Probability, belief, and proof
January 2001

Probability and belief

    Life is full of misguided questions. One germane example is, "What does such-and-such prove?" The problem here is prove, which, as you may have guessed from a separate essay, is such an ambiguous term that it is almost useless in practice unless it is clearly defined every time it is used. Recall that we noted two contradictory dictionary definitions for prove and five legal "standards" for proof.
    In actuality, we rarely or never prove anything conclusively (100%). Rather, we assemble evidence to raise the probability of the proposition in question as high as we can, and then decide what that probability means. If we could reach 100% probability, the proposition would obviously be true, and life would be easy. But most probabilities fall well short of 100%. In many cases, we may even find it difficult to assign any probability to our collective evidence.
    If we can’t prove propositions absolutely, what can we do instead? We must do something, because we don’t carry around a brainful of unresolved propositions, particularly in matters of daily life. The human animal seems to need to resolve questions, not leave them hanging. Even when definitive evidence is lacking, we find a way to "decide."
    How? We believe, that is, we choose to accept the proposition as true even when we know that genuine proof is not forthcoming (i.e., when the evidence is inconclusive). This protective device called belief allows us humans, who are creatures of action, to resolve most questions in our minds by simply acting as if they were true. We are not built to hold matters in suspension. We settle questions in our minds, then move on to something else.
    What is this act of believing? It consists of creating a threshold of belief at some probability, assembling evidence for the question, and when the probability exceeds that threshold, accepting it as true. In effect we say, "That’s good enough for me—it’s true." (A sloppy version of "I consider it to be true.") For example, what do you think about the possibility of life elsewhere in the universe? Many of us believe it exists, but nobody can prove it because no hard evidence exists. We examine the evidence, and if we think it is sufficiently compelling, we believe.

Belief illustrated
    The process of believing is illustrated in the first figure below. Four thresholds are given, from 50% to 95% probability. The 50% threshold is the lowest reasonable one, of course, for all lower probabilities point more toward disbelief. If I set my threshold of belief at 50%, I will believe any proposition whose evidence provides a probability greater than 50%. The arrow from just above the 50% level to the 100% level represents the amount by which the probability must be increased from its actual value to its accepted value of 100% by the act of believing.
    The threshold of 50% is of course is very casual. It means that I will believe nearly anything presented to me. I can be much more selective if I raise the threshold to, say, 90% probability. I will then believe only propositions whose chances of being false are <10%. If I wish to be more stringent still, I can raise my personal threshold to 95% or greater. If I choose to be a real stickler, I may require 98–99% in order to believe. (By the way, science generally requires a probability of 95% to accept an idea as being true.)
    Suppose I want to be a purist, and I decide to demand 100% probability. (I’m from Missouri—show me!) What happens to me then? I get into horrible philosophical/mathematical disputes about whether anything can be proven absolutely. Since we don’t have the opportunity to deal with such things in a short essay like this, we will avoid the question by not considering true absolutes.

Proof

Now we turn from belief to "proof." It’s not as big a step as you might imagine, because "proof," at least in the legal sense, is just a form of belief. Because the law has so permeated modern American life, we begin discussing proof from the legal standpoint.

