Is Infinite Past Duration A Problem?

One of the more significant arguments to deny that God is a being of duration, and to assert the necessity of God’s eternity being one of timelessness, is the reasoning which claims that an infinite past duration is impossible. The argument takes either the form of seeking to prove that an actual infinity is not possible, which is what an infinite past duration would be, or the form of proving that even if an actual infinity is a possibility, it could never be formed through successive addition, which is how the past is formed.

Hence God must be timeless and have created the time bound universe. I have argued for the difficulties with a timeless God creating, in an unpublished book entitled ‘The Eternal God’. What concerns us here is the accusation that God’s infinite past is an impossibility, since such a view of God’s nature is a necessary correlate of the temporal view of God’s eternity.

William Lane Craig presents this interesting attack on our thesis. The second form of the argument we will examine is also argued by Stuart C. Hackett, “The Resurrection Of Theism, (Baker Book House, Grand Rapids, MI, 1982), pg. 194-203. He argues for a cosmological proof of God’s timeless existence through the impossibility of naturalism’s eternally existent universe. It’s use in this context will interest us below. In his essay “”Creatio Ex Nihilo” Craig writes to confront Process Theology’s denial that God created the world “out of nothing.” In order to deny this theology’s claim that the universe and God have always co-existed, he seeks to show that infinite past duration is contradictory, and hence the universe must have had a beginning. 

Although his argument is directed at the eternal past existence of the universe, it is important to us since a result of his conclusion is that one cannot hold a view of God’s eternity as infinite past duration. 

Craig presents the two versions of the argument. The first (Ibid. , pg. 156) is that an infinite number of things cannot exist, which is what an infinite series of past events is, hence an infinite past is impossible. To illustrate, he refers us to the German mathematician David Hilbert’s description of the infinite hotel. It has an infinite number of rooms that are all full. Even though this is the case, room can be found for an additional guest by moving every guest up one room number. Even an infinite number of guests can be found room by moving all the guests up to a room number twice the value of their present room, clearing out all the odd number rooms. 

Interestingly, even if an infinite number of guests check out, the hotel is still just as full. All this illustrates that while infinity is a conceptual possibility, there could not be such an “actual number of things. It shows the concept of infinity is the fact that there is no limit to how many things there can be in fact, or how large they can be, but actual existing things have determinate number and size. Just so, we can divide something in half forever (assuming no limit to our ability to carry out the procedure) but no actual thing could be divided into an actual infinite number of segments.  

Craig’s second argument (Ibid, pg. 162) attempts to demonstrate that even if one assumes the possibility of an actual infinity, one could never “form it through addition.” In this case it is asserted that the series of past events has been formed by addition, such a series formed by addition cannot have reached infinity (since it can be added to), so the past cannot be infinite.  

Possible objections to Craig’s second argument suggest although beginning at a point and counting to infinity is impossible, it could be possible with no beginning, to count across infinity and end at a point. Craig’s reply is “If one cannot count to infinity, how can one count down from infinity? If one cannot traverse the infinite by moving in one direction, how can one traverse it by simply moving in the opposite direction?(Ibid. , pg. 162. ) He goes on to describe an eternal counter, counting . . . -3, -2, -1, 0. Why does this counter finish now and not earlier or later? An infinite time would have elapsed in either case. “This illustrates the fact that the formation of an actual infinite by successive addition is equally impossible whether one proceeds to or from infinity. (Ibid. , pg. 163. )  

What are we to say in response to these arguments?My own assessment is that Craig’s first argument is basically sound but unharmful because it is misapplied, and his second argument would be harmful if successful, but it is not successful. 

I think the first argument does demonstrate the impossibility of an actual infinity. Actually existing things are things with determinate qualities and are of determinable quantity. Infinity does not have quantitative application. In fact, when dealing with the concept of infinity all quantitative distinctions are dropped. Infinity is the idea of  “no limit, no number. ” It should not be considered a number greater than the greatest number. Infinity is the fact that in the process of addition or division, there is no limit to the process, even though the result is always finite. The following quotations from Israel Efros in “The Problem Of Space In Jewish Philosophy serve to illustrate this point.  

The infinite is not a product of an inconceivable number of finite spaces . . . the meaning seems to be this, namely, the removal in our thought of all quantitative determinations and limits. Israel Isaac Efros, “The Problem Of Space In Jewish Mediaeval Philosophy (Dubuque, Iowa, 196-), pg. 100.  . . .

an infinite quantity means nothing else than an infinite finitude. (Ibid. , pg. 95. ) 

That is why the current definition of infinity as greater than the greatest conceivable body, is radically wrong. The difference between infinite and finite is not merely in “degree but in essence.” (Ibid. , pg. 99. )  

But does this mean Craig is correct in concluding there could not be an infinite set of past events? Here is where the error lies, in the application of the argument against an actual infinity, to the non-existent events of the past.  

