Preliminary Discussion

                It is useful to begin by saying a brief bit on logic. Logic concerns itself with consequence, which has been referred to as truth-preservation. An analysis of consequence is performed by demonstrating the validity of arguments such that:

(Logical Consequence) Some conclusion C is a consequence[4] of a set of premises P iff in a case where all the premises of P are true, it is a case where C is true.

The “cases” referred to above are laid out by truth-conditions. Systems of logic provide truth-conditions for that which will be parsed through them[5], or rather, what will be a consequence of what. For example, I might provide the following condition (Where P and Q are the ‘things’[6] being parsed):

P ^ Q is true in some case iff P is true and Q is true in the same case.

In providing such a truth-condition I have enabled the system to demonstrate the validity of the following:

P ^ Q

_____

P

If P ^ Q is true then P is true, or in other words, P is a consequence of P ^ Q. The question is whether or not there are multiple ways to understand, or lay out, the aforementioned cases. Logical pluralism rejects the position[7] that there is only one way to determine whether or not some argument is formally valid, or put differently, that there is but one true logic[8].  It proposes instead that there are multiple ways of specifying cases (truth-conditions), all of which are true. If you were to ask the logical particularist whether some argument were valid he or she would maintain that there is only one answer to that question. The logical pluralist would reject that statement.

The Presuppositionalist’s Logical Laws[9]

                In much of the literature I have come across and in my discussions with presuppositionalists as they defend their thesis re logic they state that the non-believer cannot account[10] for the truth of the so-called Law of Non-Contradiction (LNC), Law of the Excluded Middle (LEM) and the Law of Identity (LI). These titles denote particular propositions found in, at least, Classical Logic (let the following ‘P’s stand for any sentence letter or compound sentence:

LNC: ~(P ^ ~P)

LEM: (P v ~P)

LI: A <-> A

These propositions are tautologies under Classical Logic and while their being named “laws” by some; they possess no special status over any other tautology under Classical Logic, such as:

((A v B) ^ (A -> C) ^ (B -> C)) -> C

Tautologies are formulae which are always true in their systems by virtue of the logical rules, regardless of the truth-value assignment of some sentence letter or compound sentence. That is to say, the mere syntax of the system is sufficient for the truth of tautologies. As an example, take the LEM: (P v ~P) is always true because the logical rules for Classical Logic state that a disjunction is only false when both disjuncts are false and whatever truth-value assignment we give to P, one of the disjuncts in the LEM will be true (Classical Logic only has two truth values: T/F) and that is sufficient for the truth of the entire disjunction.

I suspect that the presuppositionalist will want to disagree with my statement above, that the logical rules of a system are sufficient for the truth of that system’s tautologies. The presuppositionalist will claim that the existence of God stands in some truth-making relation to the tautologies (and everything other truth the system parses). It seems abundantly clear, however, that the logical rules are enough. I suspect the presuppositionalist would posit God as a necessary and sufficient condition, in some fashion, to the truth of the LEM (for example, and to remain consistent).

I have heard two common expositions of the truth-making relationship between the existence of God and the LEM (or any other logical truth). One maintains that the LEM is a reflection of God’s nature. I do not know precisely what is meant by this particular suggestion. What does it mean to be a ‘reflection’ in this context? How is the LEM a reflection? What is it about God’s nature that causes the LEM to be reflected? The questions are numerous. The other suggestion is that the LEM (or any other logical truth) is a reflection of the way God thinks. Similar questions arise to this suggestion as well. In order to move the discussion forward, we can at least concede that both suggestions suggest that there is something about God that makes (in some way) the LEM true.

Concerns

                Now, recall logical pluralism once more and consider some ternary logic (a three-valued logic) in which the LEM comes out false. The LEM essentially states “either true or false” but ternary logic introduces some third value (depending on the system that value might be: indeterminate, irrelevant, unknown, etc.) and so regards the LEM false. This system of logic will have a different logical rules than Classical Logic, in many ways it is a different language as French is different to English. The logical pluralist wants to maintain that this system is fundamentally no ‘better’ or ‘worse’ than Classical Logic (though different systems may in different contexts be more ‘useful’). This system will also have tautologies which differ from those of Classical Logic and the pluralist will maintain that they are true tautologies, given the particular ternary system.

Let us assume, though it may be difficult to do, that the logical rules of this system are not sufficient conditions for the truth of some proposition which entails the falsehood of the LEM, and that the existence of God is a necessary and sufficient condition of the truth[11]. If we take the relationship between the existence of God and the truth of the proposition to have something to do with his nature or thinking, then it seems that there is something about God’s nature or thinking that is making the LEM true in one instance and making the LEM false in the other. That is, where under Classic Logic God is making (a) (P v ~P) true, under some ternary logic he is making (b) ~(P v ~P) true.

The two propositions initially seem to be contradictions of each other, but because they are arising out of different logics, they are essentially arising out of different languages. If no translator were present, I think it obvious that “I am hungry” does not contradict “Je n’ai pas faim.” A contradiction only seems to arise when we parse one sentence from some other language into whichever one we are using. So, if I translate “Je n’ai pas faim” and I see that it is the negation of “I am hungry”, now I have some contradiction where prior to the translation/integration, I merely had foreign symbols. So where (P v ~P) and ~(P v ~P) seem to be contradictory, I suggest that this is only the case if taken into a common language where both are expressed and where the rules of that language determine them to be in contradiction. We should not be misled, in our example of (a) and (b) both instances use the same symbols but essentially arise from different languages. So, (a) as expressed in Classical Logic is only contradicted by (b) if it too is expressed in Classical Logic and so on.

Now, continuing along with our assumption that the existence of God (in some way) is a necessary and sufficient condition of the truth of the aforementioned propositions in their respective systems if they are to be non-contradictory, it seems that they must be non-translated. But, focusing on God’s thoughts, what might it mean to say that God’s thoughts (or thinking) act as the truth-maker for the truth of both statements, but that he thinks them in a manner analogous to thinking a statement in French and thinking a statement in English and not knowing the translation[12]? Surely if the statement is translatable, God knows the translation. Put in another way, God in some way makes (a) true in Classical Logic and (b) true in some ternary logic. Assume that by translating (a) into the system of (b), (a) is rendered false and by translating (b) into the system of (a), (b) is rendered false. Something about God (presumably an unchangeable something, according to the Reformed tradition) in this example makes (a) true and makes it false, and likewise with (b). How is one to make sense of this?

Perhaps it is the case that God possesses a system of logic which he translates both (a) and (b) into, and this logic is such that the contradiction yielded by the aforementioned translation “does not matter”. This would be to suggest that God-Logic[13] is dialtheist in some sense, permitting of contradictions in a non-explosive manner. This God-Logic however will of course have its own logical rules, but continuing with our assumption these are insufficient for any of the truths yielded, the truth-maker will have to be something about God. Now we also have something about God that makes the LNC, after translation into God-Logic, both true and false. If this is true then the presuppositionalist explanation regarding what logic is, or how the existence of God relates (in a necessary way) to logic, becomes quite unparsimonious, on one hand leaving being quite mysterious and barely serving as an explanation, and on the other having to invoke a God-Logic which all ‘subsidiary’ logics depend on for coherence.

It renders the position far less plausible, I think, than accepting that the logical rules of various logic systems are the necessary and sufficient conditions for their respective logical truths and that each system generating propositions which may conflict only when translated into another system where the logical rules generate the confliction is not a problem.

Though, at this point, the presuppositionalist may just want to rid themselves of logical pluralism. They may admit to the existence of these other logical systems but deny that they are the one true logic. In this case, as presuppositional logical particularists it seems that they would suggest there exists only one system of logic that is true and something about God stands in a necessary and sufficient truth-making relation to the truths of this system. They might further suggest then that all of this talk about other logics generating contradictions when translated is simply not a problem because that is what we should expect if the other systems are wrong. The problem with this route, I think, is that we do not appear to have any way of knowing which system of logic is the one true logic! From the various presuppositional writings it sounds like the consensus amongst them would be that Classical Logic is the one true logic, but why must one accept this? It would seem then that all of the talk about the “laws” of logic, which are just tautologies of a particular system, is quite possibly irrelevant and incorrect if there exists one true logic. We are in an uncomfortable epistemic position, the very thing from which presuppositionalism promised us deliverance.

                Thusly, the common presuppositionalist argumentation regarding logic and God’s necessity hitherto has, I think, some explanatory work to undertake. It is currently far from convincing that one should reject the sufficiency of a system’s logical rules regarding the truth of some proposition arising from that system in favor of adopting the presuppositionalist view on the matter.

[2] ‘Experience’ should be taken very loosely.

[3] This list is not exhaustive, but is indicative of the usual discussions as per my experience.

[4] One can also make sense of the principle by replacing ‘consequence’ with ‘follows from’.

[5] Provided that what is parsed is capable of being expressed given the system.

[6] Most commonly a claim of some type

[7] Hereby referred to as logical-particularism

[8] The particularist will not deny the existence of other systems of logic any more than the religious particularist denies other religions; he or she will merely deny their truth.

[9] I find it a source of confusion that presuppositionalists only seem to refer to three particular tautologies of a particular system. I do not understand the restriction, but perhaps sake of simplicity plays a role.

[10] I cannot find a conceptual analysis of their usage of ‘account’ though it seems to mean a type of explanation.

[11] Again, that is to say it stands in some type of truth-making relation

[12] Assuming the translation will yield a contradiction.

[13] Thought of as an overarching logical system.

Before I begin, I would like to make the point that the claims in my paper do not need to be true for the TAG to be defeated (with regard to logic, in this circumstance). The TAG fails due to the fact that logical conventionalism is coherent. Zao briefly touches upon this point, which I will address later, but I want to make it clear that my paper attempts to go beyond the mere claim that “logic does not presuppose God” and suggest something closer to the idea that it cannot.

The Criticisms

In my paper, I remark:

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.

Zao takes issue with this, stating:

Mitch starts off on the wrong foot immediately by proposing a hypothetical “hybridization” of two positions which is also “unique” to those other positions. So, is it a “hybrid” or is it “unique”?

I don’t think that one needs to choose between something being a hybrid, or unique. It’s doesn’t seem to be an either/or situation. For example, take gas-powered automobiles  and electric automobiles and combine the two concepts so that we create a gas-electric hybrid. In this circumstance we have a car that is unique in that there is a property that members of the previous categories do not have, namely, the property of being both gas and electric powered. Must we agree with Zao’s criteria that because this car is a hybrid, it cannot be unique or vice versa? I don’t think so, in fact it seems to me that it may be unique by being a hybrid!

Zao suggests that if there is such a system, I should present it rather than bringing it up as a hypothetical because it isn’t an objection. I think, however, if Zao understood me correctly he(?) would see that I merely rely on the possibility of a system and that this possibility is enough to make the point I wanted to make.

He also takes issue with the formal presentation of the TAG I’ve included in my paper which I’ve borrowed from Sean Choi. Zao states:

…advances have been made in presuppositionalism which have shown Choi’s position to be mistaken. Don Collett has argued effectively (in Revelation and Reason edited by K. Scott Oliphint) that Van Til’s conception of presuppositional semantics is identical to the Strawson/Van Fraasen semantics, which makes a clear distinction between “presupposition” and “implication.” (Even John Frame has accepted Collett’s argumentation in this respect.)

Choi presents his formulation of the TAG as a traditional transcendental argument (a la Kant) which would suggest (in this context) that the existence of logic implies the existence of God. Strawson in attempting to formalize a sufficient theory of presupposition proposes something similar to the following:

P presupposes Q if and only if Q is true provided P is true or P is false.

Where P is logic and Q is God, if one is to use this formulation instead of the previous, we would not say that the existence of logic implies God but that even the denial of the existence of logic also presupposes God. But what real difference does this make to our discussion? If I’m missing something then I wait to be informed, but it seems to me that even under this view the claim that “Both the truth of P or falisity of P presupposes Q” will reduce, in our discussion, to the claim that “logic presupposes the existence of God” since I am not denying the existence of logic. In other words, what difference does this make to any of my subsequent criticisms insofar as they pertain to the presuppositionalist ideas I mention?

This much can be said about the entire section of my paper where I introduce Choi’s formalism. It is of course nice to have something with which to work, but I am not dependent on this formulation. The arguments in my paper can be extended and applied to any (as I can conceive) assertion that amounts to “logic presupposes God.”

I go on to criticize Bahnsen’s idea of the “impossibility of the contrary” stating:

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 onlyproposition 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.”

Zao replies that the false-maker of the proposition is its axiomatic nature. But I cannot see any reason to accept the claim that every worldview which has the proposition “Christianity is false” has that proposition as an axiom.

He states:

If the most basic presupposition of a non-Christian worldview is “not Christianity” (which appears to be definitional, given the above framework), then it is the basic nature of the presupposition which exerts a rational controlling influence on all other worldview content. It is not merely one proposition among many, floating loose and free in a certain worldview, but is rather foundational.

Again, why is this true? It seems to me that the only reason for claiming that “Christianity is false” is the most basic presupposition of non-Christian worldviews lies simply in identifying them as non-Christian worldviews. That is to say, I might identify some worldview as being non-Mitchist because I see that their worldview does not utilize what I utilize as my axiomatic foundation but I cannot see how this entails that “Mitchism is false” becomes their foundational axiom. It also seems that depending on who is looking at Bob’s worldview, he has several other axioms! For instance, what if a Muslim is looking at Bob’s worldview, does he now have as a foundational axiom that “Islam is false?” If a Hindu is looking at his worldview, does he now have as foundational the axiom that “Hinduism is false?” It even seems that atheists can analyze Zao’s worldview under his own criteria and suggest that he has as a foundational axiom that “Atheism is false” as his most basic presupposition.

Further, imagine Bob the Buddhist who has as his foundational axiom “Buddhism is true.” If we take Zao’s criteria, then since Bob the Buddhist can be identified as possessing a non-Christian worldview it follows that he has, also as a foundational axiom that “Christianity is false.” We can say that he’d also have as foundational axioms, under Zao’s criteria, propositions such as “Islam is false,” “Confucianism is false,” and “Scientology is false.” It seems more proper to say that Bob merely has the axiom “Buddhism is true” (if even this), and that he deduces from this postulate all of the other aforementioned propositions. That is to say, “Christianity is false” is not an axiom for Bob, it’s a deduction and so like other deductions it is “floating loose and free”. If we are to follow Zao’s criteria, it seems we render the term “axiom” meaningless. In fact Bob would have possibly an infinite number of axioms about religions of which he has not even heard! I see no reason to accept such absurdity.

In further response to my mention of Fristianity, Zao responds:

Being quite thoroughly familiar with various Fristianity objections, I had to chuckle at this one. I apologize for it, but I did. Let’s be perfectly clear here: an atheist can get zero cash value out of the Fristianity objection in debate with a Christian. Are you planning on being baptized in the name of the Father, Son, Holy Spirit and “Fred” anytime soon, Mitch?

The Fristianity objection, if sound, merely shows that the central claim of presuppositionalism is false. That is, if the Fristianity objection holds then it is false that no non-Christian theistic methods can possibly justify X, Y, Z. This is all I was intending to show.

Moving right along we come to my application of a Euthyphro-like dilemma to the laws of logic. Similar to many Christians with regard to the actual Euthyphro dilemma, Zao takes the route of stating:

The Christian’s argument is that logical laws are a reflection of God’s thought which is in accordance with God’s nature, which are all necessary.

