"If I were asked what was the most disastrous moment in the history of Europe I should be strongly tempted to answer that it was that period of leisure when René Descartes, having no claims to meet, remained for a whole day 'shut up alone in a stove.' " So wrote the normally diplomatic William Temple in chapter three of his Nature, Man, and God, originally given as a series of Gifford Lectures, and published in 1934.

Temple delivered his talks while serving as Archbishop of York, and chose for that chapter the less than diplomatic title "The Cartesian Faux-Pas." For Temple, this "faux-pas" was the belief that philosophical inquiry, to be successful, should proceed according to a geometric or axiomatic model: begin with indisputable truths or axioms ("I think, therefore I am"), and from there engage in airtight logical reasoning to establish further truths—which, prior to their establishment, may have been highly disputed—such as the existence of God and the immortality of the soul. Indeed, in the synopsis to his Meditations, Descartes states, "[I]t was my aim to write nothing of which I could not give exact demonstration, and that I therefore felt myself obliged to adopt an order similar to that in use among the geometers, viz., to premise all upon which the proposition in question depends, before coming to any conclusion respecting it."

Temple thought that Descartes' strategy ("Let's pretend I don't exist and see if I can prove that I do") was a violation of common sense, and dismissed the idea that the success of the axiomatic method in mathematics could be extended to philosophy. Furthermore, he claimed that the method produced disastrous results "not only in philosophy, but also in politics and economics, with all that this means for human happiness or misery."

Carlos Bovell, in his By Good and Necessary Consequence: A Preliminary Genealogy of Biblicist Foundationalism, extends a form of Temple's thinking and argues that an axiomatic methodological mindset led to a disastrous result in theology: a clause in the Westminster Confession. For Bovell, the approach to biblical interpretation governed by this clause has resulted in the shattered faiths of many young evangelicals. It is a shattering that predictably results from an inability to come to terms with scriptural data when combined with a hermeneutic guided by a Cartesian deductivist methodology. In particular, it germinates from a belief in the inerrancy of Scripture.

The clause in question comes from the sixth article in the Confession, and at the beginning of his book Bovell displays it immediately below a similar statement taken from Descartes' Discourse on Method (bold and italics due to Bovell in both cases):

Concerning objects proposed for study, we ought to investigate what we can clearly and evidently intuit or deduce with certainty, and not what other people have thought or whatever we ourselves conjecture. For knowledge can be obtained in no other way. (Descartes, 1637)

The whole counsel of God concerning all things necessary for His own glory, man's salvation, faith and life, is either expressly set down in Scripture, or by good and necessary consequence may be deduced from Scripture: unto which nothing at any time is to be added, whether by new revelations of the Spirit or traditions of men. (Westminster Confession, 1646)

The two quotations bear a striking resemblance, especially as Bovell lays them out. To reinforce the connection between them, he orchestrates a nifty survey highlighting the development of deductive thinking that reaches a crescendo in the 17th century. The survey, which makes up more than half of his book, begins with the Pythagorean school of 500 BC.

In rehearsing the ideas of Pythagoras, Bovell is careful to point out that caution must be taken when consulting second-hand sources. Iamblichus (c. AD 300), who wrote extensively on Pythagoras, is often accused of projecting the methodological approach of his day back to the time of Pythagoras. One almost has to go back to Aristotle (c. 350 BC) to gain some confidence in the reliability of any attestations. Still, secondary sources can be useful, and those who are interested in the development of logic will find Bovell's presentation informative. To illustrate, Pythagoras and Thales (as attested by Proclus) were the first to exhibit an argument that generalizes, that is, one that holds true for a whole range of cases and not just a particular example.

Continuing his account, Bovell examines the development of deduction and dialectic in Plato's work (c. 400 BC). Where the Pythagoreans saw music as a "doorway to mathematics," Plato focused on mathematics as a doorway to knowledge. In assessing Plato's work, Bovell draws from portions in the Meno, Phaedo, and the Republic. In doing so he cites a variety of sources that indicate a growing favor on Plato's part for theoretical arguments over empirical evidence. Yet Plato was not so enchanted with deduction as were the Pythagoreans. He favored a dialectical style, as it better enabled him to re-examine initial hypotheses. Further progress in deduction would have to wait until someone could produce a refined theory of axiomatics. Aristotle's Posterior Analytics fit the bill, but Bovell points out that even there Aristotle's method amounted to a merging of the ideas of Pythagoras and Plato, not necessarily a strict deductivism.

