Reason, Chess, and the Existence of God

There’s an obvious connection between Logic and chess, this is evident from the numerous logic and debate books out there with pictures of chess boards on their covers. If you think of a chess player, you’ll think of a very logical, analytic person. When you think of a Logic professor, it’s safe to assume he or she enjoys the occasional game of chess. But what do logic and chess have to do with the existence of God? Well, I’m going to argue that logic itself can actually be seen as powerful evidence for God’s existence. I’ll make my case using three perspectives on Logic with the game of chess as my pedagogical tool.

Arguing for God from logic has traditionally been called the “Argument from Reason”, put forward most notably by C.S. Lewis. Throughout this post I’ll be using “logic” and “reason” interchangeably as he does. A Similar argument for God from logic (and intelligibility) is called the “Transcendental Argument for God”, primarily used by Cornelius Van Til and his followers. While I thoroughly enjoy them and employ both Lewis and Van Til’s arguments elsewhere, here I want to mix and match some of their insights into a triperspectival approach to the Argument from Reason.

If you’re unfamiliar with the term “Triperspectivalism”, it can sound pretty daunting, but it’s actually pretty simple. It’s just “Tri” meaning three, and “perspective” meaning a point of view. So a Triperspectival Argument from Reason is just an argument for God from three perspectives on reason.

The three perspectives involved in Triperspectivalism, as set forth by John Frame and Vern Poythress, include the “Normative Perspective”, the “Situational Perspective”, and the “Existential Perspective”. Each perspective entails the others, so if we zoom in on the normative perspective we’ll be looking out at the existential and situational perspectives. The same goes for the other perspectives. This will become evident as the argument goes on.

If I’ve piqued your interest in Triperspectivalism I suggest you take a look at my post The Golden Triangle of Freedom for a more in depth introduction. For this post, however, the game of Chess will suffice for helping to convey my point.

Chess is helpful because it can be analyzed triperspectivally. First and foremost, there are the rules of chess which constitute the normative perspective. Chess is played between two players, each piece has a set pattern by which they are allowed to move, a checkmate ends the game, etc. You can’t play chess without this normative perspective, it would cease to be chess; without set norms/rules/laws the game is nonsensical.

Next we can view chess from the situational perspective, here we look at various games of chess. When chess is played in time and space we see the rules of chess in action; the chess norms limit the amount of moves a player can make, yet there are lots of different outcomes throughout different games of chess. The situational perspective of chess views the application of the rules of chess in time and space.

The philosopher, Immanuel Kant, shows a strong connection between the normative and situational perspectives with his famous phrase, “Concepts [normative] without precepts [situational] are empty, percepts without concepts are blind.” Contextualized for us, read “The rules of chess without games of chess are pointless, games of chess without the rules of chess are nonsense.” Just like the connection between concepts and perception, there’s a strong connection between the rules of chess (normative) and various instantiations of the rules during unique games of chess (situational).

And finally, we come to the personal/existential perspective on chess: the player. In order to play the game of chess we require norms, the application of those norms in various situations, and we also require persons to understand and apply those norms in various situations. There is an immediately personal perspective to the game of chess which we can’t overlook.

While there are norms of chess that dictate which moves we can and cannot make in various scenarios in time and space, the personal perspective involves the creativity it takes to sacrifice your queen for a ten move checkmate, as well as a moral component which says “you ought not cheat”. So Kant’s phrase, while helpful, misses the existential perspective, that of the knower in who’s mind the concepts obtain and who’s perceptions give content to the concepts.

So we see from the game of chess that the three perspectives necessitate one another. From here we can begin looking at Reason, Reasoning, and the Reasoner as evidence for God.

Reason: The Normative Perspective
Starting with the normative perspective, we observe that just like the game of chess, there are rules to Reason called the laws of logic. This argument doesn’t require the affirmation of a certain set of logical laws, though I’ll be making reference to the three classical laws of logic- The Law of Noncontradiction (P is not non-P), the Law of The Excluded Middle (either P or non-P) , and The Law of Identity (P is P).

For the purpose of this argument you may substitute a different set if you hold those, or you can add other logical principles that you think are absolutely necessary, my argument hinges not on the specifics of what make up the laws of logic, but rather that there are laws of logic at all. (I follow James Anderson and Greg Welty very closely in this normative perspective, though I skip some steps, I’m indebted to them for much of this.)

