Is god infinite? (Q for theists)

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Is god infinite? (Q for theists)

 Just a quick question while taking a break from studying for exams. Smiling


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 I don't see any logical

 I don't see any logical reason why God 'must' be infinite, even within the pathetic 'logic' of theology. Very large OK, but infinite? 

Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality

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I can see why they would

I can see why they would claim 'infinite'; because it gives more wriggle room.


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Di66en6ion wrote: Just a

Di66en6ion wrote:

 Just a quick question while taking a break from studying for exams. Smiling

 

Which god? and infinite in what way?


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Ciarin wrote:Di66en6ion

Ciarin wrote:

Di66en6ion wrote:

 Just a quick question while taking a break from studying for exams. Smiling

 

Which god? and infinite in what way?

Christian god is probably the rubric but others are welcome, I'm really only interested in the concise definition of infinity that's given to these supposed beings.


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Di66en6ion wrote:Ciarin

Di66en6ion wrote:

Ciarin wrote:

Di66en6ion wrote:

 Just a quick question while taking a break from studying for exams. Smiling

 

Which god? and infinite in what way?

Christian god is probably the rubric but others are welcome, I'm really only interested in the concise definition of infinity that's given to these supposed beings.

 

I don't think the christian god exists. None of my gods are infinite in the traditional sense(as in they exist infinitely, or their power is infinite). I think time and space are probably infinite though.


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Yes and No.

Depends on how you define it, and in what sense.  Whatever caused the universe had to be infinite in one sense.  i.e. if you subscribe to the universe explodes and contracts and then explodes again (big bang repeat for eternity), then the universe is infinite in that sense.  If you subscribe to multiple universes, the mechanism for churning out the universes has to have an infinite time, or at the very least there has to be an infinite regress to a cause of some sort, be it natural or otherwise.

As far as God, I believe the christian God is infinite in a similar sense.  If he is to be considered the cause, he has to either be infinite or a link in the chain of an infinite regress. 

Also the God who would fit the description of the bible would have to be of infinite power.  However, that is not really a measurement that can be called infinite.  As there are still limitations to it given you can't do something that is contradictory.  i.e. he can't create a weight that he can't lift. 

So yeah.. infinite is a difficult term.


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Juman wrote:Depends on how

Juman wrote:

Depends on how you define it, and in what sense.  Whatever caused the universe had to be infinite in one sense.  i.e. if you subscribe to the universe explodes and contracts and then explodes again (big bang repeat for eternity), then the universe is infinite in that sense.  If you subscribe to multiple universes, the mechanism for churning out the universes has to have an infinite time, or at the very least there has to be an infinite regress to a cause of some sort, be it natural or otherwise.

As far as God, I believe the christian God is infinite in a similar sense.  If he is to be considered the cause, he has to either be infinite or a link in the chain of an infinite regress. 

Also the God who would fit the description of the bible would have to be of infinite power.  However, that is not really a measurement that can be called infinite.  As there are still limitations to it given you can't do something that is contradictory.  i.e. he can't create a weight that he can't lift. 

So yeah.. infinite is a difficult term.

The Universe does not 'have to be' infinite in any sense - this is something that would have to be determined by empirical investigation, although it may never be possible to detect, or infer, directly, or indirectly, whatever may have preceded the Big Bang.

Also, 'infinite regress' of a causal chain does not necessarily imply infinite total duration or extent - if each 'cause' in a chain is smaller in energy and duration than the following, then the total may easily be finite, in the same way that the sum of the infinite series of numbers,  1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + ...  = 2.

So an infinite entity is not logically required as a 'creator' or 'first cause' of the universe, and anyway cannot serve as the Ultimate cause of existence, since if the universe requires a cause, so does something even more powerful. Since there is no scientific impossibilty about our entire universe emerging from a point, or near pointlike structureless quantity of raw energy, 'God' is simply an unnecessary hypothesis - if there is one, it requires an explanation even more than does the Universe.

 

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what kind of infinite?

Di66en6ion wrote:

 Just a quick question while taking a break from studying for exams. Smiling

I suppose the answer all depends on how one defines infinite.

There are different "kinds" of infinity such as an actual infinite vs a potential infinite, a qualitative infinite vs a quantitative infinite, and cardinality of infinite numbers.

So...where do we start?

 

 

 

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I get all happy like a

I get all happy like a school girl every time I get to post this.

1) The probability of any entity's existence can be calculated.

2) Complexity is inversely proportional to probability.

3) Monotheistic gods are commonly defined by possession of infinite attributes: they are all-powerful, all-knowing, and/or all-good.

4) An infinite attribute is necessarily infinitely complex.

5) Therefore, Gods with infinite attributes are infinitely complex.

6) Therefore, Gods with infinite attributes are infinitely improbable.

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BobSpence1 wrote: I don't

BobSpence1 wrote:

 I don't see any logical reason why God 'must' be infinite, even within the pathetic 'logic' of theology. Very large OK, but infinite? 

If any axiom gives crediance to the absurdity to the infinite it would be entropy, and only a fool would ignore this.

God is as finite as our species and will die like any thought our pets have when they die.

Humans think they are "hot shit" but fail to consider the fact that we were not always around, and that we will not always be around.

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god is make believe

god, whatever flavor you choose, is make believe and so can't be anything existing in reality.


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Kavis wrote:I get all happy

Kavis wrote:

I get all happy like a school girl every time I get to post this.

6) Therefore, Gods with infinite attributes are infinitely improbable.

Define infinitely improbable. The axiom of choice in set theory suggests that it is possible to choose an item in a well ordered infinite set. In that case, the probability is still nonzero. Some would contend that infinitesimal probability would necessitate belief (in the Pascalian sense) because the prospect of infinite payoff and the prospect of possible evidence such a deity existence is enough to warrant such a belief.

 

 

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The Wager Again???

ubuntuAnyone wrote:

Kavis wrote:

I get all happy like a school girl every time I get to post this.

6) Therefore, Gods with infinite attributes are infinitely improbable.

Define infinitely improbable. The axiom of choice in set theory suggests that it is possible to choose an item in a well ordered infinite set. In that case, the probability is still nonzero. Some would contend that infinitesimal probability would necessitate belief (in the Pascalian sense) because the prospect of infinite payoff and the prospect of possible evidence such a deity existence is enough to warrant such a belief.

  

 

And they'd be wrong.  I calculated it out using thermodynamics at one point, and the infinitude of the improbability (exponential in time) overwhelms the infinitude of the reward (linear in time), so the expected payoff is zero.

 

a, b, c = constants

t = time

e = euler's number

Probability as a function of time:  a*e^(-bt)  <-- based on thermodynamics

Reward as a function of time: c*t  <-- heaven isn't getting any better than it currently is, so we get a constant (c) reward per unit time.

Expected payoff: limit as t approaches infinity (since heaven is eternal) of Probability*Reward, which is 0 regardless of what values are assigned to a, b, and c.

 

Also, see the sticky about Pascal's Wager.

 

 

 

For those who answer the OP with "yes," what is the cardinality of this god's infinitude?

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Infinitely improbable does

Infinitely improbable does not imply zero probability.  If I had meant "impossible", I would have said "impossible".  An infinitely complex entity would necessarily require infinitely complex causes, either at the initial onset of the entity or over its history.  If at the onset, why would we prefer an infinitely complex self-creation of an omnideity, who then goes on to create the merely finitely complex universe? If during the history of God, why should we prefer the omnideity-as-work-in-progress (and a work that will be eternally in progress)? I doubt a finite creator would satisfy the thirst for God in very many theists anyway.

The improbability proof is merely intended to demonstrate that however unlikely the course of events in the history of the universe (its state change during the BB, the rise of life and then intelligence, etc), those events are infinitely more likely to have occurred without the intervention of some omnideity than with such an intervention. 

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Subdi Visions wrote:god,

Subdi Visions wrote:

god, whatever flavor you choose, is make believe and so can't be anything existing in reality.

 

Prove it.


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Zaq wrote:And they'd be

Zaq wrote:

And they'd be wrong.  I calculated it out using thermodynamics at one point, and the infinitude of the improbability (exponential in time) overwhelms the infinitude of the reward (linear in time), so the expected payoff is zero.

a, b, c = constants

t = time

e = euler's number

Probability as a function of time:  a*e^(-bt)  <-- based on thermodynamics

Reward as a function of time: c*t  <-- heaven isn't getting any better than it currently is, so we get a constant (c) reward per unit time.

