The Infinite causal regress is an important issue in dealing with the cosmological argument, especially the kalam version, and the argument form final cause. It basically means that any infinitely recurring causality for any event is impossible, since one never actually arrives at a cause. The importance of this argument applies not only to the now largely abandoned notion of an oscillating universe, but to any finite causes of space/time. This is because in light of the impossibility it means that the ultimate cause of the universe must be a final cause, that is to say, the cause behind all other causes, but itself uncaused and eternal. These are two major issues because they indicate why the ultimate cause of the universe has to be God. Since arbitrary necessities are impossible, the ultimate cause cannot be something which is itself contingent, such as an eternal singularity. The ultimate cause, or "final cause" must be God, since God is a logical necessity.
But lately skeptics have sought to deny these principles. They have actually been denying that infinite causal regress is impossible. This causes me to suspect that they don' really understand the concept. For no one truly understanding the notion of an eternally repeating cause could seriously consider that an infinite causal regress can actual exist. But this denial takes two-forms. First, they just deny it outright. They dot' believe me. And secondly, they sometimes try to provide examples such as the number line, that's a favorite. And of course the ever popular claim that God is also an infinite Regress. That is three arguments to deal with:
1) Out right denial that ICR is impossible
2) The argument that one can find examples in Mathematics
3) The idea that God is also an ICR
Before dealing with the numberline I will just make a little argument on the impossibility of an actual infinite causal regress (that is that one could actually exist in real life).
1)A beginingless series of events is impossible.
A actual infinite is defined as A begingless series of events This is not to say that nothing actual could be eternal, but that a series of events with no begining cannot exist in reality. A thing is said to be actully infinite if part of it is equal to the whole. For example, mathematicians show that the number of fractions is equal to the number of whole numbers, even though fractions can devide whole nubers infintessimally, because its all infinity and infinity is without number. Now here I'm distinguishing between existenced in actuality, the "real world," as oppossed to existence in mathematics.
A linear Causal infinite regress is thought to be possible by Auqinas and Farther Copeleston, but only if it has a prior heirarchical cause. In other words, the causality can be not just linear but also heirarchical. A heirachical infinite regress is also impossible for the same reason, it never really has a cause since it has no begining. A liniar regress of causal nature is impossible without a hierachical cause.
The great mathematician David Hilbert argues for the notion that a beginingless series of events with no higher cause is impossible. ["On the Infinite" in Philosophy and Mathematics (Englewood Cliffs New Jersey: Prentice Hall), 1964, 139, 141.)
(2) ICR is Circular Reasoning
William Row Quoted on website below
Rowe's version of the standard answer goes as follows: Suppose we are wondering why A exists. Suppose further that A was linearly caused to exist by B and that B was linearly caused to exist by C, etc. Here is a causal series, Rowe says, which might well extend infinitely back in time. This is because we need do nothing other than point out B in order to explain why A exists; although B was itself caused to exist by C, we still need refer no further back than B to explain the existence of A. But, Ro we says, suppose we are trying to explain not why A exists but rather why a certain sort of causal activity - the activity of causing A presently to exist - is going on. Here we cannot as before merely point to B. because presumably B is itself being caus ed to engage in the causal activity of causing A presently to exist (and is thus only a kind of intermediary). Accordingly, we have to talk about C's causal activity the causal activity of causing B to cause A presently to exist. This, then, is a series t hat cannot be extended infinitely; this series must have a first member. For if there were no first member, we would never succeed in arriving at an explanation of the existence of the causal activity of causing A presently to exist. We would never be abl e to explain why this activity is going on.11
(But this author supports Aquains' and Copleston in saying that liniear cuasal regress is possible but not a hierarchical one. Easy to see why he says this, because he believed the universe to be inifinite in time, but he still asserts that there must be a higher eternal generation)
Just extend Rowe's argument a little further to see that ICR is circular reasoning. The need for a cause is granted bye ICR advocate; and that need will be supplied, so they say, by the cause of the previous event (for example in an ocillating universe, the previous Big Bang supplies the need for the casue of this universe). But, when it comes to explaining the causual relation to the whole series they will say that is uncessary, because they have that previous link in the chain and it's covered by the infinte serious of previous links, but nothing ever expalins how the previous link could be there, except a previous link.
