#771 Physicists & Philosophers Reply to the Kalam Cosmological Argument (Pt II)

Dr. craig’s response

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A

Last week we looked at criticisms of the first philosophical argument for the finitude of the past. Today we’ll look at criticisms of the second philosophical argument for the past’s finitude based on the impossibility of forming an actual infinite by successive addition. Once again, my responses are in blue italics.

B. SECOND PHILOSOPHICAL ARGUMENT

NARRATOR: Another example given to try and refute infinity are the orbits of Jupiter and Saturn.

RF VIDEO: Suppose that for every one orbit Saturn completes around the sun, Jupiter completes two. The longer they orbit the further Saturn falls behind. Now what if these two planets have always been orbiting the sun from eternity past? Which has completed the most orbits? Strangely enough, the number of their orbits is exactly the same – infinity. But that seems absurd for the longer they orbit the greater the difference becomes.

Response: This is a second, independent argument against the infinity of the series of past events. Even if you think that an actually infinite number of things can exist, an infinite collection cannot be formed sequentially by adding one member at a time. Al-Ghazali’s illustration of Jupiter and Saturn’s having completed the same number of orbits is a great illustration of how absurd this is.

DANIEL ISAACSON: If they were always orbiting then there is no notion of one being at any given point having gone twice as many times as the other. That just doesn't make sense.

Response: Thank you! That’s just my point! At any point in the infinite past they will always have completed exactly the same number of orbits, even though every time Saturn completes one orbit, Jupiter completes two.

ALEX MALPASS: The hypothesis is not that they start orbiting at some point in time and they've done zero orbits at that point, but if the hypothesis is that they'd always been orbiting then it's just the case that they've both always done infinitely many orbits. There's no sense in which you draw a graph that they start at zero and then diverge away from each other and then one of them catches up or something. They're just both always having done infinitely many.

Response: Yeah, weird, right? You think this could really happen?

NARRATOR: Infinity is accepted by mathematicians. So what about physicists?

Response: To reiterate: the mathematical legitimacy of the actual infinite is not at stake in this debate. The question is whether these mathematical concepts can be instantiated in the real world.

14:59 NIAYESH AFSHORDI: So in regards to infinities and physics, the only obstruction that we have is an observer cannot measure an infinite number because infinity is not a number. I think that our observable cannot be infinite but things like the entire volume of a space or the entire duration of time can be infinite as long as an observer cannot measure them.

Response: One of the most striking facts about modern science is that it does not employ the concept of the actual infinite. The use of the potential infinite is entirely adequate for contemporary science. There is no scientific evidence whatsoever of the existence of an actually infinite number of anything.

15:25: PHIL HALPER: Roger, why don't you start with the absurdity of a Hilbert Hotel – that you can't . . .

ROGER PENROSE: It's not an absurdity. It's just what happens if you have infinity. I mean, that was the major thing that Cantor had showed – you can talk about infinity in a serious way. And you deduce very powerful results from talking about infinity in the right way. You have to be careful when you talk about infinity but, yes, if you're careful, talking about infinity is perfectly reasonable. So I can't see a general statement about infinity is not physics.

Response: Right; “It's just what happens IF you have an infinity.” That’s a big “if.” Hilbert knew well how to illustrate the existence of an actually infinite number of things, so if an actual infinite could really exist, you could have a Hilbert’s Hotel. But in view of its counter-intuitive consequences, is that really possible?

ALAN GUTH: I think what Roger's probably thinking is what I would think is that there's certainly a well-defined mathematical description that one can imagine where there's some function that's defined for all time that describes what's happening at all time – maybe a wave function that evolves with time and is defined for all time. And the “how did we get to now” question really just doesn't arise. At the time t₀ that we call now the wave function says that certain things are happening and if that's an accurate description that's what's happening. One doesn't have to start at the beginning at minus infinity and go through all the times to get to now. One is just here now.

Response: This is evidently Guth’s attempt to respond to the second philosophical argument against the infinitude of the past based on the impossibility of forming an actual infinite by successive addition. What he propounds here is a tenseless view of time according to which temporal becoming is purely illusory. Therefore no question can arise about “how did we get to now?”—indeed, on this view there is no objective “now.” But on a tensed view of time, according to which temporal becoming is a real and objective feature of the world, that question is unavoidable. I have written two academic books on the tensed and tenseless theories of time respectively, arguing that the tensed theory of time is correct: The Tensed Theory of Time:  A Critical Examination (Dordrecht: Kluwer Academic Publishers, 2000) and The Tenseless Theory of Time:  A Critical Examination (Dordrecht:  Kluwer Academic Publishers, 2000).

NARRATOR: Craig claims that the infinite past is impossible because one can't reach infinity by successive addition - which is true if you only have a finite amount of time. But what if you have an infinite amount of time? Could you count all the numbers then?

Response: Aha! Can you count down all the negative numbers finishing today by never beginning but ending now? That seems absurd. If you could, then why didn’t you finish yesterday or the day before that or the day before that, since by then an infinite amount of time had already elapsed? At any point in the past you should have already finished your countdown. But that contradicts the hypothesis that you have been counting from eternity past!