Expected payoff: limit as t approaches infinity (since heaven is eternal) of Probability*Reward, which is 0 regardless of what values are assigned to a, b, and c.

Pardon me for asking, but what does what does thermodynamics have to do with infinite payoff? I fail to see the connection.

Second, if c is infinite, then any finite constant multiplied times c would result in c. If c = ∞, then c * t = ∞, so time is irrelevant.

 

 

 

 

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No no dear girl!

Ciarin wrote:

Subdi Visions wrote:

god, whatever flavor you choose, is make believe and so can't be anything existing in reality.

 

Prove it.

         We as atheists do NOT   have to prove ZERO.   You believe there is some kind of god hanging around,  that means you get to PROVE IT!!

 

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Jeffrick wrote:Ciarin

Jeffrick wrote:

Ciarin wrote:

Subdi Visions wrote:

god, whatever flavor you choose, is make believe and so can't be anything existing in reality.

 

Prove it.

         We as atheists do NOT   have to prove ZERO.   You believe there is some kind of god hanging around,  that means you get to PROVE IT!!

 

 

Calm down there chief. When someone makes a claim(be it atheist or theist), the burden of proof is on the claimant.

 

The claim: "god is make believe"

 

So, prove it. Atheists are not exempt. Atheism doesn't mean you get to make claims without backing them up.


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Ciarin wrote:Jeffrick

Ciarin wrote:

Jeffrick wrote:

Ciarin wrote:

Subdi Visions wrote:

god, whatever flavor you choose, is make believe and so can't be anything existing in reality.

 

Prove it.

         We as atheists do NOT   have to prove ZERO.   You believe there is some kind of god hanging around,  that means you get to PROVE IT!!

Calm down there chief. When someone makes a claim(be it atheist or theist), the burden of proof is on the claimant.

The claim: "god is make believe"

 

So, prove it. Atheists are not exempt. Atheism doesn't mean you get to make claims without backing them up.

Not quite the way it should work. If the claim is about the existence of something which is not 'obviously' a real thing,  the burden of proof is on the one claiming it does exist.

Otherwise, if I claim there is not a teapot orbitting Saturn, it would be up to me to prove it, or similarly disprove any other crazy claim someone could dream up. Now if the claim was that the Sun did not exist, that would require proof from the claimant. So that simple 'rule' about the burden being on the claimant is not workable in general. There are going to be fuzzy areas where both sides reckon their position is 'obviously' true, where each side probably should have to justify their claim, with the main burden, if any, on the person who started the discussion.

Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality

"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris

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BobSpence1 wrote:Ciarin

BobSpence1 wrote:

Ciarin wrote:

Jeffrick wrote:

Ciarin wrote:

Subdi Visions wrote:

god, whatever flavor you choose, is make believe and so can't be anything existing in reality.

 

Prove it.

         We as atheists do NOT   have to prove ZERO.   You believe there is some kind of god hanging around,  that means you get to PROVE IT!!

Calm down there chief. When someone makes a claim(be it atheist or theist), the burden of proof is on the claimant.

The claim: "god is make believe"

 

So, prove it. Atheists are not exempt. Atheism doesn't mean you get to make claims without backing them up.

 

Not quite the way it should work. If the claim is about the existence of something which is not 'obviously' a real thing,  the burden of proof is on the one claiming it does exist.

 

It's obviously real to many people. The burden of proof is still on the one making the claim.

 

If I made the claim a god exists, the burden of proof would be on me. If I make the claim that a god is pretend, the burden of proof is still on me.

 

Quote:

Otherwise, if I claim there is not a teapot orbitting Saturn, it would be up to me to prove it, or similarly disprove any other crazy claim someone could dream up.
  Except, you can actually provide evidence that the only things orbitting saturn are it's natural satellites and rings. I've heard the teapot argument before, btw. It's not really a good idea to compare mythological beings to tangible items. A better analogy would be that it would be up to you to prove an invisible pink unicorn is make believe, which would be impossible to accomplish. 
Quote:
Now if the claim was that the Sun did not exist, that would require proof from the claimant. So that simple 'rule' about the burden being on the claimant is not workable in general.
 The burden still remains on the claimant regardless of their ability to prove their claim. 
Quote:
There are going to be fuzzy areas where both sides reckon their position is 'obviously' true, where each side probably should have to justify their claim, with the main burden, if any, on the person who started the discussion.

 

 

My point of requesting proof that "god is make believe" was to get the claimant to admit that he can't know this for sure, because it's not provable. He might not accept a god belief for lack of evidence, but he can't accurately determine if any of these gods exist or not.

 


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I still stand by the

I still stand by the position that the "burden of proof" should not automatically fall on the person making the claim, it also depends on the nature of the claim. Positive claims of the existence of a thing that is not immediately and directly observable should reasonably bear the burden of proof, unless there are already well-established arguments and evidence which support the claim.

If I knew someone had a belief that the Sun is an illusion, I would not feel any onus to prove it wasn't, regardless of who raised the issue first.

For a somewhat more realistic example, if I confront a 'Flat Earther', or someone with similar sort of belief, I would regard it as far more defensible that the Burden of Proof is on them, even if I am the one to raise the issue and claim their position is nonsense.

If two people hold different positions on some issue that they both care about, "burden of proof" should only depend on which one which position has the weakest prima facie justification or general acceptance in the relevant group. There may well be no such clear agreed balance either way, so talk about "burden of proof" is just delaying and confusing the debate.

It should also not be about proof in the strict sense, that is also a distraction, since normally neither side has strict 'proof'. 

 

Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality

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Ciarin

            I put the burdon of proof on any claiment

, reguardless of who started the post.       You have made a claim that some kind of god thing exists, so prove it.

 

         My only claim is zero on top of zero:  there is nothing for me to prove ( 0 = 0  ).

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Jeffrick

Jeffrick wrote:

            I put the burdon of proof on any claiment

, reguardless of who started the post.       You have made a claim that some kind of god thing exists, so prove it.

 

         My only claim is zero on top of zero:  there is nothing for me to prove ( 0 = 0  ).

 

Show me where I made that claim.


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Cairin

 

 

       You are a theist,  if not then tell the ones who put theist under your name on the left.   You believe in some kind of god according to what you write on this site. Weather you proclaim it or not is of little interest to me  but it leaves you with a position to put up or shut up.  Now I have read your earlier posts where you claim to believe even though you have no evidence or other proofs to back up your beliefs,  yet  you still believe.

 

 

       I personaly have zero beliefs,  and no reason to believe zero is anything other then zero. Your version of zero versus anyone elses version of zero is of no interest to me 0 = 0, irreguardless of what you or any theist thinks zero is.  If you or anyother theist truely believes there is something other then zero out there;   YOU GET TO PROVE IT!!!

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Jeffrick

Jeffrick wrote:

 

 

       You are a theist,  if not then tell the ones who put theist under your name on the left.   You believe in some kind of god according to what you write on this site. Weather you proclaim it or not is of little interest to me  but it leaves you with a position to put up or shut up.  Now I have read your earlier posts where you claim to believe even though you have no evidence or other proofs to back up your beliefs,  yet  you still believe.

 

 

       I personaly have zero beliefs,  and no reason to believe zero is anything other then zero. Your version of zero versus anyone elses version of zero is of no interest to me 0 = 0, irreguardless of what you or any theist thinks zero is.  If you or anyother theist truely believes there is something other then zero out there;   YOU GET TO PROVE IT!!!

 

I don't make the claim that the existence of my gods is objective fact.

 

So nothing for me to prove, chief. Irreguardless isn't a word, btw.

 

 

so, the claim "god is make believe" still needs to be be proven, or else the claimant needs to admit it cannot be proven and it's not a factual claim. Just an opinion.


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ubuntuAnyone wrote:Zaq

ubuntuAnyone wrote:

Zaq wrote:

And they'd be wrong.  I calculated it out using thermodynamics at one point, and the infinitude of the improbability (exponential in time) overwhelms the infinitude of the reward (linear in time), so the expected payoff is zero.

a, b, c = constants

t = time

e = euler's number

Probability as a function of time:  a*e^(-bt)  <-- based on thermodynamics

Reward as a function of time: c*t  <-- heaven isn't getting any better than it currently is, so we get a constant (c) reward per unit time.

Expected payoff: limit as t approaches infinity (since heaven is eternal) of Probability*Reward, which is 0 regardless of what values are assigned to a, b, and c.

Pardon me for asking, but what does what does thermodynamics have to do with infinite payoff? I fail to see the connection.

