William Craig's Criticisms of Critiques of Kalam Cosmological ..., by Graham Oppy

[heusdens]

FEEDBACK to article(s) about the Kalam Cosmological Argument:
Professor William Craig's Criticisms of Critiques of Kalam Cosmological Arguments By Paul Davies, Stephen Hawking, And Adolf Grünbaum (1995) (http://www.infidels.org/library/modern/graham_oppy/davies.html)
Graham Oppy

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Introduction

The philosophical issue on hand, which is part of the Kalam Cosmological Argument, is a rather old subject in the philosophical debate.
Amongst others, Immanuel Kant wrote about this philosophical issue in [i]Critique of Pure Reason[i] (Kritik der Reiner Vernunft), and in which he argues that both the beginning of time and the infinity of time, can be proven both.
The argument uased in the Kalam Cosmological Argument is also known as the contradiction of the counted infinite number series. This type of argument, very similar to the one used in the Kalam Cosmological Argument, was amongst others put forward by Herr Eugen Duhring, and which was stolen almost literally from Immanuel Kant (in: Critique of Pure Reason), while rejecting the counter proof, which was also given by Kant in the same book.

Infinity of Time

The Infinity of Time is realy a very simple thing, namely that time at either end of the time line has a begin or end. Take two arbitrary points on the time line, measure its distance, and what will yield is a definite and finite number / measurement.
The infinity of time (time without a begin or end) therefore does not imply that any direct measurement of time (time difference) would yield outcomes of infinite numbers, on the contrary!
As well the Kalam Cosmological Argument as the contradiction of the infinite number series state that the series of past events, can not count up to an infinite measurement.
As we alrady have stated, the infinity of time itself, does not imply or involve infinite measurements, but only finite ones.
The infinity of time can be stated as such that there is no finite measurement that could be a bound to a measurement of time difference on the infinite time line. Proof: suppose that such a finite measurement would be a bound to a time measurement of time difference between two specific points on the time line. Now all we would have to do is take the leftmost point, and shift that somewhat to the left. Since on an infinite time line, any point is as arbitrary as the other, and the time line does not have an end to either side, that is a perfectly legal operation. What will come out is that a greater measure as the finite measurement we initially assumed can be achieved, which effictively negates the supposed fact that such a finite measurement would exist.

Contradiction of the infinite number series

Like the Kalam Cosmological Argument, which states that the series of past events can not be an actual infinite, the contradiction of the counted infinite number series states that the outcome of a measurement (count) of the time difference between a suppsed starting point and now, can never yield an infinite measurement/count.
That is of course true. The point is however that the supposed 'starting point' does not exist on the infinite time line, since all points on the infinite time line are arbitrary.
So, in fact the argument smuggles into the premise the things it has to proof, namely that the time line had a starting point at all.
Assuming that the time line had a starting point at all is already assuming that time is not infinite, since an infinite time line does not have a starting point.
What it al comes down to is that infinity can not be conceived of without contradiction. It is a contradiction that the infinite is made up entirely of finite measures, and yet that is the case.
Getting rid of that contradiction, is to get rid of infinity itself.

"The limitedness of the material world leads no less to contradictions than its unlimitedness, and every attempt to get over these contradictions leads, as we have seen, to new and worse contradictions. It is just because infinity is a contradiction that it is an infinite process, unrolling endlessly in time and in space. The removal of the contradiction would be the end of infinity. Hegel saw this quite correctly, and for that reason treated with well-merited contempt the gentlemen who subtilised over this contradiction."

Quote: Friedrich Engels (1877) [i]Anti-Duhring[i] Chapter V. Philosophy of Time and Space.


Link / Reference
For an in-depth discussion against this so-called contradiction of the counted infinite number series that supposedly "proofs" that time had a beginning (a similar objection against the infinity of time as put forward by the Kalam Cosmological Argument) please reference this link:

Friedrich Engels (1877) Anti-Duhring Chapter V. Philosophy of Nature. Time and Space (http://www.marxists.org/archive/marx/works/1877/anti-duhring/ch03.htm).

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[Graham Oppy]

The key claim made in the post to which this one is a reply is that "infinity cannot be conceived of without contradiction". ("It is a contradiction that the infinite is made up entirely of finite measures, and yet that is the case.")

I think that this is plainly wrong. There is no contradiction in Cantorian set theory; whence it follows immediately that infinity can be *conceived of* without contradiction.

Of course, this does not settle the question whether there are *actual* infinities. But it would be another gross error to suppose that this further question can be settled by considerations about what can be directly measured. We can have *theoretical* reasons for supposing that spacetime is actually infinite, as we do in standard Big Bang cosmology. (I think that physics provides plenty of support for the idea that there are actual infinities: no-one yet has the remotest idea how to construct an empirically adequate physics in which *all* quantities are finite.)

Engel's dismissive attitude towards employment of the finite/infinite distinction should be repudiated, as should the idea that *either* of the arguments that Kant gives in his first antimony is good! (There is no good a priori argument for the conclusion that time is finite, or that time is infinite. Both options are intelligible; one needs *empirical evidence* in order to settle the matter -- and it may be that the available evidence is simply insufficient to support an opinion either way.)

[heusdens]

Graham,

Thanks for your comments, and I share the conclusion that the matter can only be resolved based on emprical evidence, and that maybe there will never be sufficent evidence to support either side.