This is just circular reasoning because no matter how far back you go you have a cause that allows for any particualr link to exist. Take this example:
a => b, b => c, => d => e, e => f
Now if we say "how can f exist without a cause? They say well it has a cause in e. But e doesn't have a cause except in a equally unexplained d, and go back as far as you will, there is never an explaination for how this could be. Yet they agree that the causal principal is necessary because they keep sticking in intermeidate causes. If the causal principal is necessary, then there must be a final cause taht expalins how it could begin. Causality is linear and if they are going to argue for cyclical universe they have cover a linear concept of casu and effect.
If a series of events go back in time forever it is a beginingless series of events. IF the universe existed forever, for example, this would constittue an actual infinite. This is because the series of events that led to the current universe would be infinite. This is to distinguish it form a "potential infinite" which might be achieved by adding one event to another in a series and going on infinitely. But a series of events that has already transpired infinitely is an actual infinite.
Or let's look at the notion of finnishing an infinite series. If a man claims to have been counting for infinity and is at last about to reach zero, he says -3, -2, -1, he's finally finnished. Yet, he should have finnished eons before, an infinity of time passed enons ago, or centuries, or decades, so he should have finnished by now. Another strange paradox is that if we could check this man's counting in the past we would never find him counting. For he would have finnished an infinity ago so we could never find him counting at any time that we ever checked his counting. Yet if he never counted he could never finnish. Now may skeptics are going to say that it is impossible to count infinitley and so forth, yes, obviously. But these are the kinds of examples used in transfinite mathematics to illustrate this point.
"This illustrates once more that the series of past events could not be wihtout a begining for if you could not count numbers from eternity, neither could you have events form eternity. These examples underline the absurdity of a beginingless series of events in time, because such a sereies is an actual infinte and an atual infinite cannot exist. This means that the universe began to exist, which is what we set out to porve" (William Lane Criag in his early work, The Existence of God and The begining of the Universe Here's Life Publishers 1979 p.4 [and don't forget the empirical scientific data which also proves this same pint with the Big Bang).
3) An Actual Infinite Cannot Be Achieved by Adding one event to the series, thus the series of events in time can never be actually infinite.
This can also be understood in the fallacy to trying to count to infinity. This should be pretty obvious, because no matter how many events we add we can always add one more and continue to add events forever. One can never count to infinity. Most people understand this pretty well.So one could never add one event to another and reach infinity, it's the same thing. This is also called The impossibility of traversing the infinite.
Thus an actual infinite could come to exist only if all the memebers came to exist at the same time. As Craig points out "if an infinite number of Days existed before today, today would never come because one can never traverse the infinite." (50).
Philosopher John Hospers states:
"If an infinite series has preceeded the present moment, how did we get to the present moment? How could we get to the present moment--where we obviously are Now--if the present moment was preceeded by an infinite series of events?" [An Indtorduction to Philosophical Analysis, 2nd ed. (London: Rutledge and Kegan Paul, 1967) 434)
This First argument, the impossibility of a beginingless series of events with no higher cause was repeatedly defended and always successfully by G.J.Withrow, Professor of Mathematics at University of London's Imperial College of Science and Technology. see "The Age of the Universe,"British Journal for Philosphy of Science (1954-55) PP215-225. Natual Philosphy of Time (London: Thomas Nelson, 1961) See also Philsopher William Rowe The Cosmological Argument Princeton University press 1975
Now What if someone argues that the infinite series would be beyond time? In that case the skpetic loses the argument that there is no causality before time. IF there is no motion, causality, or change beyond time than there cannot be a series of events leading form one cause to another beyond time.
Now let's examine the three arguments.
1) Out right deniel that ICR is impossible.
Well, if they don't believe the logic, they are pretty hopeless. And if they dont' accept the word of the mathematicians that are quoted, there isn't much you can do about it. But it seems pretty obvious that if you have an ifinite series of causes leading back infinitely you would never have an actual cause, and the thing to be caused would not exist, just as you cannot count to infinity, or just as the counter claiming to have arrived at zero from infinity would never have actually counted.
2) That the number line is an exmaple from Mathematics that proves the actual infinite, or Infinite causal regress.
