Atheists will often like to pretend that logic is a self-contained system. By this I mean that the way atheists use logic is as the ultimate standard, the judge of all thinking, the epitome of rationality. Thus, we read atheists who say that Christianity is “illogical” and ought to be disbelieved.
The problem with the atheist’s worldview is that logic is not a self-contained system. Logic is dependent on something else–something that transcends logic itself–in order for it to be true.
It is actually quite simple to demonstrate this, using Gödel’s uncertainty principal. No system can prove itself true because it must assume its axioms in order to test whether it is true or not. In other words, suppose we wanted to determine whether logic was itself logical. How could we do so? We would have to use logic. Yet using logic assumes logic is true, and thus we are assuming logic is true in order to test whether logic is true.
For an illustration of this, consider the following from the novel The Outlaw:
“How do we know that logic exists? The only way to ask that question is to use logic, right? We have to logically deduce what is valid in order to test it. In other words, we have to already assume that logic is valid in order to use logic to test and see if logic is valid. That, my friend, is circular reasoning.”“I think you’re losing me again!” Broadway said. His head was starting to hurt.
“Okay, let me use another example. Suppose you want to build a machine to separate apples and oranges. So you construct this machine, put an apple in and it says, ‘This is an apple.’ You put an orange in and it says, ‘This is an orange.’ The only way for you to know if the machine is correct is if you already know what an apple and an orange is.
“Think about it. Verifying logic is the same thing as building a machine to determine if something is an apple or an orange. You are basically making a truth machine. Is something valid or invalid? That is what logic tests. But if you test out a logical sentence, you have to already know what the answer should be in order to test to see if your method is true.
“If you already have to presuppose the answer, then how can you determine if the method you used is correct? If your assumed answer is wrong, and the method gives you data that agrees with what you think, then you think that you have a working machine when you really have junk. If it disagrees, then what is to stop you from assuming that it is the machine that is wrong, instead of you?
“If you have to use logic to prove logic, then you have to assume it to be valid before proving it to be valid. Therefore, the very reason we use logic is based on circular reasoning, and logic itself would demand that logic is invalid.
“But if logic was invalid, how would we explain anything? We assume that logic is valid because of our limited observations, but we cannot prove that logic is valid using only logic. At some point, there is a step of faith where we assume it is true.”
From The Outlaw (c) 2005 by Peter Pike, p 246-247, Used By Permission. (Note: The Outlaw does have strong language and violent scenes, so if you read it beware that it is roughly equivalent to a rated R movie.)
Thus, we see that logic itself becomes self-refuting if it functions as an independent, self-contained system. Logic dictates circular arguments are falacious (due to the fact that circular arguments can prove both sides of a contradiction valid); yet the axioms of logic are themselves based on a circular argument. The only way to escape this problem is if there is something outside of logic that makes logic valid.
But whatever it is that exists outside of logic in order to make logic valid need not itself be logical. In fact, one cannot say it is logical for that would be applying a systematic term to something that exists outside the system. It is an improper use of language to do that.
Thus, if one argues that logic is a self-contained system, one is left with a self-refuted argument. If one acknowledges that there is something beyond logic which establishes logic, then one must acknowledge that whatever that is needed to establish logic is itself not logical. In both cases, logic itself cannot prove everything; instead, we must accept something as true apart from logic.
Thus, everyone at some point believes on faith instead of “reason.”
