by Scott Cherry
The law of causality is one that we must live by whether we like it or not. Everything we do and see had to have some kind of causal factor, and it will also have some kind of effect, positive or negative. That’s why our individual decisions are so important, as well as the collective ones of people. Sociologically, life and all things in society revolve around this fundamental axiom. Even our language depends upon it, which is evident every time we ask “Why?” or say “Because”. But this is not the only one in operation.
Note: I am well aware that Scottish philosopher David Hume (1711-1776) disputed the law of causality because, he asserted, it is not possible to prove the contingent relationship between effects and their apparent or possible causes. However, I find his position to be incredulous, as I think most people do. At the very least we must live by faith as though this law of causality is operative, and we can be quite certain that Hume did too. Indeed, to somehow suspend our belief in this axiom would make living impossible. And without it neither rational thought nor any semblance of science could take place.
Doubtless you affirm other axioms from my list, and perhaps some that I omitted. I would wager that you affirm at least half of them. Now, let’s consider the fundamental Law of Logic itself, including the Laws of Validity and Deduction together. These are points 3 and 4 from the list of axioms above:
3. The Law of Validity: Some kinds of reasoning are valid and some aren’t. A person’s reasoning can be analyzed and determined as valid or invalid based on the rules of reason and the laws of logic. It’s not uncommon for a person’s argument to be invalid, but this must be detected.
4. The Law of Deduction: A conclusion must always follow from its premises. Any argument may be valid or invalid (i.e. do the premises relate?), true or not true. A valid conclusion must have premises that lead to it, though it may still be false. It is only true if all the premises are true.
First, I expect number 3 to go unchallenged entirely, it’s that basic. I have alluded to this idea many times already: Good reasoning is like good math, it must obey the laws of logic. To me, this fact alone is impressive if not staggering to the mind. Why there is such a thing as good and bad reasoning that must conform to certain laws or rules is quite inexplicable in materialistic terms. (By materialistic I mean that view that rejects the metaphysical realm and any kind of metaphysical order. By metaphysical I mean that layer or dimension of Reality that is non-physical, invisible, intangible, and many say spiritual, as I do.) Again, logic is highly analogous to math, which simply is. For that matter, logic is also analogous to order, to life, to language, and to existence itself, all of which just are. As often as we depend on logic (and all these things) we can neither identify its source nor make up our own rules for it. We can only discover and utilize it. Indeed, we must, for not to do so would lead only to chaos, and nobody wants true chaos, not even anarchists. All this should be very telling. It should tell us that there is an invisible dimension of Reality that contains an order which we can recognize and to which we are completely subject. This is the Logos. That we can recognize and utilize it can only be an enigma to materialists, but to theists it is properly basic: There is a metaphysical mind from which the Logos proceeds.
Let’s drill deeper into the Law of Validity, which is logic itself. When a person forms an argument (even if only mentally) for or against something—formally or informally, consciously or unconsciously—there are always premises that lead to a conclusion, which can be explicit or implicit. And usually there must be supporting evidence for the premises. Every argument is either valid or invalid, based on these rules of thinking. What does that mean? Most of us have an intuition about it, even if we cannot express it well. It means there is a prescribed and necessary order to rational thought that must be employed in thinking and communicating. It means that some ideas follow reasonably (or relate, or connect) from other ideas, and some do not. If they do follow, then we call that reasoning or flow of ideas “valid”. If they do not we call that a non-sequitur. For example, if I say “My car has a good engine and my dog needs a flea-bath, therefore broccoli is the healthiest vegetable” we know intuitively that this is a non-sequitur. There is no logical flow of ideas here and the complete thought is nonsense. The first two ideas are the premises which may be entirely true; the third part is the conclusion, which may also be true. But premises are neither related to each other, nor do they lead to the conclusion. Thus we all recognize this complete thought as a bad one. It is invalid and it makes no sense, rather because it makes no sense. So what we are seeing the demands of the Law of Validity in action.
To correct a bad thought, or argument (which is expected), we must make the ideas or propositions of an argument conform to the Law of Validity. There might be several ways to do it. In this example we can probably only retain one of the ideas and get rid of the others. We might say, “My car has a good engine, and a good engine is the most important feature of a used car, therefore this is a good car to buy.” In this case the full idea, or the argument, is a completely reasonable one, so we say it is valid in a formal sense. Of course, the premises must also be true in order to lead to a true conclusion, but it can be valid without being true. If in fact the car does not have a good engine, the argument is valid but not true. That is why we would need some kind of evidence for the first premise about the engine.
