Authored by: Mitchell LeBlanc.

Draft version of a paper submitted for publication. The final version may include changes not present in this version.

Abstract:

I briefly trace the origin of the Transcendental Argument for the Existence of God and present both an informal and formal version of the argument. The argument suggests that the Christian God is a necessary precondition of logical principles. I present a couple of objections formulated by Sean Choi and Michael Martin and develop three of my own. I propose firstly that a Euthyphro-like dilemma regarding the principles of logic reveals an insufficient, or at least, arbitrary justification. I then show that the symmetrical relationship between logical principles and the existence of God is a severe problem for Christian theism which must either reject the necessity of logical principles, or Christian theism altogether. I conclude that the existence of logical principles cannot depend on the Christian God. Lastly, I show that the mere possibility that God justifies logical principles in any of the ways criticized by the Transcendental Argument for the Existence of God requires further explanation from the Christian theist as to how divine justification differs from human justification. My conclusion is that the Transcendental Argument for the Existence of God is not sound.

Introduction[1]

Cornelius Van Til set the foundation of an argument for the existence of God that focuses on certain tenets. Van Til believed that (i) everyone has knowledge of God, some just suppress it (ii) Natural theological arguments are ineffective because they do not prove the Christian God uniquely over any other, (iii) we all have presuppositions which either assist or defeat our truth-seeking intentions (all non-Christian presuppositions defeat such intention), (iv) it can be shown that without Christian theism as an adopted worldview, the intelligibility of the world is lost, that one cannot make sense of logic, morality, or science. Van Til’s system became known as presuppositionalism and the modern scholars which have taken up a defence of his position include Greg Bahnsen and John M. Frame.

The most intriguing part of presuppositionalism is the assertion that there is, and only can be, one argument for the existence of the Christian God. With the exception of Frame, presuppositionalists largely reject traditional arguments for the existence of God claiming, as Van Til, that they offer only the mere probability of God’s existence and not the certainty that a Christian requires[2].

As such, Van Til proposed a transcendental argument. Transcendental arguments have origins which trace back to Immanuel Kant and generally take the form of modus tollens:

P

If not-Q then not-P

Therefore, Q

We can find an example of such an argument in Descartes’ Cogito:

I am thinking

If I do not exist, then I am not thinking

Therefore, I exist

The unique purpose of transcendental arguments is in many ways geared towards addressing the skeptic[3]. The arguments begin with a premise with which even the most hardened skeptic will agree and move to show that there is a precondition of that premise which cannot, thereby, be denied. In the above example of Descartes’ Cogito, existing is found to be the necessary precondition of thinking.

In the case of Christian theism, the transcendental argument employed is one which asserts that God is a precondition for the existence, and intelligibility of logic, morality, and science (amongst other things). For the purpose of this paper, I will focus on the claim that the existence of the Christian God[4] is a necessary precondition of the existence of logical principles[5]. I will present a formulation of such an argument, but first I would like to clarify what the TAG is asserting.

Throughout presuppositionalist literature is this notion of needing to “account” for logical principles. To be sure to understand what is meant by this, it would be prudent to present an excerpt from presuppositionalist Greg Bahnsen in his debate with atheist Gordon Stein[6]:

What are the laws of logic, Dr. Stein, and how are they justified? We’ll still have to answer that question from a materialist standpoint[7]. From a Christian standpoint, we have an answer – obviously they reflect the thinking of God. They are, if you will, a reflection of the way God thinks and expects us to think.

With the argument presented informally, I now introduce a formal version.

The Transcendental Argument Stated:

Sean Choi, in his criticism, offers us the following formulation of the TAG[8]:

(1) There is a rational justification for the laws of logic

(2) It is necessary that: if Christian theism is false, then there is no rational justification for the laws of logic

(3)   Christian theism is true

In support of (2), Choi observes the justification as being:

(2a)      It is necessary that: if there is a non-Christian theistic way to justify the laws of logic, then it will be either the a priori way or the a posteriori way or the conventionalist way

(2b)      It is necessary that: neither the a priori way nor the a posteriori way nor the conventionalist way will justify the laws of logic

(2c)      Therefore, it is necessary that: there is no non-Christian theistic way to justify the laws of logic

Initial Objections

There are a number of criticisms which Choi makes in his paper. He chooses to grant premises (1) and (2a) though with regard to (2a) while he does grant the premise for the sake of argument, he notes that it may be a false trillema. I am inclined to agree with Choi’s analysis. It seems to me that some hybridization of any of the mentioned means of justification may bring about a new means of justification. For example, a hybridization of an a priori and conventionalist system may succeed in providing the justification of logic sought by Bahnsen, but in a manner wherein the new system may be thought of as unique to both previous a priori systems, and forms of conventionalism.

