Why Christianity Makes the Most Sense of Logic

What is meant by “logic”?

By logic I mean the 3 laws of logic. Namely, the law of identity, the law of non-contradiction, and the law of excluded middle. What in the world does all this mean? I’m glad you asked. I’ll try to briefly explain. You might even get a date by using these terms. They make you sound really smart.

First, the law of identity is simply stated A = A. In other words, an apple is an apple. Wow. Isn’t that profound.

Secondly, the law of non-contradiction states A cannot = non-A. Simple enough right? If the wall is yellow then I can’t also say it is not yellow and be correct. Again, profound.

Lastly, there is the law of excluded middle. That is, A must = A. Going back to the first illustration of the apple, an apple must always be identified as an apple. It cannot be an apple today and then an elephant later.

Note: The law of identity and the law of excluded middle are very similar. Here’s a helpful way to distinguish between the two. Try to think of the law of identity in the present. Imagine you are looking at an apple this moment. This moment you would identify it as an apple. Now when it comes to the law of excluded middle, try and think of it in the future. In other words, think about the apples you will eventually identify as apples in the future. If they are identified as apples now (law of identity), then they must be identified as apples in the future (law of excluded middle).

Logic is immaterial and can only be accounted for by the immaterial

Just as a real moral standard would prescribe that we “ought” to think, speak, and act according to a certain immaterial standard, so the laws of logic tell us how we “ought” to think logically, which requires immaterial rules that must be followed. In particular, this is the rule of the law of non-contradiction. If there were no such a thing as a contradiction, we would have no way to distinguish between the things we identify (using the law of identity and the law of excluded middle).

I could say the wall was painted yellow and then say it wasn’t painted yellow and be correct in both statements. I could say a duck is a duck and then say it’s not a duck and be correct in both instances. So these are rules which must be binding, otherwise, logic, reasoning, and thinking would not be possible. How can you think without associating things with other things and distinguishing between them (the laws of identity and excluded middle), and then what if you conflated the different things you identified (which would go against the law of non-contradiction)?

Therefore, these rules are required to be in place if we are going to know anything. We don’t know exactly how these laws are implied upon us, nevertheless we realize they must be implied upon us to even know anything.

Yet these are rules which we cannot detect with our 5 senses. So this demands us to ask, “where do these rules come from?”

Should we not contradict because nature doesn’t contradict?

Some will read this and say “of course there are contradictions… duh. I know this because there are no contradictions in nature. There’s no contradictions in the physical world I perceive around me. For instance, I can tell with my own 5 senses that my car is parked in my garage. Therefore, I know it’s not simultaneously parked outside my garage AND inside my garage at the same time! I don’t need “God” to know this. The laws of logic work fine on their own.”

So let’s back up real quick. What was the original question? It was “should we not contradict because nature doesn’t contradict?” Let me put it this way: “what in nature tells us that we shouldn’t contradict?” OK. So the answer would so far seem to be the ability to identify things. Right? The objector says that because they can identify what a car is, they can decide for themselves that they should not contradict. They are able to tell just fine that the car they can identify is in the garage and not also out of the garage. OK, but then here is the next question. “What in nature tells you that there is a classification known as ‘car’?”

I am NOT asking “do you know what a car is?” I grant that you most definitely do know what a car is. That is not the point. Rather, what in nature is telling you that there are classes of things, namely, “cars”? Take any class for example: trees, prime numbers, lamps, colors, etc. Classes are abstract. They are non-physical, but they identify the physical. So what in nature, or what in the physical realm, is providing these immaterial classes?

(This is why Plato had forms. He knew that classes do not exist in matter itself, but only identify matter. The non-physical is used to label the physical, in other words. Granted these non-physical classes even identify the non-physical, such as the idea of prime number, however, because we’re talking about Naturalism, we’re using mostly physical examples.)

Think about it this way. Get really close to a car door and stare at it for a long time. Try to see if the word “car” or “carro” or “chezi” appears. Try to see if the word car appears which any language on Earth could possibly provide. If it doesn’t appear, then ask the question “where did the classification of ‘car’ come from?” The objector may try to bounce back and forth between the laws of logic, namely the 2nd law to the 1st n 3rd laws and vice versa, back and forth, over and over. However, each time they land on one, they are standing on thin air. They are assuming that nature, or the physical, can account for the non-physical.

