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During episode 156 of The Skeptics’ Guide to the Universe podcast, which is the most recent episode as of this writing, the discussion turns to the question of what it would take to convince the SGU’s hosts to believe in an alternative to evolution and the existence of God. The agreed conclusion was essentially that, to quote the late Carl Sagan as the hosts themselves did, “Extraordinary claims require extraordinary evidence.”

I have a problem with this conclusion on the matter of belief in God for the simple reason that an internally incoherent concept, like God, cannot possibly exist, just as a married bachelor cannot possibly exist. God, by definition, cannot exist.

So I just wanted to point this out, again, because prominent atheists don’t seem to realize the difference between a possible and an impossible concept. Maybe if they read this blog…

Religions generally presuppose that humans have access to absolute truth. However, how do we know and, if we do, can we confirm that there definitely exists a strict division between truth and falsehood in all cases? The fallibility of perception and the limits of human ability seem to suggest that truth is not absolute.

In other words, if we define a lie as an intentional misrepresentation of the truth, then there seems to be a presupposition that truth can be known absolutely. So, if we extend the definition of truth to be contingent on human experience of reality, as a filter of sorts, and not truth as a direct statement about reality, then that seems to make truth a popularity contest, like a genetic variation of Wikipedia if you will. This makes religion’s presupposition naive.

If we cannot know everything, then can we know that something that seems impossible is, in fact, impossible?

Richard Dawkins says that we cannot be certain that God does not exist, only that this is very improbable. However, it seems to me that the very definition of a deity is inherently self-contradictory. For instance, any conceivable god is, by definition, supernatural and the supernatural is a self-contradictory concept. A supernatural being exists outside the laws of physics, but it is impossible to know this without also knowing that physics cannot possibly explain the supernatural part of the deity in question.

In other words, without being supernatural, yourself, it would be impossible to know that someone else is supernatural. So, while it might be possible for a being to be supernatural–assuming that eternally defying the laws of physics makes any sense–it is impossible to know this for certain.

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.

The Continuum of Intelligibility

No concept can be completely intelligible or unintelligible. All concepts are somewhat unintelligible because all contain unknowns. All concepts are somewhat intelligible because, at the very least, a coherent mental construct, composed of other intelligible concepts, exists in the mind.

God is a concept that is defined as unintelligible. However, it cannot be completely so, for the reason previously noted. It must be somewhat intelligible. It is no different than any other concept with regard to intelligibility and can be analyzed to the extent that it is intelligible.

To be intelligible is to be understandable and to be understandable is to be reasonable. To the extent, then, that the concept of God is intelligible, it is reasonable. In other words, it must be reasonable until it reaches a point of unintelligibility.

Furthermore, the scope of unintelligibility must be clearly defined and isolated. The intelligible area of the concept is finite and the unintelligible, by virtue of representing a singular unknown, is infinite.

An example of God’s intelligible attributes is that he is the creator of the universe. An example of God’s unintelligible attributes is that he is somehow not consumed within it, but, rather, stands outside it and is not bound by its laws. In short, we can know something about God and what we know is clearly defined and amenable to analysis, with the caveat that we will always reach a point of unintelligibility.

What God’s Unintelligibility Means

So, if we find that something about God is unintelligible, then our conclusion is not that God does not exist but that we have reached a point where we can go no further. It is often argued among strong atheists that God’s internally contradictory attributes confirm his nonexistence. However, as explained, these attributes confirm only God’s partial unintelligibility, which, again, is a feature of all concepts.

That said, it must also be said that the inability to disprove a mental construct’s extension into physical reality due to its various mutually incompatible properties in no way proves that it does physically exist. In fact, it is never the case that being unable to disprove something proves it. Neither does this inability cast doubt on disbelief in a concept’s existence or, what might be another fear, suggest that anything is possible. As far as we know, a square circle or married bachelor is never possible, and we have no reason to suppose that it might be.

A common complaint against First Cause arguments is that assuming causal contingency and the necessity of it or, in other words, that every cause must have an effect is an admission that the obverse must be true. That is, there is no effect without a cause, including God. So, the complaint goes, if every effect has a cause, then what caused God?

When considering this complaint as an argument in its own right, an unsupported assumption appears, which is, namely, that the universe is spatiotemporally finite. It is possible that the universe is spatiotemporally infinite and that “God,” or whatever one might call a point of cosmically causal origination, has created and recreated himself infinitely many times. Of course, no perfect being would have a reason to make more than one attempt at creating himself, but this does not by itself invalidate the notion of a point of origination, given that the point is arbitrary but definable via some conceivable difference, like an explosion.

I have experience of the finite and the infinite, but with respect to causation, I have only the latter. Therefore, I cannot say with any certainty that there was no first cause. All I can say is that there is no reason to believe one existed, much less still exists.