Elsewhere in his presentation[9] Choi presents a criticism of (2b) by outlining the sheer impossibility of a TAG defender showing that every possible a priori, a posteriori or conventionalist way of justifying the laws of logic fail. Of course, the TAG defender may succeed if they show that all defences of either an a priori, a posteriori or conventionalist justification depend upon a particular claim that can be shown to be false.

Bahnsen seems to think that any a priori, a posteriori or conventionalist justification of the laws of logic is incompatible with Christianity. That is to say, if one is justifying the principles of logic in any of these manners, they are employing tenets rejected by Christianity. In other words, Bahnsen believes that it follows from ‘Christianity is true’ that ‘the a priori way, a posteriori way and the conventionalist way fail to justify the laws of logic’ for if Christianity is true, the laws of logic can only be justified in the manner he presents[10]. By doing so, Bahnsen asserts that non-Christian justifications operate on the presupposition that Christianity is false. As such, in an attempt to avoid the arduous task of showing that all flavours of the aforementioned possible justifications are false (and thereby that any worldviews that employ them are false), he seeks only to show that they all depend upon a particular claim, that ‘Christianity is false’, and that this claim renders everything unintelligible. Clearly, Bahnsen has drawn a dichotomy wherein one either accepts Christianity, or wholly rejects it; no middle ground is possible. As Bahnsen states[11]:

It is absolutely crucial that transcendental argumentation begin by positing that Christian theism is either true or false…. Van Til’s defense of the faith does not require the apologist to be aware of and refute every single variation of unbelieving philosophy, but only the presupposition common to them all (namely, the rejection of Christian theism). Many apologists mistakenly imagine that there are really three options available: one may accept Christianity, reject it, or be “undecided.” But, as Van Til recognized, to be undecided about the claim that Christian theism is the presupposition necessary to make sense out of any reasoning whatsoever is to begin one’s reasoning on the operational assumption that this claim is false (and can be laid aside as one proceeds to research and develop one’s views). Since there are only two options at the most fundamental level – the truth or falsity of Christian theism as a presupposition – the refutation of the unbelieving one (in whatever illustrative variation it appears) is an indirect proof of the other.

But what might this mean for our discussion? If Bahnsen is permitted to carry on with his criteria, then if any a priori, a posteriori or conventionalist justifications of logic are shown to be false (and subsequently, the worldviews that house and depend on them) all other formulations which properly fall under those headings will also be false (worldviews included) since they employ the same proposition, namely, ‘Christianity is false’. Of course, this is not sound reasoning unless the shared proposition is what is causing the justification to be false. Bahnsen needs to show that ‘Christianity is false’ is the ‘false-making’ proposition of all non-Christian worldviews, and it doesn’t seem that this is possible by any means other than (i) showing that all possible non-Christian justifications will have ‘Christianity is false’ as the only proposition in common (for if there is even one other proposition shared by these worldviews, how might one disqualify that proposition as possibly being the ‘false-maker’?), and (ii) showing that Christianity is not false. The obvious problem is that if (ii) is shown, the TAG becomes superfluous as it is no longer needed; one has already arrived at the truth of Christian theism, and for (i) to be shown, one still has to have an awareness of “every single variation of unbelieving philosophy.”

