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    I suppose this thread is more for mathematicians than anyone else.

    My (atheist) friend and I were having a debate about the cosmological argument for God's existence.

    We agree on this much:

    There are two possibilities - there was either a "first cause" which started off the universe as we know it, or every effect has a cause, and the universe is made up of an infinite regression of cause and effect.

    He's also agreed (for sake of argument) that if there is in fact a "first cause", we can name it "God". I know that this bit isn't rigorous at all, but just suppose that we've agreed on it.

    Now:

    He thinks that there's still no reason to assume that God exists, because the universe could just as easily be an infinite regression of causes and effects.

    My argument is that, even if the universe is an infinite regression of causes and effects, it still implies that God exists, and here's why:


    Suppose the universe has existed for an infinite amount of time. Then every time-independent-event whose occurence has a probability greater than zero has occurred, because it has been allowed an infinite amount of time to occur. This is sometimes known as the "infinite monkey theorem", which you can look up on Wikipedia. Assuming that the universe has existed for an infinite amount of time, I can categorically state that at some point in time, a monkey typed out Shakespeare's Romeo and Juliet on a typewriter. I can't say when it happened, but it definitely happened.

    Similarly, the probability that God, at some point in time, said "let there be light" is also greater than zero. If the universe has existed for an infinite amount of time, then this must have happened at some point.

    Therefore, an infinite universe implies that God exists.

    Does my argument make sense, or are there any gaping flaws in my logic which jump right out at you?
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    (Original post by tazarooni89)
    Suppose the universe has existed for an infinite amount of time. Then every time-independent-event whose occurence has a probability greater than zero has occurred, because it has been allowed an infinite amount of time to occur.
    Not true. The event has occurred with probability 1, which is not the same as saying it has occurred. Analogy: flip a coin "infinitely many times" (humour me), and note down the sequence of heads and tails you get as you go. But the probability of getting that sequence was 0 (i.e. \displaystyle \lim_{n\to\infty} \left(\tfrac{1}{2}\right)^n, right?), so the probability of not getting that sequence was 1. But you got it. Oops.
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    (Original post by tazarooni89)
    Similarly, the probability that God, at some point in time, said "let there be light" is also greater than zero. If the universe has existed for an infinite amount of time, then this must have happened at some point.

    Therefore, an infinite universe implies that God exists.
    Actually, what am I doing pointing out probabilistic errors? This is a pretty gaping flaw. Every possible event will occur with probability 1, but if God doesn't exist, then his existence is not a possible event, so will not occur. The probability is not greater than zero just because we don't know whether he exists or not; either it happened (in which case the probability is 0) or it didn't (in which case the probability is 1), but we don't know which. That doesn't really give us lease to guess.

    Anyway, for the above reasons, a probabilistic argument won't work anyway. Something occurring with probability 1 isn't the same as something occurring if there are infinities involved.
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    (Original post by generalebriety)
    Not true. The event has occurred with probability 1, which is not the same as saying it has occurred. Analogy: flip a coin "infinitely many times" (humour me), and note down the sequence of heads and tails you get as you go. But the probability of getting that sequence was 0 (i.e. \displaystyle \lim_{n\to\infty} \left(\tfrac{1}{2}\right)^n, right?), so the probability of not getting that sequence was 1. But you got it. Oops.
    Surely the probability of getting that sequence was still greater than zero, because flipping a coin infinitely many times takes forever. So I can't flip a coin infinitely many times, and then retrospectively look back on it, and think "but the probability of getting that sequence was zero", because if I begin this experiment, I'll never finish it?

    Surely the fact that I've completed the experiment implies that n is not equal to infinity?
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    (Original post by tazarooni89)
    Surely the probability of getting that sequence was still greater than zero, because flipping a coin infinitely many times takes forever. So I can't flip a coin infinitely many times, and then retrospectively look back on it, and think "but the probability of getting that sequence was zero", because if I begin this experiment, I'll never finish it?
    You're the one who started going on about infinite lengths of time, not me. :confused: Anyway, no it doesn't. Flip your first coin in one second, your second coin in half a second, your third coin in a quarter of a second, and so on. Keep halving the time, and it'll only take you two seconds to flip infinitely many coins. Well, you wanted a mathematician's point of view...
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    (Original post by generalebriety)
    You're the one who started going on about infinite lengths of time, not me. :confused:
    lol, true.

    Well I believe that the universe has existed for a finite amount of time. But my friend thinks that this is a completely arbitrary belief, and it could just as easily have existed forever.

    I'm essentially trying to show that my belief in a finite universe isn't arbitrary, because infinite lengths of time cause problems like this?
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    (Original post by generalebriety)
    You're the one who started going on about infinite lengths of time, not me. :confused: Anyway, no it doesn't. Flip your first coin in one second, your second coin in half a second, your third coin in a quarter of a second, and so on. Keep halving the time, and it'll only take you two seconds to flip infinitely many coins. Well, you wanted a mathematician's point of view...
    Right, I see that this argument is much more complicated than I thought!
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    (Original post by tazarooni89)
    lol, true.

    Well I believe that the universe has existed for a finite amount of time. But my friend thinks that this is a completely arbitrary belief, and it could just as easily have existed forever.

