I do not encourage very many people to listen. There are probably only two people in the world that wouldn’t be bored to tears by it. Listen to a little bit if you want to be encouraged that there are others in the world besides yourself for whom the highlight of a vacation would be a three hour discussion of philosophy.

Listen to more if you have the Tractatus Logico-Philosophicus in hand and want to join our struggle. Don’t listen for quick answers — listen only if you are interested in going slowly and carefully, discussing each word.

1. The ancients could not explain how motion is possible. Zeno’s paradoxes have never been answered in a way everyone finds acceptable. Aristotle’s attempt using potential/actual distinction is circular when all the passages are examined carefully.

2. The early-modern period, spanning Galileo to 1900 (with a few precursors and 20^th century hangers-on) posited a mechanical and deterministic world that can be known by empirical methods. Clark’s criticism includes the standard ones (e.g. the universal claim is not itself empirically testable), as well as a cluster of objections that may be unique to Clark, centering around the fact that measurements are not precise:

• The inability to measure precisely and repeatably shows that concepts like “length” cannot be justified; but science requires these concepts.
• Procedures to overcome the imprecision of measurement, such as averaging, are arbitrary and unjustified.
• The so-called laws of Physics indicate a precise relationship between quantities which can, for example, be graphed. But doing so shows that the formula is but one choice of curve-fitting through data points out of an infinite number that could have been selected. Since there is no reason to favor any one of that infinite number of possible curves, there is a probability of one over infinity (i.e. zero) that the selected one is the right one; therefore we can say that every formula of Physics is certainly false (60, 111).

3. In the 20^th century, contradictories are asserted, such as the wave and particle model of light. Because they are contradictory, they cannot be true literally. Physicists themselves often recognize this and have proposed operationalism as the solution. This is a view that rejects metaphysical accounts of concepts, replacing them all with cook-book procedures of measurement, which procedures become the definition of the concepts. Thus, the meaning of “length” is, the procedure used to produce a number that will be called length.

In a surprising comment, easy to miss in a first reading, Clark endorses operationalism as giving the proper description and place of science (92). But since operationalism does not claim “truth” in a cognitive sense, 20^th century science too is incapable of challenging Christian theism.

Evaluation

Zeno’s arguments against the possibility of motion are interesting, and I tend to agree with Clark that differential calculus does not provide a solution to the riddle, and that the problem is still an open one. However, modern scientists are not assuming the rationalist posture, so it is not at all clear why this is an important topic in a book of this kind. One could say, “No answer to Zeno, therefore no motion,” or one can say, “Motion, therefore I’ll think about how to answer Zeno tomorrow.” As a philosopher, Clark would scoff at that attitude. But he has deferred his own answer until tomorrow also: does he believe in motion? does he believe anything physical actually exists? Tell us, Dr. Clark. Don’t just scoff at others.

What is curious about the shape of Clark’s argument in the Newtonian section is that he seems to concede a premise of certain atheist philosophes, “if mechanical determinism then no God.” For he says,

Therefore, since the Newtonian laws do not describe the actual workings of nature, they cannot be used as a satisfactory demonstration of the impossibility of God and miracles. (58)

But Lorraine Boettner, for example, is comfortable with the idea that radical Newtonian determinism would be consistent with Calvinist theism. It is odd that Clark seems to grant the major premise of the philosophes, and merely limits his argument to denying the minor. That Clark grants the validity of that conditional points, I submit, to a fundamental failure to grasp the presuppositional insight. For Clark, causality and a world are in principle understandable with or without God; an inference from that given to the non-existence of God could in principle be valid; fortunately, Clark discovers that Newtonian science does not actually deliver on its thesis of determinism, so God is safe, for the time being.

As to the “impossibility of miracles” being refuted, one wonders how miracle would even be defined in Clark’s system; it is not unpacked in this book.

The thesis that imprecision of measurement has great epistemological consequences is repeated in other places of Clark’s opus, such as Introduction to Christian Philosophy, and Christian View of Men and Things, and thus is undoubtedly what Clark regards as his best argument. I want to examine this family of objections from a variety of perspectives:

1. Clark’s exposition that there are an infinite number of curves through any finite set of points still is limited to functional (at most one ordinate per abscissa) curves. I suggest that this is because, if the universe were not of such nature, then there would be no discernible regularity at all. Clark seems to want to admit that there is some function. He should unpack why this is. If we can know that some functional relationship must be there, is Clark absolutely sure we could never discern its form?

2. Clark is agitated by the non-repeatability of measurements, and claims that methods such as averaging are unjustified (59). But this is not true. Overcoming the “noise” associated with a quantity and its measurement is itself the subject of the discipline of Probability and Statistics. By hypothesizing the noise to be subject to certain statistical properties (such as zero mean), one can derive ways to reduce the noise of the measurement arbitrarily. The success of this project confirms the validity of the hypothesis; and “wisdom is justified of her children” Matt 11:18.