Further, Choi rightly points out that this criterion for distinguishing between the Christian worldview and all others is insufficient. He shows the absurdity of the criteria when applied to another worldview, namely, Fristianity[12]. Fristianity is a worldview adopted by Choi, which is identical to Christianity with the exception of the triune godhead, to make the point that the claim that “non-Christian” worldviews cannot account for X is false, since in whichever way Christianity accounted for X, Fristianity would do so in the same manner. The distinguishing feature of Fristianity is that its godhead is a quadrinity rather than a trinity, it is essentially a “Christianity + 1”. Michael Butler, a defender of TAG, has responded to the Fristianity objection by stating that there is no guarantee that Fristianity will be a coherent worldview after it is laid out and thus cannot be an objection to the TAG[13]. Choi’s reply is that this is simply besides the point as the TAG, if successful, should prove that Fristianity will be incoherent outright and that there is no burden on the Fristian to exemplify coherence. Further, in response to Bahnsen’s statement that there can only two worldviews, “the believing one and the unbelieving one”, Choi notes:

…on the same basis the hypothetical Fristian could argue as follows: ‘There are only two worldviews, Fristian theism and the unbelieving one’—which is to say, any worldview that has as its presupposition the rejection of Fristian theism. All the alleged worldviews (and here we would have to include Christian theism) are really just variations on a common presuppositional theme that Fristian theism is false

In other words, we may not simply claim that all worldviews which share a certain proposition are false because some worldviews which share a certain proposition are such. It needs to be shown that the worldviews are false because of the shared proposition. Under Bahnsen’s proposal, an atheist could show one theistic worldview to be incoherent, and reason from this that all theistic worldviews, including Christianity, are incoherent since they all share the same presuppositional theme, that atheism is false. Clearly, an exhaustive examination of possible worldviews is still required if one wants to make the strong claim made in (2b).

The Transcendental Argument for the Non-Existence of God

I would like to call attention to a statement made by Bahnsen in the excerpt taken from his debate regarding the Christian’s justification for logical principles: “From a Christian standpoint, we have an answer – obviously they reflect the thinking of God. They are, if you will, a reflection of the way God thinks and expects us to think.” [14] This is supposed to be the factor that separates Christian worldviews from non-Christian worldviews, but the claim seems rather vague. What does it mean to say that the justification for logical principles is the fact that they reflect the thinking of God?

Michael Martin asks a similar question and formulates a Transcendental Argument for the Non-Existence of God (TANG) which he defended against criticisms from John Frame.[15]

Martin stated[16]:

How might TANG proceed? Consider logic. Logic presupposes that its principles are necessarily true. However, according to the brand of Christianity assumed by TAG, God created everything, including logic; or at least everything, including logic, is dependent on God. But if something is created by or is dependent on God, it is not necessary–it is contingent on God. And if principles of logic are contingent on God, they are not logically necessary. Moreover, if principles of logic are contingent on God, God could change them. Thus, God could make the law of noncontradiction false; in other words, God could arrange matters so that a proposition and its negation were true at the same time. But this is absurd. How could God arrange matters so that New Zealand is south of China and that New Zealand is not south of it? So, one must conclude that logic is not dependent on God, and, insofar as the Christian world view assumes that logic so dependent, it is false.

Frame’s response[17] stated that:

Logic is neither above God nor arbitrarily decreed by God. Its ultimate basis is in God’s eternal nature. God is a rational God and necessarily so. Therefore logic is necessary. Human logical systems don’t always reflect God’s logic perfectly. But insofar as they do, they are necessarily true.

Bahnsen and Frame’s defence of the TAG depend upon two claims:

(A) Logical principles (such as the Law of Noncontradiction) exist because God exists and the principles are reflections of his thinking[18]

(B)  Logical principles cannot be changed by God as their ultimate basis is in God’s nature, and God is necessarily a rational God.

A Logical Euthyphro Application

In analyzing both (A) and (B) it seems that the famous Euthyphro dilemma can be applied to the TAG, substituting notions of ‘goodness’ for ‘logical principles’. The dilemma could perhaps be expressed as the following: does God think in a certain way because it is logical to do so, or is thinking in a certain way logical because God does it? If the first horn of the dilemma holds it seems clear that logical principles exist independently of God. If the second horn of the dilemma holds logical principles seem to be under the whim of God, meaning that God could change them. A TAG defender might respond by saying that this dilemma is a false one, and advocate similar to Frame that logical principles have their basis in God’s nature and are thus neither external, nor arbitrary. Firstly, this seems to add some confusion: are logical principles based on God’s thinking, or on his nature? Frame’s above statement in response to Michael Martin seems to indicate that both are true: logical principles reflect the thinking of God and the thinking of God has its basis in God’s nature.[19]

Frame essentially makes the claim that it is logically impossible for the nature of God to change. But the standard Frame is using to identify logical possibility is allegedly the nature of God. As such, his claim appears to be represented more accurately as:

(C)  Based on God’s nature it is logically impossible for God’s nature to be different because God is necessarily a rational God

This does not seem to assist in any regard as what is rational is allegedly determined by God’s nature. So to argue that God’s nature must be the way it is because God is necessarily rational seems to only appeal to a standard of rationality that is separate from God, otherwise it is clearly circular.