But analyze what I said in the section, as Zao even quoted himself:

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.

If Zao does not think that (C) is circular, I suggest he read a bit closer. He says that my dilemma is circular in itself because the first horn “…asserts that there is a meaningful sense in which logic is independent of the thought of God.” What is the implication of the aforementioned circularity in basing them on God? It seems to me that, as a direct implication, we must conclude that the necessary principles of logic indeed are external to God just as is the case with necessary moral principles and the original Euthyphro dilemma. I have not, as Zao has suggested, assumed that they are independent to show they are independent, I’ve formulated a dilemma and shown that given the alternatives are incoherent we have no choice but to accept that logical principles exist independently of God.

We might even supplement this by raising a point that was conveyed to me by a fellow UP.net member. Zao stated that the logical laws are a reflection of God’s thought and that God thinks logically. Moving over the seemingly obvious incoherence in such a statement, one might want to ask what it even means to say that God thinks logically? Logic permits us to deduce from premises, distinguish conclusions and so on. But God, if he is omniscient, surely does not have to do any of these things to have knowledge. God does not “reason” to his conclusions, he simply knows them. To say that the logical laws are reflections of God’s logical thinking stands in opposition to the idea that God knows all there is to know. Truly omniscient beings do not require logic, because they do not require a means to apprehend knowledge. This, I think, just adds to the incoherence of stating that logical principles reflect God’s rational thought.

In my section entitled “God and the Abstract” I offered an argument which is basically as follows:

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.

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.

Zao responds:

Given the nature of the points under contention (the existence of God and the relationship between God and logic), to argue that “logical principles do not exist” counterfactually implies that God depends on logical principles for his existence is to beg the question in a rather bald and obvious sort of way. How about, “God does not exist” is a necessarily false statement? Given that TAG is intended to argue for the necessary existence of God, to assume the contingency of God’s existence upon logic in order to prove God is contingent upon logic is, well, unpersuasive (to put it mildly).

I might be mistaken, but it seems to me that Zao interprets my argument as an argument against the existence of God. This is not the case, however. I can accept both the necessary existence of God and the necessary existence of logical principles, and still deny the type of relationship that the presuppositionalist is proposing. It’s not the necessary existence of either of these things that is the issue, it’s the proposed asymmetrical relationship between God and logic. I think Zao has really misunderstood the thrust of my argument here.

After a point about my brief treatment of divine simplicity and Trinitarianism (I agree, that could be a paper unto itself!) Zao closes with a very brief criticism of logical conventionalism. Zao states:

Finally, we have a section where logic is said to be both conventional while necessary and universal. This is rather fun. It’s like something from Alice in Wonderland. “Sentence first – verdict afterwards!

This is a claim that is thrown around a lot, and it is a claim that is just simply false. There simply is no problem with logic being conventional, while having its principles be necessarily true. Zao is welcome to either read the literature cited in my paper, the brief treatment here or wait for an upcoming article I’m expecting authored by a logician.

Conclusion

Again, the arguments in my paper are not needed to show that the TAG fails, the mere coherence of Conventionalism serves as a defeater for the endeavor. What my arguments seek to show is that logic cannot be based on God in any such implied way. I can only say that Zao’s brief treatment of Conventionalism towards the end of his post seems to violate his own suggestion of “… [understanding] the matter for [one's self] before attempting to criticize…”

P.S: I’d like to politely ask that in the future Zao link to my articles rather than pasting them in full. I’d also like to ask that he adds a hyperlink to the specific post he’s writing about. Thanks!

“Like I said before, you are arguing against a straw man. The explanation you offered in your paper fails to account for the preconditions of intelligibility. You are simply making an attempt at showing how an atheistic/evolutionary world view accounts for the preconditions of intelligibility, but the fact that these preconditions exist demands that the Christian world view be true. ” (spelling corrections mine)

What I have tried to explain is that Joshua should simply take my arguments and run them as an internal critique in his own worldview, a sort of internal reductio. The soundness of my article, if truly sound, will not be limited to one worldview. That is to say, if my argument truly does establish its conclusion it will do so if parsed through his own worldview and if that conclusion is such that it shows that his worldview cannot account for logic, then all the worse for his worldview! He may not simply beg the question in favor of his position after seeing the outcome of my criticisms. To this suggestion he has responded:

The conclusion of your argument is based on your ignorance of the very foundation for the Christian world view. There were certain aspects of the Christian world view that you simply ignored, and the ones that you documented were misrepresented. Now, if its that important to you, I will go ahead and sift through your article one paragraph at a time and comment on the ones that are faulty.

This is a pretty heavy charge, but I look forward to his analysis. I do recommend, of course, that it take into account the following material.

With that said, in an effort to quell any further attempts at avoiding the ‘meat’ of my paper due to an “inability to account for the laws of logic,” I will present the conventionalist justification of logic. In my discussions with presuppositionalists they have seemed to largely misunderstand the system and in turn create strawmen of their own to argue against. We must be cognizant now that the TAG as I’ve outlined in the previously linked paper or the statement that only the Christian worldview can account for the laws of logic requires that no other justification be possibly true. If the presentation of conventionalism is coherent it saddens me to say that one will not even need to read my paper to show that TAG (and presuppositionalism) fails. Further, there are those who would assert that presuppositionalism is the true apologetic system in that it is the one that Christianity explicitly endorses. There are also those who say that presuppositionalism/TAG cannot possibly be false because of the guarantee given by scripture. For these people, there is much more at stake than merely the coherence of the TAG, they also risk the truthhood of Christianity.

If the TAG, and further, presuppositionalism, are the true exemplifications of Christianity it follows that their defeat is symbiotically a defeat of Christianity. We can demonstrate this with a simple modus tollens:

(1) If Christianity is true, then the TAG succeeds

(2) The TAG does not succeed

(3) Therefore, Christianity is not true

What of course needs to be shown is (2), and while I feel that I’ve shown it sufficiently in the aforementioned paper, as I’ve said there are those who wish to address my supposed “inabilities.” Let us analyze if the claim that conventionalism cannot possibly account for the laws of logic is true.

What is Conventionalism?

What follows will be a series of excerpts I’ve chosen from Creath’s article that I feel outline the conventionalist justification of logic quite well.

Carnap made a refreshing and welcome suggestion: the axioms can be construed as definitions (implicit definitions) and their assertion as commitment to a language containing the terms so defined. The axioms or postulates need no further epistemic justification because a language is neither true nor false, and one is free to choose a language in any convenient way. If someone else should choose other apparently conflicting postulates, there is in fact no disagreement because each postulate set is constitutive of the concepts it employs, and hence the one body of postulates is not denying what the other is asserting. In this manner the postulates are not even intended to reflect an antecedently and independently existing reality, but rather literally to create the claims they express.

It may be that some postulate sets are better than others. But the ‘betterness’ in question concerns their practical usefulness: some are more powerful or easier to use than others. In terms of epistemic justification or cognitive warrant they are all on a par. Indeed, they are the ‘meter sticks’ for the justification of anything else. Epistemically the choice among them is conventional, though the constraints imposed by pragmatic utility can be significant. For example, an inconsistent postulate set is not very useful. For most logicians of the period, including Carnap, every sentence as well as its negation would trivially follow from a contradiction. An inconsistent postulate set would therefore fail to draw any cognitively interesting distinctions among sentences or beliefs. Though the preference for consistent systems is treated as a pragmatic one, the pragmatic considerations are powerful indeed.

In this first excerpt we see some constant presuppositionalist claims addressed. If logic is conventional, can’t people just choose different conventions? If some people choose different conventions than others, they will be contradicting each other, so how do we know which one is true? The answers to these questions are laid quite simply in the excerpt. Each language or system of logic will have a set of definitions that require no further epistemic justification. Think about the English language, there are definitions of words but to ask why a certain word is defined as such rather than some other definition is a question that simply makes no sense for languages which are neither true nor false, they simply are. Further, if someone chooses some language different than ours (say, French), there is no contradiction because the French language cannot disagree with the English language because they are creating their claims independently of one another.

Pragmatism comes into play when want to decide which system to use. Now, keep in mind that Carnap is not proposing that people somehow “choose” their basic brain languages (the language upon which they would choose all other languages). This is as silly as suggesting that one should be able to choose their genetic makeup as to yield a certain eye-color. Our fundamental operating language, our basic logical brain language (logical because there is no such thing as non-logical languages) is not chosen by us, but rather is the precondition for all other choosing. For the systems we can choose, be it in mathematics or computer science, we use the ones that allow us to perform certain tasks. We would not choose a trivial system because anything follows from trivial systems, the answer to every proposition is “Yes,” clearly this is useless.

“This discussion of pragmatic usefulness and explication must not obscure, however, the epistemic core of Carnap’s doctrine. The choice among alternative postulate sets is epistemically arbitrary; the choice is a matter of convention. Moreover, the postulates themselves are the fundamental epistemic doctrine.”

Again, where choice is possible amongst systems the choice is arbitrary. Creath continues:

At this point it would be well to say a bit more about convention, for it is not always clear what is at stake in saying that something is a matter of convention (Quine, 1936). Plainly, when Carnap speaks of the semantic and epistemic features of our language as conventional, he does not mean to suggest that they are the products of some actual legislative assembly convened in antiquity. But shorn of such unhelpful metaphor, what does conventionality come to? The answer, in essence, is that to lay down a linguistic convention is to adopt a certain scheme of justification. This scheme involves two specific features: first, there are alternatives to certain aspects of the justificatory system; and, second, the choice among these alternatives is arbitrary in the sense that no justification is required for the choice. In particular, to say that postulates are laid down by convention commits one to the idea that there are alternative postulates that could have been chosen, but were not. It commits one likewise to the idea that no further epistemic justification for the choice of postulates is required. Conventions are not designed to reflect antecedent and independent facts; if they were thus designed one would have to show that they had done so. Rather, the postulates (together with the other conventions) create the truths that they, -the postulates, express.

So put, conventionalism is the adoption of a system of justification. Other systems could have been chosen, but weren’t and no justification is required for the choice. Further, conventionalist systems are not reflecting some external reality, they really are creating their truths. We will see a further explanation of this below.

Creath continues:

That the conventions constituting the system of justification are at bottom arbitrary poses no threat whatever to the objectivity of the postulates and their consequences. This was of particular concern to Carnap because he thought that all of logic and mathematics, insofar as the claims thereof can be assessed at all, is to be justified as are postulates and their consequences. Once a system of justification is chosen, i.e., once the various terms of the language are given a definite sense, it is a completely objective matter whether B is a consequence of A. It in no way depends on what any person may happen to imagine, think, believe, or know about these sentences. It is likewise a completely objective matter whether or not a given claim needs further justification. These things are no more subjective than the truth value of the claim “All swans are white”, given of course that the meanings of the terms are fixed. If the word ‘white’ has a sense different than it in fact does, then the truth value of the claim might be different, but this in no way impugns the objectivity of “All swans are white”.

Here we have an answer to the common presuppositionalist assertion that “if logical principles are conventional, they are not necessary.” As the quotation says, once we adopt a system of justification whether or not X is true, or Y is true is a completely objective matter. To quote myself in a previous discussion with presuppositionalist Chris Bolt:

There is a distinction between “object-level” and “meta-level”. Consider a meta-ethical circumstance, where an evolutionary account of morality may be charged with becoming eliminitivist. “if I do some good deed X just because I am programmed to, then X is not really good to do, it’s just part of my programming” But these statements are operating on different levels. Both the following propositions would be true: “X really is good to do” and “X really is just a part of my biological programing, and that’s the only reason I think X is good to do” A contradiction only occurs when both statements are taken to be expressing a proposition of the same level.

Applied to logic, “X is really necessarily true, everywhere, regardless of what anyone thinks, and regardless of anyone’s conventions. And X really is just part of a system of conventions I have adopted as part of my programming.”

Thus we can see that the common charges against conventionalism by the presuppositionalists are simply misunderstandings. Conventionalism does not entail that some logical systems will contradict others, nor does it entail that everything becomes subjective and that logical principles are no longer necessary. Now, so long as conventionalism is a possible justification of the laws of logic, the TAG (and for some people, Christianity) is simply defeated:

(1) If Christianity is true, the TAG succeeds

(2) If some system other than Christian Theism can possibly account for the laws of logic then that TAG does not succeed

(3) Conventionalism possibly accounts for the laws of logic

(4) The TAG does not succeed

(5) Therefore, Christianity is not true

Conclusion

In dispelling the myths surrounding conventionalism put forth by presuppositionalists it should be clear and evident that conventionalism is coherent. Further, given its coherence it is a possible justification of the laws of logic, showing that the TAG fails. Coupled with the criticisms in my aforementioned paper we are left with the possibility of a conventionalist justification and the impossibility of Christian Theistic justification. For certain Christians, these conclusions are nothing less than devastating. If their position is the one I’ve outlined in the syllogisms, not only can Christian Theism not account for the laws of logic, it is false altogether.

Smart begins with an explanation of the formal TAG I’ve utilized in my paper. He does not seem too fond of my formal representation and offers one of his own. I do think that the form I have offered is more in line with the notion of Transcendental Arguments as they have traditionally been employed, as a tool for answering the skeptic.

The Critique of the TAG

Immediately, Smart charges me with having begged the question with my utilization of Fristianity. I find this charge puzzling. Smart states:

Just as Martin did, LeBlanc simply assumes the truth of the very thing he said he would prove, a feat that is neither impressive nor rational to any thinking person. He takes as his tool of analysis an hypothetical world view called Fristianity, which is supposedly identical to Christianity in every respect but one, viz. that God “is a quadrinity rather than a trinity.” The problem should be immediately obvious: the TAG argues that it is God as affirmed by Christian orthodoxy who is the necessary precondition for the reality and nature of logic. What LeBlanc did was simply beg the question on the first premise, asserting that God as such is not the necessary precondition thereof.

The introduction of Fristianity as a possible worldview which can account for the laws of logic does not, to me, seem question begging. Recall the TAG:

(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

One possible way to analyze whether or not (2) is a sound premise is to explore possible defeaters. Fristianity was introduced as a defeater of (2) in that it shows a non-Christian theistic justification for the laws of logic and attempts to render the modal claim of (2) false. The falsehood of (2) is not assumed, it is demonstrated. Consider another example:

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

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

(3′) Fristian theism is true

Would someone be begging the question if they utilized Christianity as an example of a worldview, which is not Fristianity, that accounts for logic? I don’t think so. Again, the falsehood of (2′) is not merely assumed, it is demonstrated. I hope that I have not missed the thrust of this objection, and I trust that I will be corrected if I have.

A Logical Euthyphro Dilemma

In his next objection, Smart identifies my dilemma as being a false one. He states:

In the same way that the Euthyphro dilemma commits the bifurcation fallacy on the moral question, so too does LeBlanc’s dilemma here because it fails to present or account for a third option, which may be stated in the following way: “Logical order is grounded in the very nature and character of God and expressed revelationally in his works and word”…

Oddly enough, it seems clear in my paper that I do address such a move:

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.

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

I then go on to discuss what I feel are the shortcomings of such a move. As such, I think the claim that I’ve not presented a/the third option is clearly false.

