The following video is based on the post that follows it:
Daniel Chaney addressed Matt Slick’s Transcendental Argument for the Existence of God in his book Religion Refuted, but I was not satisfied with how he handled it. Chaney and I both agree that it is a bad argument, and he did bring up some good points, but he missed the main reason why it is a bad argument. That’s what I’ll address here. Let’s begin by taking a look at this argument. Here it is in outline form:
- Logical absolutes exist.
- Logical absolutes are conceptual by nature–are not dependent on space, time, physical properties, or human nature.
- Since logical absolutes are always true everywhere and not dependent upon human minds, it must be an absolute transcendent mind that is authoring them.
- This mind is called God.
I agree with the first premise. Slick mentions the Law of Identity (A=A), the Law of Non-Contradiction (~(A&~A)), and the Law of Excluded Middle (A ∨ ~A). To spell out what these mean, the Law of Identity says that something is identical with itself, the Law of Non-Contradiction says that something, taken in the same sense, cannot be both true and false, and the Law of Excluded Middle says that any meaningful proposition is either true or false. I agree that these are logical absolutes. Each one is absolutely and eternally true, because each one is a tautology.
I disagree with the second premise. I do agree that logical absolutes are not dependent on space, time, physical properties, or human nature. But that is not all there is to being conceptual by nature. To be conceptual by nature means to exist only as a concept. For example, the rules of a game or the details about a fictional character are conceptual by nature, because these actually do exist only as concepts. But the logical absolutes are not conceptual by nature. I may be limited to knowing them conceptually, but they are fundamentally different from products of my imagination, which exist only as concepts. These logical absolutes remain true no matter whether anyone has concepts of them. Their truth is so absolute and fundamental, there is no possible way they could be false, not even if God somehow decided to use different rules of logic. Their truth is in no way dependent upon being thought by God. Therefore, their truth does not imply the existence of God.
Besides that, Slick’s second premise contradicts his first. The logical absolutes he mentions are absolutes only if their truth does not depend upon anything apart from them. A concept is a mental construct that a mind uses to understand reality. As such, it depends on a mind for its existence. That is why Slick uses this premise to argue that these logical absolutes exist by being thought by the mind of God. In that case, these would not be absolutes at all. They would just be thoughts in the mind of God, which is the only reality that would be absolute. If so-called logical absolutes depend upon the mind of God for their existence, then they could have been something else, meaning they are not logically necessary and not absolutes. Chaney puts it this way, “If logical absolutes are contingent on God’s thoughts, then shouldn’t we call them logical contingencies?”
I have quoted from the simplified version of Slick’s argument. In the expanded version, he says, “God either exists or does not exist. There is no third option.” I agree, assuming we have a meaningful concept of God. But let me point out that this is an application of the Law of Excluded Middle. If it is only by God’s whim that the Law of Excluded Middle is true, then it cannot be used to prove that God exists. Before we could know that the Law of Excluded Middle is true, we would have to know that God exists. But using the Law of Excluded Middle in an argument for God’s existence and also using God’s existence to confirm that the Law of Excluded Middle is true would be begging the question. To get out of this cycle of circular reasoning, we have to confirm the truth of one independently of the other. I believe we can confirm the Law of Excluded Middle independently of God.
Here’s how we can do that. First, let’s define our terms. Truth is correspondence with reality. A claim is true when it corresponds with reality, and it is false if it does not. To count as a claim, a verbal expression must be meaningful. It would be meaningful to claim, “a cat suddenly grew wings and flew into the air to catch a bird,” but to say “wings air flew bird suddenly a grew and the into to a catch” would not be meaningful. Nor would it be meaningful to say “a frib suddenly grew nibs and zaroomed into the nadet to niop a wervip” unless each word in the sentence meant something. So these two sentences do not express claims. When a claim corresponds to reality it is true, and when it does not, it is false. But let’s not think that logic applies only to claims. A claim is still a mental construct. So let’s introduce a new term. A fact is a way that reality is. A claim is true when it expresses a fact, and it is false when what it expresses is not a fact. That gives the general idea, but it still oversimplifies things a bit.
Suppose we have a complex claim, such as “I am a male Protestant.” This does express one fact, namely that I am male. But taken as a whole, what it expresses is not a fact. Although I am male, I am not a Protestant. When I say that a claim is true when it expresses a fact, what I mean can more precisely be stated by saying that a claim is true when the singular claim it makes as a whole is a fact. If I assert a conjunction, such as A & B, it is true only if both parts of the conjunction, what are called conjuncts, are true. Even if A expresses a fact, A & B will not express a fact unless B also expresses a fact.
