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.

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.