Does Logic Presuppose Christianity? — Part 6: The Relation of Logic to Fact

In part 4, we discussed the epistemology of logic. There we noted briefly the issues regarding the relation of logic to facts. Here, we shall expand on those issues.

First of all, we must note that our logical systems are only useful to us as long as we can use them to gain knowledge of the world. We use logic to navigate the world, make sense of our experience, reason, and gain knowledge. A logical system that can yield no knowledge of facts is not very useful to us as knowers. If all our logical systems were good for was abstract proofs, that would not help us at all in gaining relevant knowledge. Logic is seen as a way for us to extend our knowledge. By logically manipulating the facts which we know, we can come to conclusions and new information. There is an assumption in the above line of reasoning that we must take note of, however. We have assumed that there is some sort of correspondence between our system of logic and the system of facts which exist independent of our minds. We have taken for granted that our system of logic actually tracks the system of facts. We have also taken for granted that there is a system of facts. 

What is a system of logic? A system of logic consists of certain truths, relations, and rules guiding those relations. For example, a system of classical logic has relations such as negation and implication. These are relations between truths. It also has rules such as the law of excluded middle or modus ponens. These rules determine how truths can be manipulated in that system. We can make certain observations about the nature of logical systems: (a) they are formal and abstract; they do not deal with particular truths but rather they provide general rules and principles, (b) logical relations are timeless and unchanging; the relations between a proposition and its negation, for example, do not change over time.

What is a system of fact? We may conceive of facts as states of affairs in the actual world. For the purpose of this article, we may restrict ourselves to facts about the world of experience since these are the facts which we aim to know. It is usually taken for granted that facts are related to each other. Facts are related to other facts which are in turn related to other facts and so on comprising a comprehensive, unified system. However, unlike a system of logic, a system of facts is not formal or abstract,  neither is it timeless or unchanging. The facts of the empirical world are subject to change with time. Things go in and out of existence, objects share atoms with each other, things mix and combine forming new objects, etc. In short, the world of facts is not characterized by the same unity, continuity, rigidity, and timelessness as the system of logic. The world of logic is characterized by strict timeless relations with well-defined boundaries and rules. The world of fact is not like that; boundaries between objects are fuzzy and there are no timeless relations - things constantly change.

If this is the case then we have a problem. If the system of logic and the system of facts are so radically different in nature, on what basis do we assume that there is a correspondence between them? The thoughts of Cornelius Van Til come to mind. He says:

By your own standards it can never have anything to do with reality. Your logic claims to deal with eternal and changeless matters; and your facts are wholly changing things; and “never the twain shall meet." So you have made nonsense of your own experience. [emphasis mine]

Van Til, Why I Believe in God

Our systems of logic are internal to our minds. Our minds and the way we reason may be based on logical structures. However, there is no reason to think that the world of experience and fact has to conform to this system of logic in our minds. Of course, we cannot, by the powers of our own minds, legislate for reality. Hence, the world of facts need not conform to our system of logic. Furthermore, the facts need not be related in any way, especially if we deny the existence of a sovereign personal God who controls the world. Why think that there is a system of facts? For all we know, the world is made up of purely unrelated and disjointed facts. If this is the case, then our system of logic is utterly useless with regards to gaining knowledge of the world. One cannot logically manipulate unrelated facts. The point here is that the world has to be a certain way in order for our system of logic to be useful in gaining knowledge of facts.

Let’s consider the following logical argument:

1. All men are mortal

2. Socrates is a man

3. Therefore, Socrates is mortal

The above inference is an instance of a more general rule of inference:

1. All A’s are B’s

2. C is an A

3. Therefore, C is a B

In this rule of inference, the relations between the premises and the conclusion are strictly timeless and unchanging. The individual terms (A, B, and C) are well-defined and logically related. This is the timeless continuity of a formal system of logic. However, we cannot say the same thing about the world of facts (consisting of men, mortality, Socrates, etc.) which this rule of inference is being applied to. If there is no relation whatsoever between objects in the world, then there are no objects which share similar properties (like mortality); every object would be wholly individual and distinct. There would also be no basis for grouping any set of objects under the unifying  class of “men”. Such a world makes logical inference impossible. Logical relations would only obtain in the timeless and unchanging realm of logic and would have no bearing on the realm of experience and facts. What this shows is that logic and fact are not necessarily related and in order for human use of logic to be possible, there must be something to facilitate a fruitful connection between them.

The Christian worldview provides this fruitful connection. Like we have mentioned in previous installments of this series, both logic and fact have their source in the Triune God of Scripture. Unbelieving systems of thought would always leave logic and fact in pure abstraction from each other. However, given the Christian system, logic and fact can be meaningfully brought together. God orders the world of facts to reflect the comprehensive system which eternally exists in His mind (a system which also serves as the archetype for a human system of logic). Hence, there is a necessary correspondence beteeen logic and fact. Logic presupposes Christianity because without its metaphysical picture, there can be no meaningful connection between logic and fact.