Authored by: Mitchell LeBlanc.

Author’s Note: This post is part of a series which has culminated in a scholarly paper on the topic. As such, I kindly ask that any criticism of the subject matter therein is given with a cognizance of the most recent material on the subject.

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.