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

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.

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.

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?

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.

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.

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. 

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.

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.

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.

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.

            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  ).

       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!!!

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.

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

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

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.

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.

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.

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.

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.

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".

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.

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.

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...

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...

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?

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.

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.

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

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.

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.
 

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.

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.

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.

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.