David Hilbert has prove, as quoted above, that transfinite mathematics cannot exist in life. The number line is not an actual series of events, it is ony hypothetical. Moeover numbers do not cause each other. It is not a causal regress.
3) That God is an ICR
This is merely to confusse an infinite with an infinite regress The ICR is an infinite series of events. God is not a series of events. God is not an event, God is not a recurrsion of causes, he is one final cause. God is not in time, he is eternal. So the two are not analogous at all. God is not an ICR.
The ICR is an impossibility, it cannot exist in actuality. This means the universe cannot be eternal, for the universe is an infinite series of causes, each one leading to the next. It certainly means the old oscillating universe notion of etnerally recurring big bangs and cruches is right out! Therefore, there must be a fainal cause which is eternal and is not a series of events but one fianl cause that transcends the chain of cause and effect. It causes the universe but it is not in turn an effect of any other cause.
Aristotle and Bertrand Russell agree
Robert Koons, University of Texas
Lecutre 5 Phil 356 Theism Spring 98
Another example is mentioned by al-Ghazali. Suppose that the sun and moon have each been revolving around the earth throughout an infinite past. There are 12 revolutions of the moon for every revolution of the sun. As we go back in time, the gap between the number of months and years grows ever wider, yet, taken as a whole, there are an equal number of elapsed months and years (both infinite). Cantorian set theory agrees with this paradoxical result: the cardinal number of months and years is exactly the same.
Bertrand Russell discusses a similar paradox, which he called the Tristam Shandy paradox. Tristam is writing is own autobiography. He takes a whole year to write down the events of a single day. In an infinite amount of time, Shandy can complete the task. Here's a time-reversed version of the paradox: suppose that Tristam is clairvoyent -- he writes about his own future. Last year he wrote about today's events; in the year before last, he wrote about yesterday's events. Today, he has just completed an infinite autobiography, cover all the events of his infinite past, despite the fact that, as we go farther in the past, Shandy is every further behind in the task -- i.e., 1000 years ago, he was still writing about the events of only the last three days.
Final note: The paradox of Time.
Some thinkers believe that time is an infinite series. I do not agree with this notion, I accept t=0, time begins in the Big Bang. But this is a valid viewpoint, I just dont' happen to agree. But that does not prove that a beginingless series of events with no higher cause can exist. Time can still have a higher cause, God perhaps, in heierarchical fashion.
on the Reasonable Faith Site William Lane Craig answers a question a reader had asked. This reader had recently talked ot physicsts who said that the standard model (singularity) Is no longer the preferred model.
I recently was told by some physicists whom I had the chance to interview for a paper that the standard big bang model of the universe does not include a singularity anymore. That may have been the case twenty five years ago, they said, but nowadays physicists say that the big bang extends only back to Planck time. Can you PLEASE clarify the confusion I’m having on this?
He refers to James Sinclair who is writing a cahpter for a forth comnig work on cosmology.
Indeed, Jim’s survey of contemporary cosmology reinforces just how robust the standard model’s prediction of an absolute beginning continues to be. He considers three broad research programs being currently pursued based on possible exceptions to the Hawking-Penrose singularity theorems, which support the standard model’s prediction of an initial cosmological singularity. These are (1) Closed Timelike Curves, (2) Violation of the Strong Energy Condition (Eternal Inflation), and (3) Falsity of General Relativity (Quantum Gravity). The first of these postulates an exotic spacetime which features circular time in the past and so is not taken very seriously by the vast majority of cosmologists. The real work has been on the other two alternatives.
With respect to the alternative of Eternal Inflation, it was suggested by some theorists during the 1980s that perhaps the inflationary expansion of the universe was not confined to a brief period early in the history of the universe but is eternal in the past, each inflating region being the product of a prior inflating region. Although such models were hotly debated, something of a watershed appears to have been reached in 2003, when three leading cosmologists, Arvin Borde, Alan Guth, and Alexander Vilenkin, were able to prove that any universe which has, on average, been expanding throughout its history cannot be infinite in the past but must have a past space-time boundary.