Chess would be nonsensical without laws governing the game, similarly, reasoning would not be reasoning without norms governing the reasoning process. Thinking would be impossible without logical laws. Think of the simple math equation 2+2=4, could we reason about math if 2+2=4 and 2+2=5? Could you think of your cat, Fluffy, if Fluffy was both a cat and not a cat in the same sense at the same time? Could you checkmate your friend if your queen both exists and doesn’t exist in the same sense and at the same time? Of course not.

But what and where are these laws of logic; where is the Law of Non-Contradiction? Could I go to Trader Joe’s and buy a pound of Non-Contradiction? Well, no, these laws aren’t physical, they’re immaterial. They’re propositions in our minds. But are they merely propositions in our minds, are they just conventions we’ve agreed upon? Well, if every person were to die in a worldwide cataclysmic event next week, would the whole universe begin behaving irrationally? Would Jupiter start popping in and out of existence? Would circles be squares or squares be triangles? Would it be true that there are no living persons and that there are billions of living persons at the same time? Of course not.

We depend on the laws of logic, but they don’t depend on us. As C.S. Lewis remarks in his book, Miracles, we’ve grown in our reasoning processes, we rest our minds for hours every night, and we must start with reason as an axiom, so we can’t be the ground for the logical laws.

So while the laws of logic are propositions in our minds- and indeed our minds run on the laws of logic as an operating system- we see that there’s an objectivity to the laws; while they are necessary for all of our thoughts, the logical laws transcend us.

Logic exists in every possible world. Can you conceive of a possible world where logic doesn’t obtain? Can you imagine a possible world with a square circle? The laws of logic are universal.

So far we see that the laws of logic are immaterial, necessary, and universal.

But how can we account for them? Where do they come from and how can we make sense of Reason itself? Are they derived from nature through an abstraction process by human minds? Should we affirm with Aristotle that there are no uninstantiated forms, that the universals, including the laws of logic, are abstractions sucked out of particulars? Do we see that an orange is not an apple and from such observations derive the laws of logic? I admit this line of thought is compelling, that is until we remember what Kant says about concepts and percepts. Perceptions, like the color, size, and shape of the orange in view depend on the concepts we bring to experience.

Now I’m not a Kantian and I wont argue for his categories of thought here, I think his division between the noumena and phenomena lead to skepticism, but if we don’t bring the laws of logic to our experience of the orange, then we would never have derived them from the orange. Percepts without concepts are blind. If our minds didn’t already operate on the laws of logic then we wouldn’t be able to think of a circle or orangeness or size. They would be meaningless perceptions of color and lines, but without reason we couldn’t even see them as meaningless.

So the laws of logic are necessary for thought, they are immaterial, they’re universal, and they are a priori- that is, they are prior to experience since we must bring them to experience in order to even perceive anything.

We’ve talked a bit about the laws of logic as propositions, and here I want to follow James Anderson and Greg Welty more closely in describing the laws of logic as true propositions about propositions. If the laws of logic obtain in every possible world, then they’re true in every possible word. The laws of logic necessarily obtain in every possible world (again try to conceive of a world where there are no laws of logic), thus they’re true in every possible world and in turn, they’re true in the actual world. The laws of logic are true propositions about propositions.

Take the Law of Noncontradiction for instance, P is not non-P, Anderson and Welty ask “But what exactly is the Law of Non-Contradition about? What is its subject matter?” They answer, “… the Law of Non-Contradiction is a truth about truths. Specifically, it is the truth that no truth whatsoever can also be a falsehood… In other words, the Law of Non-Contradiction is a truth about propositions: those primary bearers of truth-value. It is a truth about which truth-values a proposition can and cannot bear: if a proposition bears the value true, it cannot also bear the value false, and vice versa. So the Law of Non-Contradiction is about propositions.” (“The Lord of Non-Contradiction” Philosophia Christi, Vol. 13, #2, 2011, pg. 324-25).