The individual incidents that have past into non-existence are counted and represented as though they were still in existence, and “as though they were things with a definite beginning;  this imaginary number is then either increased or reduced. (Ibid. , pg. 98. )  

The fact is, the past does not exist. It is not something we can now enumerate in the present. Craig is correct in asserting that if time stretches back endlessly into the past,  there is no limit to the number of events which have happened. But the point is just this. They “have happened;  they are not actual events ” in the present. It would be impossible to say an infinite number of events are “now occurring” because that would be an “actual infinity. ” 

The fact is, every past event was one of a finite number of events that were happening at that time. It just so happens that there has never been a time when something was not happening and so it is impossible to enumerate the past, but this is only the problem of “un-createdness”. The fact that something exists means that something must always have existed. The timeless view does not remove the before-ness of creation. Infinite past duration is an undeniable correlate of perceived existence. The concept arises immediately with the concept of existence. 

Even if we accepted the possibility of existence “popping into existence” with no cause, we would still recognize an infinite past duration when nothing existed. All this of course assumes an objective view of time, a view not without its challengers, including Craig. For the sake of brevity I will not attempt to justify this view, since it is sufficient to our purpose to show that the infinite past duration associated with this view is not incoherent as Craig attempts to prove. This is shown by the fact that the past does not “now exist” and hence does not constitute an “actual infinity”, which it would need to be for Craig’s argument to be successful.  

Our comments also serve to show the failure of Craig’s second argument. Since time has “process” features, it is irrelevant to deny an infinite past duration could be “formed”. Nothing infinite “can be formed”, but since the past “is past”, it does not exist as a formed set. The infinite past is merely the fact that the whole of finite existence has always existed in some form, allowing of course that some of it may have been created at some time in history. My comments assume that God is a part of “existence. “At no time has the existing set of events been infinite, there merely has been no beginning to when existence in some form has been “happening.” 

Again Efros’ comments are important.  

Let us take an example from time which is supposedly Beginning-less. Up to now we have a series of moments infinite as to beginning, but limited by this present moment. A day passes by and a number of moments are added to the past. It does not mean, however, that the infinite has been ‘increased’, for this would suggest that we had a fixed calculable number of moments which we really do not have. We have a case of addition, but we cannot reduce it to a mathematical equation. What are you going to add it to? You are dealing here with unmathematical notions or metamathematical, if you will, and you have no right to subject them to mathematical treatment. (Ibid. , pg. 106-107. ) 

Having attempted a reply to the accusation that infinite past duration is not possible, and its sister accusation that therefore God’s eternity cannot be one of duration without beginning or end, I would like to qualify the strength of my conclusion. 

Although I do not believe Craig succeeds in proving the impossibility of an infinite past per se, I think a genuine objection to my view of God’s eternity does arise from my agreement with Craig concerning the impossibility of an actual “present infinity”. Even though God’s infinite past is not a problem because it “is past”, God’s memory of the past does appear to be a problem. God’s memory exists in the present, is a memory of every event from the past, and the number of these events is infinite. God’s memory would therefore constitute an actual infinity, which we have concluded with Craig is impossible. 

As to how harmful this difficulty is, I would have to stress that it is the only problem I can see with the view that God is a being of duration. If the only alternative to it is timelessness, as overwhelmed as this second view is with difficulties, then I must continue to hold the former view as the most reasonable alternative I see at present, theistically. 

However, I do see this difficulty as providing interesting ammunition for a naturalistic denial of God’s existence, since a timeless God is incoherent, and since a temporal view of God is hindered by the assertion of God’s infinite memory. Because endless past duration seems necessary and fits the naturalist scheme, one could argue for the latter’s preference. However, even here we are only faced with one difficulty for theism, whereas naturalism may well have many more problems, or more important problems facing its assertion, which would still force us rationally to prefer theism.  

There also may be some solution to the problem I have raised, although I do not at present see one. Many theists accept the possibility of actual infinity and will not see my problem as a problem. So far I am not able to join them in their enthusiasm. I am also not attracted to the suggestion that perhaps God forgets things, making his memory finite. For one thing, even if he forgot millions of things, it seems that an infinite past would still give him infinite things to remember, since there would simply be “no limit” to subtract from. It also seems quite natural to believe God remembers what he has done just like we do, and seems unnatural to suggest a blank out as the solution to such a philosophical difficulty. But I can conceive no other type of solution.  

I have raised this issue in the name of honesty and would welcome further contributions from whatever source as to a solution, if there is one. Past experience leads me to expect it eventually. Until that time I must submit the view of God’s eternity as one of infinite duration as such a satisfying view that I have found only one objection to it for which I see no solution. Such complete satisfaction is a rare commodity in philosophical inquiry.  1997 Kel Good, used by permission; this publication may be copied freely as long as no alteration is made to the text.

Copyright 2019 Kel Good. This publication may be copied freely as long as no alteration is made to the text. For more information write: Kel Good via What I Believe This Week (

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