Can God make a square-circle? The standard response is “Of course not,” since that would be a logical contradiction. Here is Ron Highfield’s response in his Restoration Quarterly Article “The Problem with the ‘Problem of Evil’”:
When we say “God cannot do a logical contradiction,” we are not placing limits on God; we are removing them…One can illustrate this principle by analyzing the statement “God cannot create a square-circle.” This statement does not limit God because the term “square-circle” refers to nothing at all, a “non-entity.” The term “square-circle” might as well be gibberish.
That seems logical, right? Yes it does, and that, I suggest, is precisely why it is wrong. Highfield’s argument is logical and a “square-circle” is in fact a logical contradiction, an idea we cannot even truly imagine with any concreteness. This proves, very definitively that beings which are bound by logic cannot create or even conceive of something quite so absurd as a square-circle. But in the formulation of that assertion lies the flaw in extrapolating it to God.
Highfield very bravely asserts that “logical contradictions do not limit God” without analyzing his presupposition that God must be logical, a presupposition which might be just as easily rephrased as “God is bound by logic.” In spite of openly rejecting anthropocentric conceptions of reality, Highfield falls prey to his own critique when he argues that God must be bound by logic since, to humanity, “square-circle might as well be gibberish.”
I can anticipate Highfield’s response to such a criticism by his connection of logic with the “nature of God.” If that is the case, then my protest is essentially vain. If God is in fact necessarily logical in His nature, then Highfield has the high ground. The real question then becomes now whether or not God can create a square-circle but whether or not God is logical by nature. I submit that He is not.
On a speculative level, the question of what logic is can serve to demonstrate this. Logic from a human standpoint is merely a descriptive practice of how the world as we experience it works. Words like “circle” and “square” are terms which we have created to describe observable phenomena, to conceptualize and categorize creation. From a religious standpoint, it may be argued that logic is our innate, God-given ability to interact with a creation which He has ordered to be understood by His creatures, but this falls dramatically short of asserting that God is by nature logical. It is sufficient to point out that God is benevolent to explain logic, because the definition of a creation without logic is one in which all rational beings are in a constant state of crippling confusion. Logic is a gift which permits functional interaction with reality. That God could not have created an illogical world is most properly explained by His Goodness and not because He is, in any sense, Logic.
But speculative arguments are, at the most, speculative. A look at the nature of God which is commonly embraced by Christians will be an even more potent proof that God is not logical by nature. Consider the paradoxical nature of almost all theology proper. For example, is the existence of an entity which is indivisibly one and equally three any less of a logical contradiction than a square-circle? Anyone who has endeavored to create a material analogy for the Trinity can testify that all which we experience, even in our minds, is unquestionably inadequate. The Trinity is no more an egg than it is three phases of water, and each of these analogies, pressed to its logical conclusion leads inevitably to the grossest heresy. Take as another obvious (or at least it should have been) example the Incarnation which presents logical contradictions on a number of levels. The most obvious is the mathematical absurdity of a savior who is 100% God and 100% man without mixture and without becoming thus 200% existent. Consider a God whose definition includes very absolutely the contention that He is uncircumscribable and is nevertheless totally circumscribed in a human, the infinite becomes finite, the immortal mortal, the eternal temporal, etc. The Incarnation is a tour de force of logical contradictions.
In the words of Vladimir Lossky: “These are not the rational notions which we formulate, the concepts with which our intellect constructs a positive science of the divine nature; they are rather images or ideas intended to guide us and to fit our faculties for the contemplation of that which transcends all understanding.” Continuing to take my cue from Lossky, the very truth of God’s suprarational character is the reason for the constant expression of dogma in the form of antinomy.
To make God logical by His nature does perhaps more than merely limit Him; it may limit Him in the most profound way possible. The suggestion that God conforms to logic, a human mode of conception, is to essentially assert that He is fully knowable. If God is logical, then He is comprehensible, and if He is comprehensible then He is circumscribable by the human mind. Even if this is accepted only in theory and never in pre-eschatological practice (as in many minds during the height of Scholasticism in the West), God has been debased in perhaps the grossest way possible. He has been made in some sense less than His creation, by suggesting that He can in any way be contained within it. If we do not fully know God it is a matter of circumstance and not of possibility. God is essentially containable, and therefore necessarily not infinite. Quite the opposite of what Highfield claims, the suggestion that God cannot make a “square-circle” actually has imbedded in it the most profound limitation on God that humanity can imagine: God is limited to our imagination of him, our ability to comprehend Him. (And if I may deliberately be alarmist, the distance is not so great between the assertion that God cannot exceed our imagination of Him and the belief that He is in fact the product of our imagination.)
In Highfield’s defense, I think the flaw in this case is more a product of the analogy chosen than the actual point He is arguing. He parallels the suggestion that God might make a square-circle to the suggestion that He might “lie, die, or be deceived.” Ignoring for a moment the most fundamental Christian belief that God did die, Highfield’s point seems to be that God cannot do that which limits. In other words, omnipotence precludes impotence. The more appropriate example that Highfield could have chosen is the old standard, “Can God make a rock so big that even He can’t move it.” Anselm answered this kind of question centuries ago (in one of the rare instance where I find myself closely aligned to Western Scholasticism). God making a rock so large he could not move it is not an act of power but of impotence. The suggestion that omnipotence requires that He can self-limit confuses omnipotence with the ability to do anything. They are certainly not the same, and on these grounds Anselm also rejects such impotent behaviors as lying or being deceived.
Those the two analogies (the square-circle and the rock) seem very similar, the questions they address are vastly different. The latter only address whether or not omnipotence, properly understood, precludes impotence. Certainly it does. The former, quite unrelated, treats whether or not God is bound by logic. There is no reason to assert that He is, and that assertion, in fact, may be the most profound limit which the human mind could conceive for God. In the final analysis, I must agree with Lossky that “the only rational notion which we can have of God will still be that of His incomprehensibility. Consequently, theology must be not so much a quest of positive notions about the divine being as an experience which surpasses all understanding.”