If pressed, I suspect most people would object to this claim. They would find examples such as positive and negative charges, good and bad, or the Left and Right in politics. Unfortunately, they would be wrong. Now, I understand why a person might believe that negations can coexist. On the surface, it would appear they exist all around us. But this is only an appearance, but that appearance is deceptive. The solution, as with most all things, lies in understanding the nature, or definition of ‘negation.’
As usual, we start with the definition of the word:
1a : the action or logical operation of negating or making negativeb : a negative statement, judgment, or doctrine; especially : a logical proposition formed by asserting the falsity of a given proposition — see truth table table
2a : something that is the absence of something actual : nonentityb : something considered the opposite of something regarded as positive
Notice that, like most words, there are many possible meanings of the word, ‘negation.’ They are all similar, but they are not all equal. So, what do I mean when I say ‘negation?’ When I say negations cannot coexist, I am referring to the notion that a negation denies the existence of its opposite. For example: If I say something does not exist, that is the negation of saying that same thing does exist. If you are aware of the Star Trek series, it might help to think ‘matter v antimatter.’ Now, let me explain why these two things cannot co-exist.
In the case of matter and anti-matter (which, incidentally, are real), when two equal particles of matter and anti-matter come into contact with each other, they cancel each other out. In the same way, if I claim that A is true, and you say A is false, our claims ‘negate’ each other. This is because something cannot be both true and false at the same time. The same applies to claiming A exists and A does not exist. By definition, they cannot both be true. Therefore, they negate each other.
Now, in matters of mathematics, this principle is easier to understand and accept. We can all see that -1+1=0 is a form of negation. By putting a +1 on the same side of an equation with a -1, they cancel or negate each other, which leaves us with 0, or nothing. When we extend this to other physical studies (i.e. physics), we find many similar situations. Few people have a problem with ‘negation’ in these areas because they are so easily seen and understood. However, when we apply this principle to matters such as human interaction, the Natural Law becomes much harder to see — but it is still there, and still in play.
For example: people generally accept the idea that there is good and evil in the world. Therefore, if these things — which are negations of each other — both exist at the same time and in the same place, this must prove that negations can co-exist, right? Well, not quite. Let’s go back to our equation, -1+1=0. What would happen is I changed the equation to this: -2+1=??? In this case, -2+1=-1. We are still dealing with negative and positive numbers, but now they do not negate each other. Why? The solution is simple: they do not exist in equal amounts. In this case, we have more negative (-2) than positive (+1). Well, it works the same way with things such as good and evil. We can have more of one than the other.
Here is where another principle of Natural Law can help us further understand the effects of my claim: negations cannot coexist. All things in the natural world seek a balance. Water seeks the lowest level. Energy states tend to do the same. It is essentially the same as saying all things decay. it is connected to the principle of entropy and the Second Law of Thermodynamics, but that gets us deeper into the weeds than we need to go. What we need to understand is that this applies even to things such as good and evil.
So long as evil exists, good cannot rest, and vice versa. So long as the political Right exists, the political Left cannot rest. So long as slavery exists, liberty cannot rest, and etc.. This means that negating concepts will be at war with each other until one side destroys the other. This can happen in one of two ways. Either one becomes so dominant that it totally eradicates the other or we achieve a perfect balance between the two such that they cancel each other out at the same time. The problem with this is, given the world such as it is, things such as good and evil can neither totally defeat the other, nor negate each other by achieving an equal balance. This is the key to understanding the nature of conflict in this world. Good and evil cannot negate each other, yet they cannot co-exist with each other. This leaves only one other option: they will constantly compete with each other in an attempt to negate each other. The same applies to the political Left and Right, liberty vs slavery, etc.. This is a principle of Natural Law, and it cannot be erased — not until the nature of this universe changes.