Book Review: Infinity, Causation, & Paradox by Alexander Pruss
The book, Infinity, Causation, & Paradox by Alexander Pruss, was published by Oxford University Press in 2018. I just finished reading it as my first book by this author. I knew of him via other philosophers’ dealing with his work and through reading his blog. My first impressions of him from reading his blog was that he was a natural born philosopher, an original thinker, creative, and a top level contemporary philosopher. Or as the philosopher William Lane Craig described him, “scary smart.”
Background on the author: Pruss is a theist philosopher and currently Professor of Philosophy at Baylor University in Texas. He apparently immigrated with his parents from Poland to Canada at age 9. After completing 10th grade, he entered the University of Western Ontario “studying physics and mathematics,” then earned a Ph.D. in mathematics at the University of British Columbia in 1996. After that he earned a Ph.D. in philosophy at the University of Pittsburgh in 2001. So he has the expertise required for the topic.
The book addresses the philosophical issue of infinities and the paradoxes associated with them in famous thought experiments such as the Grim Reaper Paradox, Thompson’s Lamp Paradox, Hilbert’s Hotel, etc.
On page 1, after briefly describing the Thompson’s Lamp paradox, he says that “potential answers” to these types of paradoxes “fall into three general camps: logically revisionary, metaphysical, and conservative.” The first posits non standard logic such as Thompson’s lamp can be both on and off at the same time, thus apparently violating the standard logic principle or law of non-contradiction. Metaphysical answers use metaphysical principles such as “there are no infinities”. Conservative answers “refuse to revise logic or posit substantive metaphysical theses” and come in two types, “Particularist” ones that argue that a particular story is impossible “e.g. precisely because it is paradoxical” and “defusing” conservative answers that say the story as given is possible, so there is no real paradox to try and resolve.
So how does Pruss answer these paradoxes himself here? He argues for a metaphysical principle he calls “causal finitism” that resolves or dissolves the paradoxes as being impossible. “The main strategy of the book” therefore is not to “opt for a number of different solutions to different paradoxes” but that “they will all be killed through the single assumption of causal finitism.”
The bulk of the book is a fairly typical philosophical analysis of the issues involved; he examines various paradoxical thought experiments or “stories” involving infinities and looks at different perspectives in the literature by other philosophers. He looks at his causal finitism principle as a solution, defines what it is and isn’t, possible modifications to it (“quasi-causal finitism”), and possible responses to/ defeaters of his position.
This brings up what, exactly, is causal finitism. First of all, he says it is not simply finitism. “Finitism is an overreach” he says, and “finitism endangers mathematics” as mathematics uses infinities and finitism would make the natural numbers “not realized” (p. 23). On page 2 he defines causal finitism by saying it “roughly says that nothing can be affected by infinite many causes.” On page 25 he says it is the position (which he says is deliberately vague and will be clarified later) that “there can’t be infinitely many causes behind an effect.” The back cover defines it as “it is impossible for a single output to have an infinite causal history.” In other words he argues “against infinite regresses” in causes (p. 2).
A Causal Finitism Based First Cause Argument
The causal finitism principle rules out an infinite causal series leading to an effect. It rules out infinite regresses. As I was reading the book and his description of causal finitism by chapter 2, I thought if it is true, one could run a Kalam style argument for an uncaused First Cause. It is similar to arguments against an infinite regress of past moments of time leading up to the present moment as in Kalam style cosmological arguments, but this argues against an infinite regress of causes (p. 184). In fact, he does offer a Kalam style argument himself for a First Cause based on his causal finitism principle at the end of the book.
The “quick” argument is (pp. 181-182):
(1) Nothing has an infinite causal history.
(2) There are no causal loops.
(3) Something has a cause.
(4) Therefore, there is an uncaused cause.
This is logically valid, so since (3) is evidently true and (4) is an inescapable logical deduction of the 3 premises, it’s a matter of wether (1), his causal finitism principle is true and (2) is true (no causal loops exists). It’s certainly a plausible argument to debate. It seems to me that if there are no causally infinite series, there has to be an uncaused first cause. Otherwise, unless you reject (1), you’d have to say something like everything (the universe) came from nothing, by nothing, for no reason at all as the philosopher Quinton Smith did. Pruss says if causal finitism is true, it leads to an uncaused first cause, but leaves open if the first uncaused cause is supernatural like God or natural like the Big Bang (p. 194).
This is a philosophical book at the top of the field, so can be technical. He marks these sections off to alert the reader with an asterisk “*” and very technical sections with two asterisks “**”. I skipped most of those myself. Also, as an academic book, the retail price is steep for a book: $60 on Amazon.
If there ever was a subject that has the potential to “expand your thinking,” it would be infinity at it’s associated “paradoxes”. Or it could just give you a headache.
I also purchased his book Necessary Existence co-authored by Joshua Rasmussen and his book from 2006 on the PSR (The Principle of Sufficient Reason: A Reassessment). I have been reading, researching, and reflecting on those two issues for a few years now, so expect reviews of these books and continuing blog posts on those issues as they are important, perennial philosophical issues, at least for me.