The Asymmetric Relationship

I think that Smart may have misunderstood this section of my paper. He states:

LeBlanc draws upon a counterfactual semantic that he cites from Matthew Davidson which states that “any proposition is counterfactually implied by a necessarily false proposition.” But for some reason he interprets this to mean that since the proposition “logical principles do not exist” is necessarily false, this somehow “counterfactually implies any proposition whatsoever.”

This is the correct interpretation under Lewis’ counterfactual semantics. So when I say that a necessarily false proposition counterfactually implies any proposition I do actually mean:

(i) If 2+2=5, then the moon is made of cheese

(ii) If circles have four sides, fish are mammals

(iii) If logical principles do not exist, pigs can fly

(iv) If three does not exist, Mitch is a monkey’s uncle

and given that, as I’ve said in my paper:

Since “logical principles do not exist” is a necessarily false proposition, it counterfactually implies any proposition whatsoever. So it is also true that if logical principles did not exist, neither would God. Thus, God depends on logical principles for his existence.

And as such, we have what I propose is an asymmetrical relationship. Smart further states:

Incidentally, LeBlanc argues that “if logical principles did not exist, neither would God; thus, God depends on logical principles for his existence.” But that is a brutal straw man mistake, for the TAG argues that logical order is grounded in the very nature and character of God and expressed revelationally in his works and word. In other words, the reason why God would not exist if logical principles did not is because the latter is grounded in his very nature and character, making LeBlanc’s point here tantamount to arguing that “not identical to P” can somehow be “identical to P.”

If logical principles did not exist, then God would not exist, for logical principles are grounded in the very nature and character of God (without which God would be not-God); i.e., God depends on himself for his existence (cf. aseity).

But I have mentioned this objection in my paper as well:

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.

I then go on to discuss what I feel are the shortcomings of this approach.

Conclusion

It seems to me that this round of objections already have their answers in the original paper. I trust that if I have misunderstood any of David’s points he will clear up my misunderstandings in his next post. I also would like to extend thanks to both David Smart and Chris Bolt for their interaction with the draft of my paper.

Note: The discussion posted is only that up until December 9th, 2009. Chris and I both agreed to end the discussion between ourselves at this point.

My posts will be colored blue while Chris’ posts will be colored maroon.

Mitch:

My mention of hybridization was not because I think conventionalism is “compromised”, it was a specific point drawn to a premise of the formulation. My paper is *not* on logical conventionalism. There are heaps of resources available should one want to explore the system, I’ve even mentioned one in a footnote for further reading.

Further, the form of TAG is not unique/indirect, it’s simply modus tollens. Even in Jamin’s article this is clear, he offers a formal representation.

As for Fristianity, the illustration is clear. I can simply add “or as close to Christianity” as possible in brackets to satisfy your problem, but it does not render it unsound.

I surely hope that this is not an attempt a full critical response to my paper.

Chris:

Since I did not state that your paper is on conventionalism, and since there are “heaps of resources available” should one want to explore the problems with conventionalism, and since conventionalism as a tenable position is at least as equally valid given your program as a “specific point drawn to a premise of the formulation”, I do not see that there is much by way of a counter in the first part of your comment. Bahnsen does not offer a trilemma, so you are arguing against a straw man, and I have shown the problem with proposing a hybrid. Since “or as close to Christianity as possible” with respect to Fristianity is not in your article, there is nothing wrong with my objection. You have a bit of a worrisome tendency to add things to your arguments after you have made them and then fault me for being faithful to your original arguments in my critiques. I critiqued parts of your article, not subsequent comments from you that are not in the article.

Mitch:

Bahnsen’s TAG from his debate with Stein, which Jamin says is a good resource, does invoke a trilemma. If you look at the subsection entitled “II. OPENING STATEMENT—BAHNSEN” I think this is quite clear.

I also do not think you can make so bold a claim as to say that you have knowledge of what every possible hybridized account of logic would “look like”. At least, if you want to, that burden is clearly on you.

As for the Fristianity point, I’ve said that I will add the bracketed note in the final draft so I would expect that you read it as such.

It’s not my intention to fault you for criticizing the original arguments, but in a dialog we move forward (so long as we’re not shifting goalposts). Oh sorry, forgot to add… the mention of hybridization was a response to premise (2a) in my paper. A premise that is drawn, again, from Bahnsen’s debate with Stein.

Chris:

If it is so clear then quote the exact portion where Bahnsen offers a trilemma. You cannot, because he does not. Bahnsen offers different ways that the atheist might try to justify logic, but he never says that these examples are exhaustive; something you would need to have him say for the argument you made concerning this portion of the debate. This is why you have put something into the text of the transcript of the debate that is not actually there.

I do like one thing Bahnsen says though that is certainly relevant here. “To say that they are merely conventions is to simply say ‘I haven’t got an answer.’”

Mitch:

In the above passage I’ve mentioned, Bahnsen explicitly makes the argument that no non-Christian theistic way to justify the existence of the laws of logic is possible, he then criticizes the a priori way, the a posteriori way and the conventionalist way.

Now it should be clear here that his point, that “no non-Christian theistic way to justify the existence of the laws of logic is possible” (premise 2 of the argument) cannot merely be asserted. But rather, from his statement we can extract the defending premises, that is where we get (2a) and (2b), they are required to make sense of (2c) and further (2).

You say that he never says his list is exhaustive, well he never explicitly says this, but in him presenting the three different ways, and asserting they must necessarily fail, and then stating (2) gives us a pretty justified reason to utilize this premise in a formal representation. In effect, (2a-c) are the required supporting premises of Bahnsen’s claim in the debate (as represented by premise 2)

Of course, if you still want to quibble with (2a) we could certainly just say that Bahnsen hasn’t/can’t provide an exhaustive list. But that does not move us from (2b) to (2c) and back to (2). If you really want to admit that the argument Bahnsen has given in his debate is invalid, that is fine with me, but such a move is not conducive to discussion (or his position).

My point against (2a) in my paper is pointing out precisely why the premise is questionable, and whether or not Bahnsen explicitly stated it, it’s tantamount to his argument in that debate. We can certainly ask for an exhaustive list, but I doubt he’d be able to provide one, and even if he did provide one it would necessarily include the three positions mentioned in the premise. If anything, we’d be attributing too little to Bahnsen’s claim, which does not give us a problem anywhere in my paper, save for where I say that a hybridization might account.

With that said, I give Bahnsen the benefit of the doubt and assume that he was not intending to (and indeed did not) make an invalid argument during his debate. Even if I am wrong in this, the majority of my paper does not depend on it. In fact, the majority of my paper (perhaps every section besides “Initial Objections” seems that it could be applied to any formal representation of the TAG so long as it attempted to establish the type of relationship between logical principles and God that has been attempted by Bahnsen/Frame.

As for Bahnsen’s quote on conventionalism, one could simply retort that to say they are part of God’s nature is also a non-answer. The reading I’ve suggested in my paper on conventionalism seems like a good place to start to understand why the ‘usual’ objections to conventionalism fail.

Chris:

Not only am I having difficulty finding this alleged trilemma in the debate transcript, I am likewise having difficulty finding the premises you are referring to. I am glad you admit that Bahnsen never explicitly states that the ways of justifying logic he mentions are exhaustive. Bahnsen provides examples of ways the atheist might attempt to justify logic. The trilemma, again, is something you are forcing into the text of the transcript. As Bahnsen mentions later, everything cannot be said in one debate. What Dr. Bahnsen has done here is analogous to what he does later in the debate in response to the question, “What solid evidence do you have to maintain that the Christian faith is the only true religion with a God?” You may read his answer there for some further insight.

With this out of the way though, what other ways might you think of to justify the laws of logic? I think Dr. Bahnsen has provided a pretty substantial list of examples, do you not? Since your hybrid example falls prey to the leaky bucket problem that Bahnsen uses in multiple other places there is no reason that I can see for either asserting it as some kind of tenable fourth option or accusing Bahnsen of having left it out in an attempt to provide an exhaustive list.
Since your argument concerning this point relies upon the premises you have mentioned, I must repeat what I mentioned at the beginning of this comment, which is that I am having difficulty finding the premises you are referring to in the debate transcript. Perhaps you could quote them for me. When I read the transcript, I see Bahnsen clearly stating his argument at the end of his opening statement.

“When we go to look at the different world views that atheists and theists have, I suggest
we can prove the existence of God from the impossibility of the contrary. The
transcendental proof for God’s existence is that without Him it is impossible to prove
anything. The atheist world view is irrational and cannot consistently provide the
preconditions of intelligible experience, science, logic, or morality. The atheist world view
cannot allow for laws of logic, the uniformity of nature, the ability for the mind to
understand the world, and moral absolutes. In that sense the atheist world view cannot
account for our debate tonight.”

This looks different from the argument you are attributing to Bahnsen and then writing about. You ascribe a trilemma to Bahnsen that he never states and then critique “him” on it, and then appeal to a formulation of an argument that Bahnsen never states in order to try and prove that the trilemma is in the text. It looks like you are not arguing against what Bahnsen said, but rather what you wish Bahnsen would have said. Another example of this is found in [7], which states, “Bahnsen erroneously assumes that if one is an atheist, they[sic] must be a materialist”. Try as I may, I cannot find this conditional in anything Bahnsen has said or written. Perhaps you could quote this for me from the text of the transcript while you are getting the other two quotations for me?

As for your conventionalism, you have written, “Conventionalism, as applied to logic, is the philosophical attitude that logical principles are grounded on agreements in society rather than any external reality” and then suggest that the case may be made that Bahnsen has misunderstood conventionalism. The suggestion is dubious, but at any rate you do not pursue this in your article, which is fine. You attempt to answer the charge of a lack of universality by writing that “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”. This is an extremely bold and unproven assertion. You continue that “Bahnsen criticized conventionalism for being arbitrary and potentially giving way to people with contradictory logical systems”. Your answer is that “it is hard to imagine someone who has adopted a logical system in which there is no LNC or equivalent mechanism”. Nonsense! I do not even have to imagine this, as there are people who claim to have done so and even attempt to live in accordance with the claim. You continue by spelling out a consequence of such a view, writing, “Such a system would be as trivial as a magic eight-ball that answers ‘yes’ to every question[25]”. Well, sure, but what does this have to do with anything? This is merely a result of accepting your conventionalist program. You continue, “It is difficult to see why Bob or any of his friends would adopt a system with no mechanism to differentiate between any propositions”. Again, who cares? Do I need to know the reason someone adopts a position to know that they do in fact do so? Of course, I do know the reason people reject logic and attempt to embrace denials of logic and positions like conventionalism; it is because they are sinners. You next write, “On pragmatic grounds, it is entirely useless”. This is just your unsupported opinion though. Useless for what? I just gave one pragmatic reason for rejecting logic; logic presupposes the existence of God whom sinners want nothing to do with apart from God regenerating them and bringing them to repentance from sin and a trusting in Jesus Christ as Savior and Lord. Two quotes from the debate transcript may be brought to bear upon this discussion. The first is from Stein and the second is from Bahnsen. Together, they answer the alleged responses you provided to the brief critique of conventionalism that Bahnsen made.

“He says that the laws of logic are the same everywhere. This is not true, although they
are mostly the same. And I wonder if he ever heard of a Zen Koan, and the answer to a Zen
Koan, is something which is like – ‘what is the sound of one hand clapping’ is the most
famous Zen Koan – The answer to that kind of question is in a different kind of logic in a
sense, or extra logical, if you want to call it that.”

“It might be appropriate in some societies to say, ‘Well, my car is in the parking lot, and
it’s not the case that my car is in the parking lot.’ There are laws in certain societies that have
a convention that says, ‘go ahead and contradict yourself’. But then there are in a sense,
some groups in our own society that might think that way. Thieves have a tendency to say,
‘this is not my wallet, but it is not the case that it’s not my wallet.’ They may engage in
contradictions like that, but I don’t think any of us would want to accept this.”

The very last sentence in the quote from Dr. Bahnsen is important. There are people who will attempt to reject the kind of logic we need for intelligibility, and in a conventionalist program there are no worries in doing this. After all, “logical principles are grounded on agreements in society”, but then, how is it that logic is necessary?

Mitch:

There’s not much more I can say that has not been said in my last comment. If Bahnsen in his debate was not using the premises I’ve outlined, his argument is simply invalid. You cannot move from:

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

to:

(3) Christian theism is true

without:

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

And further, (2) needs justification. Given Bahnsen’s criticisms in the debate, if he is attempting to construct a valid argument (which we can assume), he is doing so by the deduction from (2a-c), this is what gives him (2).

If he was not intending to give an exhaustive list, he could have just said that. But there’s no reason to infer that he did not think he was giving one, especially given how strong of a claim he was making… that *only* Christian theism can account for logic. I do think his list of examples is pretty comprehensive, but I cannot discount the possibility of some other system. It also doesn’t follow that if even these three all fail, a hybridized system containing them would also fail. That statement seems as if it would be a fallacy of composition. All I’m claiming in my paragraph there is the possibility, something Bahnsen needs to discount for the strong claims of his position to hold.

As for the justification, Bahnsen seems to assume that Dr. Stein is a materialist because he is an atheist: “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.” (p. 23)

I do not think that Stein anywhere says that he is a materialist, and as such, Bahnsen assumes it.

As for conventionalism, some people may have adopted systems with no LNC-like mechanism, but these systems are trivial.

You said: “You continue, “It is difficult to see why Bob or any of his friends would adopt a system with no mechanism to differentiate between any propositions”. Again, who cares? Do I need to know the reason someone adopts a position to know that they do in fact do so? Of course, I do know the reason people reject logic and attempt to embrace denials of logic and positions like conventionalism; it is because they are sinners.”

A system with no mechanism to differentiate between propositions would still be classified as a logical system, but a trivial logical system. So if you are saying that these people reject logic, you are entirely incorrect. Conventionalism is not a denial of logic, it’s a denial of what you believe logic to be and there certainly is a difference.

As for the pragmatic justification of logic, a trivial system is useless because it does not permit us to make usable inferences. If the answer to every question is “yes”, what do we do with such a system? We must also take into account our evolutionary history and any development of language therein. How would a trivial system aid in our survival? Again, this is discussed at great length in the book I’ve cited in my paper.

Bahnsen’s criticism of conventionalism seems quite misunderstood, that is simply not how it works. But, as a commenter said elsewhere on this site, it perhaps is not your job to educate me on the TAG, and by this virtue, it is perhaps not my job to educate you on conventionalism.

So, in short, the formal version of the TAG I present *is* based on Bahnsen’s position as espoused in the debate.He does not explicitly state the trilemma, but if his argument in the debate is to be valid, he must be assuming it. Further, I’m not quite sure that Bahnsen understands conventionalism, at least in some present forms.

Also, these objections are fine and dandy but I do not feel that they address the ‘meat’ of my paper.

Chris:

I will take your repetition of what you have already stated and the lack of quotes as evidence that you are unable to answer my concerns over your representation of the argument Bahnsen actually used. I see no reason to repeat what I have already written and the quotes that I am able to produce in support of my understanding of the transcript. I will briefly mention that so far as I remember Stein did not deny the implication that he was a materialist and while he asked how a law could be material he immediately began what appears to be an attack on the opposite position from materialism during his cross-ex time which is when he made his famous error. It might be argued that in the history of Western thought atheists have traditionally been materialists, and it may also be that Bahnsen held an argument to the effect of atheism needing to be a materialist position to remain consistent, though I doubt this was the case. In any event, the conditional is far too strong to assign to Bahnsen when he stated no such thing.

