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PART I. God and Logic: Two Popular Proposals
“God and logic” is a popular topic these days, and it certainly deserves the attention. From what I’ve seen, approaches to this topic fall into one of two complementary errors.
Many writers argue that logic as we know it (Aristotelian logic, for the most part) is the logic of God. These proposals fail to maintain distinctive Protestant commitments such as the doctrines of revelation and Scripture, and even classic, ecumenical doctrines such as the Creator/creature distinction and the aseity and triunity of God. This approach proves itself misguided when we consider its implications for theology proper. In short, if we take Aristotle’s logic to be identical to God’s logic, we end up with Aristotle’s God.
Other writers go too far in the other direction when they argue that logic is a created thing, or that logic is man-made, or something along those lines. I can sympathize with the impulse here: at many points in our theologizing we run up against what appear to be simple and intractable contradictions; if God is exempt, those contradictions become much less daunting, or they disappear entirely. Unfortunately this view disappoints as well, for at least one reason: if we accept it, we’re invited to think of God as not only incomprehensible to us, but ultimately incomprehensible (illogical, disordered), even to himself. We’re also left in the unenviable position of having to defend our devaluation of logic, while that very defense will take the form of logical argumentation. Oops.
So there are the two approaches that I see in the literature: (1) logic as we know it (Aristotelian) exists eternally with God, and is even the logic of God himself; (2) logic is a created thing and only created things can be held accountable to it in only relatively limited ways. I would like to propose a third approach.
God and Logic: A Third Approach
(3) There is an original, uncreated logic, which is the logic of the triune God. This logic is eternal, infinite, simple, triune, and personal. It is the self-coherence of God; it is the divine, triune, self-consistency. The relationship between the logic of God and logic as we know it, such as Aristotelian logic, is complex. I’ll make two suggestions:
(3.1) First, logic as we know it depends upon the original logic of God. For example, God is. Therefore, it is false that God is is false. The law of the excluded middle works in the created order because God, as uncreated, eternally is. I would go so far as to say that the act of creation and the continuing providence of the triune God are the sine qua non of logic as we know it.
(3.2) Second, logic as we know it is often falsely credited with its own self-sufficiency—it is taken to be ultimate; in other words, (3.1) is often denied, implicitly or explicitly. It is denied by non-theistic or anti-theistic writers who claim that logic is, that Christian theism violates the laws of logic, and that, therefore, Christian theism is false, or irrational. This line of thought takes logic as we know it to be ultimate in and of itself, as self-existent.
I described above those theistic philosophers who take logic as we know it to be the eternal logic of God. This is also a denial of the dependence of logic as we know it upon the original logic of God, since it describes God in terms of logic, rather than describing logic in terms of God: its methodology is creatio-centric.
The second alternative I described above had to do with those perhaps overzealous defenders of the Creator/creature distinction who claim that logic is a created thing; they also deny the organic dependence of logic as we know it upon the eternal logic of God. They claim that the two are utterly unrelated and unrelatable.
Logic as We Know It, According to the Third Approach: Facing Christ as Lord
If it is true that the original logic is the (logic of the) triune God, it would seem that one must believe in the triune God to understand logic rightly, or ultimately, or truly, or something like that—to account for it, we might say. If that is the case, the simple truths of logic like the laws of identity, the excluded middle, and non-contradiction, set before us the question of the very foundation of our thinking and our understanding of the world. There appear to be two basic alternatives: recognition of the triune Creator God as Lord and judge of all, or affirmation of the self-sufficiency and ultimacy of the laws of logic. Either God is our logic, or logic is our God.
PART II. Logic and Christianity and Alleged Difficulty
Suppose I show up at work Monday morning and begin telling my co-workers about my weekend. Suppose part of my story goes like this: “At church yesterday, we heard a great sermon from our pastor. Also, on the way to church, we got a flat tire and ended up missing the entire worship service.” My colleague might say, “Well, wait a second; which is it? Did you go to church and hear a great sermon, or did you get a flat and miss the whole thing?” If I continue to affirm both that we went to church and heard a great sermon and that we got a flat and missed the whole thing, then my colleague has good reason to doubt my story—it’s either completely false or partially false or just mixed up. Some how, he thinks, something is fundamentally wrong with the whole narrative. And he’s probably right.
