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:
- My fuel gauge is designed to tell me how much fuel I have
- I know that my fuel gauge works
- My fuel gauge says that I am low on fuel
- 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,
- The sum of the angles of any triangle equal 180 degrees
- For triangle ABC, angle A = 90
- For triangle ABC, angle B= 45
- 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
I would like to note one thing, which I am sure you will understand. When you use the name “the laws of logic,” especially in your simple examples laid out, you treat these as binding in every way. I would not like to argue that they are binding, and I wouldn’t say you’ve missed or misunderstood any of this, you may have just forgotten one small detail. As in the instance of your four statements on fuel gauges, there just isn’t enough there. You have made an unnecessary assumption in saying “I know that my fuel gauge works.” Before I had even finished reading the four statements, I had already added two in my head:
5) It is possible that a fuel gauge can be broken, or can in some other way be incorrect.
6) Therefore, the fuel might be low, or it might not be.
So we have thus proved nothing with these statements. In your later statements on the laws of mathematics, obviously mathematics in theory are less open to error than the real world, but the same thing could be done for the four statements on triangle ABC, assuming we were talking about a physical triangle being measured. In your title, “why logic always works,” you are entirely correct; logic can reliably prove nothing.
I would simply like you to note that, however many statements you may make on a topic, there are always other possibilities that could be added, and thus you can never prove anything in the physical world with mere logic. You can, however, prove quite a lot in mathematics, as that is not subject to any physical laws.
There is another, more philosophical point I would like to discuss as well. Again, in your name “the laws of logic,” I think you are treating them as overly binding. The simplest way I can explain is with the old “I think, therefore I am.” As existing, self-aware beings, any perception we have is influenced by an undeterminable amount of factors. Because of this, we can never trust any perception we make for sure, and we can never know exactly how much we can trust them. As in, for all I know, I’m actually sitting in both Moscow and New York City right now—yes, at the same time. We can never be certain. I think the implication should be clear by now; if we can never trust or senses or be certain of anything, we can never prove anything. The effect this has on the laws of logic is similarly clear; it makes them, for all scientific purposes, useless.
In fact, we could even add a couple more statements to the fuel gauge proof so as to work backwards in our theory that the fuel is low.
7) We cannot assume anything about our situation.
8) We cannot really know if the fuel gauge exists at all.
If I were speaking to literally anyone else, I would feel the need to explain myself quite a bit more. But you seem quite intelligent—I’ll leave the assumptions to you.
I think I agree with everything you said, I just want to make some clarifications.
You are certainly correct that the utility of the laws of logic is limited by our ability to accurately understand the physical universe (assuming the physical universe even exists), but, as I think you’re agreeing with, that’s a weakness in our observations, not a weakness in the laws of logic themselves. So the laws always work, just sometimes we have incorrect premises based on our faulty perceptions.
I think its important to clarify the different definitions of the term “proof.” You are using it in the most rigorous, skeptic definition: what philosophers call “strong knowledge,” but for most practical purposes, we use the term differently. I’ll use a classic philosophy example to illustrate.
1. Socrates is a man
2. All men are mortal
3. Therefore Socrates is a mortal
Most people (myself included) would consider this a logical proof. Socrates must be a mortal, but, in the strictest sense (the sense in which you are using it) it is not a proof because its possible that Socrates doesn’t even exist, or somewhere in the universe there is an immortal man, etc. That fact does not however diminish the practical utility of the laws of logic because there is no a priori reason to think that any of those alternatives are true.
To put it another way, alternatives are always possible, but they usually result in ad hoc fallacies and are, therefore, logically invalid. Its not that they are impossible, its just that it is irrational to assume that they are correct.
Occam’s razor also comes into this in a big way. You can always add alternatives, but these nearly always carry unnecessary assumptions with them, therefore they are not logically valid.
So you are correct that we cannot prove anything about the physical universe in the strictest sense, but I don’t think that either diminishes the practical usefulness of logic or invalidates a dogmatic reliance on logic.
You have not disappointed, my friend.
Oh, as a side note, I’m 14 years old.
Uh, one problem, you claim to be a Christian which would mean you believe in the doctrine of the Holy Trinity. Sorry, but human logic cannot fully comprehend that. Attempts at doing more than just repeating what the Bible says in an effort to satisfy human reason is where heresy is born.
First, I have not claimed to be a Christian, I have merely argued that science and Christianity are compatible.
Second, I really am not sure what you are arguing here. Are you trying to say that we don’t understand something, therefore it defies the rules of logic? That makes no sense (its actually a type of argument form ignorance fallacy). The fact that you don’t understand something doesn’t mean that it breaks the rules of logic. People are certainly limited and fallible, but that just means the people make mistakes and have limits, not that the laws of logic themselves are flawed.
Finally, as I explained in the post, its not “man’s logic.” The rules of logic are like the rules of math, they simply are. Again, if you’re going to say the the rules of logic aren’t universal, then you have to say that the rules of math aren’t universal.