Now if I understand you right, you are asserting that there may possibly be some other way to account for logic, but you do not have any idea what this would look like. Of course, if the three examples of attempts at justification fail, this leaves you in the position of being unable to account for logic and hence needing to accept Christianity upon pain of irrationality, but I suppose atheists must cling to such fideistic and irrational positions. If I may rip a quote from Bahnsen out of context and misapply it:

“One more interesting comment about that and we’ll let it go, he says ‘We do believe there are answers to these problems. We have yet to find them’. You see, that’s the problem: atheists live by faith.”

It appears that in light of my criticisms you have changed one of your views, for you write, “As for conventionalism, some people *may have* adopted systems with no LNC-like mechanism” which is certainly not consistent with your earlier, “it is *impossible* to think of anyone in existence who could visualize the effects of a proposition which violated the LNC” and “it is *hard to imagine* someone who has adopted a logical system in which there is no LNC or equivalent mechanism”. I suppose you may answer that it is impossible for you to think and that it is hard for you to imagine but nevertheless “some people may have adopted systems with no LNC-like mechanism”, but I will just repeat that it actually is the case that people have adopted such systems and your difficulty with it, if not based purely in ignorance, is that you are attempting to evaluate another society’s agreed upon logical principles from within your own, but why should your system be accepted rather than the other? I hope you will not make the mistake of appealing to the agreed upon logical principles of your society in answering this question.

You write: “A system with no mechanism to differentiate between propositions would still be classified as a logical system, but a trivial logical system. So if you are saying that these people reject logic, you are entirely incorrect.”

Not if I am right about logic. This aside, I am glad you agree that there could, according to your conventionalism, be other logical systems without such a “mechanism”. It is perhaps the case that you are only calling it trivial based upon your own society’s agreed upon logical principles though. Adherents to that system may not think it is trivial at all!

You continue, “Conventionalism is not a denial of logic, it’s a denial of what you believe logic to be and there certainly is a difference.” Unless of course what I believe logic to be is what logic actually is, but I did not write that conventionalism is a denial of logic anyway. For you to state that conventionalism is not a denial of logic is likewise to assume that your position on logic is correct. Also, it may be the case that in a system there is no difference between what people believe logic to be and what logic actually is, and as a conventionalist you certainly are not in a position to critique that system because you differ with it. It looks as though conventionalism is actually such a system.

“As for the pragmatic justification of logic, a trivial system is useless because it does not permit us to make usable inferences.”

This is circular, but aside from this you are again just assuming the agreed upon logical principles of your own society in making this claim, and the “trivial” system is certainly not subject to such a criticism as has already been mentioned.

“If the answer to every question is ‘yes’, what do we do with such a system?”

Yes.

“We must also take into account our evolutionary history and any development of language therein. How would a trivial system aid in our survival?”

I suppose we would use the agreed upon logical principles of our societies to try to answer this question.

The meat of your article actually does not look like it is TAG specific. Other than this, I briefly touched upon my approach in the original post.

It is not my job to educate you on the TAG when you are the one who is writing an argument against it, but then, it is “my job” to point out when you have made errors in your alleged refutation. The same may perhaps apply in the case of conventionalism, but add to this that you are supposedly using a conventionalist platform to argue from, so a reductio on the position leaves you…well, there is a picture.

Mitch:

I will likewise take your repetition of the problem to mean that you have not understood what I’ve stated. I assume that somewhere in obtaining your philosophy degree you were required to analyze texts and extrapolate arguments, in doing so, there are often times where a premise is not explicitly stated but must be assumed to maintain the validity of the argument. I will not repeat myself anymore, but this is one of those times. Now, moving on…

Yes, I am making the claim that if the three mentioned ways of justifying logic fail, it does not follow that all possible justifications fail unless these three are necessarily the only type of justifications. Your quotation just exemplifies something typical of religion in general, if I may utilize a quote of my own which I think applied beautifully here:

“Philosophy is questions that may never be answered. Religion is answers that may never be questioned.”

You said: “If course, if the three examples of attempts at justification fail, this leaves you in the position of being unable to account for logic and hence needing to accept Christianity upon pain of irrationality, but I suppose atheists must cling to such fideistic and irrational positions.”

This is no better than a God of the Gaps argument, applied to logical justifications. Why can’t epistemology rely on the possibility of there being justifications? If you’re saying that the case is such that these three justifications have been shown to be false, and Christianity has not, therefore we must choose Christianity, I think you’ve just begged the question in favor of Christianity. If the arguments in the bulk of my paper hold up, it is an incoherent notion to state that logical principles can be grounded in the existence of God.

“It appears that in light of my criticisms you have changed one of your views, for you write, “As for conventionalism, some people *may have* adopted systems with no LNC-like mechanism” which is certainly not consistent with your earlier, “it is *impossible* to think of anyone in existence who could visualize the effects of a proposition which violated the LNC” and “it is *hard to imagine* someone who has adopted a logical system in which there is no LNC or equivalent mechanism”.”

There is no contradiction here, I was making a modal claim (I should have clearly stated this), there is a possible world in which a species/society/what-not has adopted a system with no LNC (think, different evolutionary pressures, or what not), and it is likewise impossible to think of anyone in existence (actual) who could visualize the effects of a proposition that violates the LNC.

You say that some societies have (presumably, societies in this world) contradicted the LNC, well… which societies do you think have contradicted the LNC?

As for non-logical societies, Bahnsen used the example of Buddhist societies, with the use of Koans. I think if you know the answer to that hand-clapping Koan, you instantly reach enlightenment. Do you know the answer, and happen to know that it’s “extra-logical” or is it just a really hard question that might not have an answer (maybe that is even the point of the question, but I digress)

In an effort to clear up some of this misunderstanding, I have modified footnote #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.”

I think that this is where your confusion comes in, it’s not that we can actually will to change our logical system. Bahnsen famously said in his debate that logic can’t be actions in our brains, because all of our brains are different. Perhaps he means to say that our minds are different, because evolutionarily, we’re all the same species!

At any rate, as I’ve said before, a proper treatment of conventionalism was not the aim of this paper and is available elsewhere. Given that you might not fully understand this system, it is questionable as to why you’ve rejected it’s coherence outright.

The meat of my paper is specific to the claim “logical principles can be grounded in the existence of God”, a claim I would have thought you’d have embraced wholly.

Chris:

When the proponent of a view explicitly denies an interpretation of his work and you subsequently argue against that interpretation as though it is correct you argue against a straw man. Perhaps if we let Bahnsen interpret himself (as we should) he has no argument, but then it is sufficient to point this out. You have not done this, but rather ascribe an argument to Bahnsen and argue against it as though it were his own. Further, if you do not have an argument to show the impossibility of demonstrating the premise in question then you have not refuted your alleged reformulation of TAG at this point since by your reasoning there is a possibility that it can be demonstrated.

“…there is a possible world in which a species/society/what-not has adopted a system with no LNC…”

I agree, it happens all the time in the actual world.

“You say that some societies have (presumably, societies in this world) contradicted the LNC, well… which societies do you think have contradicted the LNC?”

Actually I did not say this. I do not suppose one can contradict the Law of Non-Contradiction if the system of logic wherein it is supposedly contradicted does not have contradictions, but then, trying to operate in accordance with your view on logic, that may just be the way things look like to me.

As for societies etc. that have attempted to claim a system without the Law of Non-Contradiction and have attempted to live in accordance with this I provided some examples per Bahnsen and Stein. Other examples might include adherents to Eastern religions and philosophies, pluralists, and freshman philosophy students. The quote about the Koan is from Stein, not Bahnsen, and it is illegitimate to call it “non-logical” if you are to be consistent with conventionalism.

“…it is likewise impossible to think of anyone in existence (actual) who could visualize the effects of a proposition that violates the LNC.”

Again, this is a bold assertion that has not been given any support, and it likely is just a result of the agreed upon logical principles of your society blinding you concerning other systems.

In your arguing against TAG, you argue against a claim that you admit is not a part of the traditional presuppositionalist program. In my arguing against conventionalism, I argue against the position you describe in your footnote. You have now added to but have not changed your definition of conventionalism and your addition does not affect anything I have written with respect to problems with the view. Your attempt to write me off as having misunderstood conventionalism is telling. I have not misunderstood your conventionalism and I have been quoting your definition of it. To repeatedly claim that I have “misunderstood” a simple definition is almost as bad as an undergraduate philosophy student claiming that a brilliant scholar with a PhD in the realm of epistemology “misunderstood” conventionalism. It is becoming exceedingly clear that you do not have a counter.

You write, “I think that this is where your confusion comes in, it’s not that we can actually will to change our logical system”. Again, I beg to differ that I am “confused”, I think it more likely that you are using your rhetoric in lieu of argumentation. Where did I state “we can actually will to change our logical system”? How were any of my considerations contingent upon such an assumption? A voluntary or involuntary neurological predisposition toward logical conventions via evolution and or acquisition of logic at the same time as acquisition of language that cannot be changed is perfectly consistent with the actuality of various logical systems people adhere to that factors into what I have written. What do agreed upon logical principles in a society forced upon us by evolutionary processes have to do with rationality anyway? It is nevertheless dubious that people are incapable of changing their logical schemes, and the addition to your definition does not give rise to your statement that my “confusion comes in” because “it’s not that we can actually will to change our logical system”. If anyone is confused here, it is you, for the addition to your definition only states that “agreement is not *necessarily* voluntary”, “*perhaps* is necessarily not-voluntary”, “logical conventions *may* have very well arisen via evolution”, and another “*possibility* is that we acquire logic at around the same time we acquire language”. Further, it is either ignorant or disingenuous to attribute misunderstanding and confusion to people who have encountered conventionalism elsewhere and seen it defined as, for example, “the philosophical doctrine that logical truth and mathematical truth are created by our choices, not dictated or imposed on us by the world (Cambridge 184)” in opposition to your definition of it.

“Bahnsen famously said in his debate that logic can’t be actions in our brains, because all of our brains are different. Perhaps he means to say that our minds are different, because evolutionarily, we’re all the same species!”

All of us being the same species does not necessitate all of our brains being the same. In fact, our brains are not the same.

Not only are there problems with pragmatism, not the least of which is that it does not provide epistemic warrant, but it is difficult to see how the Law of Non-Contradiction is solely of pragmatic concern even given, contrary to some of my considerations, that its denial is not useful (Why do people lie?); for its denial is apparently more than pragmatically problematic, it is logically problematic; a contradiction. This is to say nothing of the total failure of logical positivism or the inconsistency with the dismissal of the analytic/synthetic distinction in Objectivism which program you used in debate with respect to logic. Further, if “logical principles are grounded on agreements in society rather than any external reality” then logic is not necessary, even if one tries to ground it in evolution or language for we could have evolved differently; “…there is a possible world in which a species/society/what-not has adopted a system with no LNC (think, different evolutionary pressures, or what not)” and “…there is a possible world in which a species/society/what-not has adopted a system with no LNC…”

I wrote that “if the three examples of attempts at justification fail, this leaves you in the position of being unable to account for logic and hence needing to accept Christianity upon pain of irrationality, but I suppose atheists must cling to such fideistic and irrational positions” to which you respond that this “is no better than a God of the Gaps argument, applied to logical justifications”. This is simply false, for I can deny that lightning is caused by Zeus and even come up with other explanations for it, even other unscientific explanations, and not be concerned about my entire epistemology crashing down. You actually cannot, however, deny that Christianity is the precondition for logic and come up with other “explanations” for it and not be concerned about your entire epistemology crashing down. If you are actually unable to account for logic then you are reduced to absurdity and unable to even entertain allegedly possible justifications for logic. You have no place to stand.

Since I have called into question your ability to advance even one argument by my utilizing a TA in defense of the TAG, it should be understood that we are debating actual justifications for logic here rather than mysterious “possible justifications” that you have no access to in your epistemological considerations. Even if you had a place to stand in making your arguments, you have offered little more than a Naturalism of the Gaps with respect to this point. You have not offered a consistent account of our experience concerning logic, and hence the TA has done its job. Your arguments are, as I believe you wrote of TAG elsewhere, “dead upon arrival”. “Religion” is in fact your only hope for redemption of your “philosophy”.

(The Cambridge Dictionary of Philosophy: Second Edition. Edited by Robert Audi. Cambridge University Press. Cambridge. 1999.)

By the way, I would like to tell you that I have very much enjoyed the conversation and that I appreciate you taking even my “jabs” “in stride”. Even philosophers have feelings somewhere deep inside, and I do not want my attempt at the rigorous interaction that you are likely to be familiar with to come across as hateful. I am not just concerned *about* you, I am concerned *for* you.

Mitch:

I give Bahnsen the benefit of the doubt in assuming that he was attempting to make a valid argument. If he was knowingly making an argument that is invalid, and intended for this to be the case, then I have certainly erred in my inclusion of the exposition. Philosophy had to wait many years during Van Til before anything formal happened, and then some. Now, you folks complain that the formalizations are not accurate. Well, to this I say firstly that I disagree, and secondly that maybe you folks should get to work and make something cogent.

The thing about logic is that, similarly to programming languages, there might be different languages or systems and ways about going about some issue, but we can understand all of these nonetheless, we can communicate. The same is likewise the case for spoken languages, something obviously conventional in nature.

As for the Eastern Religions, pluralists and philosophy students, can be you please provide some evidence for these claims?

On the impossibility of visualizing a proposition which violates the LNC, you said: “Again, this is a bold assertion that has not been given any support, and it likely is just a result of the agreed upon logical principles of your society blinding you concerning other systems.”

Can you think of an elephant which is both pink and not pink? Can you conceive of anyone doing so? I think not, since doing so would be conceiving of it yourself!

You said: “Your attempt to write me off as having misunderstood conventionalism is telling. I have not misunderstood your conventionalism and I have been quoting your definition of it. To repeatedly claim that I have “misunderstood” a simple definition is almost as bad as an undergraduate philosophy student claiming that a brilliant scholar with a PhD in the realm of epistemology “misunderstood” conventionalism. It is becoming exceedingly clear that you do not have a counter.”

Except my statement is not an argument from authority, I’m basing it on your criticisms of conventionalism. The person with a PhD in epistemology should really not misunderstand conventionalism, and for this, one must wonder if they were just being dishonest in their presentation. As for having a counter, the counter is simply the literature on the topic, which would answer many of your questions in perhaps a much more succinct manner. My deference to the literature is due to the fact that my paper is not a defense of conventionalism, and does not rely upon a defense of conventionalism.

You said: “A voluntary or involuntary neurological predisposition toward logical conventions via evolution and or acquisition of logic at the same time as acquisition of language that cannot be changed is perfectly consistent with the actuality of various logical systems people adhere to that factors into what I have written.”

But surely you are keeping in mind the specific evolutionary pressures of our species, that is something that would be shared throughout every single human being. It could certainly give the illusion of an “abstract universal”, no?

You said: “What do agreed upon logical principles in a society forced upon us by evolutionary processes have to do with rationality anyway?”

Sounds like you are on the verge of forming a version of Plantinga’s EAAN. I’d be interested to hear some further argumentation down this line.

You said:

“If anyone is confused here, it is you, for the addition to your definition only states that “agreement is not *necessarily* voluntary”, “*perhaps* is necessarily not-voluntary”, “logical conventions *may* have very well arisen via evolution”, and another “*possibility* is that we acquire logic at around the same time we acquire language”.”

