TASC: The Transcendental Argument for Square-Circles

Hitherto it has been commonly supposed by the ill-informed that the non-existence of Square-Circles could be casually taken for granted. But demonstrating their non-existence has always proven problematic. After all, proofs are useful in demonstrating a positive, while proving a negative has always been notoriously difficult if not dubious. How exactly would one draw the conclusion that Square-Circles do not exist without begging the question or committing some other informal fallacy? What would one point to as evidence for their non-existence when everything we observe aligns so conclusively with the presupposition that Square-Circles exist? Wouldn’t one need to be omniscient to know that there are no Square-Circles existing somewhere in the universe beyond the reach of mere mortal sensibilities in order to proclaim definitively and with confidence that there are in fact no Square-Circles anywhere at all whatsoever? How would unSquare-Circulers account for logic, science and morality?

Perhaps we have in a most pedestrian stupor gone about this all wrong. Challengers often like to retort with the sneer “maybe you’re wrong!” or pester the self-confident with an endless series of the question “how do you know?” in rapid succession. Some detractors might even initiate their set of objections with “imagine that you are mistaken about everything you hold dear” (cf. here, also here). Isn’t there then at least a tiny sliver of hope that Square-Circles are in fact real, that Square-Circles do in fact exist? 

Now admittedly, because evidence of Square-Circles is in fact literally ubiquitous in human experience, attempts to construct direct arguments for the existence of Square-Circles have proven themselves to be a formidable stumblingblock for unSquare-Circulers given their anti-Square-Circles presuppositions. Because of the anti-Square-Circles bias of their unSquared-Circulerity, unSquare-Circulers have as it were a “filter [that] screens out certain features while tinting other features” (cf. here), so they do not realize that everything they actually do see is in fact evidence of Square-Circles. Because their minds are engaged in active rebellion against Square-Circles, unSquare-Circulers suppress the truth in unrighteousness.

Therefore, an indirect argument involving a reductio ad absurdam is to be called for. For it is by this method that one can clearly show precisely how a denial the existence of Square-Circles leads inevitably to the absurd conclusion that nothing at all exists, which is patently and undeniably false. And this is because denial of Square-Circles logically entails a fundamental denial of all reality whatsoever, for if Square-Circles do not exist, then nothing exists.

Thus, we can construct the following argument:

1: If anything exists, then Square-Circles must exist 

2: Things exist 

C: Therefore, Square-Circles must exist

This argument is reflexively supported by a corresponding argument as follows:

1’: If Square-Circles do not exist, then nothing exists 

2’: Things exist 

C’: Therefore, Square-Circles must exist

Clearly, then, we must confess that the soundness of the Transcendental Argument for Square-Circles is unassailable and undefeatable.

A similar transcendental argument can be drawn from causality:

1’’: If causality is real, then Square-Circles exist 

2’’: Causality is real 

C’’: Therefore, Square-Circles exist

The argument “Causality, therefore Square-Circles” speaks to such fundamental presuppositions of human thought that it would be as unthinkable to deny the reality of Square-Circles as it is to deny the reality of causality. Moreover, to the extent that unSquare-Circulers endeavor to reason in a way consistent with their faulty presuppositions, they find themselves falling into skepticism and absurdity (cf. here), and that’s not good.

If Square-Circles do in fact exist, as Square-Circulers uncompromisingly recognize, then Square-Circles would reside at the heart of our very being and occupy a fundamental role in all human cognition and experience. To deny the existence of Square-Circles, then, is to deny the very foundations of human experience and cognize in a vacuum. In short, the proof of Square-Circles is that, without them it is impossible to prove anything (cf. here). Because of this, unSquare-Circulers inadvertently prove the existence of Square-Circles by their very denial. The only rational option open to us is to acknowledge the fact that Square-Circles exist because of the impossibility of the contrary.

Now it has often been charged that defenses of Square-Circles inevitably involve the elementary logic fallacy of circular argument or “begging the question.” To this we point out the fundamental fact that all argumentation, whether for the existence of Square-Circles or for anything else, must by nature of argumentation itself presuppose the reality of Square-Circles and the truth of Square-Circularism. Apologist James Anderson explains why:

Because when one argues in defense of an ultimate epistemic authority, such as an ultimate standard of truth, then some element of circularity will be unavoidable. Consider: if the truthfulness of our ultimate standard of truth… could be established on the basis of some other standard of truth, then it wouldn’t actually be the ultimate standard. Our attempted proof would effectively disprove our position! (see here).

