Since the Kalam Cosmological Argument is being shared on social media by “everyday people,” it’s time to inquire into how the argument became so widely known. Although it does appear in Dinesh D’Souza’s book What’s So Great Christianity, D’Souza, if I recall correctly, completely ignored philosophical reasons for why the universe had a beginning. He based his argument for the finitude of the universe on a Big Bang model that is, from what I gather, obsolete. We have to, ironically, look to a book by a Christian publisher to conjecture why the Kalam argument has become so mainstream. I am hesitant to even bring up arguments found in a book written for a popular audience, but in this case, you can count the a priori arguments on one hand; so why not?
The popular book I am using is Lee Strobel’s The Case for a Creator. In its pages, we find the Kalam argument. We are informed by its defender, William Lane Craig, that it has been around in its current form for hundreds of years. In case you don’t know it:
• Whatever begins to exist has a cause
• The universe began to exist
• Therefore, the universe has a cause
I posted some notes about it in an earlier blog: Notes on the Kalam Argument
Craig only gave two or three a priori arguments for premise 2 in the popular book. Frankly, that’s not bad considering that the mainstream publisher (Regnery) that put out the D’Souza book didn’t include any. Part of the first a priori argument was included in my book Stubborn Credulity. I’ll reproduce the relevant section here:
According to the apologist William Lane Craig, the early Christian and Muslim scholars "pointed out that absurdities would result if you were to have an actually infinite number of things. … Since an infinite past would involve an actually infinite number of events, then the past simply can't be infinite." Craig is equivocating here. Although an event may be a thing in the conceptual sense, it's not a thing in the physical sense. For example, he said, "Substitute 'past events' for 'marbles,' and you can see the absurdity that would result." He's assuming that it's legitimate to substitute events for marbles. Is it? Things have properties that events don't have. As one philosopher explained,
[P]ast events are not movable. Unlike the guests in a hotel, who can leave their rooms, past events are absolutely inseparable from their respective temporal locations. Once an event has occurred at a particular time, it can't be "moved" to some other time.
Craig talked about adding and subtracting using infinity ("infinity minus infinity"), but, in this case, arithmetic doesn't make sense. As Paul Davies pointed out, "infinity itself is clearly not a number, or anything like it." If it's not a number, how can we use it for addition and subtraction?
The reason I set out to write this post is that I wanted to scrutinize, in particular, the sentence “[A]n infinite past would involve an actually infinite number of events.” In Craig's more scholarly work, we tend to see the following syllogism:
1. An actual infinite cannot exist.
2. An infinite temporal regress of events is an actual infinite.
3. Therefore an infinite temporal regress of events cannot exist.
See the similarities. "Actually infinite" appears to be implying "an actual infinite". The claim that an infinite past is an actual infinite is actually (no pun intended) controversial. Craig had to spend time in his scholarly books defending it. In an early draft of Stubborn Credulity, I rejected Craig's claim:
[Craig] conceded that "the collection of all past events prior to any given point is not a collection whose members all co-exist." ... [E]vents aren't things that accumulate in some pile. Craig mistook the fixity of the past for the actuality of the past. If time has no beginning then there is an infinity of prior moments. The events are literally countless. If you add the present moment to prior moments it would be like adding one to "countless". The sum, supposedly, is one which would make sense because only one event presently exists - the present one.
My point was that there is at the moment, not an infinite, but a moment. Assuming an infinite past, the infinite part of the timeline is horizontal, not vertical. The upshot: events are not like infinite marbles. In a paper that I recently discovered, Wes Morriston articulated what I was trying to express in my book. Whether Morriston would agree or not, even if the past is "actual," it doesn't exist. As I wrote, only one event presently exists--the present one. A physical infinite, on the other hand, would be undoubtedly real. Craig could have used the word "actual" to describe both types of infinite, but the examples he gave involve not just actual, but real infinites. There is an important distinction:
[I]t does not immediately follow that infinite sets in general are impossible. Before drawing so sweeping a conclusion, we need to consider what it is in the example that produces the (allegedly) absurd implication. The answer, I think, can be found in the way in which the number of elements in the set interacts with other features of the example. A library is a collection of coexistent objects (books and shelves) whose physical relationship to one another can be changed. It is only when these features are combined with the property of having infinitely many elements that we get this particular sort of implication. ("Craig on the Actual Infinite," Religious Studies, 38(2), 2002, 148 https://www.jstor.org/stable/20008403)
I think that we can conclude that both premises of the supporting syllogism are questionable. If we wanted to make concessions for the sake of argument, we would grant that:
1. A real infinite cannot exist.
2. An infinite temporal regress of events is an actual infinite.
3. Therefore ... ?
But, if we adopt my initial position, we don't even have to concede all of the above:
1. A real infinite cannot exist.
2. An infinite temporal regress of events is a fixed infinite.
3. Therefore ... ?
I think that I've said enough about the first a priori argument.
