1stOctober

Conceiving a Square Circle

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.

9 Comments

bipolar2 says 2nd October @ 9:52

** You’re not even Bush league **

Do you really think that you can out-think geometers silly rabbits? You’re making it so easy on yourselves. Be ashamed — have you never had plane geometry and logic?

Nonsense. We’re not talking about perception. We’re not talking about “bending” the sides of a square. Whatever that means.

A ‘circle’ can not be a ’square’ purely by the logical incompatibility of their definitions.

Here’s a better example, actually used in the middle ages as a way to think about God.

Consider what looks like a plausible candidate for a type of ‘circle’ used as a metaphor for ‘god.’ God is like an infinite circle whose circumference is nowhere and whose center is everywhere.

This is also nonsense; that is, an infinite circle can not exist given the concept of a circle. For one simple reason: a circle is a *closed* plane geometric figure. That is, it “follows” from the meaning of “closed” that any circle must have a finite radius.

So the metaphor backfires: if God is like an infinite circle; then god can not exist (because an infinite circle can not exist).

If you can’t get past making elementary blunders, you’ll never make any headway in understanding more subtle arguments, equally bad, made by xians over the last 2,000 years.

Trix are for kids. Get educated.

bipolar2
copyright asserted 2007

UK says 3rd October @ 8:47

Ad hom attacks compensate for lack of substance or, in this case, the absence of it. Please stop flaming my website.

drew says 3rd October @ 12:37

“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.”

You said it yourself. It is a composite of a square and circle. It is neither square or circle but something else. It is a new and separate concept that would need to be given a name. “Squarcle” or something. What you have presented is not a circle simultaneously being a square, it is a sensory combination of the two. How many sides does this combination have?

UK says 3rd October @ 17:43

There is a squircle:
http://en.wikipedia.org/wiki/Squircle

However, it seems to me that a new concept would not invalidate the argument above, since we are merely replacing “square circle” with another descriptor. In other words, “square circle” is itself that new concept and it is already assumed as part of the problem. The crux of the problem is whether this new concept can exist in physical reality.

The larger point to make here is that reality is a result of mind-to-world mapping, dependent not on what exists but on what is perceived and understood to exist.

drew says 4th October @ 10:14

“The crux of the problem is whether this new concept can exist in physical reality.”

I’d say there is a subtle but significant difference between the following statements:
1. Can the concept of a square - circle exist?
2. Can something simultaneously be a square and circle at the same time?

In other words, there is a difference between a. something having a combination of square and circle properties and b. something having ONLY properties of a square and ONLY properties of a circle simulataneously.

“The larger point to make here is that reality is a result of mind-to-world mapping, dependent not on what exists but on what is perceived and understood to exist.”

Well, I won’t argue with that. Despite what I said above defending the square/circle argument, I think truth is a game of probabilities.

Babs says 12th November @ 12:55

I love the way your mind works. Lol.

Mike says 13th November @ 5:35

Your reasoning is flawed. The principle that internal incompatibility cannot exist in reality is not damaged by your argument (although it can be attacked on other fronts). You see, you are finding a flaw with an EXAMPLE that is used only to ILLUSTRATE the principle of the necessary un-reality of internally incompatible things. Finding a flaw with something that is used only to help another person understand some principle does not invalidate the principle itself. It only shows that the analogy used to illustrate the principle is not a particularly good analogy.

Mike says 13th November @ 5:42

Addendum: You could however, use your analogy of an alien to illustrate the principle that mutual incompatibility is only an apparent contradiction. Since the incompatibility of two properties is necessarily determined by our perceptions & our interpretations of those perceptions, it could be argued that mutual incompatibility is itself a relative thing.

Peter Glen says 17th November @ 10:10

In reference to your particular example of a square-circle object:
You still have not shown how the thing in-itself is at the same time and place is both a square and a circle. Only that a being with two types of perception can view an item as two different things at the same time and place. It would be as if two people examined an object and at the same time came to two different conclusions: “It’s a circle” and “It’s a square.” Perception does not guarantee a true read on the object at hand.

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