This seems to be common among presuppositionalists. If your opponent is not claiming absolutely certainty, you criticize them for this. I do not see the validity of such a criticisms, and it does not arise from confusion, it arises from honesty.

You said:

“All of us being the same species does not necessitate all of our brains being the same. In fact, our brains are not the same.”

If you could, be very specific on what you mean about our brains not being the same? My understanding of neurology is that all of our brains share a commonality in the manner of their basic functions. Of course, I’m not a neurologist or a psychiatrist, so I wonder what mental illnesses bring to the discussion. Probably, as with most disabilities of that type, biological errors in development.

You said:

“Not only are there problems with pragmatism, not the least of which is that it does not provide epistemic warrant, but it is difficult to see how the Law of Non-Contradiction is solely of pragmatic concern even given, contrary to some of my considerations, that its denial is not useful (Why do people lie?”

I do not think lying qualifies as a violation of the LNC. If I steal your bike, and I tell you that I did not. It is not the case that I did and did not steal your bike, it’s the case that I stole your bike and told you I didn’t.

You said:

” Further, if “logical principles are grounded on agreements in society rather than any external reality” then logic is not necessary, even if one tries to ground it in evolution or language for we could have evolved differently; “…there is a possible world in which a species/society/what-not has adopted a system with no LNC (think, different evolutionary pressures, or what not)” and “…there is a possible world in which a species/society/what-not has adopted a system with no LNC…””

I realize now that these statements were probably the result of writing at 4am in the morning, I could have been much more clear. If it is indeed, as I have said, impossible (for us, in this world) to visualize an elephant that is both pink and not pink, then there is no possible world in which one can visualize an elephant that is both pink and not pink (since doing so would thereby mean visualizing the visualizer and subsequently the visualization in question). It seems then that it is more accurate to state that there is no possible world in which this is the case (or you can embrace RK’s hypothesis and stop a few steps earlier).

So this requires that I change my statement about a possible world where they have evolved with no LNC. I suppose it is true though that they may have evolved with a LNC-like mechanism that is different than our LNC, a mechanism by which they can distinguish different propositions. The distinction needs to be made between evolving creatures and whether or not they are *thinking* beings. A world in which no thinking creatures ever evolved would perhaps satisfy my criteria for a “species evolving with no LNC”

Even if it were the case that conventionalism is wrong, if my criticisms in the paper hold, it follows that Christianity cannot provide the preconditions either. You might say, well you were borrowing from my worldview to establish that position, well even if this were true, the fact that the position has crumbled from within shows its failure. Isn’t this precisely what you folks mean by an internal critique? If, throughout my paper, I’ve been utilizing a Christian justification for logic and the end result of the paper is the conclusion that no Christian justification is possible, if my analyses are sound, I would have revealed the internal inconsistency of Christianity.

Your last paragraph can be summed up in what seems to be a common presuppositionalist mantra:

“You didn’t do it the way I want you to do it, therefore, you’re wrong”

I also have enjoyed the conversation, though it has taken a lot of time. I suppose I should thank you for your concern, if it is indeed genuine, but I do feel it is misplaced. Cheers.

Chris:

Unfortunately there are not many more ways I can state that arguing against your own interpretation of Bahnsen which conflicts with his interpretation of himself is an instance of the Straw Man Fallacy rather than the ‘accurate formalization’ you tenaciously claim that it is. The TAG is “cogent”, but you have not interacted with it as presented by Van Til and Bahnsen. It is the case that, according to conventionalism, there might be different systems of equally valid logic since logical principles are agreed upon by societies, and I am glad that you finally agree. The Hindu tenet “atman is brahman”, Oprah’s “many ways” theology, and a freshman’s exclamation in my philosophy class “all truth is relative!” are systems held by members of each of the three groups I mentioned which attempt to deny the Law of Non-Contradiction. It is not the case that if I cannot conceive of something myself then I cannot conceive of someone else conceiving of it; you need to think this through, and on a different point you need to realize that if conventionalism is true you are thinking it through according to the agreed upon logical principles of your own society and not necessarily upon someone else’s. Having taken your definition of conventionalism and having run it through a reductio in plain sight with no direct answer from you I cannot think of any pressing need to read the literature you have recommended to me in order to provide you with a defense of your own position on logic (and why assume that I have not read it anyway?). The truth of the matter is that you have not shown where either I or Bahnsen have misunderstood conventionalism at all even though you continue to assert that we have whereas I have shown that you have misunderstood it in some respects and that you have not offered any other counter than to tell me I need to read more about it when perhaps it is you who need to do so in order to better understand the devastating critiques written on it. You are mistaken to think that your paper does not rely upon a defense of conventionalism, for once again I have offered a TA in defense of the TAG you are allegedly attempting to argue against, and this TA calls into question the very basis upon which you make your arguments, which is prior to said arguments. Even given the specific evolutionary pressures of our species there may be differences between agreed upon logical principles from one society to the next as you have conceded above, and an “illusion” of an “abstract universal” is not the same thing as an abstract universal. Since you attempted to attribute a “misunderstanding” to me concerning conventionalism at the point of the agreed upon logical principles of a society being non-voluntary (in direct opposition to the Cambridge definition I provided), the burden was upon you to provide a definition of conventionalism wherein said logical principles are agreed upon in a society in a non-voluntary fashion, which you did not do. Instead you made an irrelevant comment about certainty as though it should not strike me as strange that you would charge me with misunderstanding conventionalism on a definitional point that you have conceded you do not actually know to be the case. Each brain differs physically from every other brain, no two being identical, but this is really a side point and not overly important since it is clear that people think very differently about even the most fundamental aspects of reality, our discussion providing all the evidence we need to establish the point. There is contradiction involved in stealing and not stealing a bike, however there is also contradiction involved in someone stealing a bike and then claiming that he or she has not done so, namely the contradiction between what is said and what is actually the case; but the greater point is that it is difficult to see how the Law of Non-Contradiction is solely of pragmatic concern. Assuming we are working within the context of evolved, thinking, social beings and want to ground the alleged necessity of logic in evolution, there is still the problem that we (being these beings in this instance) could have evolved differently, not to mention that societies are contingent entities and so, again, logic is not necessary on your conventionalism, contrary to your claims and practice. It would appear that you have offered a sort of pragmatic justification for the laws of logic only, if that.

Since your paper is offered in accordance with conventionalism, if conventionalism is wrong it does not follow that your criticisms in the paper may still hold, but rather it follows that they do not. It is true then, that you are borrowing from my worldview in order to even argue against my worldview, in which case you refute yourself and prove Christianity true. What you have stated as your belief about what presuppositionalists hold with respect to an internal critique is incorrect, as we propose that the only way by which an internal critique is possible is when it is carried out upon the Christian worldview. You may again deny that Christianity is true, but then you end in self-defeating subjectivism and ultimately skepticism, as has been shown. I will be praying that you do come to see the cogency of what I have presented, as fallible and unclear as I sometimes am, and as incapable as our philosophical systems are in expressing the truth of God. All of the treasures of wisdom and knowledge are in Christ Jesus.

Mitch:

Around and around in circles we go, Chris.

The formal exposition of Bahnsen’s argument as presented in his debate is not inaccurate. It is either the case that Bahnsen’s argument is as I’ve stated, or that he was making an invalid argument. Given that Sean Choi has posted once on this blog here before, you may find it beneficial to get in contact with him and ask him about the formulation.

How precisely are the examples that you have given of the Hindu tenet, Oprah and freshman philosophy students violations of the LNC? I’m starting to wonder if we’re even thinking about the LNC in the same way (aside from the obvious differences between our positions).

Also, people who operate within a system that utilizes LNC-like mechanisms can still make false statements… humans don’t always deduce properly (like a computer would).

You said:

“It is not the case that if I cannot conceive of something myself then I cannot conceive of someone else conceiving of it; you need to think this through, and on a different point you need to realize that if conventionalism is true you are thinking it through according to the agreed upon logical principles of your own society and not necessarily upon someone else’s.”

I would wholly disagree. If you can conceive of someone conceiving P and not-P, you have thereby conceived of P and not-P. Furthermore, what is the problem of thinking about another logical system through the eyes of my own? As I said before, there is certainly communication between the different programming languages, spoken languages and also logical ‘languages’. Some research on “bootstrapping” will help to clarify these notions.

You said:

“Having taken your definition of conventionalism and having run it through a reductio in plain sight with no direct answer from you I cannot think of any pressing need to read the literature you have recommended to me in order to provide you with a defense of your own position on logic (and why assume that I have not read it anyway?).”

I have been responding to you this entire time. I assume that you have not read the literature precisely because of the criticisms you’ve been making. Similar things happen when atheists criticize the medieval version of the ontological argument, and dismiss present forms of the ontological arguments on that basis. I suspect that both Bahnsen, and yourself, may be thinking of conventionalism in a much previous form, and thus are not taking into account all of the factors. The book I’ve cited in my paper is a fairly recent explanation of conventionalism, and is beneficial for this reason.

You said:

“You are mistaken to think that your paper does not rely upon a defense of conventionalism, for once again I have offered a TA in defense of the TAG you are allegedly attempting to argue against, and this TA calls into question the very basis upon which you make your arguments, which is prior to said arguments. ”

You need this to be true so that you can avoid dealing with the bulk of my arguments, but unfortunately it’s incoherent. There would be nothing inconsistent with my paper claiming to begin from a Christian theistic account of logic. My criticisms in the sections entitled: “A Logical Euthyphro Application”, “God and the Abstract” and “The Mind of God” would still hold and if they are sound would lead to the rejection of Christian theism as an account of logic. This would not serve as a defeater to the conclusion of my argument, but rather to the system. Merely showing me that I need to “ground” logic by some other means.

Just as the presuppositionalist says if no non-Christian theistic ways can ground logic, than a Christian theistic way can, if the Christian theistic way cannot ground logic (which follows if my critique is sound), than a non-Christian theistic way can.

You said:

“Even given the specific evolutionary pressures of our species there may be differences between agreed upon logical principles from one society to the next as you have conceded above, and an “illusion” of an “abstract universal” is not the same thing as an abstract universal. Since you attempted to attribute a “misunderstanding” to me concerning conventionalism at the point of the agreed upon logical principles of a society being non-voluntary (in direct opposition to the Cambridge definition I provided), the burden was upon you to provide a definition of conventionalism wherein said logical principles are agreed upon in a society in a non-voluntary fashion, which you did not do.”

I gave you an entire book.

You said:

“Each brain differs physically from every other brain, no two being identical, but this is really a side point and not overly important since it is clear that people think very differently about even the most fundamental aspects of reality, our discussion providing all the evidence we need to establish the point.”

Sure Chris, but the fact that we can communicate is what is of the utmost importance. Even if we’re running programs written in different computer languages, bootstrapping lets me talk to you!

“There is contradiction involved in stealing and not stealing a bike, however there is also contradiction involved in someone stealing a bike and then claiming that he or she has not done so, namely the contradiction between what is said and what is actually the case”

It is not the case that Bob has both stolen and not stolen the Bike, nor is it the case that Bob has both said he has stolen the bike, and has not said that he has stolen the bike (in the same respect). You’re forgetting that key point, “in the same respect”. The contradiction between what is said and what is actually the case is not the type of contradiction the LNC deals with.

You said:

“Assuming we are working within the context of evolved, thinking, social beings and want to ground the alleged necessity of logic in evolution, there is still the problem that we (being these beings in this instance) could have evolved differently, not to mention that societies are contingent entities and so, again, logic is not necessary on your conventionalism, contrary to your claims and practice.”

This is an example of one of your statements which shows that you have not read, or have not understood the material on conventionalism.

There is a distinction between “object-level” and “meta-level”. Consider a meta-ethical circumstance, where an evolutionary account of morality may be charged with becoming eliminitivist. “if I do some good deed X just because I am programmed to, then X is not really good to do, it’s just part of my programming” But these statements are operating on different levels. Both the following propositions would be true: “X really is good to do” and “X really is just a part of my biological programing, and that’s the only reason I think X is good to do” A contradiction only occurs when both statements are taken to be expressing a proposition of the same level.

Applied to logic, “X is really necessarily true, everywhere, regardless of what anyone thinks, and regardless of anyone’s conventions. And X really is just part of a system of conventions I have adopted as part of my programming.”

There is no contradiction here because one statement is operating on the object-level, and the other is operating at the meta-level. These ideas are all integral to conventionalism and are all dealt with in the material.

In regards to your last paragraph, my mention of conventionalism was very specific and you have been somewhat taking it out of context. It is in a subsection dedicated to exploring possible ways that God might account for logic.

So all in all, I don’t find your criticisms very convincing, and even if they did hold, they would do little to the arguments in my paper. Further, I wonder why you are reluctant to deal with the very portions of my paper that would show a Christian theistic justification of logic is incoherent.

If you are indeed hinting that we should end the discussion here (your last paragraph sounds like it is), then I also thank you for your interaction and wish you the very best during this holiday season.

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.

Argument #1: That logical principles are not contingent on God

(1)    If logical principles are dependent on God, they are not logically necessary

(2)    But logical principles are logically necessary

(3)    Therefore, logical principles are not dependent on God

Chris stated:

Unfortunately, Mitch constantly employs this strawman and thinks he has thereby refuted presuppositionalism. God is a necessary being. Logic does not depend upon the existence of God; it is not contingent. Logic is necessary. Presuppositionalism is thus immune to the first argument Mitch makes.

Chris wants us to accept that God exists necessarily.  He may hold that belief as properly basic, but if he should wish to convince anyone else of this claim he’d be best served to present some type of an argument. He can either defend an Ontological Argument, or a modal formulation of the TAG. Why is it the case that God exists necessarily? If this reason finds its basis at all in the existence of logical principles and their dependence on God, he will have begged the question in affirming such a conclusion. But Chris has said that logic does not depend on the existence of God. From this, it is difficult to understand what the relationship between the propositions “Logic exists” and “God exists”, if the relationship is not one of dependence, then what precisely is the TAG stating? Without a dependence relationship, why is it that only X can account for Y? Further, without such a relationship there is no problem in affirming the existence of logical principles and denying the existence of God.

Argument #2: That logical principles are not contingent on God (and that presuppositionalism presumes an Ontological Argument)

(4)    If logic depends on God, then if God possibly doesn’t exist, then some law of logic possibly fails

(5)    No law of logic can possibly fail

(6)    So God necessarily exists

(7)    But there is a possible world in which God does not exist

(8)    Therefore, logic is not dependent on God

I fear that Chris may have misunderstood the argument here. Firstly, let me first say that there is no problem with a later premise contradicting a previous one if the premise being contradicted was established via deduction within the argument (or is an assumptive premise). An example of this is the logical problem of evil, which begins with the premise that God exists and concludes with the premise that God does not.

The purpose of this argument is twofold, it brings out the question of the dependence relationship between logical principles and the existence of God, and it questions the assertion that God not only exists, but exists necessarily. Premise (7), if even possibly true shows an obvious absurdity in the previous deductions. Of course, what I’m trying to elucidate is that the sub-conclusion of a modal ontological argument is being smuggled into the game by the presuppositionalist. One cannot merely affirm that God exists necessarily, it must be shown with an ontological argument. It could possible be shown with a modal version of the TAG as well, but it of course, could not be assumed within that argument. If that were the case, the argument would be question-begging. Chris might just flat out disagree with me on this point, but at any rate, this argument might be properly entitled Argument #1.5 as it is supplemental to the previous.

