Infinity
While I’m waiting for the YouTube videos to be posted so I can get my facts straight with regard to the debate between William Lane Craig and Bill Cooke I thought I might address the issue of the concept of infinity.
Craig introduced the cosmological argument with the notion of infinity and the fact that atheists will argue that the universe is infinite. I’d just like to put my atheistic hand up at this point and say that I’d tend to go with the ‘finite universe’ personally at this stage. I know people (both theists and atheists) who fall on either side of this argument and so this assertion was a little disappointing. This was posited right before he moved on to the Big Bang so perhaps it was an attempt to portray atheists as non-scientific.
The fact of the matter is no one knows whether the universe is infinite or not. Get used to this phrase because I’m probably going to use it a few times over the next few entries. There is stuff we don’t know; the more we find out the more we realise just how little we really do know. Making up explanations may feel satisfying but it’s not going to get us any closer to the truth.
Back to the issue of infinity. Craig argues that the concept of infinity is an absurdity in terms of logic because, for example, if you minus four from infinity you are left with infinity. And I tend to agree in principle. But there is a problem with how he’s come to this conclusion because he’s used a finite number in relation to an infinite one.
Because whenever we talk about infinity we refer to it in finite units (like time or numbers or oranges) we think that because we can just add or subtract one more as we might do in the real world that it logically follows that we could continue to do so if we had unlimited time, numbers or oranges. Which might be a bit of a circular reasoning because we’re giving ourselves infinity to prove that infinity exists.
Another angle is that if infinity in relation to time is defined as “for the full extent of time” and time can in fact be created then it would also be reasonable to define infinity as from the creation of time to its destruction.
Einstein came up with some theories where mass is equivalent to energy (and vice-versa… I can cope with this one) and - head-hurtingly - where time is equivalent to space (and vice-versa… aaaarrgh! What?!). I don’t even know what to make of this so if anyone has a succinct way of explaining the concept of “spacetime” please feel free to enlighten me.
Hawking has a nice little analogy about the limits of a dimension which I’ll see if I can completely mungle:
If a two-dimensional critter were sliding around on the face of our planet and were asked what’s south of New Zealand it would list Stewart Island (technically incorrect but we’ll leave it be because it’s just a two-dimensional critter) and then Antarctica and, finally, the South Pole. We can almost sense its outrage and confusion when we tell them they can’t go any further south than the South Pole but the fact is, within these dimensions there really is no “South of the South Pole”. Now shift the question up a dimension or two. When I ask you what happened before World War 2 you will list a number of events that occur back in time along the time axis (i.e. just like the “south” axis) until you get to a point where time starts or comes into being. Yes, we are outraged and confused when we are told that there is no such thing as “before time” because everywhere we look we can see a before, a cause. But the truth is that you can’t continue to use the word “before” once we’ve hit this point.
I don’t know if analogies that include the concept of dimensions are any more valid than the keep-adding-an-orange ones. Perhaps our concept of “dimensions” are just another way our minds have to package information about the real world in an attempt to comprehend it.
I don’t know if time unfolded out of the beginning of the universe but as incomprehensible as it seems to me I can see from the example of my two-dimensional critter that my incomprehension doesn’t necessarily make the idea wrong.
For me, the concept of infinity is either:
- A trick of the mind that doesn’t ever map against reality. Perhaps our mind can conceive of infinity because our mind is self-referencing.
- A way of describing the extent of a dimension (like “south” or “before”) that can actually have a start and an end.
- That the universe is, in fact, infinite and that my mind is incapable of comprehending it beyond describing it in terms of finite units.
- Something else altogether… [insert your reasoning here].
For the sake of argument I’m more than happy to go with Craig on this one; the universe is finite. (Until I see further evidence - always a good disclaimer to add to questions of this nature).
Tags: infinity, William Lane Craig
June 19th, 2008 at 11:09 am
The concept of infinity and the size/shape of the universe are so outside out experience that ‘common sense’ is obviously not useful - so true of a lot of things at the forefront of science. But, I think for this reason, debates are not a suitable context to make any progress on these sort of subjects.
