Does Logic Presuppose Christianity? — Part 3: The Ontology of Logic

In the introductory post to this series, we noted that the justification of the Van Tillian argument from logic can generally be categorized into: (a) the ontology of logic, (b) the epistemology of logic, (c)the ethics of logic, and (d) the relation of logic to fact. In this post, we will be examining the ontology of logic.

The justification in this case is that logic presupposes Christianity because the non-Christian systems of thought cannot, metaphysically speaking, account for logic. We find this line of reasoning in Bahnsen’s debate with Dr. Stein:

The transcendental argument for the existence of God, then, which Dr. Stein has yet to touch, and which I don't believe he can surmount, is that without the existence of God it is impossible to prove anything. And that's because in the atheistic world you cannot justify, you cannot account for, laws in general: the laws of thought in particular, laws of nature, cannot account for human life, from the fact that it's more than electrochemical complexes in depth, and the fact that it's more than an accident.

The point here is that there is some metaphysical inconsistency between an atheistic world and laws of logic. Basically, laws of logic would not exist in an atheistic (non-Christian) world. Critics of the argument have often claimed that there is some ambiguity around the phrase “account for”. It is asked what exactly it means to “account for” logic and what would an account of logic look like.

To account for logic would simply be to make the existence of laws of logic consistent with one’s metaphysical theory. It involves resolving any tension between one’s metaphysical theory and laws of logic. But why does any tension arise in the first place? To answer that question, we must consider the ontology of logic.

The Ontology of Logic 

In order for laws of logic to play the role which they are, intuitively, thought of as playing in our experience, they most possess certain metaphysical properties. Dr. Bahnsen notes:

The laws of logic, you see, are abstract. As abstract entities, which is the appropriate philosophical term, not spiritual - entities that Dr. Stein is speaking of - abstract entities - that is to say, not individual (or universal in character). They are not materialistic. As universal, they are not experienced to be true. There may be experiences where the laws of logic are used, but no one has universal experience. No one has tried every possible instance of the laws of logic.

As invariant, they don't fit into what most materialists would tell us about the constantly changing nature of the world.

Bahnsen says here that laws of logic are abstract, universal, and invariant. As abstract, they are not individual or particular in nature; they cannot be narrowed down to any particular instance or spatio-temporal location. As universal, they apply regardless of time or space; they cannot be experienced to be true because that would require universal experience. As invariant, they are not subject to change; they are fixed. We could also add that laws of logic are normative; they are standards of reasoning and they prescribe how we ought to think (more on this in part 5 of this series). Laws of logic are also necessary; that means they are not contingent. Furthermore, logic requires both metaphysical unity (unifying principles, relations and systems) and metaphysical diversity (plurality of propositions).

And if they possess these properties, then they do not just fit into any metaphysical picture. They are inconsistent with the unbeliever’s worldview. (In this case, Dr. Bahnsen’s debate opponent was a materialistic atheist). They are inconsistent because a materialistic universe does not allow for immaterial or abstract  entities. Hence, if laws of logic are abstract and universal, then they cannot exist in a purely materialistic view of the world. 

The only way the materialist can account for laws of logic is to strip them of the aforementioned metaphysical properties. In this case, Dr. Stein opted for a conventionalist account of logic, claiming that they are merely man-made conventions. Dr. Bahnsen then proceeded to argue why such an account is philosophically unsatisfactory. From this, we can get an idea of how the argument proceeds.

First, the apologist notes certain properties that logic must possess in order for the unbeliever’s appeal to logic to make sense. (In Dr. Bahnsen’s case, Dr. Stein appealed to logical binds and contradictions which indicates that he believed them to be unchanging standards of reasoning; he also admitted that they are not material). Secondly, the apologist must identify certain inconsistencies between the properties of logic and the unbeliever’s metaphysical theory. In order to resolve the tension, the unbeliever must deny one or all of the aforementioned properties of logic. The apologist, then, must always bear in mind that there are devastating consequences for denying any of logic’s properties.

Denying the abstract nature of logic makes them concrete entities. This means that one can go out into the world and observe laws of logic as they are. This is not only counterintuitive, but it strips logic of other important properties as well. Denying the universality of logic renders it inapplicable in certain contexts. If laws of logic are not universal, then we cannot be confident in our application of them beyond the narrow domain of our experience; they cease to be applicable to the future, unobserved past, possible worlds, etc. Denying the invariance of logic renders it useless as a standard of rationality. If laws of logic could constantly change, then logic loses its truth-preserving nature. Denying the normativity of logic strips them of their binding on human thinkers; all thinking becomes equally valid/correct because there is no standard by which one can differentiate rational thought from irrational thought. Every man is free to think however he wants.

All non-Christian accounts of logic deny one or all of these properties. In doing so, the non-Christian destroys logic’s intelligibility and usefulness. We can look at some unbelieving accounts of logic to illustrate this.

The Conventionalist Account

This posits that laws of logic are merely man-made conventions. This was the account Dr. Stein proposed in his debate with Dr. Bahnsen. However, as Dr. Bahnsen pointed out, if laws of logic are merely conventional in nature, then we could have different societies with different laws of logic. Logic loses its universality, invariance, and normativity. In theory, one can simply come up with his own set of laws and reason accordingly. Given logical conventionalism, one cannot say he’s wrong or irrational in doing so.

Human Conceptualism

This account states that laws of logic are merely concepts that originate in the human mind. A variation of this view conceives of logic as the by-product of electrochemical processes in the human brain. However, since human minds are finite, particular, and contingent, logic loses its universality, invariance, necessity, and normativity. Since different brains have different electrochemical processes that occur within them, then different brains would produce different laws of logic. Furthermore, the laws of logic produced in one mind is not in any way binding on other minds. Since human minds are not universal, they cannot produce laws of logic that are universal in scope.

Platonism

This account treats laws of logic as real objects that exist in what has been called the world of Forms or Ideals. On this view, logic is abstract, universal and invariant since it does not participate in the changing, temporal world. On this account, it seems the abstractness, universality, invariance, and necessity of logic is preserved. However, logic loses its normativity. Human thinkers cannot be bound to abstract ideals. If laws of logic are so abstract and transcendent as to be confined to another realm, then they have no bearing upon human life and we are not obligated to follow them. Obligation only makes sense in the context of inter-personal relations. 

A Christian Account of Logic 

On the Christian view, the absolute archetypal rationality of the Trinitarian God provides the basis for logic. Logic, as we conceive of it, is simply a reflection of the original Coherence in God Himself. God is the Archetype, human logic is the Ectype. We, as creatures, can only hope to mirror the original coherence and rationality that exists within the Persons of the Trinity. God expects us to emulate Him on a creaturely level, hence he has given us logic which mirrors His original coherence and wisdom. Logic is therefore ultimately personal given a Christian view of things. Because we are created in God’s image and expected to emulate God, we are obligated to think logically and rationally. Laws of logic are invariant because God’s internal coherence is unchanging. Laws of logic apply universally because God is not bounded by space or time. The abstract nature of logic comes from the fact that it merely reflects God’s original internal rationality which is otherwise inaccessible to us.

Only a Christian metaphysical picture can provide a suitable foundation for logic. The Trinitarian God of Christianity provides both unity and diversity. There is both unity and diversity in God and neither one takes metaphysical priority. Since logic reflects God’s own nature, then there must be both unity and diversity in logic. Since every non-Christian worldview rejects the Trinitarian God, every non-Christian worldview ultimately fails to account for logic.