In what manner would it be the case that God’s nature was not rational? It does not seem that a God who forms the basis of logical principles and thereby is the standard of rationality can ever be irrational (though he may certainly appear irrational when judged by a foreign standard). That is to say, if one wants to state that the Christian God forms the basis of rationality and the logical principles thereby in effect cannot be anything other than what they are, they must be appealing to a standard of logic that is separate from God’s nature as to appeal solely to God’s nature does not sufficiently answer the question; it is a non-answer.

God and the Abstract

In his TANG, Martin stated that if logical principles depend on God in any way, they lose their logical necessity and become contingent. Frame countered by making the claim that though dependent on God, the principles of logic have their basis in the nature of God and because the nature of God is necessary, so too are the logical principles.

An obvious defeater to Frame’s claim, and subsequently the TAG, would be to show that not only are logical principles not dependent on God, but they cannot be so dependent.

The dependence relationship between “God exists” and “logical principles exist” seems problematic. If God is the source of all things other than himself, and he depends on nothing for his existence, surely the relationship must be asymmetrical (with primacy granted to God), but it appears not to be.  It can be shown, in fact, that God depends on logical principles for his existence.

Consider:

(4)   Necessarily, x depends on y for its existence iff y were not to exist, neither would x[20]

Lewis’ counterfactual semantics tell us that ‘any proposition is counterfactually implied by a necessarily false proposition’. Since “logical principles do not exist” is a necessarily false proposition, it counterfactually implies any proposition whatsoever.[21] So it is also true that if logical principles did not exist, neither would God. Thus, God depends on logical principles for his existence.

The relationship between the existence of logical principles and the existence of God would be asymmetrical iff God depended on nothing for his being and logical principles depended wholly on him. In this regard, the relationship of dependence is one-way; logical principles depend on God but not vice versa. If dependence is asymmetrical, then logic cannot depend on God as it has been shown that God depends on logic.

The asymmetrical relationship can be depicted further: where P refers to logical principles and Q refers to God. If P depends on Q asymmetrically, then the worlds in which P is true must be a proper subset of the worlds in which Q is true. Since it is the case that the principles of logic hold in every world, and the set of all worlds is not a proper subset of any other set of worlds, the laws of logic cannot depend on anything, including God.

In order to overcome this problem, one could deny the necessary existence of logical principles. This seems antithetical to the presuppositionalist position which seeks to show that the only way to make sense out of logical necessity is through the existence of the Christian God. Indeed, the opposite becomes true; the only way that logical principles can be necessary is if “logical principles depend on God” is false. One could further deny the claim that “God depends on nothing else for his existence”, but this seems incompatible with Christian theism and perhaps even with a more general notion of God.

Another possible solution is twofold. One must first accept that abstract objects are the thoughts of God. This is not problematic for the TAG proponent as they have already explicitly stated that this is the case. One must then further embrace the Doctrine of Divine Simplicity (DDS) and accept that God is identical with each of his attributes and thoughts. Under this view, the statements “God exists” and “Logical principles exist” express the same proposition. This eliminates the problem because any proposition is counterfactually dependent on itself. But it is not clear that DDS is a coherent option[22]. Indeed it is not clear that the principles of logic can be thought to be attributes of God, in any capacity. This problem seems even more severe for the Christian. If the proponent of the TAG attempts to establish the conclusion that the Christian God exists, but has to accept the DDS to do so (as per the above objection) it is unclear as to how they would reconcile the fact that God is identical with his attributes and the belief that he is internally distinct as a Trinity. Indeed, if DDS is coherent, how can there be any distinction whatsoever between God the Father, God the Son and the Holy Spirit? The DDS seems wholly incoherent with Christian theism.

As such, in order to avoid the consequence of conceding that God is not entirely sovereign, one must either (i) deny that logical principles are necessary (ii) deny Christian theism. Both are unacceptable consequences for the proponent of the TAG.