3. A theology of probability theory would have been interesting and relevant; but it is absent.

4. Clark may still protest that since we never land on the exact value, we don’t “know” it. But let him state what he thinks the underlying reality is then. Does it have a determinate “nature” or is it random fluctuation? If the randomness is radical, then there is, to be sure, no science; but there is also not a world that man could make plans in. That fact should have alerted Clark that something was amiss.

5. Why assume that the statement of a law (the “proposition”) has to be in the form of a bare mathematical equation? Instead of saying that Newton’s First Law implies that a body in free space follows a trajectory given by

“x = v t,”

(where x is displacement, v is a fixed velocity, and t is time) why not say, the particle follows the rule

“x = v t plus or minus epsilon,”

where epsilon is specified. Then, to be sure, an infinite number of curves are included in the statement, yet the statement is still true, meaningful, and useful.

6. Clark insists that we don’t know a quantity unless we know it precisely. But that depends on our purpose.

If the football announcer says, “the ball is inside the one yard line,” he has left open an infinite number of possibilities for where the ball lies; but he has excluded an even greater infinity of impossibilities (with apologies to Cantor). I know a great deal about where the ball is and what the team should do. I am not left with a “falsehood.”

If I am talking on the phone and I say, “mercy, it’s already midnight,” my conversation partner is not going to shout out “liar! It’s only five minutes until midnight.”

Clark’s whole project was based on an unnecessarily rarified notion of what is meant by assigning lengths and positions.

The meaning of a sentence, even a “law of Physics” sentence, has an intended scope and precision, and its truth-value must be assigned with a view to that scope and intention.

Clark’s point that science does not really explain in a philosophical sense (36) is well taken; and we must be critical about existence claims that might be made for elements of a scientific theory. If gravity can be described alternatively as an all-interpenetrating field or curved geometry, then we must learn to distinguish the thing from the model. Perhaps a good analogy would be the fact that a single proposition can be expressed in a variety of sentences. We need to clarify the grammar and sense of scientific statements, but Clark goes far beyond that without really touching it.

That the universe is so governed by God that there are predictable regularities follows from the fact that God commanded man to subdue and replenish the world (Gen 1:28). From this, it could already be inferred that the thing science aims at is legitimate. Theoretically, God could have created a topsy-turvy universe, in which a plow now digs furrows in the earth against which it is set, but any moment flies off to the moon. But God could not have created such a world and also required his image-bearer to occupy it.

Clark misses this completely. For him, science is either a praxis of pure techne that works, who knows why? or a sinister activity by which men conspire to prove that God does not exist. A Christian philosophy of science for Clark means, merely, a polemic against the atheist’s bad logic; but his strategy lets a virtually self-existent universe sneak in the back door. In trying to establish a radical propositionalism, Clark is not able to close the loop and show that there is a physical universe that it is upheld by the Word of God, and that that Word can be known with progressive accuracy by man, the image of God. In effect, the physical universe becomes a brute fact, dark and unknowable and practically autonomous.

A review of Gordon H. Clark. The Philosophy of Science and Belief in God. (Jefferson, Maryland: Trinity Foundation 1987 [1964]).

- Greg Bahnsen, Van Til’s Apologetic

Throughout the history of the church, apologists and theologians have adopted (sometimes consciously, but often unconsciously) epistemological views from pagan and secular sources in an attempt to defend the truth of Christianity. But as Greg Bahnsen has warned us, these epistemologies need to be investigated in order to discover whether they comport with Christianity. Sadly, this has rarely been attempted and thus Christian apologists have rarely had a completely biblical epistemology with which to defend the faith.

Though many examples could be cited, I will illustrate the problem of employing non-Christian epistemologies in apologetics by examining the traditional Roman Catholic approach as represented by Thomas Aquinas and a compromised Reformed approach as represented by Charles Hodge.

Thomas Aquinas

Thomas Aquinas (1225-74) was perhaps the greatest philosopher of the Middle Ages. As a defender of the Christian faith he borrowed much from the Greek philosopher Aristotle. Like Aristotle, Aquinas believed that knowledge (scientia) comes through demonstrative syllogisms (basically deductive arguments with true premises). The premises to these syllogisms, in turn, must be inferred from other demonstrative syllogisms. To avoid an infinite regress of syllogisms, Aquinas argued that some premises are not conclusions of other syllogisms. Rather, there are some premises (some knowledge) that form the foundation of all demonstrations.

