Reading: Chapter 3: Self-Evident Knowledge

Foreword:

              A central problem for philosophy is how to tell whether a belief is one we're entitled to be certain of, or is merely opinion. The traditional answer worked out in the ancient world was that we're justly certain of a belief provided it is either self-evident or proven. While this seems to me too narrow an answer, I think it’s right in so far as it allows that proof and self-evidence are among the conditions that make a belief knowledge rather than mere opinion. So why are believers in God always asked for proof of that belief? Why can't the right answer be that our belief in God is a self-evident truth?    

              The answer is that long ago some very influential philosophers proposed restrictions on the experience of self-evidence that disqualify belief in God. They agreed on the observable characteristics that define a self-evident a belief, because those chaceteristics are exhibited by our experiences of self-evidence. The resulting definition was that a belief is self-evident provided that: 1) it is experienced as prima facie true, and 2) its truth is not derived from any other beliefs. It can also be noticed that many, though not all, the beliefs that meet these two conditions are also 3) experienced as initially irresistible.

For clarification: the first characteristic - being “prima facie” true - means that its truth is so obvious as not to need further reasons. The second, it’s not being inferred, means that it’s truth is in fact not known on the basis of any other truths. The third means that some experiences of self-evidence compel our belief in the way seeing it is raining compels us to believe it is raining. Such beliefs are not, therefore, matters of choice.

               To these three obvious characteristics, however, philosophers (such as Aristotle and Descartes) added that to be truly self-evident belief must also be: A) recognized as self-evident by everyone who understands it; B) be a law (a necessary truth); and C) be infallibly true. These three characteristics are not exhibited by experiences of self-evident truths, as are 1), 2), and 3) listed above. They are instead proposals – theories – about what should be allowed to count as self-evident, and they are motivated by the philosophical agenda of the people who proposed them. So despite their widespread acceptance, A, B, and C, have yet to be justified by reasons.

              In what follows I will argue that there are no good reasons for the proposed re­strictions, A, B, and C. I will show that they themselves are neither self-evident nor proven, and that there is powerful evidence that each of them is false.

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"WHAT'S YOUR PROOF OF THAT?"

How many times have we heard this question about belief in God? And at first it seems to make sense. It seems only fair to demand proof from anyone who claims to know the right answer to a question that has generated con­troversial and competing answers. In addition to seeming to be fair, this demand has been endorsed by any number of enormously influential thinkers. John Locke and David Hume, for example, have reminded us again and again that "the wise man tailors his belief to the evidence." And more recently W K. Clifford put the point forcefully, declaring that "it is wrong always, and everywhere, and for anyone to believe anything upon insufficient evidence." ¹

If all this were not enough, we could be further admonished to look at the sciences which are constantly engaged in trying to prove their theories. If scientific theories need evidence and proof, must not every other sort of belief then need it too? After all, if science is the best route to knowledge, isn’t it obvious that if we don't have proof for something, then we don't really know it?  That is, isn’t it obvious that we’d have no intellectual right to say we are certain a belief if we had no proof for it?

The view just stated is so widespread and so deeply entrenched that nowadays it is hardly ever questioned. The vast majority of my students arrive in my classes already taking it for granted because they run into it constantly. The press, cinema, TV and popular literature disseminate it continuously, as do more scholarly works by a number of prominent atheists. Nevertheless, despite this tidal wave of common acceptance that no belief can be knowledge without proof, it is a tragic mistake. First, because it is impossible that it be true; second, because it ignores the way we actually attain knowledge both in the sciences and in everyday experience. 

Please! Don't jump to the misunderstanding that I'm about to advocate blind acceptance of beliefs, reject science or condemn the questioning turn of mind that asks for reasons, evidence, and proof. Not at all! What I'm about to argue against is only the overestimation of the role of proof in gaining knowledge. If you give me the chance, I will show you why evidence and argument are not needed for some beliefs, even though they are indispensable for establishing the truth of many others. I'll begin by examining what goes into a proof. This will enable you to see why there have to be self-evident beliefs that don't need proof, and why self-evident beliefs are necessary in order to get any proofs. Then we can reflect on how we obtain such unproven knowledge. 

WHAT IS A PROOF?

Any reference to "unproven knowledge" strikes many people as self-contra­dictory. They ask: "How can we really know something unless it is proven?" But this question betrays a lack of understanding of what goes into a proof, since it is impossible that the only beliefs we have the right to be certain of are the ones that we have proven. To see why this is true, let's begin with what goes into a proof.