However, the key point in the refutation of Friedrich Engels, as I see it, was that the argumentation against the infinity of time (time without a begin) as used in the contradiction of the counted infinite set which is a similar argument also used in the Kalam Cosmological Argument) is invalid, because the argument smuggles into the premise the thing it has to proof, namely that time had a beginning. The argument can only conclude that time can not be infinite, because it already assumed a starting point of the time line, in order to count from that point to now (and thus "proving" that time was finite). The point is of course that if time is said to be infinite, this simply means that there is no point in time that was a begin. Thus, every attempt to count back from now to the past, will never arrive at "the begin".

[Graham Oppy]

I agree that many arguments against the possibility of infinite time assume what they set out to prove. In particular, there are many such arguments which assume that there is a first moment of time. If there was a first moment of time, then--as you say--the amount of time that has elapsed since then must be finite.

It is also true, I think, that one half of Kant's first antimony relies on this kind of error. (Kant's argument on the other side is no better, however, at least in my opinion. Since there has only been a finite lapse of time since the Big Bang, there can hardly be a good argument for the conclusion that past time must be infinite!)

However, I am not sure that the kalam cosmological argument *must* make this particular error. William Lane Craig has denied in print that it does. (In particular, the *empirical* support for the contention that the universe has a beginning seems quite strong. If this is conceded, then we can just ignore the--very weak (at least in my opinion!)--a priori arguments that he provides in support of this premise.

Given that the (core of the) kalam argument goes like this:

1. Everything that begins to exist has a cause of its existence.
2. The universe begins to exist.
3. (Therefore) the universe has a cause of its existence

I think that the two strongest challenges are: (a) to deny the first premise; and (b) to ask whether there is an equivocation on "begins to exist" between the two premises.

("Begins to exist" might mean "has a first moment of its existence" or it might mean "is not infinitely old". According to orthodox Big Bang theories, the universe is not infinitely old, but it does *not* have a first moment at which it exists. On the other hand, if the first premise is plausible at all, it is only plausible as the claim that everything that has a first moment of its exisence has a cause of its existence. It's only by an equivocation on "begins to exist" that the argument looks even remotely plausible. Or so it seems to me.)

Of course, as I noted above, you might still deny that everything that has a first moment of its existence has a cause of its existence; but I don't think that you need to do this in order to defeat the argument.

Cheers,

Graham

[heusdens]

Graham,

Thanks again for this reply.

I would like to make two points.

Firstly, the Big Bang theory as such does not speak about a "begin of time", it only deals with the fact, that as is observed, the universe is now expanding, and that means that in earlier cosmological times, the universe was much smaller, denser and hotter. Physical theory does not (yet) permit us to speak about time and conditions before a certain point in time.
Theories which go beyond that, and which try to explain what could have caused the Big Bang to occur, are strictly speaking seperate theories. There is for instance the idea of this instanton "pea" (hawking/Turok) which design a possible "begin" of the universe, and alternatively there is the idea of eternal cosmic inflation, which is potentially beginingless, and there are other cosmological theories, some of which are also supposing an eternal universe, without a begin.

Secondly, the core of the Kalam Cosmological argument is projecting on this term universe, as if it could be dealt with as any ordinary thing. The argument in fact assumes an ordinary logic regarding causality, in which all events that take place, have a cause. Every event is at the same time a cause and an effect, for seperate causal relationships. Causality requires that every event is an effect which has a preceding cause or causes.
But all events, both the causes and the effects, are by definition part of the universe, that is the universe in the ordinary meaning of the word. If however we use the word universe to mean observable universe, this is of course a different thing.
If we use universe in the meaning of everything that exists, then by definition the universe does not and can not have a cause, since all causes are already part of the universe. For the same reason causality itself can not have a cause, since that would assume that a cause would exist outside of causality itself.

In this sense also we can not speak about "begin of time" without violating causality, since that event would not have a possible cause. In that way, time itself could not be said to have begun, since for something to "begin" it is already assumed that time exists, and outside of time, we can not speak about anything existing.

So, the only thing we can realy talk about is a universe, which did not begin, but which history can not be traced back prior to some finite time ago. If the Big Bang theory is right (as a scientific theory, in principle it could be wrong) the Big Bang event is just that. History prior to the Big bang is unknowable in any direct way. And apart from some highly theoretical physical knowledge, there is neither a reason for us to know about history prior to that point in time. Strictly speaking however, the history prior to the Big bang is not completely unknowable, that is, some theories that theoretize about the physical conditions prior to the Big bang, can be tested against observations in the observable universe, which means that some theories can be ruled out.

[Abdul Alhazred]

While I agree with your argument when it comes to infinite time extending into the past, what about a timeline which begins at a specific point in the past and extends indefinitely into the future? It seems to me you need a slightly different argument here, though it is hard to see how it bears on Kalam. Maybe someone would like to comment on this.

I would like to note that time is a very poor choice of 'real infinite' to debate in the first place. It has a number of interesting characteristics, some of which were touched on by earlier posts, some were not.

For instance the topography of time has interesting characteristics. If we measure the 'time circumferance' of the universe by the total number of events which occur in a given clock tick then we find that its total space-time volume is a constant value (or at least the 'time circumference' increases inversely to the extent of the spacial dimensions). That is to say as space grows larger time grows 'smaller' until eventually we reach a point where rate of change approaches 0 and spacetime becomes infinite (by which I can only refer to the diameter of the light cone of an observer, since one cannot say ANYTHING about what may lie beyond that).

In a sense I thus have to see the problem of infinite time as akin to the situation which arises when calculating a current flow as resistance approaches 'infinity'. The relation between the two has meaning, but neither 'infinite resistance' nor 'zero current flow' individually do.