Joshua Rasmussen’s post “More Reflections on Bill Craig and Wes Morriston on the Kalam Cosmological Argument” (April 29, 2009), accessible at , has initiated many interesting and thoughtful comments about the merits of the KCA. Rasmussen had occasion to remark in his initial post: “My sense is that the Kalam argument is more likely to appeal to the common man or woman than to your average philosopher. From the common man’s perspective, beginnings obviously have causes; science reveals a beginning to our universe; and surely only God would be the cause of our entire universe.” (JR, April 29, 1:30 PM.) Wes Morriston “totally agree[d] that the kalam argument ‘is more likely to appeal to the common man or woman than to your average philosopher.’ I think that’s why it’s so rhetorically effective in public debates. I received a post the other day from an agnostic who’d been listening to a lot of [William Lane] Craig’s debates. He said that the kalam argument was the one that nobody seemed to have an effective reply to. He thought he was about to become a theist on account of it.” (WM, May 3, 10:09 AM) Au contraire, there is available an effective reply to the KCA that is likely to appeal to the common man or woman, and even perhaps to some philosophers whose noetic structures have not been too severely damaged due to original sin. [This last, a hopefully pardonable witticism.] I believe I have provided that effective reply.Moreover, with some tweaking, this response (potentially credible to the intelligent common man or woman) could be made accepted by some theologically conservative Christians or adherents of some other monotheistic religion who are commonsensible in their philosophical orientation. To paraphrase a passage from William Hasker’s article “What About a Sensible Naturalism? A Response to Victor Reppert,” Philosophia Christi 5 (2003) 53: “a [commonsensible theism or] naturalism … makes a really serious effort to accommodate, or at least to make sense of, our ordinary convictions about [the universe and] the mind … —the things we all think we ‘know’ about the [universe and the] mind, when we are not doing philosophy.”
I, albeit a commonsensible naturalist [see my post “A Metaphysical Naturalist Manifesto,” July 21, 2007 (accessible at , should therefore like to refer the reader to my published refutation of the Kalam Cosmological Argument. Although I am not a professional philosopher, I have written two peer-reviewed articles about the KCA in philosophy journals. [“The Kalam Cosmological Argument: The Question of the Metaphysical Possibility of an Infinite Set of Real Entities,” Philo 5 (2002) 196-215; republished (with some changes) in the Secular Web Library https://infidels.org/library/modern/arnold-guminski-kalam/; “A Critical Examination of Mark R. Nowacki’s Version of the Kalam Cosmological Argument,” Philosophia Christi 10 (2008): 377-91.] I have also authored two additional articles for the modern library of the Secular Web.[“The Kalam Cosmological Argument: The Question of the Metaphysical Possibility of an Infinite Temporal Series” (2003, updated 2005); “The Kalam Cosmological Argument as Amended: The Question of the Metaphysical Possibility of an Infinite Temporal Series of Finite Duration (2004, updated 2005). (https://www.infidels.org/library/modern/arnold_guminski/)]
The reader of my essays will discover that I substantially agree with Craig with respect to several important, relevant, principles and doctrines that the intelligent “common man or woman” upon reflection is likely to believe to be true or, at least, more probable than not given the more plausible alternatives. These philosophical principles and doctrines include: (1) the A (or tensed) theory of time; (2) the presentist version of the A theory; (3) that every bounded moment (or temporal interval) is not of zero duration, such that such moments (or temporal intervals) in a temporal series are consecutively sequenced one immediately after another; (4) the metaphysical impossibility of the traversal of an infinite set of events or entities yet to be traversed; (5) the causal principle embodied in the first premise of the KCA, according to which it is metaphysically necessary that whatever concrete entity begins to exist must have a cause, even if indeterministic.
I shall not undertake here to further explain, qualify, or defend these propositions that I believe to be true and indeed fundamental. Recall that I am interested in providing an effective reply for the common man or woman, and commonsensible philosophers, whether theist or naturalist. Hence I should like to immediately go to the heart of the matter by asserting most emphatically that I agree with Craig that an infinite temporal series of events, whether or not of infinite duration, is metaphysically impossible provided one grants that an infinite temporal series, or any set of concrete entities, has every relevant mathematical property that a mathematical denumerable infinite possesses. For, assuming that each of two infinite sets of concrete entities or events is equipollent (i.e., corresponds one-to-one) to N (the infinite set of natural numbers), it follows that they are equipollent to each other if indeed infinite sets of concrete entities or events have every relevant mathematical property that denumerably infinite mathematical sets have. (A denumerable infinite is N or any mathematic infinite set that is equipollent to it.) Building upon this, Craig has argued that infinitely many concrete entities or events are metaphysically impossible. I believe I am the only writer who has seriously attempted to refute the Kalam philosophical cosmological argument despite agreeing that Craig has convincingly argued how application of Cantorian set theory to the real world according to the received opinion generates counterintuitive absurdities, sufficient to warrant the belief that infinite sets of concrete entities or events are metaphysically impossible.
