An Informal Introduction to Covenantal Apologetics: Part 27 – Logic and the external world.

By C.L. Bolt

We have discussed a number of skeptical arguments illustrating the impossibility of the contrary. One of the more popular arguments for the impossibility of the contrary in presuppositional apologetics is based upon concerns in the philosophy of logic. Traditionally the topic of logic comes up almost immediately, often because the Christian finds it particularly rhetorically powerful to ask the non-Christian difficult questions about a perhaps mysterious topic that calls into question the very foundation of the non-Christian’s entire thought and presentation. However, the philosophy of logic is a difficult area and its discussions can become complex quickly (so quickly that I hesitate to write this part of this introduction). In my opinion, it is unfortunate that arguments from the philosophy of logic are so quickly employed by the apologist to the neglect of so many of the other illustrations of the impossibility of the contrary that we have been considering and will continue to consider. Nevertheless, the non-Christian can no more account for logic then she can for anything else.

Those who have become accustomed to responding to this argument ask, “What are the laws of logic?” By this they offer either a semantic quibble, or a misunderstanding of the argument. By offering a semantic quibble, I mean that whether we make reference to the “laws of logic” or “principles of logic” or “rules of inference” or whatever else that we are still essentially asking the same sorts of questions from the non-Christian. Perhaps to be fair and clear we should speak of “logic”. We do not limit our understanding of logic to particular laws of logic or classical logic anymore than the non-Christian does, and here is where the misunderstanding of the argument comes in. When the non-Christian asks, “What are the laws of logic?” and is not engaging in semantic quibbling, then the non-Christian has overlooked the very point in question. The non-Christian is being asked about or challenged on the answer to this question. Philosophy of logic pertains to the nature of logic itself. What is logic? The Christian and the non-Christian should ultimately have very different answers to this question.

In a Christian worldview logic reflects the thinking of God. God is our standard for everything including reasoning itself, and God expects us to think in particular ways that may be expressed through logic. Through appealing to logic understood within the context of the Christian worldview we demonstrate that we have answers to general questions concerning universal, invariant, abstract entities such as particular laws of logic like the law of non-contradiction. If we are to be like God in the obligatory rather than sinful sense, then we are to have the same sort of consistency and coherence in our thought that is in God’s. We are, as the popular phrase goes, to “think God’s thoughts after Him.”

Logic does not serve as a sort of otherworldly, divine mediator between God and the world. Rather, human logic belongs to the created order. It may be helpful to think of logic as analogous to morality (which we will discuss later). Morality is revealed with respect to the creature. Similarly, logic is normative; it is binding with respect to creaturely human thought. We may be further helped through this analogy by considering logic as decreed in accordance with the nature of God as it is with moral law. God knows propositions truly such that consistency exists between them. Logic is created upon the whole of the sets of relationships of the aforementioned consistency. God exists apart from His creation, and there is no inconsistency within God. Hence it is a mistake to suggest as some have that God might exist and not exist at the same time and in the same respect if the law of non-contradiction is a part of the created order.

It follows from what we have said that logic, just like morality, is inherently personal in the Christian view. The non-Christian will no doubt cringe at the thought of having even her most abstract thoughts inextricably tied to the personal God. We may also now consider logic in another sense. Logic, like love, justice, righteousness, wrath, and all of the other attributes of God, is related to God as an attribute best understood through the doctrine of Divine Simplicity. We should nevertheless take care to draw the distinction between the thoughts of God and our own thoughts. There is a Creator/creature distinction even with respect to what we as Christians mean by logic.

Now that we have given a brief account of an understanding of logic from the Christian worldview, we must turn our attention back to what was supposed to be the topic of this discussion, namely, the non-Christian understanding of and justification for logic. If what we have provided above is an understanding of logic available to the Christian, then the non-Christian will, as already mentioned, have an exceedingly different understanding of logic.

Of course we are already mistaken if we think that there will be only one different understanding of logic on the non-Christian view, for there are many different understandings of it. This point is not stated in lieu of or as constituting an argument in and of itself, but rather in order to emphasize for subsequent discussion that there is no one universally agreed upon understanding of what logic is. If the non-Christian wants to reject that she has anything like logic in her worldview, then we might just assume that she is saying that she does. If she wants to talk about her own view of logic, then we are on to something, for then we can begin to illustrate the impossibility of the contrary through the unbelieving rejection of the Christian worldview and its resulting problems concerning logic.

When we ask the non-Christian about logic then, we are not attempting to critique the non-Christian worldview through imposing our own understanding of logic upon it. We are, rather, performing an internal critique based upon the information provided by the non-Christian about this foundational feature of human reasoning and intelligibility. What is logic, and how is it justified?

It is readily apparent to most that a materialist view will not allow for an account of logic given that logic is not material. To merge logic with the material realm by making the two one in the same is to render logic contingent; ever changing, particular, and descriptive rather than invariant, universal, and normative. When we think of something being “contingent” we should think of something that is not necessary; it is ever changing and dependent upon other entities. If logic were material then it would constantly change, come into, and go out of existence as frequently as other material entities. There would be no sense in which logic would serve us in terms of our reasoning. Moreover, a particular principle of logic sitting on the branch of a tree might pertain to something near the tree but would have nothing to say about the man on the submarine. If the tree were trimmed we might even lose the excluded middle if that were the logical principle sitting upon the branch. Finally, the law of non-contradiction would cease to be a law at all, since we are in no way obligated to impersonal material entities like we would have on this view. For these and other reasons not mentioned here, we simply cannot accept a materialist position concerning logic.

