Certainty versus Probability

[Darrell Hougen]

Wrong. This another example of the false dichotomy fallacy which I hear so often from Objectivists: if there is some continuous scale from A to B and you deny that x = B, then x must be A (another example: if a system is not 100% deterministic it must be completely random, or: if you can't be 100% certain of anything you can't know anything).

Dragonfly's post on another thread got me interested in discussing the nature of knowledge. He apparently does not agree with the assertion that, "if you can't be 100% certain of anything you can't know anything." So, I would like to know why. First, I will put my spin on it.

As far as I know, you can either know something as a fact (i.e., be certain of it (in some sense that I will try to elucidate below)) or know the probability of it --- or at least have an estimate of the probability. There are no other ways of knowing anything.

Now, in order to know the probability of something, it is necessary to know some things for sure. For example, in order to know the probability of drawing a particular card from a deck of cards, one must know that one has a deck of cards, how many cards there are in the deck and whether the card of interest is in the deck. Without knowing those basic things, it is impossible to know the probability of drawing a card.

One cannot argue that there is a high probability that a person is possession of a deck of cards or that there is a high probability that the deck contains 52 cards, because there is no way of calculating those probabilities without knowing even more things. That is, if there is any doubt that I am holding 52 cards, I must know the probability that my perceptual faculty might be in error in order for me to calculate the probability that I am in fact holding all the cards. But, in order to know the probability that my perceptual faculty is accurate, I must know how often it is right and how often it is wrong. But, there is no way to know that unless I have some oracle that tells me when I am right or wrong. Clearly, I cannot depend upon the perceptual system itself unless the perceptual system sometimes produces results of which I can be sure.

Generally, when researchers study artificial perception systems, they characterize everything in terms of probabilities, so it is hard to imagine going from those probabilities to a state of certainty. However, there are some results from information theory and minimum description length estimation that may give us some hope.

First, according to Shannon, if the channel capacity of a communications channel is sufficiently large, relative to the amount of information it is carrying, then the probability of error can be may arbitrarily small. This is important because the channel capacity does not have to be infinite. There is a finite capacity for which the error goes to zero. So, if a perceptual system is like a communications channel, it may be that there are circumstances under which it can operate in a virtually error free manner. For example, if you get close enough to someone, you may have no doubt about who that person is, particularly if you know that person well.

The other result, from minimum description length estimation states that if you collect a sufficient number of samples from a probability distribution that can be described with a finite number of bits of information, the MDL procedure will find that solution and thereafter never deviate from that solution with probability one.

That brings us to a discussion of events of probability zero. It may be that we need to make a distinction between certainty in the absolute sense and certainty in the probabilistic sense. To be certain in the latter sense means that one knows a fact with probability equal to one, but that there may be a set of measure zero for which the fact is not true. This could roughly correspond to the notion of contextual certainty within Objectivism. That is, one can be sure, so long as really far fetched ideas are excluded.

As an example, consider my car. My car is distinctive enough, that I can be sure, when I find it and examine it closely and put the key in the lock, that it is my car. To say that my car is distinctive, means two things: First, that it has its own identity, and second that it is sufficiently different from other cars that there is essentially no chance of me making a mistake about whose car it is. Therefore, I am sure that my car is my car with probability one.

However, I cannot be sure in an absolute sense, because the KGB might have stolen my car in the middle of the night and replaced it with one exactly like it, one which they spent millions of dollars of time and effort on for the sole purpose of fooling me. This falls into the category of far fetched ideas.

Even more far fetched, are ideas that have to do with substituting people you don't know for people you do and not being able to tell the difference. Of course, this makes for interesting entertainment, but is virtually impossible in practice. Perhaps advanced space aliens could do it. Such propositions, are, in effect arbitrary since there is no evidence that space aliens even exist. Therefore, I can be certain except on a set of measure zero of arbitrary assertions.

Darrell

[John Dailey]

Ok, Darrell:

~ For a while, while such is 'tolerated' here, I'll allow myself to be seduced into responding.

~ Until you get to 'my car', I find nothing worth responding to, unless you wish to debate the worth of (supposed/alleged) 'researchers' and their alleged 'findings.' After you get to your car, and point out that when you're not looking, then a paranoic's wet-dream has done something with it, THEREFORE you have no 'certainty' that it's still the way you left it, I have a problem with your 'logic.'

~ All considerations of the worth of your 'questions' have to do with *your* 'meaning' of (given *your* use of the term) 'certainty.' May I refer you to a lecture or two by Piekoff? I assume you've maybe heard of him...and missed a lecture or two which may explicate a diff 'twixt 'omniscience' and rational-'certainty'?

LLAP

J:D

[Dragonfly]

Darrell, your whole article is about certainty in specific situations (perhaps there is a term for it, but it escapes me now), like the certainty that you're looking now at a computer screen. Now even this isn't always as clear-cut as it seems. No one less than Rand herself was "absolutely certain" that she saw a tree outside the window (when she was in hospital after her operation), while it turned out to be impossible (it was probably the reflection of an IV-pole). But when Peikoff talks about certainty he means the certainty of universal truths about the physical world. I've heard the example of Newton, that he was certain of the correctness of his theory and that this is an example of "contextual certainty". This is a prime example of a fudge term, it means that he thought that he was certain of the correctness of his theory, but he couldn't be certain, as he was simply wrong on some points, for example that time is absolute and that gravitational attraction is instantaneous. Now there is nothing wrong in being "certain" of some theory, as long as you realize that there is always the possibility that one day your theory turns out to be incorrect. It would be cumbersome and awkward to formulate that possibility every time you state something of which you are "certain", so there is good reason to ignore it in practical situations. But it does mean that you never can be 100% certain. Examples of such "absolute certain truths" are the notion that time is absolute and the same for everyone, or the idea that "particle" and "wavelike characteristics" are mutually exclusive notions. It once seemed impossible that such obvious, "self-evident" notions could be wrong, and yet this turned out to be the case. The only thing you can be really certain of is analytical truths, like the statement "2+2 = 4" or "a bachelor has no spouse", as these don't depend on empirical evidence but follow logically from the definitions, but that is not the kind of certainty we're talking about (it's also cumbersome to state this explicitly every time).

[John Dailey]

~ Maybe, in each of our usages of the term 'certainty', we should explicate the difference-as-meant as to whether we mean merely a psychological 'feeling' of certainty, vs a psychological 'awareness' of rationally-based 'certainty;' the latter being able to be demonstrated (ostensibly, or linguistically) in most (not to be confused with ALL) cases to others.

LLAP

J:D