At its core, a proof is a form of inference, and inference means deriving new information from information we already have. When we draw an inference, we come to see that if such and such beliefs are true, then some other belief must also be true. Here is an SSE (Super Simple Example) of what I mean:

1.      Joe drives 49 miles one way to his office.

2.      Joe drives to his office over 220 times a year.   Therefore

3.      Joe drives over 21,500 miles roundtrip to his office each year.

In this SSE, statements one and two (above the line) assert beliefs already known and from which the inference is drawn in statement three. You should be able to see for yourself that if statements one and two are true, there is no way statement three could be false. The relationship between the starting beliefs and the belief inferred is called entailment, and it operates, in this example, according to the rules of arithmetic which show that statement 3. must be true if statements 1. and 2. are true. It is this seeing-that-some­thing-else-must-also-be-true that lies at the heart of any proof.

The inference in another SSE should be just as obvious:

1.      All horses are mammals.

2.      Mammals all nurse their young. Therefore

3.      Horses all nurse their young.

Once again it should be obvious, even to someone without any formal training in the rules of logic, that statement three is entailed by the combination of statements one and two.

Proof-making is an old enterprise, and so has accumulated its own vocabulary. The statements of the starting information are called “premises;” the statement of the inferred information is called the “conclu­sion”. The rules by which the inference is drawn are those of logic or math, and premises together with their conclusion is called an “argument.” Most arguments are not the short, two-step affairs that these SSEs are. Most have a number of premises and thus require a chain of inferred steps to reach their conclusion. When an argument is stated along with the rules used to draw each step, and the steps end with the argu­ment's conclusion, we have a “proof” of that conclusion. And, unless a mistake has been made in drawing the conclusion, the argument shows why the conclusion must be true if the premises are true. All deductive proofs have this structure, no matter how complex they are.²

The description just given of what goes into a proof is already enough to show why any proof depends on having information that is not proven. First, because if everything needed to be proven, then the premises of every proof would also need to be proven. But if you needed to prove the premises of every proof, you would then need a proof for your proof, and a proof for the proof of your proof, and so on forever. This is why it makes no sense to demand that everything be proven: it is impossible to construct an infinitely long regress of proofs.³ So whenever the premises of an argument are themselves in need of proof, the series of arguments needed to prove those premises must eventually end with an argument whose premises are all "basic;" that is, premises not in need of proof. If that cannot be done (as is the case much of the time), we may have amassed a lot of supporting reasons for the original conclusion, but we cannot say we’ve shown it to have complete certainty. The arguments may make a good case for the original conclusion, and people may be justly convinced by them, but we do not have proof of them beyond all reasonable disbelief which is why some room for disagreement will always remain.

Notice that I am not saying we can never claim to know a belief is true unless we can trace its inference back to premises that don't need proof. In ordinary language, we don't use the word "knowledge" only for beliefs that don't need proof or are derived from others that need no proof.  We also use it for beliefs that are nearly certain, as well as those we're fully certain of. Thus, a cumulative case made up of evidence and arguments that do not rest solely on basic beliefs can still be quite overwhelming (think of atomic theory, for example). But even in such cases of near certainty, the arguments involved still depend on our having at least some basic truths that do not need proof. At a minimum, we’d need unproven rules for drawing our inferences. There are no exceptions to this point: not all beliefs need proof, and proving anything depends on having beliefs (rules) that don't need it.

The second way the description of a proof shows why not every belief needs proof, is the last one just mentioned:  arguments require rules for drawing inferences correctly. These rules of inference – the rules of logic and mathematics - cannot themselves have proofs because they are the very rules we must use in order to prove anything. If we were to use them to construct proofs of themselves, the proofs would amount to arguing in as circle because we’d already be assuming the truth of the very rules we would be trying to prove!⁴

For this reason, all proofs need belief in unproven rules. This is why the most fundamental rules of logic and mathematics were called "axi­oms": they were taken to be self-evident and therefore basic. So once again, even though gathering evidence and formulating it into arguments is very important (especially in the sciences because they debate competing hypotheses), it just cannot be true that all knowledge is obtained that way. Framing a proof is needed only for a belief that is not obviously certain already, and it is possible only when we already have some premises and/or a set of rules that are not in need of proof. And even then, a proof serves its purpose only when it is error-free and all the premises for its conclusion have more certainty than the conclusion. For if the premises of a proof have no more certainty than the conclusion they're supposed to support, how could they add to our certainty about that conclusion?