Second, if c is infinite, then any finite constant multiplied times c would result in c. If c = ∞, then c * t = ∞, so time is irrelevant.

We used the second law of thermodynamics to determine the probability of a system not drifting towards thermodynamic equilibrium (which would certainly not be heavenly) as a function of time.

Time is relevant for the mathematics.  In order to deal with infinities you need to use limits.  So you can't just have c = infinity (btw, how do you get the symbol?).  You may be able to use transfinite numbers, but I don't have any experience working with those.  Your best bet is to take the limit as both c and t approach infinity, which unfortunately is undefined.  So we get either an expected payoff of 0 in the case that c is finite or an undefined expected payoff in the case that c is infinite.  Either way it breaks Pascal's Wager (which argues for at least a positive expected payoff).

Note that the above exercise was mainly an attempt to figure out where the Wager went wrong.  I had already performed a refutation by overload, but that kind of refutation just tells you that an argument is flawed, not how it's flawed.  Our conclusion was that Pascal's Wager doesn't handle the infinities in a mathematically rigorous way, which causes a false conclusion.

Questions for Theists:
http://silverskeptic.blogspot.com/2011/03/consistent-standards.html

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Ciarin wrote:I don't make

Ciarin wrote:

I don't make the claim that the existence of my gods is objective fact.

 

So nothing for me to prove, chief. Irreguardless isn't a word, btw.

 

 

so, the claim "god is make believe" still needs to be be proven, or else the claimant needs to admit it cannot be proven and it's not a factual claim. Just an opinion.

But Ciairn, you believe in these gods.  How can you believe that they exist yet not believe that their existence is objective fact?

If you refuse to claim that your gods exist then why do you believe that they exist?

 

Always placing the burden of proof on the claimant doesn't work.  Suppose I make a claim.  You then say that the burden of proof is on me, but I don't actually need to prove my claim unless someone disagrees.  But once someone voices disagreement, they've made their own claim, a claim that my claim is wrong.  Then the burden of proof would be on both of us, which doesn't make any sense.

 

I claim that your gods do not exist.  The burden of proof is on you due to Occam's Razor.  Unless you demonstrate otherwise, your gods are unnecessary assumptions with no predictive power and thus their existence ought not to be assumed.

Questions for Theists:
http://silverskeptic.blogspot.com/2011/03/consistent-standards.html

I'm a bit of a lurker. Every now and then I will come out of my cave with a flurry of activity. Then the Ph.D. program calls and I must fall back to the shadows.


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Zaq wrote:Ciarin wrote:I

Zaq wrote:

Ciarin wrote:

I don't make the claim that the existence of my gods is objective fact.

 

So nothing for me to prove, chief. Irreguardless isn't a word, btw.

 

 

so, the claim "god is make believe" still needs to be be proven, or else the claimant needs to admit it cannot be proven and it's not a factual claim. Just an opinion.

But Ciairn, you believe in these gods.  How can you believe that they exist yet not believe that their existence is objective fact?

Because there isn't any evidence that their existence is objective fact, aside from anecdotal evidence(which isn't reliable).

 

Quote:

If you refuse to claim that your gods exist then why do you believe that they exist?

 

Because of my experiences. I interpret my experiences to indicate their existence. I just can't prove it to anyone else.

 

Quote:

Always placing the burden of proof on the claimant doesn't work.  Suppose I make a claim.  You then say that the burden of proof is on me, but I don't actually need to prove my claim unless someone disagrees.  But once someone voices disagreement, they've made their own claim, a claim that my claim is wrong.  Then the burden of proof would be on both of us, which doesn't make any sense.

 

The burden of proof would be on the original claimant, and the secondary claimant and it makes sense to me.

 

Claim 1: "The sky is blue".

Claim 2: "The sky is not blue".

 

Both would have to back up their claim.

 

Quote:

I claim that your gods do not exist.  The burden of proof is on you due to Occam's Razor.  Unless you demonstrate otherwise, your gods are unnecessary assumptions with no predictive power and thus their existence ought not to be assumed.

 

I don't require you to assume their existence. I've never made the claim that they exist objectively. The only claim I make is that I believe in them. To call them make believe like the previous poster did is to indicate that I don't really believe in them, I'm just pretending to. I'd like him to prove that. I doubt he's able to do it.

 

You can make the claim that gods do not exist, unfortunately you can not disprove the existence of deities(if I'm wrong please correct me), so your claim can not be absolutely certain. It would be more accurate to say you find no credible or reasonable evidence of a deity therefore you conclude gods probably don't exist. Which most atheists tend to say, in my experience.


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BobSpence1 wrote:Juman

BobSpence1 wrote:

Juman wrote:

Depends on how you define it, and in what sense.  Whatever caused the universe had to be infinite in one sense.  i.e. if you subscribe to the universe explodes and contracts and then explodes again (big bang repeat for eternity), then the universe is infinite in that sense.  If you subscribe to multiple universes, the mechanism for churning out the universes has to have an infinite time, or at the very least there has to be an infinite regress to a cause of some sort, be it natural or otherwise.

As far as God, I believe the christian God is infinite in a similar sense.  If he is to be considered the cause, he has to either be infinite or a link in the chain of an infinite regress. 

Also the God who would fit the description of the bible would have to be of infinite power.  However, that is not really a measurement that can be called infinite.  As there are still limitations to it given you can't do something that is contradictory.  i.e. he can't create a weight that he can't lift. 

So yeah.. infinite is a difficult term.

The Universe does not 'have to be' infinite in any sense - this is something that would have to be determined by empirical investigation, although it may never be possible to detect, or infer, directly, or indirectly, whatever may have preceded the Big Bang.

Also, 'infinite regress' of a causal chain does not necessarily imply infinite total duration or extent - if each 'cause' in a chain is smaller in energy and duration than the following, then the total may easily be finite, in the same way that the sum of the infinite series of numbers,  1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + ...  = 2.

So an infinite entity is not logically required as a 'creator' or 'first cause' of the universe, and anyway cannot serve as the Ultimate cause of existence, since if the universe requires a cause, so does something even more powerful. Since there is no scientific impossibilty about our entire universe emerging from a point, or near pointlike structureless quantity of raw energy, 'God' is simply an unnecessary hypothesis - if there is one, it requires an explanation even more than does the Universe.

 

I would like to examine your regress argument.  It seems that you are operating on a few assumptions:

A1: The change in time (t) can be made arbitrarily small.

A2: The energy E of an event can be arbitrarily small.

Now, since we are talking of an inifinite regress, the series must go backward with t->0 and E->0.  Let us describe the required sequence of events as {... e-2, e-1, e0}, where e0 is a the latest event in the causal chain.  By your description, then, each ei has a diminishing duration and energy as one moves backward in the sequence.  But if each en-1 is the cause of en then would not this violate conservation of energy?  How would an event of less energy cause an event of greater energy?

 

What is more, if each subsequent event increases in time and energy, then the duration of time for an event and the energy of the event should go to infinity as t goes to infinity.  Unless, of course, you are suggesting that the change in time and Energy converge.  Nevertheless, this seems to be a clear problem with your theory. The real issue seems to be that you have not addressed the problem of having an actual infinite (physically speaking) nor have you addressed the problem of traversing the infinite.

 

Next, you say: "So an infinite entity is not logically required as a 'creator' or 'first cause' of the universe, and anyway cannot serve as the Ultimate cause of existence, since if the universe requires a cause, so does something even more powerful."

 

What you have here is a non-sequitur.  It does not follow that if the universe requires a cause, so does something even more powerful.  Firts, what do you mean by "more powerful"?  Second, the universe is a contingent entity and so requires a cause.  Necessary things, like logic, (perhaps) numbers, etc. do not require a cause, they just are.  IF God exists, then God must be a necessary being, which does not require a cause.

 

"Since there is no scientific impossibilty about our entire universe emerging from a point, or near pointlike structureless quantity of raw energy, 'God' is simply an unnecessary hypothesis - if there is one, it requires an explanation even more than does the Universe."

 

Here I think you have missed the point.  The question is not whether it is possible for the universe to arise from a singularity, but rather whether or not it is impossible for it to do so all by itself.


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Zaq wrote:We used the second

Zaq wrote:

We used the second law of thermodynamics to determine the probability of a system not drifting towards thermodynamic equilibrium (which would certainly not be heavenly) as a function of time.