ADRIAN MOORE: Yes, if you're counting forever. If you're never finishing there is a sense in which you can count them all. And it's the following sense – given any individual counting number (however big – a million, a billion, a trillion) you'll eventually get there. It doesn't mean that you ever will reach the point that you can stop and say, “Done it! I've now finished. I've counted all the infinite numbers.” That never happens! However far into the future you go you've still got infinitely many numbers still to count. So, no, this isn't a task that ever terminates but we didn't claim that it did. The claim was only that you can count infinitely many numbers in an infinite amount of time.

Response: Of course, for any finite number, you will eventually count it. But it does not logically follow that therefore you can count all the numbers if they are infinite. Your counting generates a potential infinite, and you cannot convert a potential infinite into an actual infinite by successive addition of finite quantities.

ALEX MALPASS: OK, so sometimes the problem is supposed to be that we can't transition from the finite to the infinite. After all, if we've got something finite and we add a finite amount to it then the result is going to be finite. So no matter how many times we do that we're never going to break out from the finite to the infinite. The problem is not so much that that's false, and it seems to me that that's true, it's just that the hypothesis of the past having no beginning is such that it's always been infinite. There's never been any point in the past where there had only ever been finitely many. So there's no need for a transition.

Response: Notice the disagreement between Moore and Malpass on counting to infinity! Here Malpass seems to agree with me that counting to infinity generates a merely potential infinite. But the question concerns counting down past events from infinity. Is that really possible?

ADRIAN MOORE: So, you never get to the end of this process. You never get to the last biggest counting number. This is a sequence. The sequence of counting numbers – that is a sequence without an end. But that's perfectly acceptable. That makes perfectly good sense. The fact that you can't get to the end is indicative of the fact that there is no end.

Response: Of course, because it’s potentially infinite! But for the past to be potentially infinite, it would have to be at every point finite but growing in an ‘earlier than’ direction, which is absurd.

NARRATOR: Suppose we agree that the infinite is impossible. What does that mean for the infinite future? Supporters of the kalam are generally committed to this idea not just because religious texts seem to promise it but also because some allege that our lives have no meaning without it.

18:55: WILLIAM LANE CRAIG: . . . that on a naturalistic worldview everything is ultimately destined to destruction in the heat death of the universe. Our moral lives become vacuous because they don't have that kind of cosmic significance.

Response: This is a red herring. The kalam cosmological argument is independent of the belief in personal immortality. We have here a good example of an ad hominem objection.

INTERVIEWER: I still need to have you explain that for me better because again it seems to me it's one thing to say it lacks eternal cosmic everlasting significance, it's another thing to say it lacks significance. In fact, to give one of your examples you talked about (I don't remember the source of this quote) the torturers. Was it Nazi torturers? You say, you know, if theism isn’t true then it doesn't really matter. This strikes me as – I’m sorry, I’m sure it's going to sound rude but – it strikes me as an outrageous thing to suggest. It doesn't really matter? Surely it matters to the torture victims whether they're being tortured. It doesn't require that this makes some cosmic difference to the eternal significance of the universe for it to matter whether a human being is tortured. It matters to them, it matters to their family, it matters to us. So, again, how do you move from the lack of eternal significance to the thought that if it doesn't have eternal significance it can't have any significance?

WILLIAM LANE CRAIG: Because the victim, it obviously matters to him in the sense that he's in pain and in agony but ultimately it doesn't matter that he was ever in pain and in agony. The whole thing just degenerates into utter meaninglessness and insignificance.

NARRATOR: It's hard to see how someone can claim that infinity is incoherent and then state that our lives are meaningless unless they are eternal. After all, the infinite future seems to have remarkably similar properties to an infinite hotel.

ALEX MALPASS: If you think about the number of events in the future as like equivalent to the number of guests in the hotel and then as time passes we're removing an event from the future and putting it in the present and we can ask how many events are there left in the future. It's the same number of events in the future as there were before that event entered the present. So even though we've taken one away we've got the same number left. That's exactly the same property as adding one guest and having the same number of guests after adding it in. So if one of them is problematic so is the other.

ADRIAN MOORE: If the idea of infinity is putting pressure on the idea of an infinite past then it's going to put equal pressure on the idea of an infinite future. There's no clear asymmetry there that means that one of those is problematical in a way in which the other isn't.

Response: There is a notable asymmetry between the past and the future given a tensed theory of time, according to which temporal becoming is an objective feature of reality. On this view the past is now actual, but the future is merely potential. Moore seems to be presupposing a tenseless theory of time according to which past and future are on an ontological par.

NARRATOR: Craig's response to this problem is to suggest that an infinite past would be actual but the infinite future would only be potential.

21:41: ALEX MALPASS: It seems to me that this rests on a mistake because Craig, instead of focusing on the question “How many future events will there be if the future is endless?” to which the answer is infinitely many, Craig instead switches to “How many future events will have been?” and that – it’s true – is always finite and increasing over time and approaching infinity but never getting there. But its problem is that those two things are compatible with each other. For one thing it's changing the subject. If you say how many events will there be and to answer in terms of how many events there will have been, it's changing the subject. But also, they're both true. I mean, even though there will have been finitely many events, it's also true that there will be infinitely many events in the infinite future. Those two are not incompatible with each other.

Response: I disagree. There will never be an actually infinite number of events. For any finite number you pick there will eventually be that many events, but there will never be an actually infinite number of events. You can’t turn a potential infinite into an actual infinite by counting.

So much for their critique of the second philosophical argument based on the impossibility of forming an actual infinite by successive addition. Next week we look at scientific evidence for the beginning of the universe.