The principle at work here is something like this: nothing that is (logically) self-contradictory is believable, or even possible. And here’s the issue: it is frequently said that Christian theism suffers from precisely this problem. Critics often attempt to demonstrate logical incoherence within Christianity, and the implication is that if they succeed, Christianity will not be (rationally) believable, or even possibly true. And, in fact, it does not appear too difficult to find examples of such difficulties internal to the faith.
Here’s one example: The witty adage, “can God create a stone that is too heavy for him to lift?” is meant to point out logical incoherence at the heart of the idea of omnipotence. If we affirm that God is omnipotent (that there is no limit to what God can do, as in Matt 19:26), then we will want to deny that there is anything too heavy for God to lift, and we will want to deny that there is any kind of rock that God cannot create. Omnipotence appears to force us to affirm contradictory propositions.
If we define believability and possibility in terms of logic, if we treat logic as we know it as ultimate—even more ultimate than God—then Christianity faces tough challenges. And it should face problems if we take logic as we know it to be ultimate and self-sufficient. Taking logic as we know it as ultimate is to mistake the analogue for the original, and thus, in effect, to take the (created) world itself as ultimate and self-sufficient.
The Insufficiency of Logic as We Know It
Consider this syllogism:
All men are mortal.
Socrates is a man.
Therefore, Socrates is mortal.
Is this argument is sound? Sure it is—unless my cat is also named Socrates. Since I might have a cat named Socrates (or a dog or a gecko or an uncle), we have to clarify what we mean when we say “Socrates,” and we also have to stipulate that every time we say it, we mean the same thing: every time “Socrates” is uttered or appears on the page, it refers to the same entity, whether man or cat or gecko or uncle. (We also have to hope that the referent is the same in the speaker’s mind as it is in the hearer’s, which is not always easy to establish.) Not only that, but we also have to repeat all this to every person who reads this argument, every time it is read. Or we could simply assume that all this is the case, as we often do: that “Socrates” refers to the ancient Greek philosopher, the teacher of Plato, and that each time “Socrates” appears in the argument, it still refers to Plato’s teacher. (And that “Plato” doesn’t refer to someone else’s cat who studied philosophy under my cat or my dog or my uncle.)
Another problem arises, one that has to do not with the terms but with the things the terms refer to: What happens if, while we’re reading this argument, Socrates (the man) ceases to exist, without explanation, or if Socrates (the man) turns into a frog or a six digit number, or if Socrates (the man) turns out to be just part of a dream I’m having right now? The argument would, of course, fall apart. So we have to assume that the referent of the term “Socrates,” not the mental object but Socrates himself, also remains the same, that Socrates is self-identical through time.
One of the enduring problems in philosophy is the nature of the self: how is it the case, or what does it mean, that I am the same person that I was twenty years ago? If my, say, three-year-old self were sitting right here next to me, would we look or act or think like identical beings? Nowadays we know that each individual has his own, unique genetic code; and that helps. But when we say, “Socrates,” are we referring to an ancient Greek’s genetic code? Is Socrates, or any person for that matter, nothing more than his genetic code? “Teacher of Plato” is not in Socrates’ genetic code. And I, for one, am much more than my genetic code. There is no mention in my genetic code of my wife or my child, of my education and experiences, of my tastes, preferences, hobbies, or habits. My closest friends do not know my genetic code. Do they not know me? Logic cannot enter this morass; it must simply assume that Socrates is knowable and self-identical through time.
We now see that at least two assumptions must be maintained in order for this syllogism to work—that the terms, always and by everyone, refer to the same entity, and that referents of the terms remain perfectly self-identical. We’re beginning to see that logic operates with a kind of artificial snap shot of the world, a kind of ontological freeze-frame; it operates on the assumption that the world is ontologically flat or monotone, or mono-ontological, to coin an unfortunate term. But it’s rather obvious that reality isn’t like this. The world isn’t, ever, ontologically flat or linear or unitary or whatever. It isn’t mono-ontological.
Mono-ontological vs. Triune-o-logical
Vern Poythress has discussed this in more detail in his article “Reforming Logic and Ontology in Light of the Trinity” (Westminster Theological Journal 57, no. 1 ), and in much greater detail in his forthcoming Logic: A God-Centered Approach to the Foundation of Western Thought (Crossway 2013). In the article, he observes that, “syllogisms can operate only with unitarian ontology. Hence syllogistic reasoning is itself tacitly unitarian.” With this spurious ontology in mind, Poythress concludes that, “there is no such thing as a valid syllogism in the Aristotelian sense” (204-5). He means, I think, that logic doesn’t actually describe any actual things, because the unitarian ontology it assumes is nowhere to be found—it too, is an abstraction.