This assumes that systems have entropy. What if a system had zero entropy? If there is a heaven, then it is presumably perfect, and a perfect system would not be drifting towards any sort of thermodynamic equilibrium.

Zaq wrote:

Time is relevant for the mathematics.  In order to deal with infinities you need to use limits.  So you can't just have c = infinity (btw, how do you get the symbol?).  You may be able to use transfinite numbers, but I don't have any experience working with those.  Your best bet is to take the limit as both c and t approach infinity, which unfortunately is undefined.  So we get either an expected payoff of 0 in the case that c is finite or an undefined expected payoff in the case that c is infinite.  Either way it breaks Pascal's Wager (which argues for at least a positive expected payoff).

If we take a limit, then we are never actually dealing with the infinite, in much the same way we never actually deal with irrational numbers (such as pi or natural logarithms) but rather estimates. But we can at least project what the results would be symbolically, such as expressing numbers in terms of pi or or natural logarithms. The same hold for the infinite. But if one wants to deal with finite numbers, all I have to do is suppose some arbitrarily large or small number to offset any given function in my favor.

Zaq wrote:

Note that the above exercise was mainly an attempt to figure out where the Wager went wrong.  I had already performed a refutation by overload, but that kind of refutation just tells you that an argument is flawed, not how it's flawed.  Our conclusion was that Pascal's Wager doesn't handle the infinities in a mathematically rigorous way, which causes a false conclusion.

How did you "overload" the Wager?

What mathematical system deos handle infinities in a mathematically rigorous way? Paradoxes crop up all over the places when one starts consider infinties.

While the Wager does deal with probabilities, its function was game theory applied to pragmatic justfication for belief in a diety. It does not gaurantee the results are true, but it does serve as a heuristic of sort to eliminate middle ground.

PS...To get the infinity symbol (in Windows anyways) Start -> Run -> and type in "charmap". Look for the infinity symbol then copy and paste it into your doc.

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Di66en6ion wrote: Just a

Di66en6ion wrote:

 Just a quick question while taking a break from studying for exams. Smiling

If you are referring to the God of Christian theology, then yes. 


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QED wrote:BobSpence1

QED wrote:

BobSpence1 wrote:

Juman wrote:

Depends on how you define it, and in what sense.  Whatever caused the universe had to be infinite in one sense.  i.e. if you subscribe to the universe explodes and contracts and then explodes again (big bang repeat for eternity), then the universe is infinite in that sense.  If you subscribe to multiple universes, the mechanism for churning out the universes has to have an infinite time, or at the very least there has to be an infinite regress to a cause of some sort, be it natural or otherwise.

As far as God, I believe the christian God is infinite in a similar sense.  If he is to be considered the cause, he has to either be infinite or a link in the chain of an infinite regress. 

Also the God who would fit the description of the bible would have to be of infinite power.  However, that is not really a measurement that can be called infinite.  As there are still limitations to it given you can't do something that is contradictory.  i.e. he can't create a weight that he can't lift. 

So yeah.. infinite is a difficult term.

The Universe does not 'have to be' infinite in any sense - this is something that would have to be determined by empirical investigation, although it may never be possible to detect, or infer, directly, or indirectly, whatever may have preceded the Big Bang.

Also, 'infinite regress' of a causal chain does not necessarily imply infinite total duration or extent - if each 'cause' in a chain is smaller in energy and duration than the following, then the total may easily be finite, in the same way that the sum of the infinite series of numbers,  1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + ...  = 2.

So an infinite entity is not logically required as a 'creator' or 'first cause' of the universe, and anyway cannot serve as the Ultimate cause of existence, since if the universe requires a cause, so does something even more powerful. Since there is no scientific impossibilty about our entire universe emerging from a point, or near pointlike structureless quantity of raw energy, 'God' is simply an unnecessary hypothesis - if there is one, it requires an explanation even more than does the Universe.

 

I would like to examine your regress argument.  It seems that you are operating on a few assumptions:

A1: The change in time (t) can be made arbitrarily small.

A2: The energy E of an event can be arbitrarily small.

Now, since we are talking of an inifinite regress, the series must go backward with t->0 and E->0.  Let us describe the required sequence of events as {... e-2, e-1, e0}, where e0 is a the latest event in the causal chain.  By your description, then, each ei has a diminishing duration and energy as one moves backward in the sequence.  But if each en-1 is the cause of en then would not this violate conservation of energy?  How would an event of less energy cause an event of greater energy?

One event triggering an event which releases far more energy than the triggering even has nothing to do with conservation of energy. Think of the energy in your finger pulling the trigger relative to the energy released by the explosive in the gun barrel...

The energy released does not have to come exclusively from the trigger event. It merely has to exist, perhaps it accumulated from various sources over time. Think of the water accumulated behind a dam - opening the spillway releases far more energy than the immediate cause of the release.

How about  the chain reaction in an atomic bomb? The energy released by the fission caused by the impact of a single neutron is vastly more than the energy of the neutron.

As long as there is available energy, the energy involved in the immediate cause of a specific event does not have to be intrinsically greater that the actual energy released.

Actually, a truly infinite regress is not going to occur or be necessary, since once the 'event' is around the Planck scale of energy, it just merges into the background random uncertainty of quantum mechanics, which also allows it to occur at any 'arbitrary' time over an indefinitely large time-scale, without requiring anything more than this background 'randomness' of what is sometimes conceived of as "quantum foam".

Quote:

What is more, if each subsequent event increases in time and energy, then the duration of time for an event and the energy of the event should go to infinity as t goes to infinity.  Unless, of course, you are suggesting that the change in time and Energy converge.  Nevertheless, this seems to be a clear problem with your theory. The real issue seems to be that you have not addressed the problem of having an actual infinite (physically speaking) nor have you addressed the problem of traversing the infinite.

That is just trying to restate the original regression. If my original idea of tracing back a chain of decreasing events back in time is valid, which you have not disproved, then going forward is not going to change the math.

Quote:

Next, you say: "So an infinite entity is not logically required as a 'creator' or 'first cause' of the universe, and anyway cannot serve as the Ultimate cause of existence, since if the universe requires a cause, so does something even more powerful."

What you have here is a non-sequitur.  It does not follow that if the universe requires a cause, so does something even more powerful.  Firts, what do you mean by "more powerful"?  Second, the universe is a contingent entity and so requires a cause.  Necessary things, like logic, (perhaps) numbers, etc. do not require a cause, they just are.  IF God exists, then God must be a necessary being, which does not require a cause.

That whole statement is a non-sequitur.

OK anything 'greater' in any sense, energy perhaps, certainly structure and complexity.

Logic is not an entity, it is a set of relationships, so simply 'is'. Not relevant to actual entities containing structured 'substance' of any kind.

The last sentence simply demonstrates that 'God' is a problematic concept - implying it doesn't exist.

Quote:

"Since there is no scientific impossibilty about our entire universe emerging from a point, or near pointlike structureless quantity of raw energy, 'God' is simply an unnecessary hypothesis - if there is one, it requires an explanation even more than does the Universe."

 

Here I think you have missed the point.  The question is not whether it is possible for the universe to arise from a singularity, but rather whether or not it is impossible for it to do so all by itself.

You have missed the point. Nothing can give rise to itself. Quantum-level observations show that events sufficiently small in energy or momentum terms apparently can spontaneously occur. Given specific circumstances, they can ultimately cause much larger releases of energy. You need to get your head around this fact. This is all that is required. 

Unless you want to postulate that every radioactive decay or virtual particle event is specifically 'caused' by God, with him taking care that the timing is such as to appear perfectly random...

EDIT: The probability of an event occurring spontaneously, or a particle spontaneously popping into existence, for even a short time, is a rapidly decreasing function of its mass/energy and the duration it remains in existence. So the probability of an infinite eternal entity spontaneously coming into existence is infinitely negligible compared to a finite BB singularity...

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BobSpence1 wrote:From the

BobSpence1 wrote:

From the sublime to the ridiculous: Science -> Philosophy -> Theology

This has nothing to do with anything here, but why that order?

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ubuntuAnyone

ubuntuAnyone wrote:

BobSpence1 wrote:

From the sublime to the ridiculous: Science -> Philosophy -> Theology

This has nothing to do with anything here, but why that order?

Science is our best source of real insights from reality, continually surprising us with unexpected insights into the nature of both the external Universe, and the capabilities and limitations of our own minds.

In the case of Theology, I very much agree with the words of Sam Harris I also quote in my sig.

