Wednesday, June 01, 2011

Can proof be proved?

Someone recently asked me in the comments section of one of my posts about an article on logic on the Answers in Genesis website on the question of circular reasoning. The article was a response to a question by a reader concerning presuppositional Christian apologetics, which holds that, in contending for the truth of Christianity, one should rationally assume the truth of the Bible rather than argue for it. The folks at Answers in Genesis are clearly advocates of this position. The questioner asked how to respond to someone who accused him of circular reasoning.

Here was the response (in part):
Contrary to what your non-Christian friend said, circular reasoning is surprisingly a valid argument. The conclusion does follow from the premises. Circular reasoning is a logical fallacy only when it is arbitrary, proving nothing beyond what it assumes.

However, not all circular reasoning is fallacious. Certain standards must be assumed. Dr. Jason Lisle gave this example of a non-arbitrary use of circular reasoning:

1. Without laws of logic, we could not make an argument.
2. We can make an argument.
3. Therefore, there must be laws of logic.

While this argument is circular, it is a non-fallacious use of circular reasoning. Since we couldn’t prove anything apart from the laws of logic, we must presuppose the laws of logic even to prove they exist. In fact, if someone were trying to disprove that laws of logic exist, he’d have to use the laws of logic in his attempt, thereby refuting himself. Your non-Christian friend must agree there are certain standards that can be proven with circular reasoning."
Well, no, sorry. It's just circular reasoning. The chief problem is in the last sentence:

"Your non-Christian friend must agree there are certain standards that can be proven with circular reasoning."

The assumption here is that we need a syllogism to prove that there must be laws of logic. But the laws of logic are not proven at all--they are assumed. But they are not assumed arbitrarily. Aristotle would say they are known, but not proven--through what he would call nous, which is close to what we would call "intuition." The laws of logic are not demonstrated; they are intuited--they are not the result of logic, but of dialectic. They are nota per se: self-evident.

Every discipline (including science) has metaphysical assumptions that are not inferred from other knowledge within the discipline (and sometimes, as in the present case, even from knowledge outside the discipline). These assumptions are not themselves proven, and the idea that you can prove them is a misunderstanding of the nature of first principles--which are the analog in logic of axioms or postulates in mathematics.

The error made here was refuted about 2400 years ago. It is discussed in Book I, Part 3 of Aristotle's Posterior Analytics. He points out that some people make the error of thinking that all knowledge must be demonstrated, but in order to say this they must allow that reasoning can be circular.

Our own doctrine is that not all knowledge is demonstrative: on the contrary, knowledge of the immediate premisses is independent of demonstration. (The necessity of this is obvious; for since we must know the prior premisses from which the demonstration is drawn, and since the regress must end in immediate truths, those truths must be indemonstrable.) Such, then, is our doctrine, and in addition we maintain that besides scientific knowledge there is its originative source which enables us to recognize the definitions.

The belief that circular reasoning is valid is a foundational belief of presupposition apologetics. Cornelius Van Til makes the claim that "all reasoning is circular." This is important to that position because Van Til wants to be able to engage in circular reasoning by assuming the truth of the Bible. And he thinks that he can avoid the criticism that this belief is circular by arguing that what he is doing is no different from what everyone else does anyway.

But, alas, this is not true. First principles, being the conditions of proof, can't be proved--and don't need to be.


Singring said...

While we have some fundamental disagreements about whether or not someone's 'intuition' is any reasonable basis for making absolute claims about things, for example the existence of logic or, by extension, God, I do have to sincerely say that I rather like the way you disassemble the AiG presuppositionalist claims here.

I hope we will see more such criticism of sloppy Creationist thinking on your blog in the future.

Lee said...

I ought to know better than to go toe to toe with Martin on matters of philosophy. However, I'm probably the most sympathetic of regular posters on this blog to the presuppositionalists, so here goes...

I don't think Van Til's position can be so easily dismissed. Coming into any discussion, or so it seems to me, we are always "begging the question" at some point. Aristotle calls logic a "first principle". Really? What makes Aristotle the final authority? What makes intuition infallible? Didn't Heidegger argue that reason itself is absurd? Whether or not he proved it, or could hope to prove it, is beside the point. Obviously, he did not accept it as a first principle.

I think the crux of the matter lies not with how we can know or presume true that reason is valid, but with the nature of reason itself. What is it? What gives it its authority?

Atheists and Christians (at least the Thomist ones) alike bow toward reason, and both seem to believe that it can be perceived and appreciated starting from nothing more than man's perspective. It's that intuition thing, which is perhaps another word for instinct.

But even if the rules of reason are the same for both atheist and Christian, its nature is not and cannot be the same in both camps.

For the Christian, reason's existence and authority derive from God, as it is (as we perceive it) a (pale) reflection of His own thinking. Presuming this is true, this gives reason an objective existence apart from man and higher than man, and this is what confers authority on it. Reason does not just seem by intuition or instinct to be authoritative; it is authoritative because the Creator of this Universe has thus decreed it.

To the atheist, however, reason has no objective existence. It exists only as abstraction in (some) human minds, defined by a set of rules invented by human minds -- and physically it exists only as particles and electronic impulses in (some) human minds. When all human minds are dead and gone, so will be reason. (As an aside, I think Randists disagree with this, believing that reason is objective -- they call themselves "Objectivists", after all.)