I have real trouble getting my head around current understanding of the size and shape of the universe. But infinity is an extremely useful concept mathematically. There would be no calculus without it.
Brian Greene (Fabric of the Cosmos) discusses these issue without inlying a settled understanding. He does say that there is mounting evidence that that “the overall shape of space is not curved and that “the flat, infinitely large spatial shape is the front-running contender for the large-scale structure of space-time.”
The “big bang” concept does not necessarily imply a finite space. The ‘big bang’ could have occurred everywhere (Greene compares it to “many big bangs, one at each point on the infinite spatial expanse”). We can still get expansion and the current picture of the universe without change in overall size of space time (expanded infinity is still infinity). I guess this might imply that space-time came into existence with an infinite size.
So I think if Craig was claiming that the big bang proved infinite space wrong he is just falling back on common sense and is probably out of step with the real scientific assessment (which I understand is not completely settled).
June 19th, 2008 at 2:45 pm
Fascinating topic
There is an interesting point with the size of the universe that while it may be technically finite, if the rate of expansion is sufficiently fast (and it seems to be accelerating curiously) one could never actually reach the “edge” of it. It is suggested that the expansion is roughly at the speed of light (or faster) which means for in any practical sense the size is infinite (nothing could ever see or get to the “edge”) but technically is not infinite.
I think infinity is a by-definition incomprehensible thing that has it’s uses in certain constrained contexts (such as calculus or thought experiments or keeping the migraine medicine companies in business lol).
With regards to space-time, I think that falls into the other equally incomprehensible concept of a fourth “spatial” dimension. We can model it and use it in constrained circumstances but never actually grasp what that fourth dimension actually means.
June 19th, 2008 at 6:09 pm
My recollection is that, having dismissed infinity as a nonsense, Craig was happy to use it later in his references to his god. The recording will show if my recollection is correct.
June 20th, 2008 at 7:45 am
Yes, Des. I’ll bring that up in the next post along with his trick of everything-must-have-a-cause which he then completely drops once God has been placed at the start. And also his deliberate use of the word “begins” in the cosmological argument instead of the traditional “exists” as an effort to deflect the usual response of “well who made God?”.
June 20th, 2008 at 8:12 pm
“And also his deliberate use of the word “begins” in the cosmological argument instead of the traditional “exists” as an effort to deflect the usual response of “well who made God?”.”
Damian there are different cosmological arguments. The one Craig presented just happens to be an argument based on the beginning of the universe. It’s not avoiding anything. Moreover the traditional Leibnizian argument for God’s existence deals precisely with the “who made God” question anyways. It just argues for God’s existence being explained by his own nature (necessity).
Des says:
“My recollection is that, having dismissed infinity as a nonsense, Craig was happy to use it later in his references to his god. The recording will show if my recollection is correct.”
Yes Craig uses qualitative infinity to explain God. Many theologians do that. It’s just a way of describing God’s complete perfection and power. What Craig denies is quantitative infinity.
June 20th, 2008 at 8:52 pm
ChristianJR4, the cosmological argument is the very essence of avoidance. It shifts ‘necessity’ back one step and then calls a halt. It states that everything must have a cause (which we don’t know is true) and then declares that God is the one exception to the rule. If God doesn’t require a cause then isn’t it simpler to presume that perhaps the universe doesn’t need a cause either?
And Craig’s use of “begins” is deceptive because when the traditional “exists” is used it’s even more obvious that the “existence” afforded to God is nothing more than special pleading. We’re less tempted to ask the question of “what caused God to begin” when we’re told that God is without beginning in the first place.
ManySome Christians are aware and a little embarrassed when they see the blatant use of the god-of-the-gaps in science. I suspect this is not really because they see it as being a poor way to discover the truth of matters but more because it is highly likely they’ll be caught out when science eventually fills the gap. All Christians feel confident to insert God into the biggest gap we have though and that’s the gap before the furthest moment we’ve been able to observe. No doubt if we ever see beyond this point God will be moved once more in a never-ending but retreating dance.What will happen if the universe is proven mathematically to be infinite? Where will God go then? Will Christians all become pantheists?