Now let’s bring it home! The laws of logic are necessary, universal, and immaterial, they’re a priori truths independent of mankind and not derived from experience but rather, presupposed by experience. They exist as true propositions about propositions. So, how do we explain the laws of logic given what’s true of them in the normative perspective? The Laws of Logic exist as necessary, immaterial, true propositions in the mind of God. God is the source and the standard of Reason itself. He is necessary, universal, immaterial. God is the source of all truth. God is the necessary precondition for intelligibility. Reason itself presupposes a God like the Christian God of the Bible as it’s ground. If we want to make sense of Reason, we need God. This brings us right into the situational perspective.

Reasoning: The Situational Perspective
We now move from the norms- from the theoretical/a priori- to the situational, the more practical/a posteriori. We’re moving from the laws of chess to actual games of chess. So far I’ve sought to show that the laws of logic in and of themselves evidence the existence of God, now I’m going to argue that their application in time and space presuppose His existence.

In order for persons to apply the laws of thought/reason/logic to their experience, there must be a correspondence between the laws of thought and the laws of things.

As C.S. Lewis says, “I conclude then that logic is a real insight into the way in which real things have to exist. In other words, the laws of thought are also the laws of things: of things in the remotest space and the remotest time.” (“De Futilitate”, in Christian Reflections, pg. 78). Similarly, Van Til says, “One’s conception of reality is one’s conception of the foundation of the laws of logic.” (The Defense of the Faith, pg. 295).

In order for the laws of thought to be the laws of things what must be true? In order for us to apply logical laws in time and space what kind of metaphysic must obtain? If we take the Christian metaphysic we can see that reasoning makes sense. The Creator God, a rational, immaterial, necessary, spiritual being, created the universe in a rational-orderly way. From a Christian Theistic worldview, reasoning makes sense. If the kind of God of the Bible made the universe, then we’d expect there to be a correspondence between the laws of thought and the laws of things.

But can we make sense of reasoning without God? What about a naturalist’s explanation of reasoning? Can a naturalistic materialist worldview make sense of mankind’s reasoning capacities? I think there are lots of reasons why a naturalist can’t make sense of reasoning but here I’d like to advance my three favorites.

Starting with C.S. Lewis’s “Cardinal Difficulty with Naturalism”, we see the first reason why a naturalistic metaphysic can’t make sense of our reasoning capacities. In chapter three of Lewis’s revised book, Miracles, he distinguishes between two senses of the word “because”. This distinction shows the difference between a “cause” and a “reason” for a belief. The first sense of “because”, Lewis calls the “Cause and Effect” relation. The second sense of the word “because” he calls the “Ground and Consequent” relation. To show the difference between the two, Lewis uses two sentences about a grandfather, “We can say, ‘Grandfather is ill today because he ate lobster yesterday.’ We can also say, ‘Grandfather must be ill today because he hasn’t got up yet (and we know he is an invariably early riser when he is well).’ In the first sentence because indicates the relation of Cause and Effect: the eating made him ill. In the second, it indicates the relation of what logicians call Ground and Consequent. The old man’s late rising is not the cause of his disorder but the reason why we believe him to be disordered.” (Miracles, pg. 22-23).

A naturalistic conception of human reasoning can be represented by the “Cause and Effect” sense of because. Since the naturalist can’t allow for an immaterial soul, our mind states- if the naturalist believes in them at all- are the product of our brain states, which are ultimately the result of our cerebral biochemistry. A Christian theist will allow for interaction between mind states and brain states, for instance a brain injury can impair our mind’s ability to reason and if we use our mind to think about certain things then neural ruts can form making it easier to think about them. So we see arrows of influence go both ways. A naturalistic conception of man allows only for the arrows of influence to come from the physical.

Every event in nature has a physical causal connection to a previous event. An acorn falls from a tree, it takes root where it falls, given the right amount of water and nutrients it grown into a mature tree and repeats the process. If our thoughts are merely the results of a causal chain of biochemistry, then how could we trust them to produce truth, why would we trust our reasoning at all?

If all we had were causes for our beliefs, we’d have no reason to hold them.

If the Cause and Effect sense of because is the cause of our beliefs, then in what sense are they even our beliefs? We were forced to believe them, not by logical necessity, but rather by a physical causal chain of biochemistry; our brains fizzed a certain way and produced a belief. We didn’t choose to follow a line of reasoning, we didn’t see a logical implication, our reasoning processes don’t follow the “Ground and Consequent” sense of because.

