by Jeff McInnis
I, like many of you, love to argue with non-Christians. Each of us is always trying to find some argument, some proof of their position that will cause the other to say “Ah-ha!” Unfortunately, those ah-ha moments rarely come. Proving something to someone who willfully will not see it is impossible. It has left me asking if we humans can really prove anything.
What do we even mean when we ask if we can prove something? While there has been much philosophical ink dedicated to the question of proof of self-existence, that is not the idea I am trying to define here. I am trying to define the purpose of things outside of each of us. It is when we know about purpose, after all, that we can ascribe meaning. In other words, if we know an items purpose it can be described as having meaning. For instance, let me use an example that most Americans are familiar with - Space Mountain. Yes, I refer to the ride at Disneyland. We can ask “what is the meaning of Space Mountain?” The answer, which is something to the effect that Space Mountain is for enjoyment, is the same answer that could be given to the question of “What is the purpose of Space Mountain?” In other words, when we ask of the meaning of something, we are actually asking to understand its purpose for being. Implied also is the question of whether the item at hand satisfies that purpose.
Can we understand the meaning or purpose of anything? We can prove why some things exist. If man created something, it can be “proven.” What is meant here is that if an object or process is our invention, then we can prove its reason for being. How? By being able to explain the reason that it exists. If I invented a machine, then I can explain its purpose. I can show my thought process for determining that the object was necessary and I can explain my process of determining how to create the item. I get both sides of the equation. I am the inventor so I get to state the items intent, its reason for being. I created the item so I fully know its reason for being. Then, I get to finish the proof by showing that it fulfills its intent. I get both sides of the equation, its intent and its satisfaction of that intent.
For instance, can I show that the ottoman my feet are resting on has a purpose? Of course. Its purpose is comfort and, the present ottoman notwithstanding, ottomans fulfill their purpose fairly well. I can define the intent of the ottoman, comfort, and determine how well it satisfies that intent.
How about an automobile? The automobile was created by Henry Ford as a mode of transportation to replace the horse. It has been very successful, as seen by the relative absence of horses as a form of transportation. I can define both the intent of the automobile and can evaluate how well it satisfies that intent.
How about birds? We can enjoy watching them fly, but is that their intent? Do they exist for our enjoyment? We know that they serve some great purposes in the world such as keeping the worm population under control. But regarding their overall purpose, we don’t know. We must honestly admit that we cannot actually put our finger on why they exist. Do they satisfy their intent? Since we do not know why they were created, we have to also admit that we have no way of knowing if they have satisfied their intent. The understanding of birds, we admit, is above us. Why is understanding the purpose of birds out of our reach? We didn’t invent them. We have no knowledge of their intent and no knowledge of their ability to satisfy that intent because we were not their inventors. We are at a loss.
So the proof of reason relating to those things which are our invention is different than one of those things that are not our invention. As soon as we can no longer define the reason for being, or intent, of something, we begin to see that it is not manmade. We find that this tool is an excellent test of man-madeness. Is the item’s intent and satisfaction definable? If so, it is only because its author was human, either us or someone else.
In truth, we really don’t think much about the reason for manmade things. We don’t require proof of these items because their proof is patently clear. If they require any proof at all, the ingredients of the proof are at the ready. We know the reason for their being, and we can see if they satisfy or don’t satisfy that reason for being. Because a man-made item has man-made intent, its proof is not really necessary.
Our test of man-madeness can also be used to show that processes are or are not manmade. This is where the idea gets a bit more interesting. Many of the processes that have shaped our culture appear to be a combination of manmade ideas and non-manmade ideas. This idea can be very useful. With it, for instance, we begin to see that many of the processes we use in everyday life are based on relationships that are not manmade while being, themselves, manmade. For instance, consider the construction of a home.
The idea of creating a residence where you can be sheltered from the elements is not a manmade idea. Most every animal does it. The beaver creates a dam, the bird creates a nest in a tree, and the bear finds a cave. These ideas were not implanted in the brains of the animals by man; the idea of having a house to be in is not manmade. However, man has created a process of construction of a house using trees and nails, concrete, shingles, etc. that is all his own. No animal creates a house like the houses we create. The creation is strictly manmade, but it is based on an idea, a process, that is not manmade. The creation of shelter, then, is a combination of manmade and not manmade. The idea of having shelter is not manmade. However, the process of building with lumber, plaster, windows, etc. is what man has been able to add to the non-manmade idea of shelter.
Likewise, we discussed the automobile above. Transportation is not a manmade idea. How do we know? Because most animals have legs with which to transport themselves. Humans have legs, too, and so the idea of pedestrian transportation is not a manmade idea. We always had legs and did nothing to invent them. However, man has added to the idea of transportation their invention of the train, the car, the airplane, and several other modes. We utilized the value we found in the idea of transportation and added our own inventions to it.
Let’s turn this idea to more interesting topics. What about math? Is math man-made? The question of whether math is manmade is much like the question of transportation. Math, in its pure form, is a system to express numerical relationships using numbers as abstractions of the ideas themselves. Math at its most basic level, the relationships between quantities, is not a man-made idea. If I have 2 apples and bring in 2 more apples, the fact that I end up with 4 apples is not at all a man-made result. I had no say over the fact that 2 + 2 equals 4. If I have 4 apples and decide to give an equal amount to 2 different people, the fact that I have to give 2 apples to each person is not a manmade concept. Man had no hand in this relationship. The relationships of addition, subtraction, multiplication, and division appear to have no man-made features to them whatsoever. However, several things about math do appear to be man-made. It appears that, upon the backdrop of the basic numerical relationships that make up the world, we have placed a system of numbers that mimic the numerical relationship so closely that we begin to believe they are one in the same thing. They are not the same thing. The numerical relationships that man had no hand in making are slightly different at their most basic level than the system we have placed over these numerical relationships in order to express them. Take the symbology of math, for instance.
The number 4 itself, while representing the idea of a quantity whose invention we had nothing to do with, is itself a man-made object. The number 4 is part of the decimal system of quantity representation. Although the invention of the decimal system goes all the way back to before Christ and was invented by The Sumerians, it is a man-made system. One could argue that the two are inextricably linked, but that would not be an argument that would add up because the decimal system is not the only way we have invented to represent quantities. Man has also been able to come up with several different types of number representation systems, such as binary invented by the German philosopher and mathematician Liebniz and used in computer programming.
The decimal number system is a manmade invention to represent quantities and relationships that are not manmade. You may say that this distinction has no value whatsoever in our discussion. However, this number system that we have placed over the top of the non-manmade numerical world begins to diverge from the numerical world in the advanced forms of mathematics.
As we branch out past the most basic relationships in mathematics, we begin to see the world of manmade mathematics a bit more clearly. We see the man-madeness begin to show up because mathematics begins to diverge from the basic, non-manmade world of numerical relationships. For instance the world of algebra is a world concerned with understanding relationships between quantities. Algebra introduced the idea of being able to manipulate numerical relationships without knowing the numbers themselves. To do so, algebra introduced the idea of the variable, the dreaded x that haunts every student of math at one time or another.
From this point forward, math becomes a bit less concrete and its manmade nature becomes more apparent. Once x comes onto the scene, things start to get shaky. Man now begins to branch away from the concrete relationships that undergird math for a much more manmade endeavor. From this point forward, the use of the variable introduced in algebra becomes a central theme of mathematics. Using what the philosopher Frege pointed out to be the ideas of formal logic in equation form, mathematicians begin to manipulate multiple equations to solve functions for x and y. The idea of variables used in algebra became the jumping off point for several other schools of thought, namely probability.
Jeff McInnis is a contributing author to The Poached Egg
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