An infinite chain of causes?
It’s Islamic Awareness week this week, and apparently next week as well. I passed a stall at uni, and picked up some brochures, found a nice sunny spot and read through a few of them.
Loved it. Definitely going to lead to some interesting conversations next week.
But, one of the brochures used proved God with this sort of argument:
All we perceive depends for its existence on something else, which in turn depends on still another thing, ad infinitum, or else derives its existence from something that exists uncaused. The first alternative is false because it implies what is referred to as an infinite regression, which is impossible.
Which renewed my interest again in this question:
“Could the state of the world as we know it have arisen by an infinite chain of causes?”
Discuss.
Comments
August 13th, 2009 at 5:09 pm
SmartLX has commented here the following:
“Why exactly is it that “an infinite series of dependent causes cannot produce an effect”? … Just as there are an infinite number of negative integers, an infinite number of things can have happened before the present if time or at least causality is infinite in both directions. In this case every cause has a cause, and there is no uncaused cause.”
August 13th, 2009 at 5:13 pm
I think the thing that doesn’t satisfy me about this is that you are starting at 0 and counting back toward negative infinity. Of course, that will go on forever.
But that is not at issue. The issue is whether, starting at negative infinity and counting forwards, you will ever reach 0 again (assuming for the analogy 0 = the present state of the world).
I suggest that if you start at negative infinity, you never reach 0, and therefore a chain of causes beginning infinity causes ago would never reach the present state of affairs.
August 13th, 2009 at 5:17 pm
SmartLX also said in the comment referred to above, “Forgetting that for now and supposing an uncaused cause, why is it more likely to be a god than…anything else?”
Well, it may not. But I expect it is reasonable to think that whatever it is, it is:
a) eternal
b) uncaused; independent
c) capable of causing
Which is at least a starting point, and perhaps more characteristics could be deduced.
But let’s not get side-tracked – back to the discussion of causes!
August 14th, 2009 at 12:02 am
argh you’re hurting my brain
August 14th, 2009 at 8:58 am
Hey Hayesy.
The argument is specifically designed to hurt brains, Luke, because brains in pain tend to drop their bundle and accept things more easily.
Yep, this really is very close to VenomFangX’s argument on YouTube, in the video “Proof God Is Real”. Search YouTube for “venomfangx infinity” for a wealth of responses, many of which were made because VFX censored critical comments on his original video. Better mathematicians than me have gone at it.
Briefly, if negative infinite time exists relative to the present, you only won’t reach the present if a finite amount of time passes. That’s not the case in this scenario. If there’s infinite time before the present, infinite time has passed, and if infinite time has passed, infinite time exists before the present. A road is the same distance in both directions.
The big problem is that you’re thinking of negative infinity as a definite number we can “start” at, like zero. Like everyone, you tend to think in finite terms even when infinity is involved. Infinity of any kind is indeterminate; you can’t add to it, multiply by it or partition it, at least not very sensibly. That doesn’t mean it can’t exist, for instance as the distance you can travel (or have traveled) along the circumference of a circle without hitting a corner.
We ARE starting at zero, because one thing we’re reasonably sure of is that the present exists. We have no problem imagining that an infinite amount of time could pass after the present, and after we’ve all died. The exact reverse only gives us psychological trouble, not mathematical.
August 14th, 2009 at 9:16 am
Meanwhile, saying a hypothetical uncaused cause is “uncaused” and “capable of causing” is stating the obvious. However, by your own argument it CAN’T be eternal in terms of the past if infinite time can’t have passed before the present. Arguing from your position, if the uncaused cause is within time at all it has to have had a beginning. Hence the common escape clause that God is “outside time”.
There’s something I say a lot that applies here: whatever constraints you place upon the universe to necessitate God, you immediately have to break in order to allow for God. Even when apologists set their own rules, at times they still need to cheat. I pre-empted “outside time” so you wouldn’t have to.
August 24th, 2009 at 10:25 pm
Aren’t there two types of time? Time as in Space-time, which has a beginning with matter, and eternal time extending infinitely in each direction into which space arises.So there is a sense in which God is truely outside time because it is a feature of the material creation. But am I right in thinking that maths copes better with negative infinity than physics?
August 25th, 2009 at 8:37 am
Interesting angle, Eye Doc. There may well be systems of time AND space outside of this universe, as suggested by the multiverse theory. Also, if it turns out that our system of spacetime resulted from the Big Bang, anything that caused it must be independent of its time. If.
A minor issue is that no time we’re aware of is independent of all space. Outside of this universe we’re guessing, but the time we’re familiar with is just one dimension of a larger system. What there might well be is a line or network of causality between time systems, such as that which makes one universe produce another or bridges the gap between serial universes.