June 21st, 2008 at 1:51 pm
Surely the concept of everything having a cause went out the window ages ago? Haven’t we abandoned that with quantum indeterminacy, vacuum energy, etc.? What is for sure is that “common sense” arguments really have no place when we are dealing with huge issues like origins of space/time.
I can’t claim to understand the physics and mathematics of these issues but from my reading I understand that coming into existence is, in itself, not a problem for cosmologists. However, the physics of such high energies is. And, of course, you don’t get around problems like that using something which is only a belief.
June 21st, 2008 at 3:28 pm
Hi guys,
I’ve had quite a lot on last week and will also in the week to come (2 assignments, 2 sermons, etc.), so I’ve not been able to interact as yet, and am tempted not to, for I won’t likely be able to follow up my comments well… but alas…
Re: Infinity & Causality
Interestingly, in this topic, infinity and causality come rushing together… because the very notion of causality sets up an ‘infinite causal regress’ (i.e. ‘what caused the thing that caused the thing the thing that… repeat ad infinitum [pun intended]). This –quite simply– is why it is called the First Cause argument.
And Ken, I’m not sure how you’re proposing that our understanding of quantum indeterminacy, vacuum energy or other things has so ’surely’ caused [yet another pun intended] causality to go out the window?
Also, problelms with the word ‘began’ are unwarranted. Talking of things merely ‘existing’ is to assume those things are eternal. Either the universe is eternal or it began to exist.
June 22nd, 2008 at 3:37 pm
Damian, the cosmological argument doesn’t state that everything must have a cause. It states that everything which begins to exist must have a cause. Since the universe began to exist, it must therefore have a cause. God did not begin to exist, so the argument’s premises cannot be applied to him. It is not special pleading or avoidance to say that the argument does not apply to God. On the contrary, it is necessary to posit an uncaused causer, since otherwise you end up with an infinite regress; which Bill rightly pointed out is not a reasonable situation.
Craig also doesn’t refute himself by referring to God as “infinite”. He confuses some among his audience, evidently, but he does not refute himself. This very objection was raised at the evening Thinking Matters event in Tauranga. He was asked how he can talk about an infinite God directly after arguing that actual infinites are impossible. His answer was that God is qualitatively infinite, while his arguments are against quantitative infinite values. One cannot have an actual infinite number of discrete objects. That is what his argument is against. One can on the other hand, use the term “infinite” in a different way to describe God’s attributes, without intending to imply any such actual quantitative infinities.
Regards,
Bnonn
June 22nd, 2008 at 4:12 pm
Everything that begins to exist begins to exist. But why insist that it has a cause. Aren’t we just trying to apply ‘common sense’ from our own experience in a limited medium-sized world to things completely outside common experience - the quantum micro world or the universe?
Repeating this ‘everything has cause’ mantra opens one up to dogma - and prevents one from really understanding what is going on.
June 22nd, 2008 at 4:59 pm
Perhaps, but I’m not defending the cosmological argument. I’m just making sure that it’s properly represented.
That said, I don’t think that the major premise of the cosmological argument is unreasonable. Everything which begins to exist, it seems, must have a cause. A think cannot cause itself since it does not yet exist; and nothing comes from nothing. I know people like to cite quantum mechanics as refuting at least the latter of these, but ignorance about the cause of something does not imply that no cause exists. To the best of my knowledge, quantum mechanics by no means requires, let alone proves, that some events be genuinely causeless.
Regards,
Bnonn
June 22nd, 2008 at 10:57 pm
Good comments Bnonn.
The cosmological argument may or may not be powerful enough to provide full or near certainty that God exists, but you’re 100% right to emphasize the need to ensure that the argument is being properly represented.
Causality is fairly straightforward, I think. The nuts and bolts of it are pretty simply discussed.
-A thing that does not yet exist cannot cause itself to exist. That just makes sense (at least until we are shown anything [anywhere] that has caused itself to exist)… And I’m not even sure how the heck we could ever know that something that doesn’t exist yet had brought itself into existence anyway!
-Nothing comes from nothing. This also makes sense (at least until we see something come from nothing)… And (again) I’m not even sure how the heck we could ever know that something has come from nothing (and was not caused by something unseen or undetected by us)!