Logic: A God-Centered Approach to the Foundation of Western Thought

Vern Sheridan Poythress
Published by Crossway in 2013

Reviewed by James E. Bruce, Religion & Philosophy, John Brown University

At its best, Vern Sheridan Poythress’s Logic offers succinct arguments and thoughtful explanations. For example, informal fallacies work by counterfeiting genuine arguments, such as how the fallacy of bifurcation (or false dilemma) “counterfeits the truth that in some cases there are actually only two alternatives” (125). Venn diagrams and Euler diagrams work because they are “spatial representations of logical relations” (259), and so on. These explanations are succinct and clear. Logic also presents a thoughtful discussion of how arguments are used in the Bible (30–32) in order to undercut claims that arguments are in themselves unspiritual (43). That is helpful. Finally, Logic can be almost poetic in its description of things: “We may arrive at conclusions that become the starting point for still further deductions,” Poythress writes. “And this process may go on indefinitely. However long it goes on, as long as we stick to the rules we never arrive at anything except always-true propositions” (349).

Logic is really three books in one: (1) a logic textbook; (2) a discussion on the relationship between God and logic, and (3) a series of reflections on a variety of topics. But it is not one book after another; instead, it is a page or two of each, one after the other, jumbled together for over 700 pages.

First, Logic looks like a textbook: a cursory glance at the table of contents reveals standard textbook headings. Yet it is not a textbook, because there are only discussion questions, not real assignments, and there is no answer key for select exercises so that students can see whether or not they are doing problems correctly. Poythress occasionally places material in footnotes that is crucial for a beginning student to know. For example, he places his introductory discussion of figure (which indicates where the middle term of a syllogism is) in a footnote rather than in the body text (212n4). More troublingly, there is no formal instruction on how to do proofs in the modern sense. Examples are provided, starting at appendix B2, but the examples are incomplete. He literally places the following in the middle of a proof: “[here we take the steps to deduce ~p]” (562).

Even worse, Poythress follows nonstandard conventions. His Venn diagrams are creatures of his own design; they are rotated reverse images of what is normally seen in textbooks. He uses a checkmark (that almost looks like a square root symbol) instead of the traditional x, but then uses an x to indicate where one would shade, if one was doing things the normal way (see, for example, 217). If this all sounds very confusing, it is because it is! Elsewhere, Poythress adopts the dot notation (230) of Alfred North Whitehead and Bertrand Russell’s Principia Mathematica—only to abandon it ten chapters later, notifying the reader of his decision to do so in a footnote (309n2). The dots, he writes, “represent one more thing that would have to be learned by a beginner” (310n2). But if the dots should be abandoned from page 309 forward, they had no business being in the book in the first place.

Sometimes he just gets it wrong: Poythress uses only if in the place of if and only if “because in ordinary English the context indicates well enough that ‘if and only if’ is implied” (235n6). But that is both false and misleading. In logic, only if indicates a necessary condition, and if and only if a necessary and sufficient one. This convention makes sense given standard English: you will pass this class only if you take the final does not mean that, if you take the final, you will pass the class. After all, you may take the final and fail it, and so fail the class anyway. The teacher simply wants to indicate that, without taking the final, you will certainly fail. He is not offering a promise that if you take the final, you will definitely pass. The distinction between only if and if and only if captures this important difference, and Poythress should not have brushed it aside.

These complaints may sound like mere quibbling, but they are not. A student armed with Poythress’s Logic alone would learn a confusing and nonstandard way of doing logic. When you go into the hardware store, it is good to know that you are looking to buy a Philips screwdriver, and that people call it that. To be fair, he seems to indicate that his book is not a textbook: “Demonstrations can be found in a number of logic textbooks” (402), he writes; that is, as opposed to the thing that you have in your hands, dear reader. But if it is not a textbook, then why is all the occasional instruction there? And, whatever it is, he should get things right, and be consistent.

In and amongst the syllogisms, Poythress takes up Cornelius Van Til’s task to give logic “a distinctly Christian reading” (25n1). Aristotle, Kant, and contemporary philosophy pursue “the same old ideal of perfectly precise categories” that “implicitly rejects the Trinity and pursues human autonomy” (188–189). By contrast, Poythress’s “reformed logic will be analogically Trinitarian” (691). Poythress never makes his position entirely clear, but, in fairness, that may be because his position is so unusual.