The major issue is that even if there is some kind of external time, it’s subject to the same logic as our universe’s internal time, whichever logic you choose.
- By Hayesy’s logic infinite external time can’t have passed either, and even the external time needs to have started somewhere. Working from this, you’d have to posit an EXTERNAL external system of time to imagine any truly eternal creator entity. Then you’d need an EXTERNAL external external time, and so on. It’s not only an infinite regress, but one that results in infinite, recursive complexity. That doesn’t reflect well on any hypothesis. All you can then do is suppose that God is outside any kind of time at all, which defeats the purpose of arguing from what we know about time.
- By my logic, the external time could be infinite in both directions as you describe, and other systems of time such as ours could periodically arise from it with defined beginnings (and perhaps ends). It’s another infinite state of affairs, but at least it keeps the complexity fairly constant with respect to time.
All of these options are still a lot more complex than a single universe, or serial set of universes, which extends forever into the past and future and needs none of this stuff.
Finally, I’d like to see an actual comparison of the maths and physics of negative infinity if you have one to link. Physics in general works backwards if you reverse the rules. Working backwards from the present is how we arrived at the Big Bang in the first place. For a simpler example, if you’re watching a video in reverse you can predict to some extent what’s going to un-happen next.
All physics needs to allow negative infinity is a set of cyclical causes in unstable equilibrium, or else infinite matter with unlimited opportunities for causation. There are many ways to hypothesise either one. A third way is to suppose a completely static universe, but since my fingers are moving to type this that’s one idea we can dismiss.
August 27th, 2009 at 8:54 pm
Thanks SmartLX, now my brain is hurting. I don’t have any link but I suppposed that, whereas mathematical negative infinity is fairly easy to understand, due to causality in Physics you often end up at sigularities not infinity. But you explained that in the cases in the last paragraph.
Do you think the constancy of time logic is justified when one moves outside the present universe? Couldn’t there be alternate logics such as an eternal present?
For the Christian it gets even more complicated because not only is God supposed to be outside time in negative direction but also through time into postive eternity and also in relationship with all matter in the current universe. That is a big call conceptually.
August 28th, 2009 at 8:06 am
What do you mean by “eternal present”, I wonder? Is it perhaps a kind of infinity where infinite time doesn’t have to have passed? If so, it’s a rather direct response to the issue with Hayesy’s logic. But does it make sense? Are you saying it doesn’t have to within our logic?
That said, even though I think neither of us really has a solid concept for it, it could be the case. We can’t yet leave this universe and discover otherwise. Time, logic and everything we rely upon might only stretch to the edge of this universe, with a no-man’s-land outside where literally anything is possible.
Once you’re out there in Wonderland, though, all bets are off and no constraint is binding. If there’s an eternal present, causality isn’t beholden to linear cause and effect and perhaps something CAN or even MUST come from nothing. A god can exist, but anything else, or nothing, could also result in the emergence of a universe like ours. You make lots of room for a god to be possible, but you drown any chance of establishing His necessity in a sea of alternatives. This isn’t very useful unless someone’s arguing that gods is impossible under any circumstances, which I wouldn’t do.
The general problem with circumventing known logic to get around a particular logical issue is that you can no longer rely on the rest of the logic you’re using. If you want to advocate something with a reasoned argument, it’s all or nothing.
August 28th, 2009 at 8:11 am
Darn it. “…arguing that gods ARE impossible…”
August 29th, 2009 at 10:30 pm
Yes I agree with everything you’ve said. “But does it make sense? Are you saying it doesn’t have to within our logic?”
I was wondering what could be if our logic was only one of the possibilities. But as you say it becomes a bit nonsensical. If there is such a reality then it is beyond what we view as rational or perhaps knowable. I think this is why Stephen Hawkings doesn’t think we will get to a theory of everything. Have enjoyed the discourse. Best of luck.
August 30th, 2009 at 2:45 pm
Ditto, mate.
September 9th, 2009 at 8:59 pm
Hey SmartLX
Sorry I haven’t been engaging in this discussion – just came through a hectic period at uni.
If you’re not totally bored of this topic yet, I’d like to go right back to where I see the core of this issue as lying.
I want to sidestep the issue of whether a Creator could be the first cause, and just establish whether a first cause is needed.
I had a quick look at VenomFangX’s videos, and my argument is not quite his. He seems to be saying infinite time is impossible. I’m not concerned with that, I just don’t know whether infinite time is enough to solve the infinite regression.
Here’s my thesis: I don’t think it’s established that infinite time is long enough to count to infinity. Tonight I asked a (strongly atheist) student of Mathematics, who has studied infinity, this question: “If you had infinite time, and counted at 1 per second, would you reach infinity”
He said no.
