradoxes elsewhere LNC. They are twisted and ruined by sin like the whole of nature [major sarcasm, folks].

 

I find that if we are purely accidents of nature or products of some evolutionary process, then all beliefs are simply the result of a blind process that has been encoded into our circuitry and therefore, not necessarily correspondent with reality. That doesn't just include my beliefs, that includes yours as well. Reasoning ability is just an illusion given naturalism, both yours and mine. We are just determined by the events of our pasts and the memories stored up in our brains and how those memories output through us. So, your beliefs would be no more valid than mine.

 

Can you refute that idea?

[Ouroboros]

No, I don't believe that I am special pleading as we are discussing two different kinds of entities, a physical universe and a non-physical God.

The singularity from which the Universe came from was a non physical entity as well. At least in the sense of our present form. Time and space did not exist in the singularity. Physical only in the sense of existing and full of energy, but not time-space-matter form.

 

It is the physicality of the universe that presents the paradoxical problem. I have not argued that God is infinite in the number of parts that he contains - he has no parts. Nor have I said that God is past eternal as he existed timelessly causally prior to the existence of the universe.

There is no prior to time. The paradox argument is that there is no infinite past. No infinite past, means a beginning of time. A beginning of time means no time before that point.

 

Don't confuse the subject by throwing in false statements about the whole argument.

 

So, unless you can show that I have committed some sort of special pleading in relationship to God and infinites, then I don't think that your objection is valid.

Time didn't exist before time began. God didn't exist before time began.

 

Unless, time did exist before the Universe, and the paradox is wrong.

 

God is not, by definition self-caused as God is not caused at all, but then again, God is not a material being and matter does require a cause and, according to what we know of physics, cannot be past eternal as that would violate the 2nd law of thermodynamics.

Multiverse and panes would. Besides, I just saw some comment in some article recently which stated that quantum mechanics seems to break the laws of thermodynamics.

 

BTW, I don't engage in rock-throwing, I am simply pointing out problems with a self-caused or past eternal universe.

And past the universe exists eternal time. Time which cannot exist. A contradiction.

 

There is nothing intended to be personal about these arguments. The problem is that something has to be necessary, either God, the universe, or something else. The universe appears, according to all we know about it scientifically, to be contingent, so there needs to be another explanation as to what is necessary for its existence and God seems to be a valid possibility.

Or a multiverse with bubble-universes.

 

Either this is merely an apparent paradox or 1 does not really equal 1, which do you think? If 1 does not equal 1, then the law of identity is violated and therefore we have a logical problem.

Nothing is wrong with the argument except that it switches between common sense thoughts about infinite series and finite values. It shows the danger of mixing finite and infinite thoughts.

 

[quote

If one does equal one, then we have only an apparent paradox that is worked out somehow. However, your leap from this illustration to the conclusion that talking about causes outside of the causal world seems to be a non-sequitur.

It's targeting the approach how to understand infinite v finite paradoxes. Don't trust your senses. Mysteries exist. The world is a mystery, but it's not solved by inventing new mysteries. God is just a way of replacing one paradox or mystery, with a new one.

 

I am not sure how you make such a leap logically, you will have to explain that one to me. I also don't argue that time existed before the beginning of time, so that is a straw man.

You said, "until," and you use terms like "before." They are temporal terms. There is no zero in the natural numbers set. There is no number before 1. So if you say "before" or "until" then you're talking about a temporal God.

 

I also don't argue that the cause works outside of time, I argue that the cause and time work simultaneously. The cause exists causally prior to time, yet acts in conjunction with the beginning of time. IOW, his action begins time.

Right. So time began when he acted. The cause and time started simultaneous. Which means, there were no time before that cause. Also, God did not cause anything else before that time, since it was the First Cause, not the second, or third. He never caused a Heaven before the Universe. Neither did he cause any thoughts, ideas, planning, or design charts for his new Universe, because those are processes, which require temporal steps.

 

God is an example of a non-caused spiritual being who existed atemporally. He created and time began and now, according to some philosophers, exists temporally.

And I believe the singularity replaces your God, and quantum mechanics replaces your atemporal entity. A non-sentient and real existence of the true cause of the Universe.

 

Put it this way: God minus sentience = Natural First Cause. All attributes you give God, can be given to a multiverse.

[LNC]

What's nice is that Kalaam was (is) a Muslim philosophical school, not a Christian. In other words, Craig borrowed from a heretic, false, and devilish religion to prove his own. Hmm...

 

Oh! I think...this means Craig is not committing the genetic fallacy. Yes?

 

Phanta

 

You are correct. It doesn't matter from where an idea comes, it matters whether it is valid. Good observation.

[LNC]

..........snip

 

These and other reasons lead me to negate these three naturalistic explanations. Can you think of any that I have missed? Or, do you have a counter to my negation of any of these points?

 

I believe that God is necessary to explain the universe and therefore, does not violate Occam's Razor. Your thoughts?

 

Well, with this lengthy explanation and the added debating; I will say that Occam's Razor rules itself out as a possible solution, as it can be a complicated process.

 

Occam's Razor loses. Goddidit wins. Next.

 

I think that what I was attempting to show is that the God hypothesis does not violate OR since explanations from naturalism don't appear to have enough scope and explanatory power to account for all the data. On the other hand, I do believe that having an intelligent agent does account for the data without multiplying explanations beyond necessity.

[LNC]

I'm not sure if it's that fallacy or not, but you could be right. I think it at least points to that Kalaam doesn't prove Jesus, God, YHWH, Allah, or any of the Greek gods; even deists could use it. So lets say someone got convinced through the Kalaam argument and then converted to Islam. Would LNC see this as a victory for his argument? I think the apologists should be a little careful for what they wish for.

 

Here, I would agree with you. Theists don't use Kalam in isolation to prove the God of the Bible as it is not sufficient to do so. However, it does, I believe, get us to an intelligent agent as the cause of the universe, which is how William Lane Craig and others use it. It is part of a cumulative case argument that includes the design argument, the moral argument, and the argument for the resurrection, each of which takes us a step closer to the God of the Bible as revealed through Jesus Christ.