He certainly makes some surprising claims. “To put it provocatively,” he writes, “the Original modus ponens is not an abstract principle, but God himself in the mystery of his Trinity” (695). This claim is provocative, but it is also straightforwardly false: if it were true, then worshipping modus ponens would be worshipping God—but that is absurd. Perhaps he is just saying that modus ponens has no independent existence and that it is not even an abstract principle in the mind of God. He certainly believes that it is “at odds with the interrelatedness of the persons of the Trinity” to think that God could think of a universal without considering the particulars (148). His alternative account seems to be that modus ponens arises—perhaps on a case-by-case basis—by comparing (1) a particular argument with (2) the Trinity. If we find an analogical relation between the two, then the argument is valid. “Human instances of use of modus ponens,” he writes, “are to be evaluated according to whether they show appropriate analogical relation to the Original” (695). Let us state the obvious: this approach is extremely unusual. Additionally, Poythress offers no practical help. To make it minimally plausible, he should offer a thorough discussion of analogy and its use in establishing validity; an account of how to compare arguments to the Trinity, and so on. But he does not. So there are practical problems.

There is also a conceptual issue that serves as a decisive objection to Poythress’s approach. If modus ponens arises from the Trinity by analogy, then God ought to know about it, and he ought to know about it from eternity. Even if modus ponens is not an abstract logical principle, it would be an abstract analogical one. So there would still be an abstract principle in the mind of God, pace Poythress. Poythress may want to say that it is not an abstract principle because it is the existing God himself. But that is false: modus ponens is not God (see above), nor is it a term applied to God, the way that Father is. According to Poythress himself, modus ponens is an “appropriate analogical relation” to the Trinity. Whatever that means, it is not God, but an idea. Poythress calls the Augustinian position on this issue “superficial and inadequate” (704), but he appears to be offering a modification to the position he deplores, rather than a rival account, as he claims. Augustine is comfortable with logical relations being known by God from eternity. Poythress says that logical relations arise by analogy from the Trinity. But either God knows the analogical relations that arise from who he is, or he does not. If he does not, then we know something about God that God does not know about himself—which is absurd. But if God has modus ponens in his mind from eternity, because of its analogical relation to the divine being, then God has an abstract principle in his mind, albeit an analogical one.

There is one last part to Logic, a series of reflections on a variety of topics. Appendix F5 is a previously published essay. The rest of the occasional reflections are sprinkled throughout the work like intellectual potpourri. Poythress succumbs to a kind of literary intemperance, but he never sustains his focus on a tangential topic for more than a page or two. We get advice on what to say to people who have had bad fathers (96); a mention of the distribution of Bible translations (101); an excursus on evolutionary naturalism (102–103), and so on. It’s all very thin, and handled without discussing—or even mentioning—the intellectual heavyweights involved. Poythress discusses the problem of induction without mentioning David Hume (99); he presents something like Alvin Plantinga’s evolutionary argument against naturalism without mentioning Plantinga (103); he talks about playing “the ‘game’ of logic or the ‘game’ of playing with formal systems” (441), without mentioning Ludwig Wittgenstein, who introduced such talk into philosophical discourse; he distinguishes between “syntax” and “meaning” in order to make the case that “modern computers are mindless” (453–454), but he does so without mentioning John Searle’s exact argument along these lines. He offers trenchant critiques of Kant, and a solid swipe at Augustine, without ever working with primary texts. In fact, Augustine, Hume, Kant, and Aquinas are not even mentioned in the bibliography.

“I am writing this book” Poythress tells us, “so that we may think carefully about human achievements in the area of logic. And in so thinking, we may begin to sort through the difference between good and bad, truth and distortion, common grace and effects of sinful desires for autonomy” (175). Sadly, that is not the book he wrote.

Cite this article
James E. Bruce, “Logic: A God-Centered Approach to the Foundation of Western Thought”, Christian Scholar’s Review, 43:2 , 199-202

James E. Bruce

John Brown University
James E. Bruce is Associate Professor of Philosophy and Theology at John Brown University.