You will then say “but we invented the word ‘car’.” I will say “you are still missing the point.” I fully agree that the term, the classification, or the categorization known as ‘car’ was invented around the early 20th century. My overall point, however, is that ‘car’, or ‘carro’, or ‘chezzi’ is just a word make up of sounds. It has no intrinsic meaning. We attach meaning to it. We attach identity to it.

So where does this immaterial identity still come from? Aristotle would have said “my parents taught me what a car was (if he were alive today).” We would need to remind Aristotle that that’s not the point. Again, in a purely physical world, how do we account for immaterial classifications, categorizations, and identities? A personal mind which has these universal meanings implied upon it is needed. Further, God gave Adam the mandate to classify the animals. God gave Adam the God-like ability of being able to identify the physical with the non-physical.

Laws of logic vs. natural laws

At this point I will at least argue where the law of non-contradiction does NOT come from. It does not come from and cannot come from a naturalistic universe. In other words, this rule that we must accept in order to think logically is not tangible. It is not material. It is not physical. It can’t be tasted, touched, smelt, seen, or heard. It is not found under rocks, does not grow on trees, and is not made up of atoms.

Please keep following me here…

What do natural laws do? Natural laws “describe” unvarying uniformity in nature. Is it true that to every action there is an equal opposite reaction? From what we’ve observed, yes. We can keep performing actions to ensure this hasn’t changed.

With natural laws, the law is derived from the phenomenon. The phenomenon does NOT derive from the law! You will say “but the law explains the phenomenon.” I will say “yes, that’s all it does”. Hypothetically, if the phenomenon changes tomorrow, then the law’s explanation will adjust to the new phenomenon – that way we can explain it in mathematical terms. So again, natural laws “describe” unvarying uniformity in nature (that are at least unvarying to our limited observation). However, the law of non-contradiction does not “describe” how we think, but rather “prescribes” how we “ought” to think… in order to think! This is vastly different.

But you will say “it does too describe how we think. We don’t contradict in our thinking. That’s describing it.” And I will fully agree, but this is only half of the picture. The law of non-contradiction not only describes how we think but describes how we MUST think, hence it ‘prescribes’ how we must think. Hypothetically, if nature behaves differently then you still have nature. But if we start contradicting ourselves, then we wouldn’t be able to think! We can’t contradict ourselves, otherwise we can’t think.

The thinking process can’t behave differently, otherwise we can’t think. Hypothetically, nature could behave differently and we could still adjust our natural laws to how it was behaving. But if we start contradicting ourselves, the laws of logic still cannot change, otherwise we cannot think! This is why the laws of logic ‘prescribe’ how we ‘must’ think, not just ‘describe’ how we ‘do’ think. This is why the laws of logic aren’t derived the same way natural laws are.

Why the law of non-contradiction is not “natural”

We “ought” to not contradict in order to be logical. We do not say that actions “ought” to have equal opposite reactions, but only that we have observed actions to behave this way so far. But when it comes to being logical, we aren’t merely talking about how we “do” think, but how we “should” or “ought” to think in order to be logical! If the universe farts, and Newton’s brilliant third law of motion starts behaving a different way, then the law would adjust accordingly. Yet, this can’t be said for the law of non-contradiction. If we all start contradicting ourselves then we wouldn’t adjust our logic, we would only conclude that we were being illogical!!!

Therefore, the fact that we use logic, hence agree that contradictions are illogical, we admit that there is a rule governing the way we must think in order to be rational. Yet, this rule can’t be accounted for by mere matter. In other words, what is it in nature that tells us we MUST think according to the laws of logic in order to think rationally? Or again, how does nature alone determine that an immaterial rule must always behave that way? Natural laws don’t even determine how nature should behave. They only describe how nature is behaving, not how it ’should’ behave. There is nothing in bare matter that tells us there shouldn’t be contradictions.

The law of identity

Now let’s focus on the first and third law of logic. Namely, the law of identity and the law of excluded middle. Again, think of the law of identity as that which we identify in the present. Imagine you are presently driving your Chevy Corvere. You presently identify it as a Chevy Corvere. This relates to the law of identity.

Now think about when your Chevy Corvere will break down in the future. In the future you will still identify your car as a Chevy Corvere. This relates to the law of excluded middle. What you identify can’t change. Whatever IS a Corveres MUST always be identified as one. I can’t say that Corveres will one day be what ducks are. We identify a Corvere different than a duck. We will never say they are the same thing. Congratulations. You now better understand the laws of logic.

