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Atheism is a belief that a specific god does not exist, a belief that no gods exist, or a lack of belief in the existence of one or more gods.

Indexicals and Identity

An indexical is a linguistic expression whose meaning depends on context. For example, I can say “I” and you can say “I” but the meaning of this word changes depending on the speaker. We can think of an indexical as a relatively abstract statement that serves as a container for specific meanings applied to specific situations. The word “I” serves as a container for identity.

Our use of language is bound to personal experiences and the meaning of words changes depending on those experiences. Personal experience is, in other words, a requirement for language. Language would be useless to us without a personal perspective to give it context and meaning.

God Lacks Identity

So, it makes no sense to postulate the existence of an agent, like God, who lacks a personal identity. God is defined as being, among other things, both omnipresent and incorporeal. This paradoxical combination of attributes implies that God is everywhere at all times, but essentially without substance. God is not bound to a human body or even a finite area of spacetime.

More generally, if God can be everywhere at once, then he cannot be only one place or only some places at once, which means that he cannot experience reality from a single perspective. Similarly, if God is incorporeal, then he cannot experience reality sensorially, having that experience processed through a physical brain.

If God cannot experience reality from a unique and limited perspective, then he cannot use language from a unique and limited or, as we humans say, personal, perspective. And if God cannot use language, then he cannot communicate to us through language, which means, among other things, that he could not have helped write the Bible.

A Classic Defense of Strong Atheism

The strong atheist position is supported in part by the argument that no concept with internally incompatible properties can exist in physical reality. A common example is the concept of a square circle. It is argued that, just as a square cannot simultaneously be a circle or a circle a square, God cannot exist if he is defined as having attributes x and y, where x and y are mutually incompatible.

I have read this argument in a few writings, perhaps originating with Baron D’Holbach in The System of Nature, but I discovered it several years ago in George H. Smith’s book, Atheism: The Case Against God. I highly recommend this book to agnostics and weak atheists. It presents the most powerful set of arguments I have read on behalf of strong atheism. In fact, if twentieth-century atheistic literature could be said to have a work of genius, Smith’s book would be it, followed closely, I might add for reference, by J. L. Mackie’s The Miracle of Theism: Arguments For and Against the Existence of God.

A Potential Flaw in the Defense

However, I have discovered a potential flaw in this defense and I feel obligated to share it with others who, like me, lend this argument great importance. Specifically, I have found a way to conceive of a square circle. This suggests, although it does not prove, that a concept’s existence might not be determined by the limits of our imaginations or reasoning ability.

There is a way in which the concept of a square circle can exist. Imagine that you are an alien with two sets of senses, each of which must simultaneously experience the same phenomenon to produce conscious awareness of it. This is similar to the way in which each of our eyes must see the same object to form a three-dimensional, stereoscopic image.

Imagine that I draw a square on a sheet of paper. When you look at it with one set of eyes, it looks exactly as I see it, with four equal sides. Yet, when you look at it with your other set of eyes, it looks like a circle. Suppose that from a direct, frontal position, your second set of eyes bends the square’s four sides outward just enough to create a perfect, seamless curve.

So, one pair of your eyes sees a square, while the other pair sees a circle. And it happens simultaneously. When your brain merges or otherwise processes these two ordinarily distinctly different images, it produces an indescribably unified third image, which is a composite of a square and a circle.

The fundamental point to be made here is that bending the sides of square can produce a circle. Conversely, pulling in four curves of a circle can create a square. A square circle, in other words, is conceivable.