I see Philosophy as covering the whole spectrum in between. Some philosophy usefully extrapolates from various scientific fields into the speculative and subjective world of ideas related to the 'hard' insights from various sciences. At the other end it merges with the purely imaginary nonsense of Theology. In between it occasionally comes up with some ideas which may help us think about the nature of life and different ways to live it, but just as often, if not more, leads us off into worse than useless verbal nonsense. I say worse than useless because it typically leads away form real understanding, riddled with obsolete concepts and 'arguments'.

I read a lot of philosophy a long time ago, and I still have a few 'heroes', such as Bertrand Russell, David Hume, and Daniel Dennett. But I have repeatedly contrasted more and more really exciting discoveries and theories at the frontiers of Science with sterile discussions on the same general topics from Philosophers whose understanding is decades to centuries behind...

Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality

"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris

The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me

From the sublime to the ridiculous: Science -> Philosophy -> Theology


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BobSpence1 wrote:Science is

BobSpence1 wrote:

Science is our best source of real insights from reality, continually surprising us with unexpected insights into the nature of both the external Universe, and the capabilities and limitations of our own minds.

I see Philosophy as covering the whole spectrum in between. Some philosophy usefully extrapolates from various scientific fields into the speculative and subjective world of ideas related to the 'hard' insihts from various sciences. At the other end it merges with the purely imaginary nonsense of Theology. In between it occasionally comes up with some ideas which may help us think about the nature of life and different ways to live it, but just as often, if not more, leads us off into worse than useless verbal nonsense. I say worse than useless because it typically leads away form real understanding, riddled with obsolete concepts and 'arguments'.

I read a lot of philosophy a long time ago, and I still have a few 'heroes', such as Bertrand Russell, David Hume, and Daniel Dennett. But I have repeatedly contrasted more and more really exciting discoveries and theories at the frontiers of Science with sterile discussions on the same general topics from Philosophers whose understanding is decades to centuries behind...

I suppose I'd put philosophy before science....I guess I find it hard to do science without doing good philosophy...that is what make good science, good science and distinguishes it keep psuedo-science and junk science, and just plain nonsense.

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ubuntuAnyone wrote:

BobSpence1 wrote:

Science is our best source of real insights from reality, continually surprising us with unexpected insights into the nature of both the external Universe, and the capabilities and limitations of our own minds.

I see Philosophy as covering the whole spectrum in between. Some philosophy usefully extrapolates from various scientific fields into the speculative and subjective world of ideas related to the 'hard' insihts from various sciences. At the other end it merges with the purely imaginary nonsense of Theology. In between it occasionally comes up with some ideas which may help us think about the nature of life and different ways to live it, but just as often, if not more, leads us off into worse than useless verbal nonsense. I say worse than useless because it typically leads away form real understanding, riddled with obsolete concepts and 'arguments'.

I read a lot of philosophy a long time ago, and I still have a few 'heroes', such as Bertrand Russell, David Hume, and Daniel Dennett. But I have repeatedly contrasted more and more really exciting discoveries and theories at the frontiers of Science with sterile discussions on the same general topics from Philosophers whose understanding is decades to centuries behind...

I suppose I'd put philosophy before science....I guess I find it hard to do science without doing good philosophy...that is what make good science, good science and distinguishes it keep psuedo-science and junk science, and just plain nonsense.

It becomes a question of semantics or definition. You can consider questions of methodology of science part of science, or part of the "philosophy of science". I do consider that "Philosophies of" some other more specific discipline the most defensible forms of philosophy, but that makes them secondary aspects of other disciplines.

The requirements of replication, peer-review, etc, are what filters out bad or junk science.

'Philosophy' as an independent discipline lacks its own such check on its arguments and conclusions. That makes it intrinsically incomplete, but it also allows it to come up with new ideas without inhibition. So it occasionally generates concepts which find real application -  logic and math stand out, but they are now their own fields.

I see "junk philosophy' much more of a problem than "junk science", because Philosophy, by its necessarily open nature, lacks the specific tools that Science employs to weed out "junk science"

I see it as an area of speculation, but until the ideas are checked against reality, they have no claim to truth. Once you start testing ideas, that is merging into Science.

 

Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality

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From the sublime to the ridiculous: Science -> Philosophy -> Theology


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Re: Ciarin

How is believing in X any different than believing that X is true?  What I'm getting (correct me if I'm wrong) is that you believe that certain gods exist but you do not believe that their existence is objective fact.  Does this mean that you believe that their existence is subjective, in that they exist for some people and not for others?  Or are you just differentiating between believe and claim?  If you believe in gods but are unable or unwilling to claim that their existence is true then this just sounds like an unfounded and unconfident belief.

 

Ciarin wrote:

Both would have to back up their claim.

But this means that both sides have the "burden of proof" in all cases, which makes "burden of proof" useless terminology.

 

In a complete lack of evidence, nonexistence is the default due to Occam's Razor.  Therefore it is up to the claimant of existence to provide evidence proving existence.  The only "evidence" required for the nonexistence claim is a lack of evidence for existence.

 

I suppose I should modify my innitial claim.  Using the same reasoning as before, I claim that either your gods do not exist or they are meaningless.

 

Re: ubuntu

Using the second law of thermodynamics assumes that the system is capable of having entropy.  I think a system with constant zero entropy would have to be completely empty.

 

ubuntuAnyone wrote:

If we take a limit, then we are never actually dealing with the infinite, in much the same way we never actually deal with irrational numbers (such as pi or natural logarithms) but rather estimates. But we can at least project what the results would be symbolically, such as expressing numbers in terms of pi or or natural logarithms. The same hold for the infinite. But if one wants to deal with finite numbers, all I have to do is suppose some arbitrarily large or small number to offset any given function in my favor.

Limits are one of the very fundamental ways that mathematcis handles infinity.  Infinite sums are calculated by taking the limit of the sequence of partial sums, and can be used to solve things like Zeno's Paradox.  The problem is that Pascal noticed the infinite reward and then said obviously we have a positive (probably infinite) expected payoff without doing the proper math (which may not have even been developed at the time).  But if the probability is infinitely small, then you have a case of infinity over infinity which could result in infinite, finite, zero, or simply undefined.

No matter how large one makes c, or how small one makes a and b, if a, b, and c are all finite and positive (forgot to label them as positive constants earlier, my bad) then the limit is zero.  If c is infinite then the limit is nonexistant.  Either way Pascal's conclusion does not follow.

 

ubuntuAnyone wrote:

What mathematical system deos handle infinities in a mathematically rigorous way?

From what I've learned, limits and cardinality.  Paradoxes crop up all over the place when infinities aren't handled properly (for instance, Zeno's Paradox), but math can make sense of at least some previously paradoxical infinity-involving statements.

 

ubuntuAnyone wrote:

How did you "overload" the Wager?

 

Nicholas Yee wrote:

The being we call god is merely a pawn working for a powerful and rational force in some far-off galaxy.  This force is trying to weed out people who are irrational by seeing who would be stupid enough to believe in his god illusion so easily.  Those that believe in this illusion, he will send to eternal damnation and he will deliver the rational beings, those who stoically refused to believe in a god, to heaven.

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By Pascal's own reasoning, no matter how improbable the above statement is, the infinitude of the possible reward and punishment implies that everyone should be an atheist.

1: Assume Pascal's Wager works

2: Note that neither the deific God nor the pawn God can be disproven, and thus neither has a zero probability.

3: Conclude that theism offers a higher expected payoff than atheism (same reasoning as Pascal's Wager)

4: In the same way, conclude that atheism offers a higher expected payoff than theism

5: We have just reached a contradiction.  Conclude that something is wrong with Pascal's Wager

 

EDIT:  I have no idea why it spit out formating junk, but it doesn't appear in the editor so I have no idea how to get rid of it.  Must've been the result of my copy-paste.

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http://silverskeptic.blogspot.com/2011/03/consistent-standards.html

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BobSpence1 wrote:It becomes

BobSpence1 wrote:

It becomes a question of semantics or definition. You can consider questions of methodology of science part of science, or part of the "philosophy of science". I do consider that "Philosophies of" some other more specific discipline the most defensible forms of philosophy, but that makes them secondary aspects of other disciplines.

The requirements of replication, peer-review, etc, are what filters out bad or junk science.

'Philosophy' as an independent discipline lacks its own such check on its arguments and conclusions. That makes it intrinsically incomplete, but it also allows it to come up with new ideas without inhibition. So it occasionally generates concepts which find real application -  logic and math stand out, but they are now their own fields.

