In recent years Westminster New Testament scholar Vern Poythress has proven to be something of a philosophical polymath publishing whole books on topics as varied as philosophy of science and philosophy of language. His seemingly unabated flow of output continues with a new and very large book on logic (the largest book I know of on the subject).
Poythress’ new work is so comprehensive that at first its table of contents may strike one as something of an eclectic hodge-podge. But though grand in scope, Poythress’ Logic has a very clear layout of three broad sections. §1 focuses upon explaining the elementary ideas and concepts of logic. This section is also the heart of the book in that Poythress emphasizes throughout various theological issues as they bear on the subject of logic. §§2 and 3 will probably be of less interest to readers of this journal since they focus upon later developments in the history of logic and provide more detailed discussions on various approaches to logic. Since §1 is clearly Poythress’ main concern, I’ll summarize these sections in reverse.
The latter two sections of the book are for those individuals who find the subject of formal logic interesting in itself and wish to pursue more in-depth studies. These sections are very informative. Poythress surprised me (though a philosopher of logic myself) by introducing some ideas that I was unfamiliar with (particularly lattice theory). As with §1, Poythress continually touches upon the theological issues and problems that relate to these various approaches. Most of his theological comments in these sections are repetitions of what he says in more detail in §1. There are also several appendices that address some deeper and more philosophical issues for those so inclined.
§1 though will probably be more of interest to pastors and theological students. One could read this section alone, without loss, if the latter sections hold little interest. §1 of the book is obviously Poythress’ main concern as the title of the book claims. Here he seeks to show how Christians should think about logic and provides biblical argumentation for its theological foundations. This is where Poythress is at his best showing not only how logic is introduced and used in the Bible but also how it glorifies God. Throughout Poythress shows how modern understandings of logic contrast and contradict this biblical understanding of logic.
Since to my knowledge there are very few books that treat the subject of logic from an explicitly biblical perspective, Poythress’ text is a refreshing gift. I heartily recommend this book (and primarily its first section) to those who wish to think more biblically about the intellectual and theological fabric of rational thought. One should not be intimidated with all of the charts and mathematical formulas that a cursory search of the pages will show. Poythress does an exceptional job at explaining complex logical notions very slowly, and in clear ways. This book is very much aimed at those who are new to the formal study of logic. And again, most of the more complex formalizations appear in the latter two sections of the book.
However, Poythress’ book is not without shortcomings, especially from a more scholarly viewpoint. For example, though Poythress’ knowledge of the subject is well-informed, it’s clear that he is not very familiar with recent research and literature on logic. He gives far too much space to older formal systems, like Russell and Whitehead’s, even though natural deduction systems are clearly the more dominant means of teaching and disseminating logic today. Also, though Poythress explores (and is surprisingly somewhat sympathetic towards) intuitionistic and fuzzy logics, he gives no hint that other non-classical logics such as relevance logic exist.
Another narrowness here is that Poythress’ footnotes overwhelmingly cite mainly two individuals: John Frame and the late Cornelius Van Til. Both of these are respectable Reformed scholars whom I hold in admiration. Nevertheless, it’s somewhat troubling that Poythress’ scholarly well seems to be primarily filled mainly with these two scholars’ ideas. Though scholars should have heroes like anyone else, there’s a lurking fear here that a scholar’s output can be overly dependent or parroting of those he primarily focuses upon. Many times our critics (not our heroes) can be our best scholarly help.
However, the biggest shortcoming I had with Poythress’ Logic was his discussion of analogy—the idea that our words, and especially our predicates, apply to God only analogously (as opposed to univocally or equivocally). Poythress rightly notes that formal logic claims that valid argument forms assume that terms are used univocally throughout the form. But, again as Poythress rightly points out, we cannot use terms univocally in an argument that applies to God. However, Poythress correctly maintains that we must not fall into either a non-Christian view of transcendence (i.e., logic doesn’t apply to God) or a non-Christian view of immanence (i.e., we can capture God with logic). Thus, we must maintain that our reasoning does apply to God without becoming gods and making God subject to our reasoning. Though I completely agree with this conclusion, as far as I could see, Poythress never explains how we can use logic correctly concerning God. More detail would have been greatly helpful here.