In my Philo article, I proposed and defended the thesis that infinite sets of concrete entities or events, although each is equipollent with N and thus has the same cardinality (i.e., aleph-zero), are not necessarily equipollent with each other. Thus in a possible world in which there are infinitely many humans each with two and only two hands it cannot be the case that the infinite set of all humans is equipollent with the set of all hands. To take up Craig’s favorite scenario involving Hilbert’s hotel, I maintain that if all the rooms are and must be occupied by one and only one guest and there are infinitely many rooms, then the hotel management can not possibly accommodate another guest unless another room was provided, unless one of the guests checks out. But according to Craig, the application of Cantorian transfinite arithmetic to the scenario entails the conclusion that an additional guest could have a room after each occupant moves to the next adjoining room ad infinitum. And so, to take another example, if the temporal series constituting the history of this universe is infinite then the set of infinitely many years ending at midnight, January 1, 1000 is not equipollent with that set of years ending at midnight, January 1, 2009, according to my version of how Cantorian set theory applies to the real world. However, according to Craig, although the set of first set of years is a proper subset of the second, since each is equipollent with N it follows that both temporal series are equipollent—another counterintuitive absurdity.
My Philo article shows that my theory that two infinite sets of concrete entities or events are not necessarily equipollent to each other does not result in counterintuitive absurdities. In no way do I challenge Cantorian transfinite arithmetic. What I challenge is the opinion commonly held amon
g philosophers that the only way to apply Cantorian transfinite arithmetic to the real world of concrete entities and events is to posit that sets (or, if you will, aggregates) of such entities or events have every relevant property that denumerable mathematical infinites possess. Quentin Smith, then editor of Philo when I submitted my article, wrote the following in his message of acceptance of July 15, 2002: “Your paper has been studied thoroughly for some time and there is agreement that it is at least an under-cutting defeater of Craig’s beliefs about real infinites, probable even an overriding-defeater. More importantly, it introduces a novel metaphysical theory of the relating of transfinite arithmetic to concrete reality.” To be sure, a successful refutation of the KCA leaves untouched other arguments for God’s existence. Indeed, rejection of the KCA is not limited to naturalists as many Christian philosophers and theologians also reject the argument.
My second KCA article, “The Kalam Cosmological Argument Yet Again,” addresses Craig’s second philosophical argument that any temporal series of events must necessarily be finite even were it assumed (for argument’s sake, at least) that an infinite set of entities is not necessarily metaphysically impossible. My third KCA article, “The Kalam Cosmological Argument as Amended,” addresses the question whether an infinite temporal series of finite duration is metaphysically impossible and concluded that such is the case. In so doing, I showed that Craig in presenting his scientific argument (based upon Big Bang cosmological models and the second law of thermodynamics)in some writings subsequent to his The Kalām Cosmological Argument (1949) has in substance admitted (without any qualification that he is assuming something for argument’s sake only) the metaphysical possibility of an infinite temporal series of finite duration in order to accommodate his second premise of the KCA (i.e., the universe began to exist) with various Big Bang cosmological models. However, I hold that that the deliverances of the natural sciences, or rather the deliverances of some natural scientists, are insufficient to warrant the conclusion that the temporal series constituting the history of this universe is of finite duration. (See my “The Kalam Cosmological Argument as Amended,” pars. 55-62.) Although I have yet to author one more paper discussing the question of the scientific version of the KCA, suffice it to say for now that if this universe began to exist in the requisite sense, then the nature of whatever caused the universe to exist cannot be determined by reliance upon the alleged metaphysical impossibility of an infinite temporal series of whatever duration.
Alas! Craig has never answered me although it is notorious how ever since the appearance of his The Kalam Cosmological Argument he has otherwise made every effort to refute other critics of his arguments, however implausible their objections might be in his opinion. He has had plenty of time to respond to my writings; and I do not think he can credibly claim that my writings are beyond the pale of respectable philosophical scholarship. I more than suspect that Craig has not answered me simply because he cannot undertake a successful refutation. Of course I could be wrong but I would like to know why. One thing cannot be said against my refutation of the KCA, and that is the reproach by J. Brian Pitts directed to atheistic critics. According to him, they “not infrequently mix with their good points various unhelpful moves such as denying ex nihilo, nihil fit and thus perhaps ceding the rational high ground, introducing premises that strike the theistic apologist as question-beginning, or writing in atone suggesting that rejection of the theistic conclusion plays an undue role in motivating the rejection of the argument.” (“Why the Big Bang Singularity Does Not Help the Kalām Cosmological Argument for Theism,” British Journal for the Philosophy of Science 59 (2009) 675-708, 676.) To be sure, some naturalists might well reproach me for living dangerously by agreeing too much with Craig, as if the nonexistence of God is somehow self-evident or the subject of a properly basic belief. No, on the contrary, a commonsensible argument against the KCA, one that agrees that the received way of applying Cantorian set theory to the real universe of concrete entities and events generates counterintuitive absurdities, is what is polemically dangerous for adherents of the KCA.