How then do we come to know these foundational propositions? Without getting bogged down into the details of his theory, Aquinas, who held to a form of empiricism, tells us that we can know these propositions only through sense experience. We perceive an object (say a man) and then, through our cognitive faculty known as the active intellect, abstract the essence or universal from it (in this case, rational animal). Leaving aside the question of how our minds can abstract universals from particulars, Aquinas is faced with the problem of how men can come to know God. If all knowledge is acquired through sense perception and since God is not sensible, how can we even form a conception of God through our active intellect, let alone prove his existence?

The answer that Aquinas’s gives is unconvincing. He asserts that while we cannot know God directly, we can know him (both form the concept of God and know he exists) by analogy. Sensible objects, in that they are finite and contingent are said to reveal God’s infinity and necessity.

As it stands this is a mere assertion. Assuming Aquinas’s epistemology for the moment, why does it follow that because the objects of our experience are finite and contingent there must be a God behind them who is infinite and necessary? It is at this point that Aquinas resorts to his famous proofs for God’s existence.¹ These proofs run as follows. Since all objects of our senses are contingent, it is possible for all these objects not to exist. Aquinas then adds, “But it is impossible for these always to exist, for that which is possible not to be at some time is not. Therefore, if everything is possible not to be, then at one time there could have been nothing in existence.”² He then infers that if this were true, nothing would exist now since if all things were contingent and at one time nothing existed, then contingent things would not have come into existence. Next he argues that since something does exist, there must be something that is necessary. This necessary thing must have its necessity in itself and not from anything else, since this would entail an infinite number of necessary things. He concludes by identifying this necessary thing with God. Hence we can have knowledge of God’s existence even though this knowledge of him is indirect.

Many things can be said about this type of argument. (1) Even if we grant that something necessarily exists, why does this have to be God. Could not the universe be necessary? (2) Just because each particular part could possibly not exist does not mean the whole could not exist.³ (3) Furthermore, just because it is possible for all contingent things not to exist does not mean that at one time they did not exist. (4) Why is an infinite number of necessary things deriving their necessity from other things impossible? In a debate with Jesuit Frederick Copleston on the existence of God, Bertrand Russell said he could imagine an infinite chain of contingent things causing one another. Whether he could or not is beyond the point. What should be noted is that it is not, prima facie, clear that there could not be an infinite number of necessary things. (5) Even if this argument proved the existence of a god, it does not prove the existence of the Christian God.

What we can conclude from this brief discussion of Aquinas is that the epistemology he adopts from Aristotle controls his apologetical argument. However, the conclusion that Aquinas wishes to reach, that the Christian God exists, does not follow from this epistemology. The irony is that the very epistemology by which Aquinas tries to explain knowledge precludes him from having knowledge of God.

Charles Hodge

Though far apart theologically, Charles Hodge (1797-1878), the great Princeton scholar, fell into the same epistemological pitfall as Aquinas. An ardent Calvinist, Hodge was arguably the most powerful advocate for the Reformed faith in America during the 19th century. Proponents of rival theological outlooks and heretical doctrines were sure to be challenged by his trenchant biblical arguments. In settling theological disputes, Hodge referred to the Bible and the Bible alone as the final judge.

Hodge’s apologetic approach, however, differed greatly from his theological methodology. When dealing with unbelieving opponents, Hodge put down his Bible and defended the faith with a compromised epistemology. Rather than allowing Scripture to provide its own epistemological foundation, Hodge adopted the position known as Scottish Common Sense Realism.

Common Sense Realism claims that common sense is the basis for all human knowledge. The mind of man is, by nature, constituted in such a way that it will lead him into the truth about the world and morality; metaphysical speculation is to be avoided. Rather, humans should go out into the world to collect objective (neutral) facts from which, by use of inductive reasoning, general laws are to be inferred. Hodge summarizes this view by stating, “The Bible is to the theologian what nature is to the man of science. It is his store-house of facts; and his method of ascertaining what the Bible teaches, is the same as that which the natural philosopher adopts to ascertain what nature teaches.”⁴Nature is viewed as a teacher and its lessons are the bare facts. By use of the principles of induction mankind can take the teachings of nature and agree upon how the natural world operates.

On this epistemological stance, Hodge attempted to prove the existence of God by the traditional arguments. Hodge, like most adherents to Common Sense Realism, took it for granted that unaided human reason would lead to the establishment of the truth of Christianity.⁵ Science, after all, showed that the world was wonderfully designed. The only way to explain the fact of this design was to infer (through induction) that there is a Designer. Speaking in confident terms, Hodge asserts: “On this ground we are not only authorized, but compelled to apply the argument from design far beyond the limits of experience, and to say: It is just as evident that the world had an intelligent creator, as that a book had an author . . . “⁶

The problem with this epistemological outlook became apparent with the publication of Darwin’sOrigin of Species in 1859. Darwin, looking at the same “objective” facts and using the same “neutral” logic, concluded that there was only the appearance of design in the natural world. This appearance is accounted for by the process of evolution by means of natural selection. No longer was a god necessary to explain the orderliness of the world, because nature itself could account for this.

