I used to really love logic puzzles when I was a kid. I’ve mentioned the professional logician Raymond Smullyan a few times as a big influence of mine, and I highly recommend his puzzle books. Here’s a complete list of what Amazon carries, and I’ll highlight some, roughly in order of personal preference:
- Alice in Puzzle-Land
- What Is the Name of This Book?
- The Lady or the Tiger?
- The Chess Mysteries of Sherlock Holmes
Also noteworthy is his book of philosophical essays, The Tao Is Silent. Smullyan, like fellow mathematician Bertrand Russell, dabbles in philosophy a bit, and this book is a westerner’s perspective on eastern religion. I’m sure it takes a lot of liberties with the subject matter, and I imagine if I reread the whole thing now I’d find I agree with him a lot less than I used to in my teens and twenties. But still, his style is playful and entertaining, and there are a couple of essays in that book which I love to reference: “Is God a Taoist?” and “An Epistemological Nightmare.” The first is one of my favorite speculations I’ve ever read on the nature of the “god” concept.
But I digress. I wanted to talk for a minute about Smullyan’s logic puzzles in order to illustrate a point about religious arguments.
Among many other puzzle frameworks, Smullyan authored numerous little puzzles that take place on an imaginary island where all the residents are known to be either knights, who always tell the truth, or knaves, who always lie. In these stories, some people would come up to you and make various statements, and you would have to deduce what kinds of people you’re really talking to. An example from Wikipedia:
John and Bill are residents of the island of knights and knaves.
John says “We are both knaves.”
In this case, John is a knave and Bill is a knight. John’s statement cannot be true because a knave admitting to being a knave would be the same as a liar telling the lie “I am a liar”, which is known as the liar paradox. Since John is a knave this means he must have been lying about them both being knaves, and so Bill is a knight.
The puzzles get very intricate and fascinating, and I recommend them for anyone who is aspiring to gain a deeper understanding of logic, critical thinking, and the ways that formal mathematical systems can be used to represent the truth of a claim. In fact, I even did a team project for a graduate school computer engineering class, in which we wrote a program to read and parse these puzzles and generate possible solutions.
However, you also have to recognize their limitations. Knight/knave puzzles can be solved only if you accept the premise that everyone you talk to is either a knight or a knave. Characters must be either 100% truthful or 100% liars, no exceptions. Later in the puzzle section, Smullyan would often introduce “normals” who, like any other person, can say true or false things at will. Once those people show up, the rest of the logic mostly goes out the window. A normal can say anything at all, and the truth value can’t be determined by any means. Unlike knights and knaves, a normal can lie and say “I am a knave” and there’s no contradiction. Or a normal can tell the truth and say “I am not a knave,” and that’s also just fine. The only way you can solve any puzzle with normals present is if the author helps you out by providing additional information, such as “this group of people contains at most one normal” or something like that.
The reason I’m mentioning these puzzles is that many bad arguments seem to operate under the assumption that we live in a world of knights or knaves. To give a simple example, a fallacious argument from authority is implicitly based on the assumption that the person is a knight. “A famous person says X, and the famous person is often right, so we can be sure that X is true.” In a world of knights and knaves, that makes perfect sense! Once you can establish that a resident of the island has said at least one true statement, it follows that he is a knight, therefore every sentence he ever utters is true! So X is true, end of discussion.
Religion is full of oversimplifications like that, but the real world is a lot more messy. Since every real person is actually a normal, capable of saying either true or false things at any time, no amount of generalization about their tendency to tell the truth can be enough to guarantee that the last thing that came out of their mouth was still true. Thus, somebody can be a brilliant scientist in their own particular field, and right about most or all things, and yet they can still be a complete crackpot when saying things about a subject they haven’t studied. When an authority figure is talking about the field that they are actually an expert in, we can definitely use their expertise as a guideline to suggest that they are making claims that are very likely true. But that person is still not a knight, and is still capable of saying things that are false — whether through ignorance, malice, or bad communication.
Other examples of faulty knight/knave assumptions are all over the place in religious logic, once you start looking for it. Here are a few examples I encounter regularly, off the top of my head.
- CS Lewis’ “Liar, Lunatic, or Lord” trilemma. Jesus Christ claimed to be God; therefore either he is God (being a knight), or he is lying or crazy (being a knave who, having said something untrue, must say or believe untrue things at all times). The problem is, even if we assume that the reports of Jesus making such a claim are accurate (which we can’t really be sure of), he could have been partially or temporarily deluded, mistaken, or lying; and yet he could still have made many other true statements.
- The Bible mentions some cities that don’t exist today; but archaeologists discovered the remains of those cities. Therefore the Bible is accurate that those cities existed. Therefore (can you see the logical transition coming?) the Bible is accurate, so we can trust anything else we read in it.
- Ray Comfort’s favorite apologetic, “Are you a good person?” is quite obviously based on proving that you are a knave. “Have you ever lied? Yes? What does that make you? A liar.” The sleight of hand is that a liar is not a knave, but a normal. Lying some of the time doesn’t make you a knave, any more than telling the truth some of the time makes you a knight.
- Stating that the pope, or anyone else, is infallible — making him a knight.
Here’s an example that’s a little bit trickier: the ontological argument for God basically starts by conditionally assuming that God exists. Then it broadly defines the properties of this hypothetical God, and leverages the implications of these properties to prove that God does, in fact, exist. In a world of knights and knaves, proofs like that aren’t always just wheel spinning. In fact, Smullyan’s books include a number of puzzles in which the very fact that somebody said something about a proposition, makes that proposition true. For instance, we can prove that when a knight or knave says “If I am a knight, then God exists,” it logically follows that the speaker is a knight, and that God does exist. [Note: See the comments section for this proof.]
…If the speaker is definitely a knight or a knave. Which, again, is not a condition we ever have to accept in reality.
In reality, not only do people frequently say things that are unpredictably true or false, they can even say things that are neither true nor false. For instance, when I say the well known paradoxical statement, “This sentence is false,” is it true or false? It’s only an impossible statement under a strictly binary logical system: if the sentence is false then it’s true, and if it’s true then it’s false. But the real answer is, in fact, that the statement is neither true nor false. It just occupies a space where those words don’t apply or have meaning.
In the world of apologetics, many arguments are con games, in the most literal sense of the word: Someone is trying to give you “confidence” in the reliability of a source, and then relying on what the source says to prove things true. By proving that the authority has said at least one true thing, they hope you’ll accept their claim that all the rest of it is true. “Hi, I’m Russell. The sky is blue. Also, God exists.” Two of those sentences are true. That doesn’t tell us anything about the third sentence. In a world of normal people, it is frequently a waste of time to try to find things out by evaluating whether the speaker tells the truth or not.