Legal aspects of "proof"
    A legal proceeding first decides on its threshold of belief (which it calls "standard of proof"), then assembles and evaluates evidence for the accusation. If the evidence exceeds the standard of proof, the legal body accepts the accusation and convicts the defendant. (It believes the proposition that he is guilty.) In so doing, the legal body is simply choosing to raise its probability from its demonstrated (actual) value to 100% . Has the legal body proven the defendant guilty in our absolute sense of the word? No. They have only chosen to believe that he is guilty ("considered" him guilty). Unfortunately, the law uses the word "prove" or "convict" for all these decisions, regardless of threshold probability. This causes great confusion until the process is diagrammed.
    The five "standards of proof" (thresholds of belief) found in the law are shown in the lower figure below. "Preponderance of the evidence" is the lowest, at 50% probability. It is used in most civil proceedings, and requires only that the plaintiff (accuser) outprove the defendant. Probabilities of 51% vs 49% produce the same "guilty" verdict as 99% vs 1%.
    The second standard of proof is "clear and convincing." It is also used in civil proceedings (equity cases), but less frequently than "preponderance of the evidence." Its threshold probability lies somewhere between 50% and 90%. For simplicity, I have set it at 75% in the figure.
    The third standard of proof is "beyond a reasonable doubt." It is the common standard of criminal proceedings, and requires roughly that "all reasonable doubt about guilt of the accused be removed from the mind of the ordinary person." This standard is generally considered to correspond to a probability of at least 90% (although some lawyers would claim ≥95%). For convenience, I have used 90% in the figure.
    The fourth standard of proof is "to a moral certainty." It is also used in criminal proceedings, and requires jurors to be "confident enough about the conclusion to rely on it in matters of the greatest personal importance." Its level of probability falls somewhere between "beyond a reasonable doubt" and "certainty". I have represented it here as 95%. Sometimes these last two standards are lumped together, as in "beyond a reasonable doubt and to a moral certainty." To my mind, this further confuses the uninformed observer of the legal process. "To a moral certainty" means exactly the same. (Note the unfortunate use of "certainty" with probabilities of <100% here.)
    The fifth standard of proof is "absolute certainty." Although the law recognizes this standard of proof, it explicitly never requires it, because the law considers absolutism unworkable (i.e., no criminal would be convicted if 100% proof were required).

How shall we view "proof"?
    Since we here are not addressing the Kennedy assassination legally, there is no reason for us to restrict ourselves to legal definitions and procedures. How then should we understand "proof"? What should we mean by "proving something"?
    I suggest that to keep our terminology as pure as possible, we reserve "prove" for establishing a probability as near 100% probability as humanly possible, which for all practical purposes means the scientific standard of ≥95%. When we fall short of this level, we simply cite the probabilities we have reached rather than calling them "proof."
    I also suggest that we use "strong evidence" to mean that which creates probabilities of ≥95%, i.e., that give rise to "moral certainty" in the law and "scientific proof" in the rest of life. In other words, strong evidence must be truly strong. "Weak evidence" will mean that which is "without significant probative value," and will correspond to probabilities of <<90%, and certainly <75%. We will accept the idea that weak evidence by itself demonstrates nothing that we can or should rely on. ("Strong" and "weak" evidence are discussed further in a separate essay.)
    In practice, this will mean that we can confidently retain propositions supported by strong evidence and we can confidently reject propositions supported by only weak evidence. But we take as a guiding principle that we will always seek the strongest possible evidence in support of propositions.
    Lastly, we will agree to apply these standards objectively and consistently. We will challenge our favorite ideas just as vigorously as we challenge those "crazy" ideas put forth by the other person, and maybe even more vigorously.
    In short, we will accept no proposition that we cannot prove. Whenever someone proposes a new idea to us, we say simply, "Prove it to me (show me strong evidence for it) and I will accept it. Anything less, and I will reject it." We will be like the person from Missouri who says, "Show me."
    Only with these operating principles can we be truly intellectually honest in our quest to understand the Kennedy assassination.

A new view
    The world viewed in this way will look very different from the world that most of you know now. I submit that this new world is the only defensible one—all others involve greater or lesser amounts of "fudging," a polite word for intellectual dishonesty.
    Of course, there is more to making our way through this new world than just proving or disproving things. For maximum efficiency, we must follow the optimum sequence of intellectual steps in our reasoning. That sequence will be the topic of a separate essay ("The Critical Method"), which will be best considered only after we have practiced accepting or rejecting a few things.

Proof versus disproof
    For the record, it can be argued that we can never really prove anything; we can only disprove things. (See essay by Sir Karl Popper on falsification.) This is because to prove a proposition (normally an explanation for some problem we are facing), we must not only show that it is always correct, but also that it is the only correct explanation (i.e, that every other potential explanation is wrong). Obviously, it is feasible to disprove something once, whereas it is unrealistic to disprove every alternative explanation, except perhaps where mathematical laws are involved. Accordingly, we retain and reject propositions (akin to statistical procedures) rather than prove and disprove them. I wish that we could explore ideas like this here, but it is impossible. So keep these things in the back of your mind as we proceed to "prove" and disprove various aspects of the Kennedy assassination.