To Hodge’s credit he did publish a critique of Darwin’s theory.⁷ However, given his epistemology, he was in no position to offer a cogent refutation of evolutionary theory since he, like Darwin, appealed to the same facts and to the same type of reasoning. The trouble is that the facts said one thing to Darwin and another thing to Hodge. Who was observing the facts correctly? Who was using induction correctly? Under the principles of Common Sense Realism, there is no way to decide.

Hodge’s teleological argument, and the epistemological foundation on which it stood, could not withstand the pressure that Darwin and others brought to bear upon it. Like Aquinas’s Aristotelianism, Hodge’s Common Sense Realism proved to be ineffective and indeed contrary to the faith he was so adamant to defend.

Reformed Epistemology

Aquinas and Hodge represent two different and rival traditions of Christian theology. The whole of Aquinas’s theology is polluted with pagan categories. Essentially it is Aristotelianism with a Christian veneer. Hodge, on the other hand, presents us with a truly biblical theology. Speculation about God and man are not countenanced. Scripture alone defines God and man, as well as creation, the fall and redemption. When it comes to defending the faith, however, the two have more commonality than differences. Both take their epistemologies from autonomous philosophy and not the Bible. And both, ultimately, undermine the faith that they seek to defend.

Against both Aquinas and Hodge, the Bible alone is the source from which Christians are called to draw their epistemology. Scripture is adequate for every good work, including defending the faith (2 Tim. 3:16-17). In Christ are all the treasures of wisdom stored (Col. 2:3). The Christian is called to take every thought captive to the obedience of Christ (2 Cor. 10:3-5). The only biblically acceptable apologetic is therefore one which is drawn from the Bible and acknowledges the epistemic lordship of Christ. Any position other than this is merely knowledge falsely so called (1 Tim. 6:20).

Not only are epistemologies derived from sources other than Scripture dishonoring to Christ, but they lead to an abortive defense of the faith. Whether one’s theory of knowledge is grounded in demonstrative reasoning, common sense or something else, this, and not Scripture becomes the ultimate authority of the one who adheres to it. It becomes surer than the sure word of God. But Scripture teaches us that Scripture itself is to be our final authority (2 Pet. 1:19, 21; 2 Tim. 3:16, 17; 1 John 5:9; 1 Thess. 2:13). If Scripture is the final authority, and if one proves the authority of Scripture on the basis of something else other than Scripture, then one proves that Scripture is not the final authority. In other words, to prove the authority of Scripture on something other than Scripture is to disprove Scripture.

Christian apologists are morally and logically compelled to defend the faith with an epistemological outlook that accords with the faith. Not only is it wrong to defend the faith with an autonomous epistemology–Christianity must be understood on its own terms–but, in the nature of the case, blending Christian theology with non-Christian epistemology always serves to undermine the Christian’s ability to defend the faith. As Christians we need to be much more epistemologically self-conscious; we need to develop a truly Reformed epistemology.

Quoting again from Greg Bahnsen again:
Our Christian epistemology (or theory of knowledge) should thus be elaborated and worked out in a way which is consistent with its own fundamental principles (or presuppositions), lest it be incoherent and ineffective. Our “method” of knowing is determined by our “message” as a whole–thus being influenced by, even as it influences, our convictions about reality . . . We ought not to espouse one thing theologically, then practice something else in our scholarship. One way to say this is to say that Christian scholars and apologists must be thoroughly “self-conscious” about the character of their own epistemological position, letting its standards regiment and regulate every detail of their system of beliefs and its application. They need always to form opinions and develop reasoning in light of their fundamental Christian commitments.

NOTES

1. I am speaking of logical order, not Aquinas’s actual order of presentation in his works. In Summa Theologica, for instance, Aquinas give his proofs for God’s existence at the very beginning (Ia, 2) and reserves his general epistemological discussion for later sections (Ia 79, 84-86).

2. ST, 1a, 3.

3. In informal logic, this is called the fallacy of composition. Just because the parts of a whole possess a certain property, does not mean the whole possesses that same property. Each part of my car weighs less than 20 lbs., but it would be fallacious to conclude from this that my car weighs less than 20 lbs.

4. Systematic Theology (Grand Rapids: Eerdmans, 1989), vol. 1, p. 10. [Emphasis mine.]

5. For further elaboration on this form of Realism, see S. A. Grave, The Scottish Philosophy of Common Sense (Oxford: Clarendon Press, 1960)

6. Systematic Theology, vol. 1, p. 217.

7. What is Darwinism? (New York: Scribners, Armstrong, and Company, 1874).