The law of identity assumes the “one and the many”

So what is so significant about the fact that we identify things? Well this ties into “the problem of the one and the many”. What in the world is that? I’ll try and simplify. First, let’s ask, “what is the problem of the problem of the one and the many?” Here is the problem: How do we account for classes of things (one), ie. cars, dogs, people, etc. within a universe made up of pieces of something (many)?

First let’s specifically look at a universe that is many. This would be a Naturalistic universe. The bare bottom substance of everything, whether it be Chevy Corveres, ducks, planets, people, etc is pieces of something. Everything is said to be made up of some ultimate substance. What is the substance we are all made up of? Is everything at its basic level particles of some kind? Many believe everything to be atoms and electromagnetism. No one really knows for sure. Let’s pretend it’s marbles for the sake of illustration.

Pretend the universe and everything in it is made up of marbles at its most basic level. Now let’s say you’re walking through this universe of marbles and you notice that many of the marbles are arranged in different ways. Now let’s take our transcendent a-priori of logic out of the picture. In other words, imagine you have no ability to identify things and distinguish between things. You have no intelligence. With no existing intelligence there would be no way for any of the marbles to be identified as anything, no matter their arrangement. Some marbles would move and bump into each other, but nothing could be identified as anything other than marbles moving around. This is the “many”. It describes a Naturalistic universe where everything is ultimately mindless matter in motion.

Now let’s look at the “one” within the many. The “one” is shorthand for identifying the same things within the many. It’s the fact that we group material objects into immaterial classes. Going back to the marbles. If the marbles are arranged in a certain way, let’s say like a duck, then I must place this arrangement of marbles into the category of “duck”. Yet, the marbles themselves do not create the identity duck. Remember, there is no intelligence in the marbles themselves.

Let me use a more abstract example. How about what we identify as being an “odd number”. 3 is identified as an odd number. The marbles may align themselves so I have 3 ducks, but the marbles themselves do not create the concept of “odd number”. The identity of “duck” does not exist within the marbles themselves. It exists when certain arrangements of the marbles can be distinguished between other possible arrangements and be called something. In addition, the identity of “odd number” does not exist within the marbles themselves. It only exists when quantities can be distinguished from other quantities, thus can be called something specific.

So again, “the problem of the one and the many” states that there is a universe of marbles (the many), and that things can be identified within the marbles (the one). Now, the problem OF “the problem of the one and the many” is trying to account for the “one” within the “many”. In other words, trying to account for having classes, groups, and types of things in a universe of marbles. Everything is changing, exists in different locations, and acts differently within time. A cat that lives, dies, and decomposes is still the same cat, even though its matter is arranged differently at different times. If there is a cat in China and a cat in Brazil both belong to the classification of “cat”, even though they consist of separate matter. A cat that sleeps all day as opposed to a cat that runs around outside is still a cat, even though each one’s matter is behaving differently.

Conclusion

In conclusion, there is nothing about “marbles”, or matter, in and of itself that can bridge the gap between itself and what we identify it to be. All matter constantly changes over time, exists in different locations, and no two things behave exactly identical. Yet, we look at matter and identify things.

So what enables us to identify things? A universe made up of “marbles” wont suffice. We can’t just say the universe is “many” mindless things. A universe just with the “one” wont suffice. We can’t just say there exists abstract identities without anything to actually identify. We must somehow account for both the “one and the many”. There really exists things we really identify.

I account for the one and the many because of Yahweh, the Lord Jesus Christ, or the Triune God of Christianity. He is the creator of all actual and possible things. Thus, He has knowledge of all that is identifiable. Lastly, because God is eternally logical, the fact that we shouldn’t contradict in our reasoning stems from Him. Because God is eternally distinguishable within Himself, hence God eternally consists of the Father, the Son, and the Holy Spirit, the possibility of contradiction eternally exists. There are 3 distinguishable persons which cannot be said to be the same person. The law of non-contradiction exists within God’s own nature and because of His own eternal knowledge of Himself. Thus, the law of non-contradiction can be instilled in those who are created in His likeness, namely, us. Therefore, we can acknowledge contradictions, distinguish between things, and think logically! Praise be to God!