This is true not only for simple conjunctions but for long ones. Consider a historical drama, such as HBO’s Rome. Is it true or false? It may tell about events that really happened, portraying people who were actually involved in those events. In that sense, it would be true. But it would also be fictionalized, including fictional characters, fictional portrayals of real people, fictional dialogue, and fictional details, such as what clothes they were wearing, what they looked like, the finer details of how they acted during the events they were involved with, etc. In that sense, it would be false. In this case, it would be accurate to say that it is false overall but still contains true details. If I assert that HBO’s Rome is true, I assert that everything it portrays as fact is fact. HBO’s Rome is a work of fiction that blends together fact and fiction, which makes it false as a whole. This certainly isn’t to deny that it is partially true or to deny that one can learn something of history from watching it. It’s just to say that understood as a conjunction of multiple truth claims, what it asserts as a whole is not a fact.
As I was saying earlier, logic applies to more than just claims. It also applies to facts. A fact is true if it corresponds to a fact. And since every fact corresponds to itself, every fact is true. A fact differs from a claim by being a feature of reality, not a construct of a mind, and by always being true, never false. Even though there are no false facts, logic still applies. When a fact is true, there cannot be another fact that contradicts it. This is the expression of the Law of Non-Contradiction in reality. The Law of Identity may be expressed as a fact is identical with itself. And the Law of Excluded Middle asserts that the disjunction of a fact with its contradiction is a fact. A disjunction is an or-statement. If A is a fact, then so is A ∨ ~A. A fact does not have to be known to be a fact. There are countless facts unknown to anyone. In fact, there is an infinite number of facts, and no one, not even all knowers as a whole, can know all facts. The logical absolutes brought up by this argument are facts. They are just a way things are. But more than that, they are a way things must be. They are necessarily true, and that is what makes them absolute.
We could try to object that these are true absolutes. Although this would fly in the face of the first premise, it would help support the second, which, as I said, contradicts the first. One objection we could make is that there are systems of Three-valued logic. In looking over the article on these, it is not evident to me that the third truth value they introduce is actually a meaningful third option. In Kleene logic and Łukasiewicz logic and some other three-value logics, the third value means unknown. An unknown would actually be true or false. It’s just that we wouldn’t know which. But something may count as a meaningful third truth value only if it can be said that something with it is neither true nor false. In the event that we did have a meaningful third truth value that excluded both true and false, we would still have analogues to the Laws of Excluded Middle and Non-Contradiction that each included a third term. So we would still have logical absolutes whose truth did not depend upon anything, including God. I think a three-valued logic could be an interesting intellectual exercise, but I don’t believe it has any application to reality. The distinction between fact and non-fact is binary.
Another objection is to bring up Gödel’s Incompleteness Theorem. Chaney brings this up, and I think this is why he doesn’t take the same approach to this argument as I am taking. I am not an expert on Gödel, but I do suspect that some people interpret his theorem to mean more than it is saying. I understand it to be about powerful logical systems, and it is saying that one cannot be both complete and consistent. A complete system is one that can prove every true theorem. When you have a contradiction, you can prove anything. That’s why you can have a complete system if you introduce a contradiction into it. But a logical system with a contradiction in it wouldn’t be very logical. The alternative we’re left with is a consistent system that cannot itself prove every true theorem. I believe that’s why it’s called an Incompleteness Theorem rather than an Inconsistency Theorem. In my symbolic logic lessons on conditional proof and indirect proof, I have given a proof of each rule of replacement without using that rule in the proof, but I have not given proofs of the rules of inference, which I simply established with truth tables, or of the rules of Conditional Proof or Indirect Proof. Indeed, it may be impossible to prove something as basic as the rule of Conjunction1 without using a truth table. I tried doing an Indirect Proof of this2, but after I got contradictory premises on separate lines, I realized I needed the rule of Conjunction to put a contradiction on the last line of the Indirect Proof. Nevertheless, the rule of Conjunction does follow from the truth-functional definition of the conjunction symbol, which can be illustrated as a truth table.3 So I don’t interpret Gödel’s Incompleteness Theorem to mean that logic is questionable and that we cannot establish the truth of any logical absolutes. Besides that, it would be unreasonable to expect that any consistent system could prove every theorem. A logical system has to begin with a foundation that is established outside of itself. In trying to demonstrate the logical absolutes mentioned in this argument, I have not appealed to a larger system of logic to prove them. Instead, I have appealed to the definitions of the terms I use to explain them. If you understand what claims, facts, truth, conjunctions, disjunctions, negation, identity, and correspondence all are, then you should understand why these logical absolutes are logically necessary.
Putting that aside, if God is the source of logic, then logic is not absolute, and it is nonsense to speak of anything as necessary. It would even be nonsense to speak of God as necessary. If God is the author of logic, he cannot be subject to it, and that means God cannot be logically necessary. This undermines any argument for God’s existence which tries to show that God’s existence is necessary. So, if the Transcendental Argument can establish God’s existence, the Modal Ontological Argument cannot. But more than that, it undermines any argument that tries to use logic to prove God’s existence. As long as logic depends upon God, God’s existence is beyond all reason and cannot be established by it. This undermines every argument for God’s existence, including the Transcendental Argument. Since an argument that undermines itself cannot be a good one, the Transcendental Argument fails once again.