Why Atheists Can’t Know That 2 Apples + 2 Apples = 4 Apples...
The title of this article may be a bit misleading. There are obviously very capable and very knowledgeable mathematicians who are atheists. Such people do not only know that two apples plus two apples equals four apples, they can also provide elaborate proofs of the various mathematical theorems that undergird such a truth. This post is not meant as an attack on the intellect of atheists but rather as an attack on atheism as a philosophical system. A more accurate title would be “Why Atheists Can’t Know that 2 Apples + 2 Apples = 4 Apples If They Were Being Consistent With Their Philosophical System”. I know, not very catchy!
But what is it about atheism as a philosophical system that precludes knowledge of a truth so basic and fundamental that even children know it? The short answer is that atheism commits one to an autonomous epistemology—an epistemology that rejects the necessity of divine revelation. Believing that two apples plus two apples equals four apples is easy enough. The problem arises when one is asked to account for that knowledge. How do we know that two apples plus two apples equals four apples?
Well, one obvious answer is that it is an instance of the more general mathematical truth that 2+2=4. We are simply applying this truth to the realm of apples. This raises another question, however: how do we know that 2+2=4? This is where things get a bit tricky.
One might say that we know that 2+2=4 by repeatedly experiencing instances of its truth and then extrapolating to the more general truth. In other words, we repeatedly observe that two things (apples, oranges, books, etc.) plus two things equals four things and from these observations we make the generalization that 2+2=4. There are a host of problems with this however.
Firstly, for this approach to work, we would need to possess the mathematical concepts of twoness, fourness, addition, and equality prior to our experience of the world. If not, then there would be no way to even know that there are two things in front of us. But how do we obtain these concepts? It cannot be through inductive generalizations since we must possess them prior to experience. Perhaps we obtain them a priori (that is, wholly apart from experience). We shall see the problem with this in a bit.
Secondly, such an approach would imply that 2+2=4 is not a universal truth. A universal truth or principle is one that holds true for all members of a class and whose application is not restricted by spatio-temporal constraints. For example, “all bachelors are unmarried” is a universal truth because it applies to all bachelors regardless of time or place. Basically, there are no exceptions to universal truths. However, if 2+2=4 is known through generalizations from experience, then it cannot be said to be universally true because human experience is not universal in scope. No one has observed all instances of such a truth. At best, what can be said is that, as far as we know and have experienced, 2+2=4 holds true. We would have to allow for possible exceptions and admit that there may be some instances where 2+2 is not equal to 4.
But if it is not a universal truth, then we cannot even say whether or not it applies in our narrow domain of experience. Even in areas where its truth has been previously verified, it could turn out that it no longer holds true. Without universality, 2+2=4 becomes like any other particular fact of history. Saying “2+2=4” would be just like saying “it is raining”—true at some times and in some places, false at others. As such, applying this truth to the realm of apples becomes impossible because we can never know whether or not it is true for those apples or not. We still do not know whether two apples plus two apples equals four apples.
What other answer could be provided to the question of how we know that 2+2=4? It could be said that we know it’s true apart from experience. This answer may come in different forms—intuition, self-evidence, analyticity, the incoherence of its denial, etc. The main idea is that we can know that 2+2=4 without having to go look into the world. There are problems with this as well.
The biggest problem with this approach is that, although it preserves universality, it severs any connection between the truth that 2+2=4 and the facts of history. 2+2=4 becomes a purely formal, abstract principle with no relation to the realm of apples, shoes, chairs, etc. Why think that its truth is ever instantiated in the world of facts? There’s no reason to think that. If we bring this truth to experience and interpret experience according to it, then we would surely encounter what appear to be instances of its truth. However, we could simply be deluded. The objects of experience (apples, oranges, etc.) may be such that they cannot be numerically categorized. If so, then it’s futile to try and apply such a mathematical truth to them. We still do not know whether two apples plus two apples equals four apples.
Atheism as a philosophical system does not have a solution to this epistemological predicament. This is because, on atheism, there is no God and man is left totally on his own in epistemology. A God who eternally relates all facts into a system and who reveals certain universal truths to man so he can be able to mirror that system would surely be an indispensable ally. Atheism has no such God. And as such, knowledge of such a basic truth is precluded.