We have spoken of the problem of skepticism as a problem of connection. It is no different when we come to logic. The worry of the philosopher of logic is to bring logic into contact with the contingent, material realm without sacrificing the law-like nature of logic or its applicability to the contingent realm. Already people will disagree with me here, but this is to be expected. There are consequences for rejecting this understanding of the matter, and one must learn to exploit these consequences to the full. We have looked at materialism as a first example of attempting to bring logic into conversation with the contingent realm, and found that making logic a part of that contingent realm results in rather absurd consequences.

The type of evidence that is brought to bear upon the truth value of some proposition concerning logic will be determined by one’s view of logic, and as we emphasized before so we will emphasize again that there is no one universally agreed upon understanding of what logic is. Different types of truths are justified in different ways, and logic is certainly no exception. Even the given of the differences between the different sciences serves to corroborate our point, since practitioners of these disciplines cannot perform in fields that they have not been trained in to the same extent that they can in their respective fields. We must ask ourselves not only what evidence a person has for believing some particular point or view about logic, but what kind of evidence it is, and if it fits in with that individual’s worldview as a whole. A person who believes that logic consists of inferences that are conceptual judgments will view these matters differently from a person who thinks logic is merely a term given to particular brain activity. When features of logic like universality, abstractness, and invariance are sacrificed to the presuppositions one holds as an integral part of a worldview there are consequences which follow with respect to the worldview and the apologetic discussion itself which must be taken into account and sifted through to test for consistency.

For example, if logic is justified apart from experience (a priori) then we must still ask why logic applies at all in the contingent realm of experience. There is a problem of connection. While in the Christian worldview God imposes logic upon the contingent realm there is no such imposition of order or norm in a non-Christian or non-theistic view. Even if the connection were there the question would immediately be raised as to why some unchanging a priori truths like those of logic continue to apply in an area where everything is in constant change.

As another example, suppose that logic is allegedly justified by appealing to experiential and observational data so that we experience some phenomenon over and over again and then make general statements on the basis of this repeated experience. Unfortunately it is difficult to imagine how this might play out in actuality. Learning or creating logic by way of “experiencing” it in its particular manifestations in the contingent realm of experience is problematic, and the complexity of some logical relations makes it dubitable that logic of this nature has ever been experienced in this manner at all. This potential worry aside, note that tying logic to contingent experience contextualizes logic to the extent that it cannot be applied to anything which has not been experienced. Again, there is a problem of connection. Most notably, logic is no longer taken to apply to the future or the past, much less to “possible worlds” where there is no contingent experience. On this view logic is no longer necessary, universal, or invariant, and deeper considerations of these consequences render the view unusable and harmless in a context like the apologetic encounter.

An increasingly popular view concerning logic is that it is merely conventional. This view is immediately non-intuitive and suggests that there could be many various conventions upon which or within which we find particular logics. Again we may point out analogous problems with a conventional understanding of ethics. For example, if logic is merely convention, then surely it is also culturally relative, much like what some people have suggested concerning morality. But then all of the problems of moral relativism, which will be discussed later on in this introduction, come into the picture and create problems for the advocate of a conventional account of logic. Completely contradictory systems (whatever that means!) of logic might be considered equally valid, sound, rational, etc. Of course it also follows that logic is largely if not completely arbitrary and stipulative. But even setting these aside, if logic is merely conventional, then one must ask by what right we ever think they could or should be applied to our contingent realm of experience.

While arguments pertaining to logic and the non-Christian worldview can in some encounters be helpful, fruitful, and successful, the apologist must take care to describe his own position in a consistent manner while representing the contrary position fairly and making sure that his critiques of that position do not fall back on his own. In my opinion, this is extremely difficult and better left up to those more familiar with the philosophy of religion and the philosophy of logic, but at the very least we have shown that things are not always so simple and straightforward with respect to the nature and justification of logic as people sometimes think, and hence there is plenty of room for the covenantal apologist to go to work concerning those topics that may have provoked a “matter-of-fact” appeal to logic in the form of an objection from an unbeliever. Finally, it is often the case that inconsistencies and errors regarding logic and the non-Christian worldview are immediately knowable, and it is best not to let such inconsistency and error remain unaddressed. 

< Previous | Next >


3 Comments

VazScep

This is the best article I’ve read on the matter of logic and what I understand of presuppositionalism, and clears up a lot of my confusion. Great stuff!

One point: when I ask “what are *the* laws of logic?” I am not trying to quibble. The way I understand logic doesn’t leave much room for asking about *the* laws or *the* inference rules in such a general way. And questioning specifically the three classical laws is a point I do frequently because I consider them particularly banal: I’ve never used the principle of non-contradiction in a formal proof, and think there are very elegant ways to unfold the principle into something less law-like and much more pragmatic. I don’t care for the law of excluded-middle, and am not convinced that it is “true”. Finally, I’ve used fully workable formal systems where the law of identity is rejected because it is believed that most people’s reasoning doesn’t use such a law.

Anyway, if a conversation begins with the question “how do you account for the [three classical] laws of logic?”, I know I am engaging with someone who doesn’t understand logic as I do, and doesn’t have my experience of formal logic. That puts a serious strain on communication, and I’m left not knowing how to answer the original question. But if, as you suggest, I should start from the beginning, and give my understanding of logic in full, rather than trying to answer curt questions about the three classical laws, then I may well make some progress!

pat

How would you respond to an atheist who says the laws of logic are axioms of existence?

defectivebit

This is a better question for the chat channel than the comment box. But I would simply ask him why he/she accepts those axioms to be the way reality is simply making the laws of logic axioms commits oneself to some epistemological and metaphysical presuppositions.


Leave a Comment