Lewis argues that this fundamentally discredits our processes of reasoning, creating a “proof that there are no such things as proofs”. In showing the self-referentially absurd nature of naturalism, he quotes J.B.S Haldane, “If my mental processes are determined wholly by the motions of atoms in my brain, I have no reason to supposes that my beliefs are true… and hence I have no reason for supposing my brain to be composed of atoms.’” (Miracles, pg. 22)

In one of his most powerful and succinct summations of this argument, Lewis says, “Supposing there was no intelligence behind the universe, no creative mind. In that case nobody designed my brain for the purpose of thinking. It is merely that when the atoms inside my skull happen for physical or chemical reasons to arrange themselves in a certain way, this gives me, as a bye-product, the sensation I call thought. But if so, how can I trust my own thinking to be true? It’s like upsetting a milk-jug and hoping that the way the splash arranges itself will give you a map of London. But if I can’t trust my own thinking, of course I can’t trust the arguments leading to atheism, and therefore have no reason to be an atheist, or anything else.” (The Case For Christianity, pg. 32). So if Lewis’s argument holds, then the naturalist conception of reasoning fails.

Next we’ll look at a related argument from Alvin Plantinga known as “The Evolutionary Argument Against Naturalism”. Plantinga’s argument, while similar to that of Lewis and Arthur James Balfour, can be traced back to Charles Darwin himself. In an 1881 letter to William Graham, Darwin wrote, “the horrid doubt always arises whether the conviction of man’s mind, which has been developed from the mind of the lower animals, are of any value or at all trustworthy. Would any one trust in the convictions of a monkey’s mind, if there are any convictions in such a mind?”

Following Darwin’s doubt, Plantinga develops a skeptical threat against a naturalistic account of reasoning such that to believe both naturalism and evolution- two beliefs usually held as bosom buddies- would be self-referentially incoherent.

Plantinga argues, “that (from a naturalistic perspective) what evolution guarantees is (at most) that we behave in certain ways- in such ways as to promote survival, or survival through childbearing age. The principal function or purpose, then,… of our cognitive faculties is not that of producing true or verisimilitudinous beliefs, but instead that of contributing to survival by getting the body parts in the right place. What evolution underwrites is only (at most) that our behavior be reasonably adaptive to the circumstances in which our ancestors found themselves; hence (so far forth) it does not guarantee mostly true or verisimilitudinous beliefs. Of course our beliefs might be mostly true or verisimilitudinous… but there is no particular reason to think they would be: natural selection is interested not in truth, but in appropriate behavior.” (Warrant and Proper Function, pg. 218).

Plantinga’s EAAN (Evolutionary Argument Against Naturalism) punches a major hole in a naturalistic account of reasoning in that if evolution (a major tenant of Naturalism) produced our thought processes, then it would have tended towards adaptive survival thoughts rather than thoughts that are “true”. For instance, let’s say a frog eats dragonflies because he thinks that doing so will turn him into a prince and he’ll win the hand of a fair princess. As long as he keeps eating dragonflies he’ll survive. His thoughts, though untrue, still provide him with beneficial survival habits.

If our reasoning is the result of a long series of evolutionary biology, then our reasoning would be directed at survival rather than truth. Since truth is harder to come by than falsity (a math equation has one correct answer but thousands of incorrect answers), it’s more likely that, given naturalistic evolution, our reasoning processes give us survival beliefs that are false but beneficial. If this is true then we have no reason to believe in a naturalistic evolution of our reasoning processes. Thus, instead of undergirding our reasoning capacity, naturalism erodes it’s foundations.