I see "junk philosophy' much more of a problem than "junk science", because Philosophy, by its necessarily open nature, lacks the specific tools that Science employs to weed out "junk science"

I see it as an area of speculation, but until the ideas are checked against reality, they have no  claim to truth. Once you start testing ideas, that is merging into Science. 

Science in and of itself is good at making discoveries, but what we do with those discoveries...that's when, at least in my evaluation, science stops and discussions become more philosophical. For example, science discovered how to harness nuclear fission. In and of itself, fission is nothing more than a natural process, but what one does with it...that's where I think science is ill equipped to handle such things. The science behind nuclear warfare is the same science behind a cheap, viable energy source. One could laud one and decry the other, but this to me hardly seems scientific. What mechanism does science, strictly speaking, have to make ethical judgments about such things? This is but an example, as I think there are other areas. Even judging the utility of science as reason for embracing it does not really seem to be all that scientific, unless of course we want to broaden our definition of science.... which then goes back to what I was getting at: what defines good science?

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Zaq wrote:Using the second

Zaq wrote:

Using the second law of thermodynamics assumes that the system is capable of having entropy.  I think a system with constant zero entropy would have to be completely empty.


Either that, or its unlike the world as we know it. I suppose theists would say it was the latter. Another possibility is that the there is no thermodynamic limit in heaven, that is the 1st law does not exist.  A god, being omnipotent, could supply limitless amounts of energy in a higher state and destroy energy that reaches a lower state.

Zaq wrote:

Limits are one of the very fundamental ways that mathematcis handles infinity.  Infinite sums are calculated by taking the limit of the sequence of partial sums, and can be used to solve things like Zeno's Paradox.  The problem is that Pascal noticed the infinite reward and then said obviously we have a positive (probably infinite) expected payoff without doing the proper math (which may not have even been developed at the time).  But if the probability is infinitely small, then you have a case of infinity over infinity which could result in infinite, finite, zero, or simply undefined.

No matter how large one makes c, or how small one makes a and b, if a, b, and c are all finite and positive (forgot to label them as positive constants earlier, my bad) then the limit is zero.  If c is infinite then the limit is nonexistant.  Either way Pascal's conclusion does not follow.


Limits don't really solve Zeno's Paradox...they avoid it. Limits were imposed to compensate for the would be infinite regresses caused by things like division my zero or multiplication by infinity. One can do integrations, derivatives, and differential equations all day long, but to actually get some sort tangible results for such things, one has to impose limits. By definition, you're right, the infinite does not have a limit, but that's the point. In the Pensees Pascal does grapple with the infinite, and realizing how difficult it is to grasp the infinite, he went to a second mode of justification, namely pragmatic justification, for belief in a god.


Zaq wrote:

2: Note that neither the deific God nor the pawn God can be disproven, and thus neither has a zero probability.

Don't really need this...Why wager if one has this?

Zaq wrote:

4: In the same way, conclude that atheism offers a higher expected payoff than theism


I'm not really sure how an atheist would conclude this, unless you're supposing there is some sort of infinite eschatological reward for atheists.
 

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ubuntu, the conclusion that

ubuntu, the conclusion that atheism offers a higher expected payoff comes from the quote I put up.  The idea is that the atheist can easily turn the wager around by saying that maybe there's some rational being that will reward us infinitely for NOT believing in God.  Number 2 is necessary because from 1 and 2 we conclude 3 and 4 and thus arrive at a contradiction.

 

I'm aware that theists will simply claim that thermodynamics doesn't apply to heaven, but then the probability of heaven's existence just becomes unknown, which still causes the wager to fail by generating an unknown payoff.  Anyway, the main point was to demonstrate that an infinite reward does not necessarily indicate a positive expected payoff.

 

Zeno's Paradox was originally proposed as "OMG Hercules will never catch up to the tortoise," but limits demonstrate that it's actually "OMG Hercules will never catch up to the tortoise before some specific time," which is no longer a paradox.  The paradox was never in the infinite regress, it was in the idea that such a regress constituted infinite time, and thus Hurcules could never catch up.  Also, aren't solutions to paradoxes often just means of avoiding them, i.e. demonstrating that no paradox actually occurs?

 

We did integrals with limits of plus/minus infinity in my quantum course.

 

Also using the concept of a limit never really implies that infinity has a limit.  The whole idea is that sometimes even an infinite regress doesn't lead to infinite results.  1 + 1/2 + 1/4 + ... will approach but never pass 2 no matter how many terms you add.  Using the epsilon definition of equality (a = b iff for any epsilon > 0, |a-b| < epsilon) we can demonstrate that the infinite sum is equal to 2.

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Zaq wrote:ubuntu, the

Zaq wrote:

ubuntu, the conclusion that atheism offers a higher expected payoff comes from the quote I put up.  The idea is that the atheist can easily turn the wager around by saying that maybe there's some rational being that will reward us infinitely for NOT believing in God.  Number 2 is necessary because from 1 and 2 we conclude 3 and 4 and thus arrive at a contradiction.

The only way for one to actually wager on such a belief as the one you are proposing is to actually believe that there was a god that rewards unbelief, which would then thwart the means of payoff. Also, one cannot expect such a payoff if one never bets on it either. So in either case, this would not be a "live" option in the Jamesian sense. The only way an atheist could receive the payoff is through dumb luck, which is hardly rational. If one wanted to compare it with the theistic beliefs, one would have to ask, which one makes sense in and of itself? I'm afraid that the theistic version does...

Zaq wrote:

I'm aware that theists will simply claim that thermodynamics doesn't apply to heaven, but then the probability of heaven's existence just becomes unknown, which still causes the wager to fail by generating an unknown payoff.  Anyway, the main point was to demonstrate that an infinite reward does not necessarily indicate a positive expected payoff.

An unknown probability is not a zero probability. But if I could know, then I would have no need to wager would there? Besides, the Wager is not concerned about the probabilities of such things actually existing, and as many have rightly pointed out, that Pascal's wager does not prove the existence or nonexistence of a deity. It simply provides a pragmatic justification for belief in a deity.

Zaq wrote:

Zeno's Paradox was originally proposed as "OMG Hercules will never catch up to the tortoise," but limits demonstrate that it's actually "OMG Hercules will never catch up to the tortoise before some specific time," which is no longer a paradox.  The paradox was never in the infinite regress, it was in the idea that such a regress constituted infinite time, and thus Hurcules could never catch up.  Also, aren't solutions to paradoxes often just means of avoiding them, i.e. demonstrating that no paradox actually occurs?

Also using the concept of a limit never really implies that infinity has a limit.  The whole idea is that sometimes even an infinite regress doesn't lead to infinite results.  1 + 1/2 + 1/4 + ... will approach but never pass 2 no matter how many terms you add.  Using the epsilon definition of equality (a = b iff for any epsilon > 0, |a-b| < epsilon) we can demonstrate that the infinite sum is equal to 2.

Avoiding a problem does not solve actually solve the problem...If I ask, "What is the exact numerical value for pi?" You'd have to say, "I don't know." But if I ask, "What is a good approximation of pi?" You could then give me  a calculated answer to whatever precision I so desire, but the approximation is not the actual value. And the original question still stands. But if I take a limit as something approaches infinity, I get pi. (Pi is not a rational number like 2, a thus why I chose it) Limits make the infinite tangible, but limits themselves are finiite. If one was to add as such, 1/2 + 1/4 etc. all simultaneously then one would get 2. (This is an aside, but generally if one can express an equation in terms of a limit, the cardinality of the operations performed is said to be transfinite, rather than infinite. Georg Cantor describes this as being less than an actual ifinite but more than a finite number.) But if I add 1/2 to 1/4, then add that sum to 1/8, then etc. then one would never arrive at 2. This is traversing the invinite which is why we cannot neccesarily compute pi and also what Zeno's paradox is talking about.

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The numbers dealt with by

The numbers dealt with by Cantor are all real infinities, by the normal usage of the term. "Bigger that a finite number" => "not finite" => "infinite". He didn't want to imply that such such numbers are 'truly' infinite, since he wanted to reserve that concept for God, apparently. It is not commonly used to refer to such numbers themselves, except in the Cantorian context.

Despite this hangup about God,, his work was extremely important in showing that there are different 'levels' or degrees of infinity, probably an 'infinite' number. Categorizing the set of 'infinite' numbers as 'transfinite' to distinguish them from the set of natural numbers is still useful, as well as avoiding some of the baggage attached to the word 'infinite', such as all the religious crap.