The Mind of God

There is yet another respect in which the TAG is vague. It states that the Christian worldview can account for the laws of logic because they have their basis as reflections of God’s thought. Presumably, this means that the reason why the Law of Non-Contradiction (LNC) is the way it is depends on the fact that God cannot avoid thinking in accordance with it due to his nature as logical. Even temporarily disregarding the previous objections, this claim seems dubious. This justification or grounding of the principles of logic does not seem to necessitate any transcendental reference. Consider Bob the Conventionalist[23]; he is a normal human being. Even as a conventionalist, Bob cannot help but think in accordance with the LNC, for how could Bob visualize the effects of a proposition that is both true and false simultaneously? If, as per Bahnsen’s statement, logical principles are reflections of the way God thinks and further if it is true that the LNC exists and holds because God cannot think that p and not-p, surely Bob’s own inability to think that P and not-P fulfills the same justification requirement.

One foreseeable objection is that Bob’s self-grounding does not explain the seeming universality of the LNC. However, it is impossible to think of anyone in existence who could visualize the effects of a proposition which violated the LNC[24] and in this regard the LNC is universally self-grounded.

In the aforementioned debate, Bahnsen criticized conventionalism for being arbitrary and potentially giving way to people with contradictory logical systems. Though it is hard to imagine someone who has adopted a logical system in which there is no LNC or equivalent mechanism. Such a system would be as trivial as a magic eight-ball that answers “yes” to every question[25]. It is difficult to see why Bob or any of his friends would adopt a system with no mechanism to differentiate between any propositions. On pragmatic grounds, it is entirely useless.

One may make the case that Bahnsen has misunderstood conventionalism[26], and one might further make the more interesting point of asking how God accounts for the laws of logic. If it is even possible that God justifies his use of logic in either an a priori, or conventionalist manner[27] premise (2b) of the TAG can be further rejected.

What might it mean to say that God justifies logic in an a priori manner? Bahnsen’s criticisms of an a priori justification can be found in his debate with Stein:

But if you don’t take that approach and want to justify the laws of logic in some a priori fashion, that is apart from experience, something that [Stein] suggests when he says these things are self-verified. Then we can ask why the laws of logic are universal, unchanging, and invariant truths – why they, in fact, apply repeatedly in the realm of contingent experience.

He argues that an a priori justification of the laws of logic does nothing to explain their universality. But, the fact that the laws of logic would be known a priori to be logically necessary does seem to explain the universality in a ‘self-verifying’ manner; they are necessarily true. One might further press to ask why it is the case that they are necessarily true rather than not and one possibility is that they are justifiable in some Platonic manner, existing as brute, primitive facts. In essence, this is presumably how God would view his a priori justification. For God, these logical principles are “just there” even if necessarily “just there”.

It may also be possible that God justifies logical principles conventionally, assuming them for a purpose.  One possible objection is that if this is the case, God could have done otherwise (chosen a different convention). It seems that if there are multiple sufficient conventionalist justifications of logical principles, God certainly would possess the capability to select the best possible and employ it on pragmatic grounds.

If these justifications are even possible, then (2b) in its current form becomes demonstrably false. Of course, it may be reworded to state:

(2b*) It is necessary that: no human forms of either a priori, a posteriori or conventionalist justification will justify the laws of logic

It would be the duty of the TAG proponent to develop an explanation as to why it is either impossible that God justify logical principles in the aforementioned two manners or why a human version of the same justification must necessarily fail.

One might object to (2b*) stating that a divine form of a priori justification or conventionalism would not differ sufficiently from a human form but space does not permit a treatment of this claim here.

Conclusion

Given (i) the initial objections, (ii) the vague and troubled explanations of what it means for God’s nature to be logical, (iii) the lack of asymmetry in the relationship between logical principles and God’s existence, and (iv) the possibility that God accounts for logic with the same justifications criticized by the TAG, it is my proposal that, pending further defence, the Transcendental Argument for the Existence of God be considered unsound and unsuccessful in its goal of establishing the existence of the Christian God[28].

[2] Not all Christians may agree that they require certainty of their position.