If you are accustomed to thinking that only what is proven counts as knowledge, you may be surprised to hear that what I have just said is not controversial in science or philosophy. The major theories about what counts as genuine knowledge have long acknowledged all these same points, and it is all standard fare in logic textbooks. Some theories hold that a belief can be knowledge without proof if it is either (1) about what is evident to the senses or (2) is self-evident (Aquinas, Locke, Hume). Others, such as Descartes, have dropped the "evident to the senses" part. But either way, there has always been and still is general acknowledgment that while some beliefs need proof, many others don't.

THREE ARBITRARY RESTRICTIONS ON SELF-EVIDENT TRUTH

We have now seen the central characteristics of beliefs that can be knowledge but don't need proof: it is that we experience them as prima facie true without deriving them from other beliefs.⁵ Here are a few examples: memory beliefs such as your name, address, and telephone number; perceptual beliefs such as that it is sunny today; introspective beliefs such as your belief that you have a slight ache in your left foot; and beliefs that arise by what I’ll call “reflective intuition” ⁶  such as your belief that 1 + 1 = 2 or that “Things equal to the same thing are equal to each other”, or that other people have minds. None of these have proof, but none of them needs proof if they are self-evident to you. They can be known for sure, and known without your deriving their certainty from any other beliefs.

But, as I forewarned you, some very influential philosophers proposed restrictions on which of our experiences of self-evidence they would allow to count as the real thing. The first of these, the one designated as A) in the introduction, I call the “Everybody Requirement.”⁷ This requirement has so thoroughly won the hearts and minds of thinkers that came after its defenders (Aristotle and Descartes), that for over a century now most philosophers have defined a self-evident belief by this restriction on it! They have taken self-evident beliefs to be ones we need only understand to see that they are true, and which everyone sees as true once they understand them.

I find this to be a seriously misleading way of defining self-evidence, for two reasons. First, saying we need only understand a self-evident belief to see its truth denies that there are cases in which someone may need to have acquired other information, or to have had certain previous experiences, or to be in a certain frame of mind, or to have acquired certain skills, or even to have become an expert in some field, in order to see a particular belief as a self-evident truth. Surely there are beliefs that are self-evidently true to experts that are not to non-experts! So it seems plainly false that if someone understands a belief that is really self-evident, he or she will invariably also see it to be self-evident.

Moreover, I also find the definition faulty for its inclusion of the term “everyone.” How could we ever know - for any belief we experience as self-evident - that no one has ever in the past understood it but denied its self-evidence, or that no one will ever will do so at any time in the future? For these reasons, I conclude that defining genuinely self-evident beliefs as those that need only to be understood to see them as true is too weak a requirement, while requiring that everyone must agree about every self-evident belief is too strong a requirement. Like Jack Spratt and his wife, the two parts of this requirement lick the platter clean and leave us with no self-evident truths at all! But we all know it is false that there are no such beliefs, because we all experience a host of beliefs as self-evident every day. In fact, anyone now reading these words is experiencing their appearance on this page as a self-evident truth.

In addition to the fatal flaws just mentioned, it is also the case that the Everybody Requirement doesn’t pass its own test for self-evidence. Since it’s not self-evident to me, it cannot count as self-evident to everyone and therefore not in need of proof. And the fact is, no one in the 2300 years since Aristotle proposed it has ever offered a proof of it, so it lacks both self-evidence and proof. Nor has anyone, so far as I know, offered any other sort of justification for it. And the reason they haven’t appears to be that no one can so much as imagine what could justify it.

The second requirement imposed on the experience of self-evidence - the one designated as B) in the introduction - is that all genuinely self-evident beliefs must be laws (“necessary truths”). I call this the “Necessity Requirement.” Now there are plenty of laws we do experience as self-evident; 1 + 1 = 2, for example, or “All bachelors are unmarried.” These truths are not derived from other beliefs and are experienced as prima facie true. But the fact that there are self-evident laws is no proof that only laws can be self-evident. So why should we think that? What are the arguments in its favor? Well, the fact is, that although Aristotle insists on this restriction and Descartes endorses it, neither of them gives a single argument to show it is true. Nor, once again, has anyone given a reason in its favor in the 2300 years since Aristotle first proposed it. So why should anyone believe the Necessity Requirement? This question is especially made urgent by the fact that you are – as I said a moment ago - experiencing right now a self-evident fact that is not a law, namely, the belief that you are seeing these words on this page. That’s not a necessary truth, but it surely is self-evident!