I think it is still debated whether Zeno 'really' understood that there is no true paradox in his story, and was just dramatizing the conceptual difficulties that arise when dealing with infinities.

 

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BobSpence1 wrote:The numbers

BobSpence1 wrote:

The numbers dealt with by Cantor are all real infinities, by the normal usage of the term. "Bigger that a finite number" => "not finite" => "infinite". He didn't want to imply that such such numbers are 'truly' infinite, since he wanted to reserve that concept for God, apparently. It is not commonly used to refer to such numbers themselves, except in the Cantorian context.

I suppose "smaller" is a poor choice of words. But how does on "compare" infinite numbers to one another?  Aleph-null is not finite, but niether is it an actual infinite...it's somewhere between. As you said, Cantor wanted to reserve the actual infinite for a god, as he thought that only a god could be an actual infinite. Godel used these concepts to develop what he thought was a deductive ontological proof for an actual infinite, and he called it "God". He was so scared of the results, he did not publish them, but one of his colleagues did after he died.

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ubuntuAnyone

ubuntuAnyone wrote:

BobSpence1 wrote:

The numbers dealt with by Cantor are all real infinities, by the normal usage of the term. "Bigger that a finite number" => "not finite" => "infinite". He didn't want to imply that such such numbers are 'truly' infinite, since he wanted to reserve that concept for God, apparently. It is not commonly used to refer to such numbers themselves, except in the Cantorian context.

I suppose "smaller" is a poor choice of words. But how does on "compare" infinite numbers to one another?  Aleph-null is not finite, but niether is it an actual infinite...it's somewhere between. As you said, Cantor wanted to reserve the actual infinite for a god, as he thought that only a god could be an actual infinite. Godel used these concepts to develop what he thought was a deductive ontological proof for an actual infinite, and he called it "God". He was so scared of the results, he did not publish them, but one of his colleagues did after he died.

Aleph-null is an infinite number, and you compare them by the math Cantor used. What is your problem?

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BobSpence1 wrote:Aleph-null

BobSpence1 wrote:

Aleph-null is an infinite number, and you compare them by the math Cantor used. What is your problem?

There is a difference between an actual infinity and a transfinity...Yeah...it's infinite...but notice the qualifier...actual infinite.... any actual infinite is unbounded non-discrete entity. Aleph-null describes the cardinality of set well ordered discrete elements....they are not the same thing.

My problem is that if one tosses out the word infinite, they may as be talking gibberish without defining the context in which they are using the word. If I say, "that's infinitly larger this," that could go any number of ways...qualitatively, quantitatively, transfinite sets, actual numbers, actual infinities, potential infinities, etc, etc, etc.

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ubuntuAnyone wrote:There is

ubuntuAnyone wrote:

There is a difference between an actual infinity and a transfinity...Yeah...it's infinite...but notice the qualifier...actual infinite.... any actual infinite is unbounded non-discrete entity. Aleph-null describes the cardinality of set well ordered discrete elements....they are not the same thing.

Then by your definition the set of real numbers would be an actual infinity (its cardinality is c, so c being "the 'number' of real numbers" would be an actual infinity).  Why are you calling for a need to be non-discrete though?  Are there not infinitely many integers?

 

The point of the overload refutation is that the validity of the argument leads to a contradiction.  You can't prove that a God that rewards atheism is impossible anymore than you can prove that a God that rewards theism is impossible.  Thus if Pascal's Wager has any merit then theism and atheism are both the appropriate choice.

It's not irrational to concieve of a payoff through dumb luck.  If you set up a game where I payed 1$ to roll a 6-sided die, and you payed me $100 if I rolled a 6 and nothing if I rolled anything else, then it'd be rational for me to play the game as much as I could even though the results are determined by dumb luck.

 

Pascals Wager basically goes:

1P. The probability of a heavenly reward for theistic belief is nonzero

2P. The reward one might attain is infinite

3P. Thus one should be a theist

 

Zaq's Counter-Wager basically goes:

1Z. The probability of a heavenly reward for atheistic lack of belief is nonzero (via the quote + the reasoning for 1P)

2Z. The reward one might attain is infinite

3Z. Thus one should be an atheist

 

Arguing that 1Z is true is just as easy as arguing that 1P is true, as both hinge on the fact that their respective gods are impossible to disprove.  So either both are false or the validity of the argument structure leads to a contradiction.  Either way both wagers fail.

 

"An unknown probability is not a zero probability."

I never said that.  The point is that if the probability is unkown then the expected payoff is unknown, in which case the possibility of a heavenly reward can't be used to make a rational desicion.  If you have absolutely no idea what the expected payoff of either decision is then how can you argue that one decision is better than the other on the basis of payoffs?

 

"Avoiding a problem does not solve actually solve the problem"

Then there's no way to actually solve a paradox.  A "solution" to a paradox is just an avoidance of said paradox, a demonstration that it's not really a paradox.  I suppose we could say that rather than solving paradoxes we demonstrate that there's nothing to solve.

 

The exact numerical value of pie is c/2r (circumfrance over diameter for a Euclidean circle).  The fact that we can't determine pi computationally with exact precision doesn't mean that we can't describe it or represent it with exact precision, or work with it mathematically with exact precision.

For instance, even though I can't compute pi exactly, I can still determine that 2pi / pi is exactly 2.  Similarly, even if it were impossible compute an infinity exactly, this doesn't mean that there aren't some cases where (infinite function)/(infinite function) can be determined exactly.

 

"But if I add 1/2 to 1/4, then add that sum to 1/8, then etc. then one would never arrive at 2."

But the "solution" to Zeno's Paradox is that if the time it takes you to add one number is half the time it takes you to add the previous number (which would be the case with Hercules and his half-speed twin), then the statement "one would never arrive at 2" is false.  Infinite steps does not imply infinite time.  One would arrive at 2 after twice the time it took one to arrive at 1/2, which fits well with the physics of constant velocity objects.

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Zaq wrote:Then by your

Zaq wrote:

Then by your definition the set of real numbers would be an actual infinity (its cardinality is c, so c being "the 'number' of real numbers" would be an actual infinity).  Why are you calling for a need to be non-discrete though?  Are there not infinitely many integers?


It's the differences between something like a line and a set of all possible coffee cups. A line is non-discrete entity, meaning if I divided it up, I still have an infinite number of points. no matter what segment I take. But I can't take a coffee cup, split it in two, and get two coffee cups. (I suppose technically, one could, but not without destroying the original coffee cup). Nor can one have a "negative" coffee cup--that would be nonsense. The set of all possible coffee cups is a set of discrete entities. Aleph-null describes the cardinality of this set of coffee cups, but not the cardinality set of points that comprise the line. An actual infinite would be non-discrete, like the line, albeit more complex.

Zaq wrote:

It's not irrational to concieve of a payoff through dumb luck.  If you set up a game where I payed 1$ to roll a 6-sided die, and you payed me $100 if I rolled a 6 and nothing if I rolled anything else, then it'd be rational for me to play the game as much as I could even though the results are determined by dumb luck.

Pascals Wager basically goes:

1P. The probability of a heavenly reward for theistic belief is nonzero

2P. The reward one might attain is infinite

3P. Thus one should be a theist

Zaq's Counter-Wager basically goes:

1Z. The probability of a heavenly reward for atheistic lack of belief is nonzero (via the quote + the reasoning for 1P)

2Z. The reward one might attain is infinite

3Z. Thus one should be an atheist

 

Arguing that 1Z is true is just as easy as arguing that 1P is true, as both hinge on the fact that their respective gods are impossible to disprove.  So either both are false or the validity of the argument structure leads to a contradiction.  Either way both wagers fail.




I think this would be bifurcation -- that is saying it is this wager or that wager. I think game theory applied properly would pose all three options as possibilities:

(1) Belief that a god rewards infinitely

(2) Belief there is no god

(3) Belief that a god rewards (2) infinitely.

If one believes (3), then one rejects (1), but in order to embrace (3), on has to believe in in a god, so that person could never recieve the payoff of (3). If one blieves (2), then one rejects (1) and (3) in either case (3) does not seem like a good bet for an atheist. The only way to win on (3) is to bet on (2), but one cannot rationally bet on (3). (3) is not one's best bet, but it is possible to win on dumb luck...

Zaq wrote:

The point is that if the probability is unkown then the expected payoff is unknown, in which case the possibility of a heavenly reward can't be used to make a rational desicion.  If you have absolutely no idea what the expected payoff of either decision is then how can you argue that one decision is better than the other on the basis of payoffs?