[3] Baggini, Julian and Peter S. Fosl. 2003. ’2.10 Transcendental arguments’. In The Philosopher’s Toolkit: A compendium of philosophical concepts and methods. Oxford: Blackwell Publishing

[4] Many will be confused as to why the Islamic or Judaic God cannot satisfy the requirements put forth by the TAG. A good discussion of this is available in the section of James Anderson’s paper “If Knowledge Then God” entitled “Argument #1: The One-Many Argument” published in the Calvin Theological Journal, Vol.40, No. 1 (2005), 49-75

[5] This may entail some overlap as to the precondition of intelligibility.

[6] A transcript of the debate is available at: http://www.bellevuechristian.org/faculty/dribera/htdocs/PDFs/Apol_Bahnsen_Stein_Debate_Transcript.pdf (the spaces in the PDF title are underscores)

[7] Bahnsen erroneously assumes that if one is an atheist, they must be a materialist.

[8] Choi, Sean. “The Transcendental Argument.” Reasons for Faith: Making a Case for the Christian Faith. Illustrated. Geisler, Norman L., and Chad V. Meister.  Good News Publishers, 2007. 238-243. Print.

[9] Ibid. 241-244

[10] As is usually the case with religion, there may be disagreements within a tradition. Many who identify as Christians may disagree with what Bahnsen believes are tenets of Christianity. In this respect, one may not agree, for example, that a conventionalist justification of logic is a non-Christian justification. For the purpose of this paper, I will assume, with Bahnsen, that if Christianity is true then the laws of logic are justified in the manner he has stated.

[11] Bahnsen, Greg L. Van Til’s Apologetic: Readings and Analysis. P & R Publishing, 1998. 277. Print.

[12] I do not seek to offer a defense of the ‘Fristianity Objection’; I only seek to utilize it to demonstrate the shortcomings of Bahnsen’s criterion.

[13] See: http://butler-harris.org/tag/

[14] This quotation is taken from the aforementioned debate.

[15] Their online discussion can be accessed at http://www.infidels.org/library/modern/michael_martin/martin-frame/

[16] http://www.infidels.org/library/modern/michael_martin/martin-frame/tang.html

[17] http://www.reformed.org/master/index.html?mainframe=/apologetics/martin/frame_contra_martin.html

[18] It is difficult to understand precisely what is meant by “reflections of his thinking.” Presumably, the TAG defender is claiming that the reason the Law of Non-Contradiction (LNC) holds is that God thinks in accordance with the law, or rather, the manner in which God thinks is such that the LNC can be derived from his thinking processes.

[19] One way to make sense of this claim is that God’s thinking is a property/attribute indistinguishable from God himself. I will explore this idea, and offer some objections shortly.

[20] Davidson, Matthew, “God and Other Necessary Beings”, The Stanford Encyclopedia of Philosophy (Fall 2008 Edition), Edward N. Zalta (ed.)

[21] Ibid.

[22] See: Plantinga, Alvin. Does God Have a Nature? Milwaukee: Marquette University Press, 1980.

[23] Conventionalism, as applied to logic, is the philosophical attitude that logical principles are grounded on agreements in society rather than any external reality. This agreement is not necessarily voluntary (and perhaps is necessarily not-voluntary); of course, logical conventions may have very well arisen via evolution, giving us a neurological predisposition to the conventions we do hold. Another possibility is that we acquire logic at around the same time we acquire language, and once it’s in our minds, it can’t be changed.

[24] Surely if I could, I’d be one example of such a person. I’d need to conceptualize a person conceptualizing the contradiction, thereby conceptualizing it myself.

[25] Such a demonstration is beyond the scope of this paper. For a proper treatment of conventionalism, see: Syverson, Paul F. Logic, Convention and Common Knowledge: A Conventionalist Account of Logic. Stanford, California: Center for the Study of Language and Information, 2002. Print.

[26] Martin lays this charge on Bahnsen in his article, “Does Logic Presuppose the Christian God?” (http://www.infidels.org/library/modern/michael_martin/logic.html)

[27] I have excluded the possibility of an a posteriori justification as I’m unsure how this would apply to God

[28] Special thanks to Phil Scott, Research Postgraduate Student at the Centre for Intelligent Systems and their Applications at the University of Edinburgh, and Dr. Klaas J. Kraay, Associate Professor of Philosophy at Ryerson University for their invaluable assistance in this paper.