Since Square-Circles are absolute, everything else depends on them for its own reality, including our own mental activity such as that used in developing proofs as such, for nothing else could exist independently of Square-Circles. Hence:

We simply prefer to reason in a circle to not reasoning at all, for only circular reasoning is even possible to man. Unless we are larger than Square-Circles, we cannot reason about them in any other manner, than by transcendental or circular argument. The refusal to admit the necessity of circular reasoning is itself an evident token of opposition to Square-Circles. (see here)

After all, “’Circularity’ in one’s philosophical system is just another name for ‘consistency’ in outlook throughout one’s system. That is, one’s starting point and final conclusion cohere with each other” (Greg Bahnsen, Van Til’s Apologetic: Readings and Analysis, p. 170n.42). For this reason, “we should not tone down the validity of this argument to the probability level. The argument may be poorly stated, and may never be adequately stated. But in itself the argument is absolutely sound” (Cornelius Van Til, The Defense of the Faith, p. 197).

For more nimble thinkers, the similarities between the trinitarian deity of Christianity and the notion of square circles have been hard to miss. For example, the Trinity is supposed to be three and yet one, and yet one but three, a puzzle with which even deeply invested Christian theologians have had a tumultuously difficult time wrestling. For example, John Frame explains that “the Christian God is three in one. He is Father, Son and Holy Spirit… Somehow they are three, and somehow they are one… The fact is that we do not know precisely how the three are one and the one is three” (Apologetics to the Glory of God, p. 46). Those looking for a thorough explanation must accept the fact that they’re in for some dissatisfaction. As Frame explains elsewhere: “The greatest mystery in Scripture and Christian theology is, of course, the mystery of the holy Trinity.” At the end of the day, it’s a mystery, and that’s all that can ultimately be said about it. Similarly, more restless thinkers are likely going to find the concept of Square-Circles to be similarly problematic. But this stumblingblock is a symptom of man’s enmity with Square-Circles. Enmity with Square-Circles could not exist if there were no Square-Circles in the first place with which to experience enmity! So in just this way puzzling over the nature of Square-Circles is testament to their reality.

What unSquare-Circulers tend to ignore is the fact that Square-Circles are holly square, wholly circular, and thus not at all contradictory as they often claim. This is demonstrably not a contradiction because a circle does not have a hole while a square does where a square does have a whole while a circle does not. Hence we say holly square, wholly circular, not wholey square, wholey circular. This trips up those who are darkened in their thinking, for they are not mindful of such rudimentary distinctions. But clearly this can only mean that Square-Circles are not wholly square and wholly circular in the same sense, thus not contradictory.

Since the objection to the very existence of Square-Circles that is most commonly raised is that the very idea of a Square-Circle is self-contradictory, this is worth exploring a bit further. Now, while such an objection is clearly absurd, it is so common that it is necessary to put this concern to eternal rest. To test the claim that Square-Circles are self-contradictory, we can use the same criteria which Marc Cortez uses when considering the question Is the Incarnation a Contradiction? (Yes, the original blog has been removed from the internet – however, I found the entry on the Way Back Machine.) According to Cortez,

a statement is only truly contradictory if it affirms that two contrary propositions are both true at the same time and in the same way.

Of course, in reaction to this one might point out that Square-Circles are not simply statements, but actual concretes that exist in what William Lane Craig would call “space-time reality”; they even exist outside “space-time reality”! This means that Square-Circles are not statements to begin with! Nor are its constituent elements mere “propositions.” So the very rudimentary conditions necessary for a contradiction are not even in play here. Now, it may be supposed that certain statements about Square-Circles on their surface seem self-contradictory, but that would be a problem with those statements, not with Square-Circles themselves. Insistence that there is something contradictory about Square-Circles, then, can be traced to some moral deficiency: unSquare-Circulers simply do not want Square-Circles to be real! And as everyone knows (or should know): Square-Circle denialism is the root of all evil and depravity. It is because unSquare-Circulers have unresolved depravity in their lives that they are so susceptible to the conclusion-delusion, a most insidious expression of vanity exemplified in such crass denialism.

Like reason, logic, the laws of nature and moral laws, Square-Circles are immaterial. They are also infinite, transcendent, sovereign, authoritative, self-attesting, immanent. Without Square-Circles, there could be no intelligibility whatsoever. Since Square-Circles are the necessary pre-condition to all intelligibility, Square-Circle denialism is like a man chasing his own tail in quicksand: he just goes around and around, not realizing that his very action affirms Square-Circles while sinking in his own absurdity. Pointing this out to an unSquare-Circuler is sure to pour hot coals on his head.

Do you have unSquare-Circulers in your life? Do you have unSquare-Circulers in your family? Take them to TASC with the Transcendental Argument for Square-Circles and help them get on the straight path. Challenge them to look deep into the rounded corners of their hearts. They too will see the light.

by Dawson Bethrick