From Aristotle the survey continues over the next several chapters by examining Euclid's Elements (c. 300 BC), Proclus' deductive metaphysics (c. AD 400), Boethius' use of axiomatics (c. AD 500), and Aquinas' commentary on Boethius (c. AD 1250). In each case Bovell provides an extensive analysis, and his bibliography of over 400 items provides ample fodder for investigating some of his more provocative conclusions. He states, for example, that the rigor of Aristotle's axiomatics served "anagogical rather than epistemological" ends, and that the axioms the Greeks used for doing their mathematical work were chosen not because of "self-evident truth and unprovability. They are rather theoretical and practical permission to take a specific direction of thought, an expository tour of the discipline in question." In particular, Euclid's axioms are validated because they lead to a well-known and accepted result: the Pythagorean theorem. Doing so helps "confirm the hypotheses [i.e., the axioms] listed at the beginning of Book I [of the Elements]."

While most mathematicians would agree that axioms (from the Greek axios, meaning worthy) are chosen in part because they enable the construction of a useful system, they might well judge it a stretch to argue that the Greeks had only that end in mind and were not concerned with epistemology. Euclid's proof of the Pythagorean Theorem is the 47th proposition out of a total of 467 spread across 13 books. A substantial number of those propositions are not at all obvious to the point that their proof would justify the axioms in Book I. Rather, their conclusions are justified precisely because of the trustworthiness of the axioms.

Mathematicians might also take issue with Bovell on some smaller points. For example, he illustrates the (Pythagorean) idea of generalization with a particular case. He begins with the (true) inequality that 6 > 5, then multiplies both numbers by -1 to get -6 and -5. What relation do they now bear to one other? Obviously, -6 < -5. In other words, the inequality is reversed when multiplying by minus one. The result holds true for the numbers 6 and 5, but what about other numbers? Bovell's generalization proceeds as follows: begin by supposing that -x < b. Next, add x to both sides of the inequality to get 0 < x + b. Finally, subtract b from both sides to get -b < x, which can be rewritten as x > -b, thus proving (for arbitrary numbers) that multiplying by minus one reverses the inequality. Okay, but why begin by supposing that -x < b instead of (for an equally easy proof) supposing that x > b, and then concluding that -x < -b? The latter approach would look more like the concrete example, and be just as valid. Moreover, Bovell's illustration might lead readers to think that the Pythagoreans dealt mainly with numbers. Although numbers were important to them, the Greeks in general worked mostly with geometric ideas; and in any case negative numbers did not hit the mathematical scene until the 1500s. A better illustration would have been a proof, attributed to Pythagoras, of the Pythagorean Theorem: given any right-angled triangle, the (area of the) square (that is drawn) on the hypotenuse equals the sum of the (areas of the) squares (that are drawn) on the other two sides.

There are other instances where mathematical explanations could be a bit better laid out. So depending on one's training in logic or mathematics, judgments regarding Bovell's survey of deductive thinking might range between fascinating and frustrating (and between important and irrelevant). Such judgments must keep in mind, however, Bovell's ambitious task of painting a broad picture of the development of deductive thinking. For Bovell, the climax of this progression occurs in the 17th century, and his first chapter ("The Seventeenth Century Context") gives good documentation of that era's ethos. As a bookend, chapter ten contains a summary of the ensuing survey.

But what are we to make of the consequences that Bovell deduces from his analysis? Are they good and necessary? The comparison of the Westminster Confession with Descartes' Discourse looks impressive, but the only evidence Bovell provides for any connection between the two documents is circumstantial. It can, after all, be debated how familiar the Westminster divines were with Descartes' work. They first convened in 1643 during the English civil war for the purpose of producing a tract that would set out a unified theology and polity for the Church of England. Bovell's project would be improved if he could find a more direct connection. Even if such a connection could be made, one might still dispute the primacy of epistemology that Bovell claims this clause conveys, for the quotation only constitutes the first part of the article in question. The second part reads, "Nevertheless, we acknowledge the inward illumination of the Spirit of God to be necessary for the saving understanding of such things as are revealed in the Word: and that there are some circumstances concerning the worship of God, and government of the Church, common to human actions and societies, which are to be ordered by the light of nature, and Christian prudence, according to the general rules of the Word, which are always to be observed."