Take the law of identity for example, which says that A=A. It is true in an obvious sense that God is self-identical, or that if you have God, then you have God. But how exactly is this the case? Consider the persons of the Trinity. If you have one person of the Trinity, you have God. But if you have God, it is not so obvious that you have one person of the Trinity.
In God, self-identity is fundamental, basic, rock-bottom. If not, we are tri-theists. But in God, non-identity is also fundamental, basic, and rock-bottom. If it isn’t, we are modalists. The law of identity in God, that God eternally and unchangeably is who he is, is so sure that we say it is a se, of itself or to itself. But God’s identity is a rich and incomprehensible, Triune, personal identity. Logic as we know it should be used with an understanding that behind it lies the irreducibly triune personality of God. But often, as we’ve seen, it is not.
Cornelius Van Til wrote, “God has determined whatsoever comes to pass. Man’s moral acts are things that comes to pass. Therefore man’s moral acts are determined and man is not responsible for them.” And so, he says, “From the point of view of a non-Christian logic the Reformed Faith can be bowled over by means of a single syllogism” (Common Grace and the Gospel, 73). If we are treating logic as the self-sufficient determiner of possibility, we’d have to surrender either moral responsibility or the full sovereignty of God. (See Rom 9:19ff.) The simple fact that Scripture won’t allow us to surrender either of these to the demands of logic is an indication that logic as we know it must be leading us astray somehow.
The way through such apparent difficulties, I think, is to understand logic as (3.1) derivative and reflective of the original uncreated logic of the eternal triune God, and to remember that [~(3.2)] we should not, therefore, take logic to be the independent determiner of possibility and believability, particularly when Scripture invites us not to.
Triune Theism and the One-and-Many Fabric of Reality
According to the Christian Scriptures, the triune God is the creator of this one-and-many universe. It is because the one-and-many God is self-consistent and self-existent that logic works. At the same time, it is because God the creator and sustainer is himself essentially one-and-many that reality is too rich to be captured, or much less governed, by syllogisms and propositions and laws of logic.
After the flood, the Lord renews his covenant with Noah. Part of the re-creation language in that renewal goes like this: “While the earth remains, seedtime and harvest, cold and heat, summer and winter, day and night, shall not cease” (Gen 8:22). This is an extraordinary utterance. It appears to be a divine utterance that is essentially and irreducibly one-and-many: In a single word and with a unified declaration God has determined that history should be a certain way, and that way, notice, is change and variation—plurality. As far as I know, there is nothing intrinsic to winter that produces the spring, nor is there anything intrinsic to summer that invites the fall. These changes are neither naturally nor logically necessary. Although, I think, seasonal changes are attributable to the motion of planetary bodies—the earth, the moon, and the sun—and to gravitational force, gravitational force is not logically or naturally necessary either, nor is the existence of any of these bodies. (I’m sneaking in a bit of the cosmological argument here!) And if this is the case, in Gen 8:22 God sovereignly and singly ordains variation and genuine historical change. We may, I think, marvel as the seasons change throughout the year at this stable flux and unified variation, this basic one-and-manyness of the natural world; it is a deeply Christian reality.
The richness of the one-and-many fabric of the created order is beyond the explanatory power of logic, but logic is a tremendously powerful tool; indeed, it is sublime, and, if understood rightly, reflective of the nature and the majesty of God. Van Til says somewhere that “the unbeliever takes for granted the ultimacy of the universe.” This is a helpful insight. Problems emerge when logic as we know it is treated as ultimate, as self-sufficient and self-existent, particularly when we’re dealing with Scripture. Logic itself is sometimes thought to be the first and the last, that through which all things were made and in which all things hold together; but that honor belongs to Christ alone.
- “Thought Thinking Itself? Christianity and Logic,” by Scott Oliphint
- “Believing Contradictions,” by Nathan Sasser
- “Does A=A?” by Nathan Shannon
- “Reforming Ontology and Logic in Light of the Trinity,” by Vern Poythress WTJ 57 (1995)