Logic

Vern Sheridan Poythress, Logic: A God-Centered Approach to the Foundation of Western Thought (Wheaton: Crossway, 2013), 730pp., $45.00

The term "polymath" seems to have arrived in English by way of Greek; it combines the Greek words for "many" and "learner." Hence, it means someone who is learned in many different areas. Curiously, the word for "learner" is also the word commonly translated "disciple" in the New Testament.

In Prof. Vern Poythress all three terms meet: he is a fervent disciple of Jesus Christ and learned in many different things. Few scholars can boast his credentials: a PhD in mathematics from Harvard, a Master of Letters from Cambridge, two master's degrees from Westminster, and a theological doctorate from Stellenbosch thrown in for good measure. Poythress is a man of wide and deep reading, voluminous publication, and thirty-plus years of teaching experience. He is well qualified to write on just about any subject--and he has. From science to sociology, many topics have found themselves under the capable investigative eye of Dr. Poythress.

Enter his present work, a gargantuan undertaking indeed. The subtitle says it all: Poythress aims to cover the labyrinthine subject of logic, while arguing that the entire discipline itself needs a new foundation. Poythress's aim is thus ambitious and welcome. Given the current postmodern apathy towards anything that smacks of "Enlightenment rationalism" (threadbare terms if there were ever ones), one can only hope that a book on logic will gain a wide audience among Christians, if for no other reason than to encourage critical thinking that will spot the (ample) fallacies of postmodern irrationalism.

Poythress divides his work into three main parts, with a fourth section entitled, "Supplements." In addition to the main body of the book, there are dozens of illustrations and tables. The intended audience therefore seems to be advanced high school students, if not undergraduates. Coming in at right around seven hundred and thirty pages, even the most studious layman would not be faulted for feeling intimidated by such a book. Nevertheless, as with Poythress's other writings, study is repaid with rewards plus interest.

As a good pedagogue, Poythress introduces the usually insomnia-curing subject of logic by way of a clever Star Trek illustration (yes, this may push the Geek-o-meter into the red for some).  Using Spock and McCoy as his examples, Poythress notes how the former seems to most people the ideal of logic: cold, calculating, alien. By way of contrast, McCoy seems the ideal of the truly human being: passionate, persuasive, personal. Yet, as Poythress notes, neither man stays put; both struggle with logic and passions. Thus, Poythress argues that we need a Christian account of logic, one which can do justice to both Spock and McCoy. One might say that, according to Poythress, a Christian view of logic is therefore the real McCoy!

Readers familiar with Poythress's previous works will find some familiar themes in part one. The usual cast of characters make their cameos: the necessity of God for thinking anything at all, Trinitarian adumbrations in logical syllogisms because of unity and diversity, the devastating effects of sin on our thinking--all are here in the present monograph. I don't say that dismissively at all, far from it. Poythress has done a great service here and elsewhere by pointing out that the presuppositional issues of any discipline must be examined for the discipline to stand. He does the same kind of presuppositional analysis with logic and finds it wanting if it is not based on Christian theism.

Part two guides the reader through aspects of symbolic logic. Those unfamiliar with the various symbols and tools of this subdivision of logic might begin to be discouraged here. But Poythress demonstrates his skill as he walks readers through everything from Venn diagrams to Boolean algebra. Poythress argues that, given the complexities introduced by modern logics, a perspectival view (as Poythress contends for elsewhere) is most helpful. And perspectivalism itself only makes sense within a Trinitarian worldview. Hence, the reader is directed again to consider the necessity of Christianity to ground any study of, in this case, symbolic logic.

Part three begins with a study of predicate logic and proceeds from there. Predicate logic further investigates the pieces of the propositions represented in symbolic logic (364). When it comes to discussing things like quantifiers, the reader could easily find his head swimming, trying to keep straight all of the upside down "A's" and backwards "E's," but Poythress once again proves to be a sure guide through the morass of modern logic symbols. Poythress also takes the reader to his wheelhouse, as it were, examining logic in relation to mathematics.

Part four looks at the supplements for the various types of logic studied thus far. Readers will find Poythress's examples helpful and illuminating for the previous discussions. The final section of part four, the appendices, contains an extended discussion of logic and philosophy. What stands out here is Poythress's groundbreaking 1995 article, now republished in this book, "Reforming Ontology and Logic in Light of the Trinity: An Application of Van Til's Idea of Analogy." This is an article to be read and pondered, more so than it has been in the past. In it, Poythress demonstrates a mathematician's precision, combined with a linguist's analysis, all informed by an exegete's care.

I have not come close to doing justice to some 600 pages of argument in my brief review. But hopefully the reader's interest is piqued. I will conclude by offering what I take to be some comparatively mild criticisms. Before I do so, let me make clear that I think every Christian college student, seminarian, and pastor should own this book. On to the criticisms.

First, contrary to Poythress's intention, I'm not sure the intended audience is going to find this book a good introductory text to logic. Sometimes it seems that there is a bit of a "halting" (for lack of a better tem) feel to the work. I think this arises from the fact that many chapters are only five to six pages in length. It strikes me that it would have been more useful to write longer chapters on fewer aspects of logic for it to be serviceable as a textbook on the subject.

Second, and following from the first, I wonder if Poythress would have done better to write two (maybe three!) books. The first could have been an introduction to logic, with maybe ten chapters. The second monograph could have been a sustained argument for his proposal to rethink the foundations of Western thought along Trinitarian lines. In other words, one could ask, "Is Poythress writing a textbook or is he arguing for a particular view of logic?" I think it is both and hence I think both need more focused attention over a shorter span. 

Thus, I would have liked to see Poythress write a book about logic and then an argument for why logic must be placed on a Christian foundation. As it stands, Poythress sprinkles his arguments for Trinitarian foundations for logic throughout the present work. Given the sheer size of this book, logicians who might otherwise be inclined to give Poythress a hearing will likely find themselves frustrated by a few pages here and a few pages there of reasoning, instead of a book-length treatment into which they could sink their teeth.

I think Poythress's overall goal in the current work is admirable; namely to challenge the study of Western logic from an explicitly Reformed stance. Particularly for those who share Poythress's appreciation of the thought of Cornelius Van Til (as I surely do), this book represents a substantial contribution to current apologetics scholarship. But it does so in the way of suggestions and directions for further research projects. 

Accordingly, I think Poythress's Logic will serve its intended audience well, provided that they have a few other logic textbooks on the shelf beside it. His contribution will provide a handy reference tool for scholars, pastors, and Christian logicians. And I look forward to reading how Poythress (and others, hopefully) develop his project, that the triune Creator of logic might get all the glory by such endeavors.