The second argument is found on p. 104 of The Case for a Creator:
"In fact, we can go further. Even if you could have an actual infinite number of things, you couldn't form such a collection by adding one member after another. That's because no matter how many you add, you can always add one more before you get to infinity. This is sometimes called the Impossibility of Traversing the Infinite."
In my book I mention that in a debate, Craig's friend, J. P. Moreland, actually said, "It would be impossible to traverse the [infinite?] past going backward in your mind." Notice that Craig keeps saying "you ... you ... you". What we can do isn't relevant. As I wrote in my book, "if we ignore the red herring about whether we can synthesize an infinite series and, instead, focus on whether such a series can be synthesized, then the answer is clear" (Stubborn Credulity, 38). If you disagree, then let's ignore that. Perhaps my analysis wasn't radical enough. It may be absurd to ask, but is it really the case that we can't go through the infinite past in our mind? Couldn't we conceive of going through it? Do you really have to live a century in order to go back one hundred years "in your mind"? Regardless, a general response usually resembles the words found in an article that I recommended in my book: "[I]t is inconsistent to suppose that an infinite series of events elapses in a finite amount of time, but consistent that they elapse in an infinite amount of time" (Quentin Smith, "Reply to Craig: The Possible Infinitude of the Past," International Philosophical Quarterly, 33(1), 1993, 113). Anything else I can think to say about the above argument has been said elsewhere.
The next argument is related to the last one. Craig thought that it too demonstrated the impossibility of traversing the infinite. He continued, "But if the past really were infinite, then that would mean we have managed to traverse an infinite past to arrive at today. It would be as if someone had managed to count down all of the negative numbers and to arrive at zero at the present moment. Such a task is intuitively nonsense." That's how his argument ended. He appealed to intuition. His argument is about as sophisticated as someone saying "It stands to reason!" (Isaac Asimov once quipped, "Never trust an argument only because it stands to reason.") I know that I'm quoting from a popular book, but even popular books have arguments. If you have read my book, you would know that I agreed with Quentin Smith, not Craig. Smith wrote, "It may be the case that we must start at - 1 and can only count some ways backwards, but a logically possible counter could have been counting at every moment in the past in the order in which the past events occurred. And this logically possible counter in relation to any present would have completely counted the negative numbers" ("Infinity and the Past," Philosophy of Science, 54 (1), 1987, 74). Of course, one could have misgivings about the last sentence. One might wonder why the counter would finish at this moment and not the previous one. The best answer that I'm aware of was given in the Morriston paper that I just discovered. He wrote, "It is true that at any moment in the past, the man had already counted off infinitely many numbers, but it does not follow that he had already counted off all the numbers or that he had already reached zero. Perhaps that could have been the way the man's count went. But it was not..." ("Craig on the Actual Infinite," 150).
Those who have read my book know what mathematicians say about the infinite. According to them, in the case of infinite collections, "a part contains as many terms as the whole" (Bertrand Russell, Wisdom of the West, ed. Paul Foulkes, Crescent Books, 1959, 281). As Isaac Asimov put it, "the phrase 'as many' doesn't have the usual everyday meaning when we're talking about things that are endless" (The Realm of Numbers, Fawcett Premier, [1959] 1967, 131 & 132). Mathematicians use the term "aleph-null" to refer to the infinite that is relevant here. Aleph-null "corresponds to the endlessness of the series of integers" (Ibid, 140). The a priori Kalam argument hinges on the presumption that actual things can be numbered using all of the real numbers (the positive integers). I suspect that the "man on the street" wouldn't have a problem dropping that presumption. My suspicion would explain why Craig didn't mention it in the popular book and why D'Souza didn't even bother with philosophical justifications for a temporally finite universe. We have no problem conceiving of a timeline with numbers going in reverse order. Ironically, the Christian calendar essentially has years that are labeled with negative integers (for example, 300 B.C.). Even believers may be leery of saying that an actual infinite cannot exist. Wouldn't such a claim put limits on God? As we saw above, even Craig was willing to drop the premise for the sake of argument. If D'Souza's book is an indication, most non-philosophers never accepted the premise to begin with.
Comments