    I'm essentially trying to show that my belief in a finite universe isn't arbitrary, because infinite lengths of time cause problems like this?
    Mmf, that's the start of your problems. Even if you do manage to prove the universe has only existed for a finite length of time (which I think is what scientists are agreeing on now, though I'm not sure), just because you call the first cause "God", and talk about it as if it's a person, that doesn't mean you've actually proved it is anything like what you call a deity. I could quite happily call the Big Bang "God" if I wanted, but that wouldn't make me a theist, it would make me an atheist who liked to misuse theistic terminology. You need to show it has some kind of property of being a deity.
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    (Original post by generalebriety)
    Mmf, that's the start of your problems. Even if you do manage to prove the universe has only existed for a finite length of time (which I think is what scientists are agreeing on now, though I'm not sure), just because you call the first cause "God", and talk about it as if it's a person, that doesn't mean you've actually proved it is anything like what you call a deity. I could quite happily call the Big Bang "God" if I wanted, but that wouldn't make me a theist, it would make me an atheist who liked to misuse theistic terminology. You need to show it has some kind of property of being a deity.
    Yes, I realise that - the God thing was just the start of the conversation really.

    My actual aim is to prove that my belief in a finite universe is not arbitrary. Seems to be harder than I thought though

    (This is ignoring science and focusing mainly on philosophy by the way).
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    (Original post by tazarooni89)
    Yes, I realise that - the God thing was just the start of the conversation really.

    My actual aim is to prove that my belief in a finite universe is not arbitrary. Seems to be harder than I thought though

    (This is ignoring science and focusing mainly on philosophy by the way).
    Good luck. Meanwhile, I'm off to bed. :p:
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    (Original post by generalebriety)
    Not true. The event has occurred with probability 1, which is not the same as saying it has occurred. Analogy: flip a coin "infinitely many times" (humour me), and note down the sequence of heads and tails you get as you go. But the probability of getting that sequence was 0 (i.e. \displaystyle \lim_{n\to\infty} \left(\tfrac{1}{2}\right)^n, right?), so the probability of not getting that sequence was 1. But you got it. Oops.
    If "the event has occurred with probability 1" does not mean the event occurred (and of course, this means that an event with probability 0 can occur), then what is the right interpretation of a probability?

    (Also, an easier example would be throwing darts on a dartboard. If the dart lands on (0,0) for example, then the probability that it doesn't land there is 1, the probability that it does is 0, and yet it did.)
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    Hmm. This is a rusty philosopher's view -

    You don't need to suppose God to suppose a first cause. As we cannot explain how or why God exists, we can just as easily suppose that the universe caused itself. To suppose a being that must have existed infinitely or created itself is in defiance of Ockham's Razor, which suggests that if we already have a weird entity that may have existed infinitely or caused itself, we are not solving the problem by adding another one to explain the first.

    Anyway, I think generalbriety's maths is correct. I'm a bit poo at maths. It is also 5am and I'm stuck pissing about with quantum mechanics. I'm tired =(
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    (Original post by tazarooni89)
    Suppose the universe has existed for an infinite amount of time. Then every time-independent-event whose occurence has a probability greater than zero has occurred, because it has been allowed an infinite amount of time to occur. This is sometimes known as the "infinite monkey theorem", which you can look up on Wikipedia. Assuming that the universe has existed for an infinite amount of time, I can categorically state that at some point in time, a monkey typed out Shakespeare's Romeo and Juliet on a typewriter. I can't say when it happened, but it definitely happened.
    General already said this, but only those events that are possible will occur. In this analogy, the monkeys will never type up a japanese novella.
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    You're still stuck on two sides of belief...there's nothing you can do about it in my view..but then that's just what I beleive...

    Logic can't help you here really, and the same goes for your friend.

    Also, if there has always been a universe, then isn't it impossible for it to have been created by god (or any other means)? When you look at the universe as infininate then it becomes impossible to pinpoint when things have happened/do happen/will happen...maybe it's infinate in that time goes round in a loop...or maybe not - just don't ask Stephen Hawkins what it's shaped like...
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    Hm, the best interpretation I've been able to think up (of the probability of an event) is that if you repeat the experiment, the probability is the proportion of times that the event occurs... and eventually the limit as you keep doing so.

    Not sure if this is good or not. But, for example, if the probability that an event occurs is 1 then, under this interpretation, it might not occur in some particular experiment. It just has to occur enough times that the limit of the proportion is 1. (Likewise, something with a probability of 0 might occur within a particular experiment. But it has to not occur enough times that the limit of the proportion is 0.)
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    (Original post by tazarooni89)
    Similarly, the probability that God, at some point in time, said "let there be light" is also greater than zero. If the universe has existed for an infinite amount of time, then this must have happened at some point.

    Therefore, an infinite universe implies that God exists.

    Does my argument make sense, or are there any gaping flaws in my logic which jump right out at you?
    Theorem:

    "A monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a given text, such as the complete works of William Shakespeare."

    Your interpretation:

    "A monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely cause the Earth to spontaneously transform into a delicious blancmange."

    I'm sure I needn't elaborate further.
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    (Original post by tazarooni89)
    My actual aim is to prove that my belief in a finite universe is not arbitrary. Seems to be harder than I thought though

    (This is ignoring science and focusing mainly on philosophy by the way).
    Well, if you don't ignore the science, you're going to have a really hard time with that. (Another link, thanks to Bear)
 
 
 
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