I explained why I was asking, he said “there had to be a first cause”. He looked like he was in a hurry, so I didn’t push him to hypothesise a first cause, but I’d like to follow it up later.
“The big problem is that you’re thinking of negative infinity as a definite number we can “start” at, like zero.”
No, I’m clear that you can’t “start” at infinity (though I see how my poor expression lead you to think I was unclear here) – but that’s the whole point. You can’t start at infinity.
It’s this fact that causes the problem.
“Infinity of any kind is indeterminate; you can’t add to it,”
Again, this is what causes the problem. Negative infinity + 1 = negative infinity. You never get to 0.
In a very simple form, here is the problem: You will never get to infinity by adding anything finite. Ever.
September 10th, 2009 at 11:34 am
Your last sentence is your problem in a nutshell: “You will never get to infinity by adding anything FINITE.” By only counting 1 at a time, you’re trying to partition infinity into finite amounts, and essentially count to infinity. Of course you’ll never exhaust infinity that way, because subtracting from it is firstly borderline nonsensical and secondly futile.
It’s similar to Zeno’s paradox. He explained that if you divide a finite amount (e.g. 1) into progressively smaller partitions (e.g. 0.9 + 0.09 + 0.009 + …), you will never reach even the finite amount by counting through them (in his famous example, only taking stock each time the arrow has caught up to where the tortoise was last time). Regardless, there are several mathematical proofs that 0.9999 recurring is exactly equal to one. In practical terms, the arrow will catch and overtake (or kill) the tortoise.
Therefore, just because you can’t count to a number in a certain way doesn’t mean the number isn’t a practical reality. Like Zeno, you’ve chosen a method of counting to your target (i.e. a progressive series of finite numbers) which will never fully add up if you go piece by piece. I said very early on that infinity can’t be partitioned. Infinity divided by any finite number is infinity. You’d have to count in infinities, and then there’d be no point.
You might not think of infinity as a number to start at, but you do still think of it as a number you can or can’t “get to”, “count to” or reach. It’s an almost identical (merely inverse) perspective on the concept. It’s the underlying assumption you make when you use infinity as an arithmetic value, e.g. “Negative infinity + 1 = negative infinity.”
Here’s another angle. As well as a first cause, would you argue that the universe also has to have a last effect? If we can’t count forward to infinity any more than we can count backward to negative infinity, does that mean the universe must come to an end as surely as it supposedly had a beginning? (Going further if you like, does that mean there must be a powerful Destroyer waiting to be the Uncausing Effect, or Ineffectual Effect?) Does the fact that we can’t reach infinity by counting mean that we have to slap an arbitrary terminus on time in this direction too? If not, why are the mathematics or physics of the supposed beginning of time not fully reversible?
Moving into theology for a moment, does the unattainability of infinity mean the saved can’t actually spend forever in Heaven if they die in the present?
Be careful about attacking infinity. You might need it.
September 10th, 2009 at 1:01 pm
Slight confusion there. The tortoise is chased by a sprinting Achilles, not an arrow. The arrow paradox is something else entirely.
September 10th, 2009 at 6:52 pm
I’m not interested in what I need, I’m interested in truth. If infinity threatens eternity, we’ll need to deal with that. I’m not saying infinity is impossible, either. I’m just saying you never reach it; which is entirely consistent with eternity if you ask me.
But I think I’m going to throw in the towel on this argument. I caught a PhD Maths student at dinner – He’s only just got back from lecturing in Europe, Oxford, Cambridge etc. And I asked him some of these questions. I learned:
a) that the more you understand about infinity, the more you realise you don’t understand.
b) that infinite time doesn’t solve the infinite regression.
c) that a first cause doesn’t help either
d) that his answer was “I don’t know”
e) that mathematicians commit suicide if they think about this for too long.
So I’m going to say, this is over my head. I don’t know.
September 11th, 2009 at 7:44 am
Well, there you go. You might be right, in the end, but you’re trying to establish the impossibility of past infinity in order to necessitate a beginning, and like so many other things there’s no way to conclusively disprove the reality of it.
I’d just say that an infinite regression need not be “solved” if that’s the way things are.
September 11th, 2009 at 7:58 am
Just to clarify, I’m not “trying to establish the impossibility of past infinity in order to necessitate a beginning”
I was trying to say, even given past infinity, you couldn’t produce the present by an infinite chain of events.
The PhD I spoke to last night saw it as something that needed solving, but didn’t know how.
September 11th, 2009 at 9:27 am
Okay, substitute “the impossibility of an infinite chain of events before the present” for “the impossibility of past infinity”. Regardless, you want to necessitate a beginning with a view to putting God there. Of course you do.