An Introduction to Logic

In debates, I often find that people are unwilling to accept the rules of logic, and they make foolish comments like, “well you’re entitled to your opinion.” In reality, the rules of logic are like the rules of mathematics. They are an inherent and immutable property of existence, not opinions. Just as 2+2 always equals four, the rules of logic are always true and must always be followed. To illustrate, the most basic rule upon which all other rules rely is known as the Law of Noncontradiction. It states that something cannot be A and not A simultaneously. In other words, two mutually exclusive things cannot exist simultaneously. For example, you cannot have a circular triangle, because a circle, by definition, has no straight lines and no corners, and a triangle, by definition, has three straight lines and three corners. An object cannot simultaneously have zero corners and zero lines and three corners and three lines. That’s not an opinion, it’s an immutable property. If you reject the rules of logic, then you have just acknowledged the possibility of a triangular circle, and, in fact, all rational thought disintegrates. You see, we all inherently and intuitively know that the rules of logic work, and we apply them in our daily lives, we just don’t often think about them in technical terms. For example, suppose that your fuel gauge shows that you are low on gas, and you know that your fuel gauge works, what do you conclude? Obviously, you will conclude that you are low on fuel, but why did you reach that conclusion? Without you even knowing it, your brain did the following:

1. My fuel gauge is designed to tell me how much fuel I have
2. I know that my fuel gauge works
3. My fuel gauge says that I am low on fuel
4. Therefore I am low on fuel.

That’s plain and simple deductive logic. If, however, you deny the laws of logic, and claim that they are just opinions, then you have just denied that syllogism. In other words, if the rules of logic don’t work, then the fact that your fuel gauge works and is currently showing that you’re low on fuel does not mean that you are low on fuel. Cause and effect relationships operate because of the rules of logic. So, if you deny the rules of logic, then you deny cause and effect.

I mentioned earlier that the rules of logic are like the rules of math. In fact, they aren’t just like math, math relies on them. For example, anyone who has taken geometry has probably been introduced to proofs. These are simple logical syllogisms. For example,

1. The sum of the angles of any triangle equal 180 degrees
2. For triangle ABC, angle A = 90
3. For triangle ABC, angle B= 45
4. Therefore, for triangle ABC, angle C = 45

Notice, the conclusion is made absolutely necessary by the premises. If 1–3 are true, then 4 absolutely must be true. Angle C cannot be anything other than 45. That is logic. It’s not an opinion, it is an inherent property of the universe that absolutely must be accepted. If you reject the rules of logic, then you must also reject the rules of mathematics.

Do Christians Have to Follow the Rules of Logic?

It may seem odd that I am singling Christians out in a blog about science, but on scientific issues like climate change and evolution, I often find that Christians are hesitant to accept logical arguments and often respond to them with statements like, “Logic is just man’s wisdom, but God is higher than man, therefore we shouldn’t trust man’s logic and should rely on God instead.” I want to address this argument, because I encounter it frequently, and it often seems to be an underlying reason for rejecting science. To be clear, I’m not going to enter into a debate about theism or atheism, rather I am simply going to address the issue of whether or not a belief in God somehow makes you exempt from the rules of logic.

First, this argument is obviously dependent on the belief that God is actually real. So the argument is predicated on faith, which is problematic to say the least (again, I’m not telling you what to believe, but you should be aware that this argument is based on a premise which cannot be proved, which means that it is going to be completely unconvincing to anyone who does not share your faith). Nevertheless, for the sake of argument, let’s assume for a second that Christians are right, and God does actually exist. If he is real, then he, like everything else, must be bound by the laws of logic. I can prove that via that law of non-contradiction. Consider the following hypothetical dialogue between two Christians:

1. (Christian 1) “Can God do anything evil?”
2. (Christian 2) “No”                                                                                                                              3. (Christian 1) “Why not?
4. (Christian 2) “Because his inherent nature is perfectly good.”
5. (Christian 1) “Why does his inherent nature prevent him from doing anything evil?”
6. (Christian 2) “Because, it’s impossible to be perfectly good and do something evil.”

Does #6 look familiar? It’s an affirmation of the law of non-contradiction. If God was not bound by the laws of logic, then he could be evil and perfectly good simultaneously, but every Christian agrees that he cannot do anything evil, therefore if he exists, he must be bound by the laws of logic (note: this is also the appropriate response to creationists’ absurd and ad hoc allegation that logic would not exist without God, clearly it would since, if he exists, he must be bound by it).

What I have just argued often makes Christians irate because they see this as an assault on God’s omnipotence, but that is only because they misunderstand the concept of omnipotence. Philosophers universally agree that “the ability to do anything” is a terrible definition for omnipotence. The most widely accepted definition is, “The ability to do anything logically possible if one wanted to.” The reason for this definition becomes obvious if we return to the example of a triangular circle. No matter how powerful a being might be, he wouldn’t be able to make a triangular circle because it’s not logically possible for such an object to exist.

So, in short, even an omnipotent being would have to be bound by the laws of logic, and would not be capable of doing anything that is not logically possible. Therefore, claims that we should not follow the laws of logic because, “they are just opinions,” or “they are man’s wisdom,” or “all things are possible with God,” are silly and invalid. The laws of logic always hold true and must always be followed in all rational conversations and debates, regardless of your religious beleifs.

Other posts on the rules of logic:

• The Rules of Logic Part 2: Good vs. Bad Arguments
• The Rules of Logic Part 3: Logical Fallacies
• The Rules of Logic Part 4: The Laws of Noncontradiction and Transitive Properties
• The Rules of Logic Part 5: Occam’s Razor and the Burden of Proof
• The Rules of Logic Part 6: Appealing to Authority vs. Deferring to Experts
• The Rules of Logic Part 7: Using Consistent Reasoning to Compare Apples and Oranges