So the question is raised, why should human beings treat something conceived of and invented by other human beings as authoritative? Reason does not stand over us in judgment; rather, it sits under us, like a lap dog, waiting for our command. Actually, it's probably more like a toolbox than a dog. It helps us get what we want. Sometimes. But that's no reason, so to speak, to hold it in any great esteem when adherence to it does not serve our purposes. It is, after all, just particles and impulses, in that regard not any difference than non-reason.

So I think what Van Til is saying is, forget this talk of instinct. No one is denying that atheists perceive reason and the fact that it carries validity with it. Of course they see it; God made it, after all, just like he made the air and grass. But to call it a "first principle"? No -- not if God created it; that would make *God* the first principle.

Van Til believed that Christianity explains satisfactorily why reason exists and why we can with confidence rely so much on it. He also believed that the atheistic world view gives no accounting of reason's existence or authority -- and therefore it is appropriate to require them to provide an accounting for their reliance on reason.

Lee said...

> But to call it a "first principle"? No -- not if God created it; that would make *God* the first principle.

I should have added: If God did not exist, there is no "first principle," but just the misleading braying of our instincts. Heidegger would not have been wrong to denounce logic as an "invention of schoolteachers, not of philosophers."

Thomas M. Cothran said...

Two things should be noted in addition. For Aristotle, "demonstration" is a technical term that does not cover every kind of argument that might establish something as true. Science A may presume principle X but be unable to prove it, but science B may be able to prove that principle. (Aquinas uses the example of arithmetic and musical theory: musical theory presupposes arithmetical principles that it cannot prove; however these can be demonstrated in the science of arithmetic.) So something may be called a first principle relative to one science but not another.

The important point is that while first principles are not demonstrable (in Aristotle's sense) that does not mean they are simply assumed as matters of intuition, nor does it mean they cannot be established by argument. A number of other methods may be used to establish a first principle, and many of these methods fall under the rubric of dialectic.

The problem with the presuppositionalists, as I see it, is that they construe all reasoning as deductive reasoning--the sort of reason whose conclusions are only as strong as the premises. But even modern philosophers are not chained down to deductive or demonstrative reason--after all, Kant has his antinomatical dialectic. Not all forms of reasoning need assume the truth of their premises.

Lee said...


I have a couple of questions, if you have time and inclination, that might help me understand your position...

1. Is the purpose of reasoning to establish truth?

2. Is there any type of reasoning that, ultimately, is able to completely shuck the chains of logic?

Thomas M. Cothran said...


The purpose of reasoning is important to get to the truth of a matter. (It's good to remember that truth is a manifold concept, referring to experiences, sentences, mathematical formulas, an attribute of God, and so on.)

And no sort of reasoning operates contrary to logic. But, again, it's important to remember that logic is also a manifold concept: it refers to the science of syllogisms, to the forms of mathematical logic, and to the structure of the world (the sense in which Hegel speaks of logic and what Thomists often call "material logic".) One has to know when to employ what method and in what way.

Lee said...

> The problem with the presuppositionalists, as I see it, is that they construe all reasoning as deductive reasoning--the sort of reason whose conclusions are only as strong as the premises. But even modern philosophers are not chained down to deductive or demonstrative reason--after all, Kant has his antinomatical dialectic. Not all forms of reasoning need assume the truth of their premises.

You may be right about the presuppositionalists on this, I can't really say. I don't have a "philosopher's license" -- which is to say, on many matters of philosophy, I don't know what I don't know.

What the presuppositionists are asking, though, seems to me like a reasonable question. It is certainly a simple question: if you don't believe in God, then, arguing from your own premises, can you please justify your use of reason and explain why (when used properly) it is authoritative in any discussion?

I think the "authoritative" bit is the key. It is easy to argue that reason, whatever it is, is useful at least on the small stuff. But when discussing the more vast questions, why should we cede to it the role of authority figure and accept its conclusions? (I could perhaps draw a parallel to physics here -- i.e., perhaps reason, small "r", is like Newtonian physics, useful within a proscribed arena, but less useful at the extremes of reality.)

Anyhow, a Christian accepts many things because an authority has ordained them. We accept reason as authoritative because we have a reasonable God. But atheists don't believe that. Therefore, if they're going to use reason against us, we don't want them borrowing from our premises. An accounting of their use of reason, then, seems proper, at least to me.

Martin has proposed in earlier threads that the presuppositionalists confuse ontology with epistemology -- I take that to mean, they confuse questions about "how something came to be" with "how we can know something." I can't be sure his criticism is faulty, but can only explain what my faith tells me:

1. If something is not eternal, then it doesn't matter.

2. Without God, nothing can be eternal.

3. Therefore, if God does not exist, then nothing matters.

And if nothing matters, then certainly epistemology doesn't matter either. From what I know of the solipsists and the existentialist philosophers, they tend to agree with me on that; though they take the opposite tack on God's existence, we are led to the same conclusion.

Without God's existence, our own existence is futile. Epistemology? What good is it to know anything when a fragile chemical matrix is the difference between being and not being, and tomorrow those chemicals return to dust forever? Without God's existence, the reductionists are right. We all agree that man is at some level chemistry, but without a God in Heaven, chemistry is all there is, it's the whole thing. Somehow, chemistry may have succeeded in giving us notions of eternal truths and conceits of having a consequential life, but all that means is we are dust with delusions of grandeur.

No wonder the 20th century philosophers seemed always on the brink of despair. I have noticed, however, that most atheists don't go there. Like Sam Harris, they are happy to piggyback on our notions of transcendent truth and ethics without justifying their use of it, and to proceed to expound on things that they think matter.