Suppose, however, we accept Bovell's claim that the good and necessary consequence clause was motivated by a desire to gain some kind of epistemological advantage and thus thwart religious skeptics. A lingering question remains: does it follow that such a theological outlook is a faux-pas?

Bovell's answer is a resounding yes. His belief is that the outlook he critiques ("biblicist foundationalism") falls under its own weight: "And not only is there disagreement regarding consequences, but also about express statements too! This raises some honest questions about the nature of the 'necessity' allegedly provided for by biblicist foundationalism. In my view, biblicist foundationalism cannot possibly deliver what it promises." To be sure, Bovell believes that drawing deductions can be useful in certain respects, such as pointing out inherent contradictions in doctrinal statements one might make. His main concern resides with the conclusions one is forced to make by accepting Scripture as inerrant.

Such language may remind readers of this journal of Christian Smith's The Bible Made Impossible: Why Biblicism Is Not a Truly Evangelical Reading of Scripture (reviewed by Bob Gundry[1]). A difference between Smith and Bovell, however, is exemplified in Bovell's chapter eleven ("A Consequence of Biblicist Foundationalism"), where he comments extensively on the well-known story of Bart Ehrman, the once conservative Christian who no longer professes the faith. In recounting this story it is apparent that Bovell is objecting not so much to an inerrant doctrine of Scripture but to a wooden literalism, one that refuses to admit that Scripture displays a variety of literary forms. These days most evangelical Christian colleges welcome hermeneutics that take those forms into account, while at the same time including inerrancy language in their doctrinal statements: "[t]he Bible, consisting of the Old and New Testaments, is God-breathed and true, without error in all that it teaches" (Westmont College); "the Scriptures of the Old and New Testaments are verbally inspired by God and inerrant in the original writing" (Wheaton College); "[t]hey constitute the only infallible guide in faith and practice" (Gordon College).

Bovell's message might have been more relevant to those institutions some time ago, and in a private e-mail exchange he acknowledged that schools such as the ones mentioned above may well have a view of Scripture that, for him, is genuinely compatible with biblical data. He doubts, however, that evangelical churches would be comfortable with ideas that scholars at those institutions may espouse, such as biblical authors redacting historical events to make theological points. Of course, that depends on the church, and in that regard evangelical colleges and seminaries may do well to consider establishing some kind of dialogue that will help themselves and the Church (writ large) avoid the shattering of faith that Bovell laments.

So what does Bovell regard as the proper approach to Scripture? In his last chapter he exhorts Christians to adopt a Husserlian strategy ensuring an emphasis on origins. To illustrate, he draws an analogy with the loss of mathematical talent among high school students. With calculators, they have become unaware of the original meaning of many terms, such as the sine of an angle. As a result, their mathematical ability suffers. Likewise, Christians accept certain doctrines (that there are four canonical gospels, that the Scriptures are inerrant) with little investigation of or appreciation for "the Bible's epistemic origins with its genetic origins." Thus, Christian leaders would profit greatly from learning in an environment that allows and encourages such investigation. Good counsel, but does such a strategy imply, as Bovell indicates, that a Cartesian biblicist foundationalism is misguided?

In answering this question we might again draw from William Temple's Nature, Man, and God. His fourth chapter bears the title "Mathematics and Logic." In concluding it he remarks, "It is important to determine the use of our terms. We might decide … to confine the term Logic to what is recognised to be a very subsidiary discipline; or we might keep it with a modified significance to represent the discipline that represents accurate and adequate thinking. What always leads to dangerous confusion is to use it with an undefined significance, as is commonly done by persons who say that Life is wider or richer than Logic … and their meaning is that we often get on better if we stop trying to think accurately. Well, we may; but if so that is because we think badly, not because good thinking can ever be misleading." With that understanding, and with a rich view of Scripture, the good and necessary clause may well be something for evangelicals to take with renewed seriousness, rather than abandoning it.

Russell W. Howell is Kathleen Smith Professor of Mathematics at Westmont College.

1. Robert Gundry, "Smithereens!", Books & Culture, September/October 2011, pp. 9-11.

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