Impossibility of the Contrary

This portion of my post is too long to paste here so I will simply paste the entirety of Bolt’s criticism:

Mitch immediately gives chase to a rabbit and asks his readers to consider four “worldviews”: Christianity, Christianity without the incarnation (C1), Christianity with four persons in God (C2), and Christianity with an extra disciple of Jesus (C3). Mitch writes that these, “are, in effect, non-Christian worldviews that match Christianity point for point in every regard, save for one difference”. Unfortunately for Mitch this assertion is false, as may be easily demonstrated. If there is no incarnation, then Jesus has not been raised from the dead. If there are four persons in God, then baptism is to be performed in the name of more than just Father, Son, and Holy Spirit. If there is an “extra” disciple of Jesus, then the risen Christ was seen by more than “the Twelve” as the term was understood. Thus C1, C2, and C3 are not non-Christian worldviews that match Christianity point for point in every regard save for one difference and the statement Mitch makes is false. It is therefore doubtful that the rest of whatever Mitch argues in this regard makes sense. Sunday School teachers refute these kind of “worldviews” all the time, especially in cases where the class is made up of children. Since C1, C2, and C3 accept the authority of Scripture but contradict what Scripture teaches they are to be rejected as incoherent. Now I suspect that Mitch might change his argument, but really none of this should be of any concern anyway as will be seen in a moment.

This largely misses the point and I’ve addressed this issue in the previous post.

I stated:

It’s the job of TAG to show that all worldviews (actual and possible) incompatible with Christian theism are incoherent. If TAG is successful there should be a guarantee that [C1-4] (and every other possible worldview) will be incoherent. The proponent of TAG must show that all possible ways of tinkering with the contents of Christian theism, to create [any other view] are bound to fail, and must fail, necessarily.

As such, the objector to TAG needs not provide a positive proof for the coherence of [C1-4] as all that is needed to defeat TAG is to argue that for all we have reason to believe, a fully developed Fristianity seems coherent. Of course, it may sound odd and bizarre but judgments about oddness and such are governed by one’s presuppositions and are not reliable indicators of incoherence.

Clearly it is the job of the TAG defender to show us why the worldview must fail necessarily.

Bolt further states:

To begin with, Mitch is not entirely clear concerning what he believes about logic. Mitch writes that it “is clear and evident that logical principles exist as logically necessary abstractions…” but elsewhere writes in a self-contradictory fashion that logic “isn’t a thing, it’s a referrer to things” and argues that logic cannot be referred to as it is not an abstract object or entity.

As has usually been the case, Bolt charges me with being contradictory. Unfortunately for him, there is no contradiction here. Saying that logic exists as a necessary abstraction is not the same as saying that it’s a thing; why does Bolt think this? Logic may not be an abstract object or entity, but they certainly seem to be abstractions. I was not making a claim about the ontological status of abstractions. Surely, just as justice is an example of an abstraction, one must not be immediately understood to be saying that “Tennis exists, out there!”

To clarify any future misunderstanding, my position on logic falls under the heading of conventionalism.

Bolt further criticizes the notion of “Fristianity” (see above linked post):

What is Mitch standing on when he raises the Fristianity objection? What would Mitch have us to believe concerning the laws of logic, and how are they at all consistent with his worldview? How can such immaterial entities exist in a materialist universe? Why does logic continue to apply in a contingent realm of experience? How is logic imposed upon the world? Why should anyone care about adhering to the laws of logic? How is the universal and absolute nature of such laws consistent with the existence of only particular and finite minds? Such questions are only the beginning of an internal critique.

Presumably, Bolt is asking about my position rather than the hypothetical Fristian position. All of the questions which he has asked have been answered in various places throughout conventionalist literature.

Conclusion

It should be noted that Bolt did not address the last argument in the post which he criticizes. I’m not entirely sure what Bolt’s post accomplishes, perhaps it’s merely to satisfy those who have requested that he reply to me. I am, however, puzzled when Bolt states:

Mitch may continue to parrot old arguments against TAG, but what has been offered in reply is a TA in defense of TAG. I, for one, do not think Mitch is quite able to answer it. This may be the reason for the prolonged discussions concerning apologetic method as well as the search for anything on the Internet which might be used against the presuppositionalist method.

Is Bolt honestly saying that my discussion regarding apologetic method comes out of some insecurity with regard to the TAG? I don’t see any reason to make this claim, but perhaps it’s merely a joke.

I have been relatively silent on the TAG as of late, not because I am ignoring it, but rather because I am preparing a paper for submission. The topic is indeed the TAG, and I will post the paper once it has gone through the review process. Until that time, I can only say that it would be interesting to hear Bolt offer his own analysis of the relationship between logical principles and God.

The article to which I initially responded criticized William Lane Craig’s apologetic approach on the grounds of his plea to examine claims objectively. Objectivity is something the presuppositionalist deems impossible, and they subsequently deem that Craig in asking for such is leaving Christ on the sidelines while trying to show his existence.

I posted a quotation from J.P Moreland and one from Richard Howe. Bolt has chosen to respond to my comments in an article of his own, and it is this to which I am responding.

It would be prudent to note, firstly, that I have nowhere claimed that Bolt is an evil presuppositionalist nor have I claimed that presuppositionalism is evil. I have made clear my objections to the apologetic system but I do not seek to draw conclusions about the person professing the system. It may very well be that Bolt is a nice person, or perhaps he is evil. In any respect, I’ve not asserted one or the other.

As I’ve said, I made use of two quotations:

Take as an example the illustration of a map to Atlanta. In the order of being, there would have to be the city of Atlanta before there could be a map showing one how to get to Atlanta. Thus, in the order of being, Atlanta is first. However, in order to find one’s way to Atlanta, one might need a map. Thus, in the order of knowing, the map is first. In the theistic argument debate, the theist certainly sees that in the order of being God is first, since, if God is the creator of all things besides Himself, then, if there was not a God, there would be nothing else at all, not even an argument for God. But in the order of knowing, it might be the case that one would need a “map” to God, i.e., a theistic argument. Just as using a map to find Atlanta says nothing amiss about the metaphysical priority of Atlanta to the map, likewise, to use a theistic argument to find God says nothing amiss about the metaphysical priority of God to the argument. The presuppositionalist is wrong to think that if an argument leads on to a belief in the existence of God, this God could not be the God of Christianity… It does not imply that somehow the being of God is secondary. Presuppositionalists mistakenly assume that to have the argument first in the order of knowing is to tacitly deny that God is first in the order of being, it does not.

and

Even if one granted that human beings are estranged from god by virtue of man’s rebellion, it does not follow that human beings are estranged from reality itself. Surely even the most extreme Calvinist would admit that gravity affects the sinner as much as the saint. It is from this common ground of reality that the Classical tradition has built its natural theology.

Both quotations can be found in this essay. The former is attributed to J.P Moreland whereas the latter is that of Richard Howe.

Bolt takes issue with the first quotation. With regard to the statement that “in the order of being there would have to be the city of Atlanta before there could be a map showing one how to get to Atlanta” Bolt objects that this need not necessarily be the case. He offers an example of a map to Candyland.

There are a few problems with this objection. Firstly, the existence of CandyLand as espoused by his map is presumably not representative of an actual state of affairs. Similar to a map of Middle Earth, the plotted locations represent their co-ordinates in some possible world, the references need not be actualized. In this regard, his map to CandyLand and a map of Middle Earth are not necessarily false constructs, they simply represent a non-actualized reality, that of a fictional world.

But is it possible for someone to map something that doesn’t exist at all? I’d argue not. I could pick up a sheet of blank paper and begin to map a small town, while this town may not possess actual existence it possesses existence in the form of a possible state of affairs. In this regard, the existence of this small town remains first in the order of being as it must be conceptualized prior to plotting, even if this world is fictional.

As such, in regards to the actual world, the city of Atlanta holds primacy over the map showing its location in the order of being. It just so happens that Atlanta exists actually and the map corresponds so in turn. The matter of a map representing an actual or a possible state of affairs is wholly besides the point. The fact is, to be plotted on a map the object/location being plotted must possess either actual or possible existence. In both respects the existence holds primacy over the plotting in the order of being.

Next Bolt objects to the statement that “in order to find one’s way to Atlanta, one might need a map. Thus, in the order of knowing, the map is first” by responding that:

Knowledge of Atlanta and knowledge of how to get to Atlanta are two different things. Moreland is equivocating. It has already been granted that in order to find one’s way to Atlanta, one might need a map. It has not been granted that in order to know that there is an Atlanta one needs a map.

But the weight of this objection is questionable. With specific regard to the map example, knowledge of Atlanta would necessarily entail knowledge of how to get to Atlanta at least in a primitive form. For the person who was not aware of the existence of Atlanta, in looking at the map, could at least discern that (i) Atlanta exists (ii) I either am in Atlanta, or must move to get to Atlanta (provided the person new their position on the map). But I fail to see the relevance of this objection. It is only relevant in light of his next criticism.

In response to Moreland’s claim that “…in the order of knowing, it might be the case that one would need a ‘map’ to God, i.e., a theistic argument”, Bolt states:

Moreland implies that presuppositionalists present no theistic arguments, which is false. He is also blatantly contradicting the claim of Scripture that everyone knows God without theistic arguments. The phrase “it might be the case” is false as according to Scripture it is certainly not the case.

The presuppositionalist does not just state that God must exist in order for there to be knowledge, but that God must be known. J.P. Moreland has never presented an argument for the existence of God which did not already presuppose the knowledge of God.

It is interesting to note here that Moreland does not claim that one needs a map to KNOW God, but rather needs a map to find God. This answers Bolt’s criticism that it blatantly contradicts scripture. Moreland, Craig and most Christian philosophers I am aware of all embrace the notion that belief in God is properly basic, that is to say, they accept Plantinga’s philosophical notion (which is consistent with the Bible) that belief in God requires no argument and is rather a gift from God Himself in the form of self-evidence. As such, Moreland is not claiming that one needs an argument to KNOW that God exists, but rather that one may require an argument to FIND God, or reveal such known knowledge. This is not inconsistent with Christianity stating that all men have an innate knowledge of God.

To briefly touch on the first portion of Bolt’s objection, it can be debated amongst philosophers as to whether or not what presuppositionalism provides meets the criteria for an argument, but if we are to grant that TAG is such a formulation it is true that presuppositionalism at least presents one argument. But this is not inconsistent with what Moreland has said, and rather it diverges into a separate discussion on whether or not the argument given by presuppositionalists is sound. I discuss this in my recent article, “The Case Against Presuppositionalism: Part III“.

Where Moreland states that:

Just as using a map to find Atlanta says nothing amiss about the metaphysical priority of Atlanta to the map, likewise, to use a theistic argument to find God says nothing amiss about the metaphysical priority of God to the argument.

Bolt says:

First, Moreland is equivocating as “finding God” must mean something quite different from “finding Atlanta” since both are not “found” in the same way at all, the one being a particular location. Second, Scripture does not allow any room for the view that people are able to “find God” through theistic arguments, as God is already “found” or known. Third, the necessity of theistic arguments with respect to some people results in all sorts of absurdities regarding those who lived prior to such theistic proofs were formulated and those who are intellectually incapable of grasping such proofs. Fourth, there is at the very least a claim that there is an epistemological priority of God to the argument which Moreland has not touched upon at all.

The notion of equivocating the term “finding God” is one where I see no problem, the map example is after all an example and similes are being drawn. Bolt’s second and third objection have been dealt with above. The question of the epistemological priority of God is the question of presuppositionalism as a whole, of course, and cannot be dealt with here. Just briefly, however, even the Classical/Evidentialist philosopher would agree that there is an epistemic priority of God for all existent things exist contingent upon God’s necessary existence. That is to say, not only could nothing be known without God, there would be nothing to know and nobody to not know it! I do not see where the non-presuppositionalist disagrees with this statement.

Where Moreland states:

The presuppositionalist is wrong to think that if an argument leads on to a belief in the existence of God, this God could not be the God of Christianity…

Bolt responds with the claim that the God in which Antony Flew believes cannot be the Christian God. It is true that Flew was led to belief in a God through argument, and that his concept of God is deistic. It is puzzling though, precisely how many Gods does Chris Bolt think exist? If it is the case that only one God exists, and that it is the Christian God then anyone professing belief in a God as a result of argument must believe in the Christian God insofar as the presented arguments are sound. They would simply fail to grasp his nature properly. This might sound peculiar at first, but it seems to logically follow from the statement that there is only one God. That is to say, there is not another God existing beside the Christian God whom Flew has been convinced to believe in as a result of argument. If the premises of the argument were sound, they must be expressing qualities of the existent God, and if that existent God is the Christian God then Flew is believing in him without knowing it, but believing in him to a lesser degree than say, a Christian would. In fact, it seems that any notion of God conceivable would at least grasp some quality of the Christian God (if the Christian God exists as the totality of all), for what positive quality could God lack?

In fact, the error is not one of the argument, but would be one of the person acknowledging the conclusion. Flew’s belief that he believes in God X is incorrect, but his belief in God X is not incorrect, just underdeveloped or misguided.

But does this then necessitate that God could be attributed false properties? Could an argument establish that God is evil and lead someone to believe in an evil God? How then would this be representative of the Christian God. Well, the issue is an interesting one to ponder but all arguments I know which have attempted to show that God is evil have failed miserably, they are horribly unsound. Evil is in fact a negative quality and God does not possess negative qualities. These attributions are in fact at odds with our basic philosophical notions of God as possessing maximal greatness.

So unless Bolt believes in a pantheon of Gods it is necessarily the case that any belief in God is a belief in the Christian one insofar as it is necessarily the case that the Christian God is the only God which exists! Miscategorizations or misattributions would be due to a sort of “seeing through a glass; darkly”, a fault not of the argument but of the interpreter.

But is it not the arguments fault for not attempting to express the full reality of God’s nature? I do not think so. In fact, I do not think that any Classical/Evidentialist Philosopher would seek to establish all the attributes of God with one argument, they present cumulative cases (that is except for proponents of the Ontological Argument). It is thereby unfair to extract these arguments from the set in which they are intended for delivery and criticize them on a one by one basis for not establishing a thorough enough conclusion. In fact, one could make one argument out of all of Craig’s arguments (for example), but what a long winded argument that would be and you’d probably need a degree to read along!

The quote which Bolt presents from Moreland is indicative of such usage of one theistic argument as a “magic bullet”:

In summary, it is most reasonable to believe that the universe had a beginning which was caused by a timeless, immutable agent. This is not a proof that such a being is the God of the Bible, but it is a strong statement that the world had its beginning by the act of a person. And this is at the very least a good reason to believe in some form of theism. (J.P. Moreland. Scaling the Secular City: A Defense of Christianity. Baker Books. Grand Rapids, MI. 1987. Pg. 42.)

This is representative of the pivotal first step in a cumulative case. One must walk before they run and it is difficult to see how one should be faulted for this.

In response to the notion of reality being the common ground between the believer and the non-believer (where it was stated that gravity effects the sinner as much as the saint), Bolt states:

The unbeliever cannot account for the knowledge of something like gravity because she will not accept that Jesus is the Lord of gravity. Of course, Moreland might not either, and that is the problem pointed out in my previous post.