The third argument I want to advance against a naturalistic conception of reasoning comes from Richard Taylor, we’ll call this argument the “White Stone Argument”. Taylor’s argument is similar to those of Lewis and Plantinga but it’s much simpler. In his book, Metaphysics, Taylor starts out the argument by showing two interpretations of a greeting,

“suppose that you are riding a railway coach and glancing from the window at one of the stops; you see numerous white stones scattered about on a small hillside near the train in a pattern resembling these letters: THE BRITISH RAILWAYS WELCOMES YOU TO WALES. Now you could scarcely doubt that these stones do not just accidentally happen to exhibit that pattern. You would, in fact, feel quite certain that they were purposefully arranged that way to convey an intelligible message. At the same time, however, you could not prove, just from a consideration of their arrangement alone, that they were arranged by a purposeful being, It is possible – at least logically so- that there was no guiding hand at all in back of this pattern, that it is simply the result of the operations of inanimate nature. It is possible that the stones, one by one, rolled down the hill and, over the course of centuries, finally ended up in that interesting arrangement, or that they came in some other accidental way to be so related to one another. For surely the mere fact that something has an interesting or striking shape or pattern and thus seems purposefully arranged is no proof that it is. There might always be some other explanation.”

Taylor uses this premise to set out his argument. Given the placement of these white stones, we have basically two options in explaining how they came to be there. The first is the most obvious: someone placed them there with the intention of welcoming you to Wales. The second is the more improbable, but not necessarily impossible: the stones came to be there, in that pattern, by accident.

He goes on to argue that if you believe someone placed the stones there on purpose, in order to convey a message to you, then you’d be perfectly rational in reading it for content. However, if you believe that the stones ended up on that hillside by accident, you’d be foolish to read the rocks together as a message and conclude that you’re entering Wales.

This analogy can be applied to human reason itself. If you believe that human reason is the result of a Rational Being, like the God of Christianity, then you’d be justified in using your reason to search for truth and meaning in the universe you believe He created. However, if you believe that human reason is ultimately the result of random chance acting on matter over time, then you’d be irrational to trust your reasoning processes in order to find truth and meaning in a universe of meaninglessness.

So we’ve seen some serious problems with a naturalistic conception of human reasoning, whether it’s Lewis’s argument against causal determinism which erodes reasoning, Plantinga’s argument that shows the irrationality of holding both evolution and naturalism together in the same conceptual framework, or Taylor’s argument that shows the irrationality of using reason to find truth and meaning while believing that reason is ultimately the result of accident and chance. Christianity, on the other hand, makes perfect sense of human reasoning. If we take the Christian doctrines of God and Creation, we can make sense of the correspondence between he laws of thought and the laws of things. We can make sense of man as reasoner, which bring us to our third perspective.

Reasoner: The Existential Perspective
So far, I’ve argued that the normative perspective of reason evidences the existence of God, that the situational perspective of reason presupposes the Christian doctrines of God and Creation, now I’m going to argue that the existential perspective of reason also presupposes the God of Christianity and the Christian doctrine of Man.

To return to our chess analogy, chess requires rules or norms and individual games of chess involve the application of the rules of chess in time and space. Now we come to examine the chess player: the reasoner. The idea of man as reasoner is multifaceted, but again I want to take a look at just three aspects: 1. the necessary preconditions of human thought, 2. our access to logical laws, and 3.the ethics of inference. (The astute reader might see these as a sub-triad, of the existential perspective: 1. Normative-Existential, 2. Situational-Existential, 3. Existential-Existential)

Starting with the necessary preconditions of human thought we return once more to C.S. Lewis. Lewis argues that there is no such thing as “human reason”, but rather we should speak of “human thought” which presupposes an objective standard of “Reason”. In his essay, De Futilitate, Lewis says,

“… there is no such thing (strictly speaking) as human reason: but there is emphatically such a thing as human thought – in other worlds, the various specifically human conceptions of Reason, failures of complete rationality, which arise in a wishful and lazy human mind utilizing a tired human brain. The difference between acknowledging this and being sceptical about Reason itself, is enormous. For in the one case we should be saying that reality contradicts Reason, whereas now we are only saying that total Reason- cosmic or super-cosmic Reason- corrects human imperfections of Reason… To say that Reason is objective is to say that all our false reasonings could in principle be corrected by more reason.” (Christian Reflections, pg. 83-83).

Lewis points to the fact that human thoughts can be true or false, rational or irrational, and thus our thoughts can’t be the ground for reason. Similar to the argument above in the normative perspective, there must be an external, objective Reason by which we can judge our subjective thoughts. This means that all of my thoughts throughout this post, and all of your thoughts about it, presuppose what Lewis calls “Reason”.