All of us expect someone’s reasoning to be both true and valid; there are no exceptions. I think that’s really interesting. In other words, if someone is going to convince me of something they must form a true and valid argument, or at least one I believe to be true and valid. By argument I do not mean a verbal quarrel but a set of propositions, or premises, that lead to a conclusion. For every argument we expect both true and valid premises. It’s like math. With respect to the former, if you know any of the premises of my argument are not true, you will reject my argument as a whole. You’ll be unconvinced because you naturally expect and demand true premises. In all good reasoning you know they are non-negotiable. The truth value of one’s premises is fundamental and axiomatic to the function of reason, so much so that I doubt you could believe an argument for which you knew one or more premises to be false. This applies equally to the validity. If you know the form of my argument (i.e. valid premises that lead to a conclusion) is not valid you will reject it even if the premises are true. As in a mathematical equation all the parts have to be correct. The propositions, or premises, must be both true and valid.
But it’s the expectation of validity that is the focus of our attention here. Let me illustrate this with a story about my son Cameron in which this idea was very poignant. When I wrote this particular section he was 18 and close to the end of his senior year in high school. One night in the kitchen I was having an intense discussion with him about his lackluster performance in the AP Lit class he was taking. Cameron is very smart but he did not like the class at all, and he saw no reason to invest any more effort than the bare minimum required to pass. I was of the opposite opinion and I was trying to convince him of the merits of literature and why he should apply his full potential. I gave him my best fatherly arguments, but at one point he said, “Dad, that is not even valid!” So I reconsidered my premises. Wow, I thought, is he right? I was indignant, but that’s not the point.
What is the point was his expectation of rational validity on my part. He wasn’t questioning the truthfulness of my premises, but rather their validity. Cameron apparently believed that my premises did not lead to my conclusion, so even if they were true my argument failed to convince him. It was invalid, or so he thought. I think I lost that match, but still I pondered his statement for weeks. To the best of my recollection he had never said that to me before so explicitly, though if he had it’s likely that I would have simply assented to it and let it pass as a given. On this occasion, however, I wondered where he had specifically learned this law and acquired his expectation of it. He had never had a logic or philosophy class, but he didn’t need to. He learn
ed it from rational life, or Reality (not just culture) which depends on this and other laws.
The Law of Validity is so basic to Reality that it turns up everywhere, in every subject, in every sphere of life. From the time we begin to think and reason we learn that arguments must be valid, and by degrees we become adept at conforming to it (or at least appearing to). We also learn to detect invalid logic on some level. (Even now you are analyzing the validity of my thinking.) The question driving much of our discussion is why? Why is the Law of Validity a law at all? Why do we expect it, and we expect others to expect it? Why does all meaningful communication seem to hinge on valid reasoning? Where does it come from? Like math, and other laws of logic, it seems to just be and binds us to it, all our thinking and all our doing. Here again we come face-to-face with the Logos principle, for the Logos itself gives meaning to the notion of validity and explains its demands. It imposes a truth claim upon those who wish to understand how anything could just be, but also on those who do not. It asserts that there is a Metaphysical Source and structure of all that is with laws that shape and govern our Reality in every detail. It does not solve every mystery but without it there is only mystery. The Logos is not only the comprehensive order of Reality by which and to which we are bound, but also the Orderer.
Chapter 8
Objections to the Logos Principle, part 1
Now we come to some objections. There are always objections in philosophy, and they fall into two broad categories: those that assert the premises are not true, and those that assert they are not valid, or both. This demonstrates very nicely the main idea of the preceding discussion. Some may argue, for example, that the laws of logic such as Validity are an outgrowth of language or that they would have pre-existed God so that He could not have created them, similar to the Euthyphro dilemma about moral laws. In any case, no argument can be made without first presupposing the absoluteness of logic. My whole argument thus far is either logically valid or it is not. And this is precisely my point!
I came upon a paper by a writer named Michael Martin who is a strong critic of the Logos principle that I have been propounding. His paper is called, “Does Logic Presuppose the Existence of the Christian God?” His answer to this question is a resounding negative. In it he attempts to refute the argument of Greg Bahnsen and associates, proponents of what’s called the Transcendental Argument for God (TAG)—that logic, science, and objective ethical standards presuppose the existence of the Christian God, which he says “has been repeatedly used by a small group of Christian apologists operating within the Orthodox Presbyterian tradition.” Bahnsen did a series of debates with Gordon Stein and George Smith in which he argued that deductive logic presupposes the existence of not just any God but the Judeo-Christian God portrayed in the Bible. Martin introduces his counter-argument as follows:
Let us understand deductive logic to be the study of valid deductive arguments [thus the idea of validity is reinforced once again]; that is, arguments in which the premises necessitate the conclusion. On this common understanding IF the premises of an argument are true, THEN the conclusion must be true. Deductive validity is determined by the form of the argument and not the content of the premises.