This brings us right back to whether or not presuppositionalism is a coherent philosophical system, and sadly Bolt misses the point. The common ground of reality affect both the believer and the non-believer, and this is a common ground from which dialogue may begin. Knowledge of gravity is not required for the effects of gravity. We do not see babies flying because they do not understand physics! The point is that reality is something that effects us all, God-fearing or not. The notion of whether or not one can “account” for gravity should be illuminated through sound, reasoned, argument. It is not difficult to see the move an atheist who experiences the effects of gravity may move towards establishing the existence of God. Perhaps it is the case that gravity exists and that gravity is a natural law and that the best explanation for the natural law of gravity is an intelligent designer. If the non-believer will accept such “natural” theological propositions, they have establish a creator of the Universe, the first step in what could be a cumulative case for Christian theism. I do not think such a move is warranted, but it is not impossible to work from common ground to belief in the Christian God as the presuppositionalist so states.

I have been asked to deal with an argument Bolt presented in his initial post on Craig’s argumentation:

(1)If the Christian worldview is true then Christ is Lord of all.
(2)According to Craig, Christ is not Lord of all.
(3)Therefore according to Craig, the Christian worldview is not true.

I think the issues have already been addressed. I shall grant (1), so the obvious issue is (2). It’s obviously untrue for anyone who has read Craig’s work, but the justification Bolt presents is shoddy at best. William Craig has said numerous times that he does not believe on the basis of argument. He is in agreement with Plantinga that belief in God requires no argument to be justified, as it is properly basic (a tenet of reformed epistemology). His arguments do not validate his faith, they only seek to demonstrate said rationality.

After Bolt’s argument, he says:

Now obviously Craig holds that the Christian worldview is true and he seeks to prove portions of it. The point here is not that Craig is actually an unbeliever, but rather that even before Craig begins his arguments he undercuts them all and concedes the debate with his methodology.

Bolt undercuts (2) on his own at this point. Thus, we cannot grant (3). What is really at discussion is whether or not Craig’s apologetic method acknowledges Christ as ‘lord of all’. Bolt says that it does not because he attempts to establish an objective ground from where to begin. But this does not necessitate that Craig has stopped accepting that his existence, and subsequently his thinking is contingent upon God. In fact, to establish this from his position Craig would have to make the fantastical argument that he exists necessarily rather than contingently. The presuppositionalist says that without God, nothing can be proven. It’s even more dire than that under Classical/Evidentialist apologetics as without God there is absolutely nothing. God is the necessary precondition for everything, the disagreement lies with how presuppositionalists attempt to show this.

When Craig makes his arguments he has not forsaken knowledge of Christ, which God does Bolt think Craig is representing? There is nothing inconsistent with Craig making the arguments the way he does, acknowledging that the unbeliever has an innate knowledge of God (he references this in his writings) and that they may need arguments to uncover or accept what they already know just as one needs a map to find Atlanta.

It is verging on incoherence to say that if one attempts to speak about God from a mutually accessible sphere (that of reality between the believer and unbeliever) that they have then undercut their position. It is perhaps even more absurd to say that no sphere exists, for surely, as said before, gravity effects both the believer and the non-believer in the same way. Even Paul himself offers evidentialist arguments for the Resurrection in his writing, did Paul somehow undercut his position?

No classical apologist that I know of denies matters of “presupposition”, if the presuppositionalist position just seeks to establish that without God, nothing could be demonstrated, then all classical apologists agree with presuppositionalism on the conclusion and disagree on the method. What differs is whether or not presuppositionalism formulates a sound argument for the existence of God and whether or not it is sound as an apologetic method.

All in all, I feel the points of Bolt’s argument have been addressed by my previous points, but as he requested I’ve added this previous portion to deal with it directly.

In my previous posts, The Case Against Presuppositionalism and The Case Against Presuppositionalism: Part II, I have outlined a couple of arguments against presuppositionalism and answered some objections. In this article, I would like to further refine my previously presented formal arguments (thanks to the help of the UrbanPhilosophy user VazScep), present two additional arguments, including one from Jason Streitfeld.

I have previously presented two main arguments against the claim that logic depends on God’s existence, the following are the same arguments with minor revisions to presentation:

Argument #1: That logical principles are not contingent on God

(1)    If logical principles are dependent on God, they are not logically necessary

(2)    But logical principles are logically necessary

(3)    Therefore, logical principles are not dependent on God

The key premise is, of course, (1). In my previous article I have outlined a brief defense against the claim that “though logic is part of God’s nature, it’s still logically necessary”. I’ve seen no reason to abandon (1) as most of the objections are bare assertions that something can be both logically contingent/necessary.

Argument #2: That logical principles are not contingent on God (and that presuppositionalism presumes an Ontological Argument)

(4)    If logic depends on God, then if God possibly doesn’t exist, then some law of logic possibly fails

(5)    No law of logic can possibly fail

(6)    So God necessarily exists

(7)    But there is a possible world in which God does not exist

(8)    Therefore, logic is not dependent on God

The key premise here is (7). Surely the presuppositionalist will state that there is no possible world in which God does not exist, and thus, God is logically necessary.  A defeater of (7) must be some type of Ontological Argument, showing that God exists necessarily because of the type of thing that he is. In the absence of such an argument one should not be expected to accept a denial of (7). The presuppositionalist may assume the falsity of (7) but this refusal should be rejected if it is not established soundly. That is to say, if (7) cannot be negated by virtue of anything other than presuming that it is false, it must hold. If the presuppositionalist wishes to simply presume that (7) is false by virtue that God is a necessary precondition for logic, they have in effect committed a vicious circularity; God being a necessary precondition for logic is precisely what is at issue and they should therefore not beg that question.

Argument #3: The absurdity of Christian logical necessity

As we should all understand by now Christian presuppositionalism states that no other worldview can account for the laws of logic. Their approach to suggest such is twofold. The alleged proof of this statement is the “impossibility of the contrary”, which states that if all non-Christian worldviews fail at accounting for X, the Christian worldview is able to account for X. Of course this in itself does not follow as it may simply be impossible to account for X, that is to say the presumption of justification may not be valid.

But in this respect, it is a peculiar notion and indeed a bold claim which suggests that all non-Christian worldviews are illogical.

Let C be standard Christianity. Consider worldview C1 which matches Christianity point for point sans the fact that the second person of the trinity became incarnate. Consider worldview C2 where the Godhead is quadripersonal rather than tripersonal. Lastly, consider C3 where Jesus had an extra disciple.

It is clear that C1, C2, and C3 differ from C in ways that make the definitionally non-Christian. They are, in effect, non-Christian worldviews that match Christianity point for point in every regard, save for one difference. Is one to understand that the differences, however seemingly minute, cause a collapse of rationality? Is it true, then, that all the truths of Christianity, every single line of the Bible is a necessary truth; that is to say that in all possible worlds C must obtain? That is to say that it is logically impossible that Jesus was born elsewhere, that is logically impossible that the Godhead be quadripersonal and that it is logically impossible that Christ have had one more disciple. Even the most seemingly trivial facts become logically necessary, consider all the Bible stories, it is not the case that they could be any other way, such is logically impossible.

But the implications of this view are grave, for if it is logically impossible that things have occurred in a manner other than what is reported to have occurred through the Bible this entails that not even God could have made them so. General understandings of Divine Omnipotence state that God can produce any conceivable thing or arrangement of things. And it follows that since such deviations from our current state of affairs are logically impossible, they are as inconceivable as a square circle.

But this entails that God could not have made it so that Peter denied Jesus twice, or four times. God could not have made it so that Mary was named something else. God could not have made it that there was one more guard at Jesus’ tomb. This seems to be an absurd notion: (i) why should one accept these as logically necessary facts, (ii) why do they directly affect the ability of God to account for logic?

The Christian presuppositionalist, to defend their position, must argue for the following:

(9) All non-Christian worldviews are not even possibly true

To analyze whether or not the presuppositionalist meets this challenge, let us bring forth a version of the Christian TAG to analyze (This is Sean Choi’s reformulation of Bahnsen’s argument as espoused in the Bahnsen vs. Stein debate and subsequent analysis – the full version can be found in “Reasons for Faith: Making a Case for the Christian Faith”):

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

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

(11a) 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

(11b) Neither the a priori way nor the a posteriori way nor the conventionalist way will justify the laws of logic

(11c) So, there is no non-Christian theistic way to justify the laws of logic

At this point, one can grant for the sake of argument that (11a) and (11b) are true, but such a grant does not seem to establish the truth of (11). It has been proposed that one could establish the truth of (11) via:

(11d) Necessarily: if there is a rational justification for the laws of logic, then it will be either Christian theistic or non-Christian theistic.

The claim is that the addition of (11d) to (11a)-(11c) may appear to allow the valid derivation of (11), but this is mistaken. It is the case that (11c) follows from (11a) and (11b) by modus tollens (if p then q; not-q, so, not-p), but the inference from (11a), (11b), (11c), and (11d) to (11) is logically invalid. Even with (11d) which is plausibly true, one cannot derive the necessary proposition (11) as a conclusion because (11a) and (11b) are contingent.

This is a clear modal defect and to solve it one must take (11a) and (11b) to be necessary truths:

(11a*) 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

(11b*) It is necessary that: neither the a priori way nor the a posteriori way nor the conventionalist way will justify the laws of logic

It now follows from modal modus tollens (it is necessary that: if p then q; it is necessary that not-q; so, it is necessary that no-p) that:

(11c*) Therefore, it is necessary that there is no non-Christian theistic way to justify the laws of logic

Thus, from (2a*), (2b*), (2c*) and (2d) it validly follows that (11) and given the granted premise (10), which in itself may be assuming to much, and the new transcendental premise (11), it follows that:

(12) Christian theism is true

So, now that there exists a logically valid formulation of this argument, the question falls onto the reasons to accept (11a*) and (11b*). If there are such reasons, the Christian TAG will be valid and sound.

Let us consider (11b*) once more:

(11b*) It is necessary that: neither the a priori way nor the a posteriori way nor the conventionalist way will justify the laws of logic

Even if one is to grant that this premise is not a false trilemma (for the sake of argument), (11b*) might still be false. As mentioned earlier, it is not the case that the presuppositionalist has exhaustively examined and refuted every possible a priori, a posteriori and conventionalist way or justifying the laws of logic! As such, the only sound premise to make would be:

(11b**) All the a priori, a posteriori, and conventionalist ways of justifying the laws of logic thus far examined have failed

But this premise is wholly coherent with (11b*) being false, ergo (11b**) does not entail (11b*) and insofar as this argument relies upon the truth of (11b*) it cannot establish its conclusion. As such, there is a need for an argument from the presuppositionalist that shows that every possibly a priori, a posteriori, or conventionalist way of justifying the laws of logic must fail. This argument would have to establish that these systems not only fail, but fail necessarily. I am not presently aware of any such argument.

To quickly recap, the Christian presuppositionalist TAG takes the following form:

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

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

(12) Christian theism is true

Premise (11) is the key premise insofar as (10) is granted and (12) follows logically from (10) and (11), which it does. Much work was needed, however, to support (11), so that the argument became:

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

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

(11a*) 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

(11b*) It is necessary that: neither the a priori way nor the a posteriori way nor the conventionalist way will justify the laws of logic

(11c*) So, it is necessary that there is no non-Christian theistic way to justify the laws of logic [from (11a*) and (11b*)]

(11d*) Necessarily: if there is a rational justification for the laws of logic, then it will be either Christian theistic or non-Christian theistic

(12) Christian theism is true

We have already seen that the truth of (11b*) has not been established, but what of premise (11a*)?

We can begin to analyze whether or not (11a*) is true by looking at a negation of it:

~(11a*) It is possible that: there is a non-Christian theistic way to justify the laws of logic and it is neither the a priori way the a posteriori way nor the conventionalist way

There are not, to my knowledge, any reason to reject this possibility, and in fact, if ~(11a*) is merely possible then (11a*) must be false. As such, we must find discern whether or not there is a reason for thinking that ~(11a*) is impossible.

The first glaring example that this is not the case would be the absence of evidence against the following proposition:

(A) It is possible that: there is a worldview distinct from Christian theism and which is such that if it were true, it would provide a sufficient justification for the laws of logic

Consider my previous example of worldview C2 wherein is it identical to Christianity in every respect sans the fact that the godhead is quadrinitarian rather than trinitarian. This means that in whatever way Christianity accounts for the laws of logic, C2 does so in like manner. Perhaps the presuppositionalist will argue that C2 is not an actual worldview. But this is besides the point, the presuppositionalist seeks to establish the rational necessity of Christian theism. To defeat such a necessity claim, possible worldviews are fair game. To argue otherwise is simply to make an act of special pleading that one side may use modal logic whereas the other may not, this would be absurd.

Michael Butler has offered an argument against the notion of C2 or what he calls Fristianity (due to the fourth person of the Godhead being posited as Mr. Fred). The presuppositionalist will be quick to say, again, that they need not refute every opposing worldview as they can simply be sorted in terms of Christian worldviews and non-Christian worldviews; those that presuppose Christ and those that reject him. This is simply far too absurd and juvenile of a claim. For the hypothetical Fristian could argue: “There are only two worldviews, Fristian theism and the unbelieving one” – which is to say that any worldview that has as its presupposition the rejection of Fristian theism. All of these worldviews (which would include Christian theism) are just variation on a common presuppositional theme that Fristian theism is false. As such, this criteria cannot be rationally held to absolve the presuppositionalist of the need to address worldviews.

But with further regard to Fristianity, Butler states:

…that the only way we know that God is a Trinity is that He revealed it – mere speculation or empirical investigation would never lead to this conclusion. But for the Fristian, which is, ex hypothesis, identical to Christianity in every other way, asserts that its God is a quadrinity. But if Fristianity is otherwise identical to Christian, the only way for us to know this would be for the Fristian god to reveal this to us. But there is a problem with this. Supposing Fristianity has inspired scriptures they would have to reveal that the Fristian god is one in four. But notice that by positing a quadrinity, the Fristian scriptures would be quite different from the Christian Scriptures. Whereas the Christian Scriptures teach that, with regard to man’s salvation, God the Father ordains, God the Son accomplishes, and God the Spirit applies, the Fristian scriptures would have to teach a very different order. But exactly how would the four members of its imagined godhead be involved in man’s salvation? ore fundamentally, whereas in the Christian Trinity we read that the personal attribute of the Father is paternity, the person attribute of the Son is filiation, and the personal attribute of the Spirit is spiration, what would be the person, distinguishing attributes of the members of the Fristian quadrinity? What would their relationship be to each other? Further questions flow out of this. How would the quadrinity affect the doctrine of man’s sin? How would redemptive history look different? What about eschatology? This all needs to be spelled out in detail. This illustration reveals a general problem. One cannot tinker with Christian doctrine at one point and maintain that other doctrine will not be affected. It does no good for the proponent of Fristianity to claim that the only difference between his worldview and the Christian worldview is over the doctrine of the Trinity. Christian doctrine is systemic, and a change in one area will necessarily require changes in other. It is necessary, therefore, that the advocate of Fristianity spell out how this one change in doctrine affects all other doctrines. But once this is done, there is no guarantee that the result will be coherent.