At this point you might be asking why we can’t be the ground of this Reason, why must we posit some external ground? To which Lewis replies,

“… it is clear that my Reason has grown up gradually since my birth and is interrupted for several hours each night. I therefore cannot be that external self-existent Reason which neither slumbers nor sleeps. Yet if any thought is valid, such a Reason must exist and must be the source of my own imperfect and intermittent rationality. Human minds, then, are not the only supernatural entities that exist. They do not come from nowhere. Each has come into Nature from Supernature: each has it’s tap-root in an eternal, self-existent, rational Being, whom we call God.” (Miracles, pg. 43).

So we see, then, that a necessary precondition for the truth or falsity, the validity or invalidity, soundness or unsoundness, of our human thought is an objective Rationality, i.e. God. This leads us into accounting for our access to logical laws.

In helping us understand our access to the logical laws, we can look, yet again, to Immanuel Kant. Kant argued that we perceive an orderly world in the way we do because we all have 12 categories of understanding. We uses these categories to sort out raw sense data into meaningful perceptions.

John Frame summarizes a common critique of Kant’s categories which will be helpful for us, “Students sometimes ask, given today’s emphasis on the sociology of knowledge and the diversity of ways in which people think: why did Kant think that everyone reasoned with these same categories?” (A History of Western Philosophy and Theology, pg. 260). How can Kant account for all humans having the same categories of understanding if we haven’t been designed to think in these categories? The same question can be asked of those who would seek to account for our access to logical laws without relation to God.

As we’ve seen above, reason is a priori, that is we bring it to experience rather than derive it from experience. How can we make sense of mankind’s a priori access to objective reason? The best explanation is some sort of preformation theory: “…knowledge is possible only because God has endowed humans with certain innate ideas along with dispositions or aptitudes to think in certain ways. These forms of thought correspond to the real world, which is also a creation of God.” (Ronald Nash, Life’s Ultimate Questions, pg. 267). If God- the ultimate source and ground of Reason- has created the universe in a rational way and created us in His image with the ability to think His thoughts after Him, then it makes sense to see humans thinking and reasoning in time and space. If we haven’t been created by that kind of God, in that kind of way, then we’re left in a similar position to Kant.

Finally we come to the most controversial portion of this whole argument: the ethics of inference. The ethics of inference can be summed up by the phrase “be reasonable”. Most of us have at one time or another pleaded with someone to be reasonable. This imperative or injunction isn’t a logical demonstration of the truth or necessity of reason itself, rather, it’s force is felt when the unreasonable person is made to see the irrationality of their position. A tacit presupposition of the call to “be reasonable” is an ethical ought: people ought to be reasonable.

Similarly, if you see that a logical syllogism is sound, that the conclusion necessarily follows from it’s true premises, then you ought to affirm that conclusion. You ought to believe the truth. But where does this “ought” come from? It’s not from the realm of logic alone, oughts come from ethics!

John Frame helps us more fully understand this argument,

“We have seen that people do hold contradictory beliefs sometimes. But the fact that someone believes “not-p” is no proof that he does not also believe “p”. The law of noncontradiction says that he ought not to believe contradictory propositions, but it does not prevent him from doing so. But there is a second sort of necessity. The logical “must” indicates a moral necessity. To say that someone “must” accept a conclusion is to say that he ought to accept it, that he has an obligation to accept it.” (The Doctrine of the Knowledge of God, pg. 248).

So we see that “Logic, therefore, can be viewed as a brand of ethics.” If we ought to affirm the truth, if we ought to affirm a conclusion from a valid argument with true premises, then to whom do we owe this duty? Again, the answer is God. As image bearers of God, we ought to represent Him as He is, in truth. God is not a liar, and as His image bearers here on earth, we ought not lie, we ought to think His thoughts after Him in truth. We ought to believe the truth.

If we believe in God, then we can make sense of the ethics of inference. If we don’t believe in God, we’re left trying to derive an ought from an is, also known as the naturalistic fallacy.

On that note, let’s see if we can wrap it all up. Reason, as seen from three perspectives, evidences the Christian God of the Bible. We’ve seen that just as chess has rules, games, and chess players, so reason has rules, reason can be applied to various situations in time and space, and reason requires reasoners such as God and His image bearers. If the argument is successful, then all of our thoughts are evidence that God exists.

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