At this point our discussion will become more ‘technical’. Like every discipline and field, philosophy has its own professional ‘language’ unique to it with its own vocabulary and formulas. The language of formal Logic, for example, is a lot like math and is way over my head even though I took a course in it 30+ years ago! Parts of many languages seep into the public square lexicon and even become ‘street language’, especially among those who have had college education at any level. This is true with the language of philosophy. It will especially seem familiar if you have had a philosophy course or two (or teach them). For you I realize a definition is unnecessary but for others I offer this: The following form is called a syllogism, albeit a very simple one (and they can get very complicated). It is a representation of the way we all think and form arguments. It is built on ‘propositions’, statements of truth or possible/ probable truth. A proposition is always intended to be true (or it is called a lie). This, to me, is telling. A syllogism is a form of expressing an argument in clear and concise terms with math-like qualities insofar that it attempts to list in a linear fashion all the propositions and premises, of an argument which lead to the conclusion. The person who formulates the syllogism intends all the premises to be both valid and true (unless he is being deceptive).
Using the following syllogism Martin continues to make his point. An example of a valid deductive argument is this:
All dogs are brown. [Premise 1 or P1]
Rover is a dog. [Premise 2 or P2]
______________________
Therefore, Rover is brown. [Conclusion or C]
Of course we know that all dogs are not brown, so this argument is false, but it is valid. It is valid because if the premises are true the conclusion must also be true. That’s how deductive logic works per law #4. Deductive validity contains premises that lead inescapably to their conclusion, whether true or not. Isn’t that fascinating, if not annoying? Therefore, deductive validity must not be confused with truth. Once an argument is shown to be valid it must then be shown to be true or false, as the case may be. If any of the premises of the argument are false the conclusion must be false, even if the argument is valid. Therefore, Martin observes, the argument's validity is not a function of the truth of the premises but [only] its form which is:
[P1] All Ds are B
[P2] x is D
________________
[C] Therefore, x is B
So interpreted, Bahnsen's claim is that the validity of deductive arguments presupposes the existence of God, that both deduction and validity are immutable and inextricable laws of logic that presuppose a supremely logical being who created the 'formula' for Reality.
In other words, Bahnsen argued for the same point that I have already asserted above with respect to validity, but in more explicit terms: The Law of Validity in general, and of deductive validity in particular, can only be made sense of if there is a God who has established it—for the purpose of our discussion, the Logos. To elucidate Bahnsen’s argument further Martin puts it in terms which he says Bahnsen often used himself: “To say that A presupposes B is to say that we could not ‘make sense’ of A without assuming B.” That is to say, Logic presupposes God because it could not be made sense of without assuming a Supreme Logician, a Source of the Law that makes it binding.
I agree. But Martin doesn’t. So we need to explore this idea more methodically to see who’s right. We need to get into the weeds, as they say. I am going to try to show that Logic does presuppose God, a super-intelligent being who established the laws of logic as necessary components of reason.
The core of Martin’s rebuttal is the assertion that even if “one must assume B to make sense of A, it does not follow that B is true.” Here I will offer my first commentary: well, yes and no. It depends on the details. If I see a boy that is dripping wet (A) we cannot assume that the person went swimming and just got out of the pool (B). That is one of the options, but there are other possible explanations. So in this case Martin would be quite right: A does not presuppose B. But we can assume that the person got water on him somehow (or some liquid), because getting covered in liquid is what makes a person wet. So with one small adjustment to the proposition we see that A does presuppose B. Martin makes it seem as though nothing presupposes anything else, but there are hundreds of examples we can think of to show that some things, no, many things, presuppose others. When we see a person we can presuppose that person has or had biological parents. When we see a computer somewhere we can presuppose it had a maker and a programmer. If a there is a cooked meal on the table when we get home we can presuppose someone prepared it. When I communicate with someone I use language I presuppose that my listener uses language also. We can rightly presuppose certain things.
To strengthen his rebuttal M
artin offers these two examples:
1. If I am trying to communicate to an audience by speaking to them in English [A] my action makes no sense unless they understand English [B]. But it does not follow that they do [E]. They might only understand Chinese.
2. Scientists listening to radio signals from outer space [A] in order to make contact with extra-terrestrial life [B] presuppose that such life is possible. But it does not follow that it is. [C]
Each of these arguments is valid and true, but they both contain the same logical error. (Note that I’m attempting to use logic to analyze logic because I assume it as a permanent standard of right thinking, and I presume you do too.) They confuse the actual thing that is dependent on something presupposed with that which is not the actual thing, which I will illustrate below. Also, there are one or more missing premises in each of them. Example 1 has four: First, all speakers who address an audience desire and expect to be understood; second, no speaker would use a language to communicate to his/her audience that he knows they do not understand; third, no speaker would reasonably speak to an audience before ascertaining their language needs or if he had reason to believe would they not understand him; fourth, if their proficiency in the given language was in question a pre- or post-test would resolve that. (The availability of an interpreter, of course, would be a mitigating factor in all of these.) Therefore A does presuppose B, at least inductively. We will delve more deeply into this below.