Besides that, there is another excellent reason for supposing the Necessity Requirement is not true. The reason is that whenever anyone denies a genuinely necessary truth, they are forced to make an assertion that is plainly self-contradictory. For example, consider the denial of “All bachelors are unmarried.” Its denial is: “There is at least one married bachelor.” Is a married bachelor an absurd self-contradiction? It sure is. But now use this same test on the Necessity Requirement itself. Its denial is: “There is at least one self-evident belief that is not a law.” Is that self-contradictory? Is it as obviously an impossibility as a married bachelor? Clearly not. We have already noticed that your present experience of the words on this page generates in you belief in the self-evident truth that they are there, and the truth about that fact is not a necessary law. Therefore I find that there is no more a good reason to accept the Necessity Requirement than there is to accept the Everybody Requirement.

Finally, I’m also going to reject the Infallibility Requirement, designated as C) in the introduction. Why should we think that it is utterly impossible for any genuine experience of self-evidence to be mistaken? We can and do make mistakes when we reason; we make mistakes about what we perceive, and what we remember. We even make mistakes about what we gather from introspection (when we introspectively report our own motives, for example.) So what reason could possibly be given for thinking that our reflective intuitions of self-evidence are utterly immune from error? Besides, the self-evidence of a belief of reflective intuition seems to be good enough grounds for believing it. What is to be gained, then, from adding that it is impossible for such beliefs to be mistaken? So far as I can see, adding the Infallibility Requirement to a belief that is already self-evidently certain is a fifth wheel. We don’t need it, and it is an extremely dogmatic distraction.

But besides these objections there are, once again, excellent reasons to think the Infallibility Requirement is false. These reasons are the many incompatible beliefs that are both experienced as self-evident by reflective intuition. Since incompatible beliefs cannot both be true, every pair of incompatible beliefs that are experienced as self-evident is proof that self-evident certainty is not the same as a belief’s being infallible. In fact, examples of such conflicting beliefs are common. And the most shocking thing is that many of them occur not only with respect to perceptual beliefs (such as whether a player committed a foul in a game), or to memory beliefs (such as whether I locked the front door when I left the house), or to contrary divinity beliefs, but with respect to the very sciences that are supposed to be the epitome of rational infallibility. I mean the laws of mathematics and logic!

One striking example of such a conflict concerns the logical axiom called the “law of excluded middle.” The law says that for any belief whatever, it must be either true or false whether or not we can discover which it is. This means that statements we have no way of deciding such as those about the future or how the past would have differed had not a certain event not taken place, are nevertheless either true or false. This law has been regarded as a basic axiom of logic for centuries, and was held to be self-evident by a long list of logicians, including Aristotle, who regarded it as one of the three fundamental axioms of thought and reality. But in the twentieth century a number of thinkers denied that the principle of excluded middle is a law at all. The denial first gained adherents by a group of mathematicians led by Luitzen Brouwer. For Brouwer and his associates, the law of excluded middle not only isn’t self-evidently certain, in some cases it’s false. They developed an impressive system of mathematics that omits the law, and its denial has now spread out-side mathematics. More recently their position was the subject of a close examination and defense by philosopher Michael Dummet.⁸

By now, such disagreements are not only widely known but are (in part) responsible for the rise of different “schools of thought” in math that have become notoriously intractable. As one historian of mathematics has put it:

              The current predicament of mathematics is that there is not one but many mathematics                       and that for numerous reasons each fails to satisfy the members of the opposing schools.                                It is now apparent that the concept of a universally accepted, infallible body of reasoning –                          the majestic mathematics of 1800 and the pride of man – is a grand illusion… The dis -                                     agreements about the foundations of the “most certain” science are both surprising and, to               put it mildly, disconcerting. The present state of mathematics is a mockery of the hitherto             deep-rooted and widely reputed truth and logical perfection of mathematics.⁹

At this point defenders of the Infallibility Requirement may wish to object: even if self-evidence isn’t always infallible, it may sometimes deliver specific truths that are. What of the logical law of non-contradiction? What of the belief that “I am conscious”? Aren’t these beliefs ones we are entitled to say cannot be false? ¹⁰