Thus, without providing the details of Fristian theology, this objection loses its punch. It can only be thought to be a challenge to Christianity if it, like Christianity, provides preconditions of experience. But without knowing the details, we cannot submit it to an internal critique. Until this happens, we can justifiably fall back on the conclusion that there is no conceivable worldview apart from Christianity that can provide the preconditions of experience. (Butler, “The Transcendental Argument”, 118-119)

Is it the case that Butler has disposed of the Fristianity objection? Not quite. Consider Butler’s claim:

(*) If Fristianity is otherwise identical to Christianity, the only way for us to know [that its God is a quadrinity] would be for the Fristian God to reveal this to us

Butler proposes that (*) is true, but there seem to be good reason to accept it as false. That the Fristian God is a quadrinity is something we know to be true in virtue of stipulation. It is such by the very virtue that it was introduced as such. Whereas when one says:

…consider Fristianity, which is a theistic worldview that holds to the doctrine of the quadrinity (one God in four persons) and is otherwise identical to Christianity, or as similar to Christianity as possible (given its quadrinitarian tenet)

there can be no question as to what Fristianity is. It’s come to mean what it does precisely because in offering a possible defeater to presuppositionalism, Fristianity was defined as a possible worldview that includes a quadrinitarian God. There is no need for a mysterious revelation to teach us that the Fristian God, a God of a merely possible worldview Fristainity, is a quadrinity. Also, insofar as the content of Fristianity is identical to the content of Christianity (sans the quadrinity), this does not entail that the means by which we know about God in one worldview is the means by which we know about God in the other. Christianity is actual, in that it is a worldview that exists and Fristianity is possible and our methods for knowing about actual states of affairs are different from knowing about a possible state of affairs. Also, the numerous unaswered questions that Butler espouses is not an argument for anything. Many of his questions erroneously assume that worldviews need revelation and are as such, irrelevant.

But what about this notion that once Fristianity is spelt out, it might be incoherent? This isn’t quite the issue. It’s the job of TAG to show that all worldviews (actual and possible) incompatible with Christian theism are incoherent. If TAG is successful there should be a guarantee that Fristainity (and every other possible worldview) will be incoherent. The proponent of TAG must show that all possible ways of tinkering with the contents of Christian theism, to create Fristainity are bound to fail, and must fail, necessarily.

As such, the Fristian objector to TAG needs not provide a positive proof for the coherence of Fristianity as all that is needed to defeat TAG is to argue that for all we have reason to believe, a fully developed Fristianity seems coherent. Of course, it may sound odd and bizarre but judgments about oddness and such are governed by one’s presuppositions and are not reliable indicators of incoherence.

I am currently only aware of an objection to Choi’s criticism from Josh Walker of “Bring the Books”. Though, it is difficult to see the appeal of his objection.

Josh Walker states:

Thus, Choi offer “Fristianity” as an alternative worldview to Christianity that, as he claims, would account for the preconditions for intelligibility. This argument is not substantial to the TAG for at least two reasons. First, we are not concerned about hypothetical worldviews that can be made up to fit the preconditions; rather, we are interested in actual worldviews. In other words, the TAG is concerned with actual worldviews that can stand this criticism. If no one holds to “Fristianity”, at the end of the day, it is really irrelevant to the presuppositional project.

But clearly, as Choi himself has said, in order for the TAG to succeed it must show the impossibility of any worldview contrary to Christ. This must include hypothetical worldviews as TAG’s claim attempts to establish supremacy over such hypotheticals. To be as bold to say that the TAG does not deal with hypotheticals is to offer a defeater on that very premise. If the TAG is not making a modal claim, then it becomes largely useless even if we grant that the laws of logic actually need “accounting”. This uselessness arises by virtue of the fact that there would be no basis to make the claim that “Christianity is the only worldview which can account for the laws of logic” without modality.

Walker’s second objection is largely similar to Butler’s:

Second, and much more substantial, Choi has failed to provided acoherent worldview to account for intelligibility. The worldview that Choi sets forth is identical to Christianity with one major alteration, the Trinity is gone. But what Choi does not understand that worldviews are not disconnected propositions—as if one doctrine can be changed and the system remains largely in tack. Instead, worldviews are organic. One part flows into the other. By changing one part the whole system will change. Thus, if the doctrine of the Trinity is changed the entire worldview is altered. Take for instance the doctrine of the Scripture. The Christian worldview teaches that the Bible is the final and complete revelation from God about himself. If the Trinity were altered, the Christian Bible would have to be altered significantly to make room for the “quadrinity.” At the very least, sections would have to be added introducing us to this fourth person. Or take the doctrine of salvation; it would have to be changed. As it stands, Christianity holds that all three person of the Trinity are directly involved in the salvation of God’s people—the Father chooses his people, the Son dies for his people and the Holy Spirit sanctifies his people. If a fourth person were added to the Godhead, a role for this person would need to be added to the doctrine of salvation. These are but a few of the many examples that could be given to show that adding the “quadrinity” is not as nice and neat as Choi would like it to be and as such, Choi fails to understand the organic nature of worldviews.

Again, of course Fristianity might be incoherent, but it is the duty of the TAG to establish this outright. Should the TAG be wholly successful, one could establish today that all future worldviews will fail. If the TAG cannot make this claim, it can be dismissed by mere pragmatism and a denial of its claim to omnipotence.

Argument #4: Argument from Invalidity

Jason Streitfeld, in 2008, published an argument against presuppositionalism. For the purpose of this argument validity does not refer solely to formal validity as petitio principii is an informal fallacy, but no less an egregious error of reasoning. With that said, “valid argument” refers not only to the formal validity but the informal validity as well:

(13)    All valid arguments do not beg the question

(14)    All knowledge presupposes the existence of God [Presuppositionalist premise]

(15)    If one presupposes the existence of God in an argument, one begs the question against atheism

(16)    All valid arguments presuppose knowledge

(17)    All valid arguments beg the question against atheism

(18)    But then, all valid arguments beg the question

(19)    But this is absurd and either (13) or (14) must be rejected

To this argument Paul Manata, a defender of the presuppositionalism offered an objection. Primarily, the objection was a series of parodies which replaced that which was claimed as being presupposed (note that I have replaced valid with sound for specificity):

(13*) All valid arguments do not beg the question.

(14*) All knowledge presupposes the existence of knowledge.

Global skepticism (e.g., the former Unger) may here be defined as any explicit or implicit denial of the existence of knowledge.

Thus, if one presupposes the existence of knowledge of in an argument, one begs the question against global skepticism.

Now consider that all valid arguments presuppose knowledge.

Combining this with the second claim above, we find that all valid arguments presuppose the existence of knowledge.

Therefore, all valid arguments beg the question against global skepticism.

Therefore, all valid arguments beg the question.

This contradicts Streitfeld’s first claim. Therefore, at least one of the two claims is invalid.

To avoid contradiction, Streitfeld must abandon one of his two claims.

To this objection Streitfeld replied:

It does not make sense to say “all knowledge presupposes knowledge.”

A proposition cannot presuppose itself. That is, if X presupposes Y, then Y does not equal X. So the statement “knowledge presupposes knowledge” is just wrong.

Perhaps the idea you had in mind was more like this: For every true proposition X, there exists some true proposition Y, such that X presupposes Y. Let’s call this idea A.

Maybe you don’t want to postulate A. Maybe you do. But let’s say you do, for the sake of argument.

I could list a number of reasons why A is not a valid defeater for my argument, but I will mention only one—one which your own position binds you to accept

First, let’s go over the logic of presuppositions for a moment.

Again, as I noted, a proposition cannot presuppose itself. That is, if X presupposes Y, then Y does not equal X.

Furthermore, if (X presupposes Y) and (Y presupposes X), then X and Y are identical.

As a presuppositionalist, you maintain that all propositions presuppose that God exists. In other words, for all propositions X, X presupposes that “God exists.”

Of course, X cannot contain the proposition “God exists.” So, we can restate it as follows: For all propositions X (such that X is not “God exists”), X presupposes that “God exists.”

We can also add that the proposition “God exists” does not presuppose any other proposition. For, if it did, it would be equivalent to that proposition, and so would presuppose itself—an impossibility.

Now, you say that you know God exists. This means there is some proposition, the knowledge of which does not presuppose any other proposition. This means you cannot use A as a defeater for my argument.

I agree with this analysis from Streitfeld though I do not think that Manata has come to accept it. Of course, the presuppositionalist will perhaps state that all arguments for epistemologies beg the question. Then surely it stands to reason that there can be no sound arguments for epistemologies. That entails then, that there can be no sound argument for presuppositionalism and no, non-question begging way for the presuppositionalist to argue against atheism.

Of course, one can claim that such an argument can be used on atheism and state that all arguments beg the question against presuppositionalism (insofar as they assume that God does not exist). But as Streitfeld accurately notes, the atheist is not solely committed to the denial of God as traditionally understood. Should an atheist be more accurately defined as an Ignostic (theological non-cognitivism) and accept that a coherent definition of God must be presented prior to meaningful discussions on God and that such has not yet been accomplished, then the Argument from Invalidity as applied to Ignosticism (and any atheists within) fail.

Conclusion

If any of the above arguments are sound one can safely conclude that Presuppositionalism has been defeated and subsequently that logic does not presuppose the existence of God in the manner espoused by presuppositional apologists.

I have received some feedback on my previous article, The Case Against Presuppositionalism. I have decided to outline some received objections and deal with them accordingly. If you have not done so already, you should read the previous post before continuing.

I presented quite a lengthy criticism of presuppositionalism in my previous post and I am operating under the assumption that you have read the material. As such, I will condense and reformulate my arguments and answer some received objections afterwards:

Argument #1: That logical principles are not contingent on God

(1) Logical principles are either dependent on God or not dependent on God (premise)

(2) Logical principles are dependent on God if and only if (i) logical principles are created by God or (ii) logical principles are part of God’s nature (premise)

(3) If logical principles are dependent on God they are not logically necessary, they are contingent (premise)

(4) It is logically necessary that the principles of logic be necessarily true (premise)

(5) Therefore, the principles of logic are necessarily true (from 4)

(6) If the principles of logic are necessarily true they are not contingent (premise)

(7) Therefore the principles of logic are not contingent (from 4, 6)

(8) Therefore logical principles are not created by God nor exist as part of God’s nature ( from 2,3,4,5,6,7)

(9) Therefore, logical principles are not dependent on God

The above argument is a summation of many points in my previous article and shows the absurdity in claiming that logical principles depend on God for their existence.

The deduction proof is:

1. G(l) v ~G(l) (tautology)
2. G(l) <-> (Cr(l) v Na(l))
3. G(l) -> (~N(l) ^ C(l))
4. N(T(l))
5. T(l) conclusion
6. T(l) -> ~C(l)
7. ~C(1) conclusion
8. ~Cr(l) ^ ~Na(l)
9. ~G(l) conclusion

Argument #2: That presuppositionalism presumes an Ontological Argument

(1′) Logical principles are either dependent on God or not dependent on God (premise)

(2′) Logical principles are dependent on God if logical principles are part of God’s nature (premise)

(3′) If logical principles are a part of God’s nature there can be no logical principles if God does not exist (premise)

(4′) If there are no logical principles without the existence of God the proposition ‘God does not exist’ entails that the LNC fails (premise)

(5′) There is a possible world, w1, in which God does not exist (premise)

(6′) In w1 the LNC must hold as logical possibility is determined by the LNC (from 5)

(7′) It is the case that in w1 the LNC holds even though God does not exist (from 5,6)

(8′) Is not the case that logical principles are dependent on God

This argument is sound insofar as (5′) is true. If the presuppositionalist wants to assert that (5′) is false, they MUST present an Ontological Argument which exemplifies that God exists necessarily (that he exists in every possible world), they may not merely assume that conclusion.

Argument #1: Objections and Replies

1. Even if logic is part of God’s nature it is still logically necessary

It simply cannot be the case that logic is both contingent upon God’s existence and logically necessary, it MUST be one or the other. It seems to be the understanding of presuppositionalists that nothing can exist independently of God but this is a very elementary mistake in the philosophy of religion as logically necessary abstract objects MUST exist independently.

To quote Keith E. Yandell

“It is logically consistent with monotheism that there exist abstract objects that possess logically necessary existence. Abstract objects have no causal powers, are not self-conscious or even conscious and exercise no creation of providence. They are of little if any religious interest. It is a necessary truth that if X has logically necessary existence then there is nothing Y such that Y is distinct from X and X depends on Y for X’s existence. So if ‘there are abstract objects that have logically necessary existence’ is true, it is also true that there exists something whose existence does not depend on God. God’s status as Creator and any coherent notion of divine sovereignty, does not require that something that cannot depend for its existence on anything else depend for its existence on God or deny that the existence of such things is logically possible. But the only candidates for being something of this sort would seem to be things that exist with logical necessity.” (Philosophy of Religion: A Contemporary Introduction pg. 373, Keith Yandell)

As Yandell says:

It is a necessary truth that if X has logically necessary existence then there is nothing Y such that Y is distinct from X and X depends on Y for X’s existence

As such:

It is a necessary truth that if logic has logically necessary existence then there is no God that can exist distinct from logic and it be the case that logic depend on God for its existence

One might argue that Yandell’s statement does not apply here as it was not asserted that logic and God exist distinct from each other but rather that God’s nature is logical. This simply characterizes yet another misunderstanding of logic. Logic is not attributable to one being or concept but rather only to the relationships between two or more concepts or arguments. Thus, whereas it may be possible that when God’s nature is analyzed, it is coherent and orderly this is not to say that God’s nature IS logic. In fact, it is to say something wholly different.

Assume a situation where God performs an action, A. God’s action must presuppose the LNC as God cannot do act A and not A at the same time. God cannot also have property P and not P at the same time. In this respect, it is the case that God’s nature corresponds to necessarily existent logical principles. So whereas God MUST presuppose logic, it is not clear that logic presupposes God, rather we have good reasons to reject that logic presupposes God.

Argument #2: Objections and Replies

1. This entire possible world matter is just silliness

Possible world semantics (or modal logic) is simply a form of reasoning to discern logical necessity/contingency. The fact that we say there is a possible world where X does not mean that there is an actual world where X, merely that X could possibly be the case (even though it might not be). For an easy to understand overview: Modal Logic on Wikipedia

2. The premise, (5′), can be shown to be false from the mere fact that without God you cannot prove anything!

This is, of course, the precise issue being discussed and so one should not beg this question. However, it is not the case that if without God nothing can be proven, God must exist necessarily. Such an argument:

(1”) Without God, one cannot prove anything

(2”) Therefore God exists necessarily

is a complete non-sequitur.

Why must God exist in all possible words because without him, nothing can be proven? There can exist a possible world in which there is nothing to be proven and as such, according to the criteria assumed by such a formulation, God would not exist in such a world or his existence would be arbitrary.

Non-argument specific: Objections and Replies

1. You still have not accounted for logic

The notion of “justifying logic” is a peculiar one. It is clear and evident that logical principles exist as logically necessary abstractions, furthermore, logical principles are axioms and as such they are not subject to any proof or justification outside of themselves.

(10) If something needs justification/accounting from an external source that thing is logically contingent and not logically necessary

(11) The principles of logic are logically necessary

(12) The principles of logic are not logically contingent (from 11)

(13) The principles of logic do not require justification/accounting from an external source

It is difficult to see what is even meant by “justifying/accounting” for logic.