One does not have to know the probabilities to wager, just that the probabilities exist. If I assign them all equal probabilities, then all things are equal, so the odds of being right are the same as the odds of being wrong. But even if it is not an equal wager, so long as the probability is nonzero probability, then it makes sense to wager on something with infinite payoff.

Zaq wrote:

For instance, even though I can't compute pi exactly, I can still determine that 2pi / pi is exactly 2.  Similarly, even if it were impossible compute an infinity exactly, this doesn't mean that there aren't some cases where (infinite function)/(infinite function) can be determined exactly.

But the "solution" to Zeno's Paradox is that if the time it takes you to add one number is half the time it takes you to add the previous number (which would be the case with Hercules and his half-speed twin), then the statement "one would never arrive at 2" is false.  Infinite steps does not imply infinite time.  One would arrive at 2 after twice the time it took one to arrive at 1/2, which fits well with the physics of constant velocity objects.


I never said one could not infer what the result may be if I could simultaneously add a series of fractions, but the point was that I am doing simultaneously, not iteratively. If I did it iteratively, then I'd do it eternally. Now, going back to the discussion about a non-discrete entity--a line for instance, better yet, a number line. If I want to go to one, I have to pass over 1/2, but to pass over 1/2, I have to pass over 1/4, etc. etc... One cannot get to point 1/n  without first getting to point (1/n-1). In short, I'd never get off the starting point of 0...that's what Zeno's paradox was getting at. If I can leap from 0 to 1, great! But that does not solve the problem...as I mentioned, it avoids it which is essentially what calculus is doing.

 

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ubuntuAnyone wrote:It's the

ubuntuAnyone wrote:

It's the differences between something like a line and a set of all possible coffee cups. A line is non-discrete entity, meaning if I divided it up, I still have an infinite number of points. no matter what segment I take. But I can't take a coffee cup, split it in two, and get two coffee cups. (I suppose technically, one could, but not without destroying the original coffee cup). Nor can one have a "negative" coffee cup--that would be nonsense. The set of all possible coffee cups is a set of discrete entities. Aleph-null describes the cardinality of this set of coffee cups, but not the cardinality set of points that comprise the line. An actual infinite would be non-discrete, like the line, albeit more complex.

Your analogy breaks down when you talk about splitting the number line being like splitting a single coffee cup.  You instead need to talk about splitting the set of coffee cups, because nobody's claiming that a single coffee cup is infinite.  If you split the set of real numbers you can get two infinite sets.  If you split a set of discrete objects you can get two infinite sets.  For instance, the set of integers is the set of even integers combined with the set of odd integers.  Both of these subsets have cardinality Aleph-null.

You still haven't really given any reason why an actual infinity must be non-discrete though.
 

ubuntuAnyone wrote:

I think this would be bifurcation -- that is saying it is this wager or that wager. I think game theory applied properly would pose all three options as possibilities:

(1) Belief that a god rewards infinitely

(2) Belief there is no god

(3) Belief that a god rewards (2) infinitely.

If one believes (3), then one rejects (1), but in order to embrace (3), on has to believe in in a god, so that person could never recieve the payoff of (3). If one blieves (2), then one rejects (1) and (3) in either case (3) does not seem like a good bet for an atheist. The only way to win on (3) is to bet on (2), but one cannot rationally bet on (3). (3) is not one's best bet, but it is possible to win on dumb luck...

No, one just has to recognize that 3's belief is just as possibly true as 1's.  Then belief in 2 becomes rationalized by the possibility of 3, not by a belief in 3.  I'm not saying it's this wager or that wager.  I'm saying that if either wager is valid than the other is.  Thus if 1 is preferred then 2 is also preferred, which of course is a contradiction.



ubuntuAnyone wrote:

One does not have to know the probabilities to wager, just that the probabilities exist. If I assign them all equal probabilities, then all things are equal, so the odds of being right are the same as the odds of being wrong. But even if it is not an equal wager, so long as the probability is nonzero probability, then it makes sense to wager on something with infinite payoff.

But this is my exact point!  You're making the same error as Pascal.  Nonzero times infinity is NOT NECESSARILY positive.  Just because one payoff is infinite doesn't mean that any non-zero probability will rationalize that payoff.


ubuntuAnyone wrote:

I never said one could not infer what the result may be if I could simultaneously add a series of fractions, but the point was that I am doing simultaneously, not iteratively. If I did it iteratively, then I'd do it eternally. Now, going back to the discussion about a non-discrete entity--a line for instance, better yet, a number line. If I want to go to one, I have to pass over 1/2, but to pass over 1/2, I have to pass over 1/4, etc. etc... One cannot get to point 1/n  without first getting to point (1/n-1). In short, I'd never get off the starting point of 0...that's what Zeno's paradox was getting at. If I can leap from 0 to 1, great! But that does not solve the problem...as I mentioned, it avoids it which is essentially what calculus is doing.

FIrst, you don't need a line for this demonstration.  In fact, all the numbers you used in this example are rational numbers, and the cardinality of the rational numbers is Aleph-null.  This just refutes your first claim.

"If I did it iteratively, then I'd do it eternally."

The whole point of the "solution" is that this is NOT TRUE.  Infinite iterations does not imply infinite time.  While it may take you infinite iterations to get to 1, it will not take you an eternity when each iteration is an exponentially decreasing amount of time.

Also, if we can't add the numbers iteratively then what's wrong with adding them simultaneously (as you call it)?  If I can do them simultaneously then why don't I just do them simultaneously and stop worrying about itterations?  And since addition is commutative adding numbers simultaneously would yield the same result as adding them iteratively.  So we could say that I know what you would get by adding the numbers iteratively if you could do so.  The point is that even if going through all the iterations is impossible, we could still figure out what you would get if it were possible.

I'm not suggesting that you leap from 0 to 1.  I'm pointing out that if your iterations are fast enough then even all infinity of them won't take you an eternity.

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Zaq wrote:You still haven't

Zaq wrote:

You still haven't really given any reason why an actual infinity must be non-discrete though.

An actual infinite is a technical term.  I'm not trying to argue for or against its existence....I'm trying to describe it to you. Maybe I'm not doing a good job and some outside reading on the subject would help you understand what I'm talking about.

Zaq wrote:

No, one just has to recognize that 3's belief is just as possibly true as 1's.  Then belief in 2 becomes rationalized by the possibility of 3, not by a belief in 3.  I'm not saying it's this wager or that wager.  I'm saying that if either wager is valid than the other is.  Thus if 1 is preferred then 2 is also preferred, which of course is a contradiction.

Read William James' essay, "The Will to Believe" and the chapter 233 in the Pensees concerning the wager. In a Pascalian (and really a pragmatic since), one's belief is one's wager. One cannot rationalize 2 without believing in a pragmatic sense 3, and if one believes 3, he or she believes in a deity, thwarting the counter wager.

Zaq wrote:

But this is my exact point!  You're making the same error as Pascal.  Nonzero times infinity is NOT NECESSARILY positive.  Just because one payoff is infinite doesn't mean that any non-zero probability will rationalize that payoff.

All probabilities are 0, 1 or a number between the two. The expected payoff is a positive infinity. The only thing times that would not result in a positive infinite payoff is a zero probability. How can anything other than a positive infinity if I have a positive probability greater than 0 and an infinite greater than 0?

Zaq wrote:

I'm not suggesting that you leap from 0 to 1.  I'm pointing out that if your iterations are fast enough then even all infinity of them won't take you an eternity.

Start counting all numbers iteratively between zero and one. Let me know when you're finished.

Calculus does not traverse infinites...It infers the results of a traversed infinity. In a since, Calculus asks the question, "What if I could divide by zero???" That is, in my attempt to approximate the some of the areas under a given curve, what would happen if my delta-x got infinitely small -- that is it became zero. Time aside, an iterative algorithm would never logically finish the approximation.

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The sum of an infinite

The sum of an infinite converging geometric series is finite. That can be demonstrated explicitly, without using calculus-style limit theorems.

No element of the series can be shown to be zero, yet the sum is finite.

So counting an infinite series could in principle be done in a finite time, as long as each successive count takes half the time of the previous one. This is unrealistic for a real physical process, but valid mathematically.

You can treat this as either an example of how math, especially when it deals with infinities, does not adequately model reality, or that 'infinities' are not 'real' quantities, but only exist as concepts within the synthetic world of math.

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