Dedicated to the devotional, exegetical and philosophical study of theological paradox in Conservative, Thoroughly Biblical, Historically Orthodox, Essentially Reformed theology . . . to the glory of God alone!

Wednesday, September 01, 2010

You Already Believe in Square Circles

Inevitably, the classic geometrical argument against Biblical and theological paradox comes up in conversation.

The incredulous questioner scrunches up his face and says, "Are you trying to get me to believe in square circles?"

Sometimes the tone of the question imparts a sense of rationalistic condescension. I've even seen the "square circle" invoked as the penultimate refutation of any and all paradoxical thinking. It's a philosophical, "So there!"

In spite of its perceived force and intended effect, the argument is completely bogus. We will see why in a moment. In the process, we shall demonstrate that it serves as an effective illustration of the very concept it tries to destroy. In other words, the "square circle" completely backfires as an attempt to dismantle the arguments validating theological paradox. A simple lesson in geometry turns it on its head. I answer it this way:

"Why yes, I am saying there are square circles. You already believe in them, and Geometry proves they exist." (So there!)

Squares and circles are, by definition, 2-dimensional objects. As such, they cannot exist in 1 dimension, but can exist in 2 and 3 dimensions. It is true that within a two dimensional field a shape cannot possibly be both square and circle at the same time, because squares and circles are (by any logic) mutually exclusive. However, on a three dimensional field things change radically. We can have square triangles (pyramids), circular triangles (cones), and - YES - square circles (cylinders)! View any of these objects from certain angles, and some of their shape characteristics disappear. From some angles, a cylinder with equal height and width looks just like a square. From other angles, the same cylinder appears to be a perfect circle. This doesn't make the cylinder self-contradictory - though it may appear that way when viewed two-dimensionally.

When we translate dual-shaped 3-dimensional objects onto two dimensional fields, we are forced to eliminate some of the dimensionality and thereby reduce the object to one of three possible shape types. Let's illustrate using the cylinder:

1. We can eliminate the axis that reveals circularity, and reduce it to a mere square.
2. We can eliminate the axis that reveals squareness, and reduce it to a mere circle.
3. We can retain aspects of all three axes, and reduce it to a shape which is properly neither a square nor a circle, but contains aspects of both.

Let's say divine sovereignty and human responsibility are circle and square, respectively. Some portions of Scripture only reveal God's sovereignty (perfect circles). Other portions of Scripture only reveal human responsibility (perfect squares). And some portions of Scripture mention both divine sovereignty and human responsibility in varying degrees (odd shapes made of squared angles and curves). Because we cannot see all three dimensions at once, God shows us the same issue from various angles. In our minds, they sometimes appear to contradict, but this is only a result of our limited vantage point.

The "square circle" argument against theological paradox overlooks the fact that one additional dimension makes the seemingly impossible possible. That extra dimension makes the apparently contradictory totally tenable. We must come to grips with the fact that God's logic - God's Truth, God's thinking, God's knowledge - exists on a higher plane than ours. He has infinite dimensions. So it is really amazing that we do not find more paradoxes in the eternal realities He has revealed. He has finely tuned His Word to be rationally intelligible to our wee little human brains - yet its revelations point to realities that are beyond our grasp and super-rationally True.

Compatibilism proposes that God plainly declares His absolute sovereignty because He wants us to hold it firmly, and He sometimes reveals human freedom without qualification because He wants us to hold it firmly. He reveals both together because He wants us to recognize that they interact in ways not fully discernible from our human point of view. Compatibilism says when we see squares and circles in the same place we can rationally believe there is a cylinder there (a 3D square circle).

In the Bible, God is not describing 2-dimensional concepts to 3-dimensional creatures. He is describing multi-dimensional concepts to comparatively 2-dimensional creatures living in a comparatively 2-dimensional world, with nothing but 2-dimensional logic to work with - and broken brains to boot. Our attempts to grasp His self-revelation ought to melt us down to the most humble confession: "I am insignificant! God is GREAT! I am a blockhead! God is WISE! I am limited! God is INFINITE! I am of the dust! God is ETERNAL!"

So, the next time someone asks you about square circles, just hand him the nearest cylindrical object and walk away without saying a word.


  1. I love this, Derek. What a great explanation of how we should view our, ummm limited point of view! I'm going to bookmark this post...

  2. Blaine,

    Thanks. I love good illustrations, and it's nice to know when they actually makes sense to someone besides me!

    BTW - I don't recommend the square circle t-shirt, the THEOparadox shirts are much more stylish. :)

    Part two of this post should be publishing in a few minutes. My only regret is I haven't had time to list the actual Scripture passages that support these thoughts.



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