The answer to this is that we must try not to confuse two distinct, but similar, issues. To say a belief is self-evident is to say we can be certain of it, not that it is infallible. To claim infallibility for a belief is to claim that we have a power of forming it that can never go wrong, and that the belief in question was formed by that power. I have already given one famous example of a belief that some philosophers thought infallibly true, while others thought it was self-evidently false (the law of excluded middle), and there are many more. But since no belief can be true and false in the same sense at the same time, not even the reflective intuitions of self-evidence that arise in logic and math can claim infallibility. Even if some are beliefs are individually undeniable – such as “I exist” - they are not formed by a capacity that can never be mistaken. Much as we may wish otherwise, we are forced to leave infallibility to God alone.                                                                                                                                                                                                                                                  

 

For all these reasons, I'm going to stick with the description we get by listing the characteristics of self-evident beliefs that are exhibited to our experience, and reject the traditional restrictions placed on it. I’m going to hold that a self-evident belief is one that is: 1) experienced as prima facie true 2) without being inferred from any other belief, and that some of them also have the characteristic of being 3) initially irresistibly certain. These are the characteristics we get by abstracting from our experiences of self-evidence, without the addition of anyone’s faulty proposals.

 

According to this view, then, self-evident truths can arise from normal sense perception, from memory, from introspection, and from reflective intuition. Among the beliefs formed by this last capacity are not only the necessary truths of math and logic, but also such important beliefs as: 1) the existence of other minds, 2) the existence of laws that govern the orderliness we experience in the world around us, and 3) divinity beliefs - including belief in God. As I see it, the reason early Christians didn’t answer the question about their belief in God by saying they experienced it as a self-evident truth, was that they were buffaloed by the restrictions put on self-evidence, namely, restrictions A, B, and C.

It is not unfair to point out, in addition, that it is not only competing divinity beliefs that were disqualified as genuinely self-evident by these restrictions. The fact that normal sense perception was also ruled out, led to centuries of attempts to prove that the objects we perceive really exist independently of us! The same restrictions also led to attempts to prove that other people have minds, that there are objective moral laws, that God exists, that humans have free will, and a host of other beliefs all of which were in fact believed because they were experienced as self-evident, but which were instead treated as needing proof. Not only were they thought to be in need of proof, but century after century the proofs of them were all shown to fail! To this day it is generally conceded in philosophy that there is no successful proof that the objects we experience really exist independently of us (or not), that other people have minds (or not), or that God is real (or not). Moreover, the conclusion drawn from these failures by a number of contemporary thinkers is not that something is wrong with the traditional restrictions, but that there is therefore no certain knowledge about anything! This self-refuting nonsense has been dignified by the name “post-modernism,” and is worn as a badge of honor by those who consider themselves to be brave souls who have the courage to admit that there is no sure and certain truth whatever.

Finally, there is one last reason why the Necessity Restriction on self-evidence is to be rejected. It is especially striking that Aristotle, who is famed for backing up his hypotheses with reasons, gave no argument whatever to show that only laws of rationality could be genuinely self-evident. The motivation that led him to propose this restriction does, however, rear its ugly head in his famous work, The Metaphysics. There he explains that that since the laws of rationality are the highest sort of reality so far as the order of being is concerned (because they are self-existent and divine), it seems only right that they alone should also be the most certain realities in the order of knowledge (be self-evident). In other words, he wanted there to be a parity between what is most real and what is most knowable, so he simply asserted it without argument! Aristotle himself put the point this way: “… that which causes derivative things to be true is most true. Hence the principles of eternal things must always be most true… nor is there any cause of their being, but they themselves are the cause of the being of other things, so that as each thing is in respect of being, so it is in respect of truth” (Meta. 993b 26-30, emphasis mine). The upshot is that Aristotle proposes the Necessity Restriction so that no other divinity belief is allowed to be self-evident; but his only “reason” for that was his (dogmatic) pronouncement that only his divinity beliefs could be truly self-evident. With respect to belief in God, then, his argument is religiously circular.

If the arguments I have just presented are correct, the consequence that should be drawn is not that there is no certain truth whatever, but that the traditional restrictions on the experience of self-evidence are among the most unjustified dogmas ever to burden (and destroy) a philosophical tradition. And that goes equally for the belief that is central to thesis of this chapter: it was the restrictions on self-evidence that drove Christians into the misguided project of constructing proofs of God’s existence.¹¹