What makes their proof so powerful is that it holds regardless of the physical description of the universe prior to the Planck time. Because we can’t yet provide a physical description of the very early universe, this brief moment has been fertile ground for speculations. (One scientist has compared it to the regions on ancient maps labeled “Here there be dragons!”—it can be filled with all sorts of fantasies.) But the Borde-Guth-Vilenkin theorem is independent of any physical description of that moment. Their theorem implies that even if our universe is just a tiny part of a so-called “multiverse” composed of many universes, the multiverse must have an absolute beginning.
Vilenkin is blunt about the implications:
It is said that an argument is what convinces reasonable men and a proof is what it takes to convince even an unreasonable man. With the proof now in place, cosmologists can no longer hide behind the possibility of a past-eternal universe. There is no escape, they have to face the problem of a cosmic beginning (Many Worlds in One [New York: Hill and Wang, 2006], p.176).
Some current cosmological speculation is based upon attempts to craft models based upon possible exceptions to the Borde-Guth-Vilenkin condition that the universe has on average been in a state of cosmic expansion. In his article Jim provides the following chart of possibilities:
this graphic is from his article
The first case involves an infinite contraction prior to the singularity, followed by our current expansion. The second case postulates an unstable initial state followed by an inflationary expansion. The third case imagines a contraction followed by a super-expansion fueled by ‘dark’ energy, with the universe breaking into a multiverse. The fourth case postulates two mirror-image, inflationary expansions, where the arrows of time point away from the cosmological singularity. Jim shows that these highly speculative models are all either in contradiction to observational cosmology or else wind up implying the very beginning of the universe they sought to avert.
The other alternative to the Hawking-Penrose theorems that has been vigorously pursued is Quantum Gravity models. Jim provides the following chart of such models:
The first class of models postulates an eternal vacuum space in which our universe originates via a quantum fluctuation. It was found that these models could not avoid the beginning of the vacuum space itself and so implied the absolute beginning of spacetime. These models did not outlive the early 1980s.
The second class, string theoretical models, have been all the rage lately. They are based upon an alternative to the standard model of particle physics which construes the building blocks of matter to be, not pointlike particles, but one dimensional strings of energy. Jim discusses three types of string cosmological models:
The first of these string cosmologies, Ekpyrotic cyclic models, is subject to the Borde-Guth-Vilenkin theorem and so is admitted to involve a beginning of the universe. The second group, Pre-Big Bang models, cannot be extended into the infinite past if they are taken to be realistic descriptions of the universe. The third group, the string landscape models, feature the popular multiverse scenario. They are also subject to the Borde-Guth-Vilenkin theorem and so imply a beginning of the universe. Thus, string cosmological models do not serve to avert the prediction of the standard model that the universe began to exist.
The third class of Quantum Gravity models, Loop Quantum Gravity theories, features versions of a cyclical universe, expanding and contracting. These models do not require an eternal past, and trying to extend them to past infinity is hard to square with the Second Law of Thermodynamics and seems to be ruled out by the accumulation of dark energy, which would in time bring an end to the cycling behavior.
Finally, fourth, the Semi-classical Quantum Gravity models include the famous Hartle-Hawking model and Vilenkin’s own theory:
These models feature an absolute beginning of the universe, even if the universe does not come into being at a singular point. Thus, Quantum Gravity models no more avoid the universe’s beginning than do purported Eternal Inflationary models.
In sum, I think you can see how misleading the physicists’ statements to you were. The prediction of the standard model that the universe began to exist remains today as secure as ever—indeed, more secure, in light of the Borde-Guth-Vilenkin theorem and that prediction’s corroboration by the repeated and often imaginative attempts to falsify it. The person who believes that the universe began to exist remains solidly and comfortably within mainstream science.
It doesn't' seem that the old occilating ICR is of much use in cosmologies of today. That seems less used than the standard (singularity). All of these theories suggest an absolute beginning.
Of course we really don't even need that. Even if we assume eternal universe has no beginning that still doesn't get around necessity and contingency. The concept of an eternal necessity is not unheard of. At times I have given the impression that contingent is synonymous with temporal. Necessity is synonymous with eternal. That would be true in terms of purely naturalistic causes. But the idea of an eternal contingency was advanced by Aquinas. this works, if and only if, the necessity upon which is pinned is also simultaneously eternal as well. Take the example of an eternal flute player. As long as the timeless musician plays, the music is eternal. If he were to stop the music would not be eternal. If he always places the music is eternal and yet contingent.