Certainty and Probability
The words "certainty" and "probability" do not apply to propositions that are either true or false. These propositions entertained by us with suspended judgment should never be qualified as either certain or probable.
In the Anglo-American common law there are degrees of certainty and doubt. Certainty attaches to judgments beyond the shadow of doubt; not certain are judgments made with a reasonable doubt; and less certain still are judgments made by a preponderance of the evidence.
The last two are judgments to which some degree of probability must be attached, the former more probable, the latter less probable.
The propositions in each of these two cases, when entertained with suspended judgment, are either true or false. Certainty and probability qualify our judgments about the matters under consideration on the propositions entertained with suspended judgment.
This statement brings us to consider what happens by chance and what is causally determined. Here we must distinguish between the mathematical theory of probability and the philosophical theory of what happens by chance. In the mathematical theory of probability, which begins with an essay by Blaise Pascal, one can calculate the chances of anything happening by the number of possibilities present; for example, in the toss of a coin, the chance of its being heads or tails on any toss is fifty-fifty, because in the long run, with many tosses, that is how one should wager on the next toss, if we know that the coin being tossed is not affected by an extraneous factors.
In the philosophical theory of probability, what happens by chance is what happens without a cause. Consider the coincidence of two individuals who happen to meet on a particular street at a particular time. Why do we call this a coincidental meeting, and regard it as an uncaused event?
The answer is that each of the two individuals is caused to be at the spot where the chance meeting occurs by all the causal factors operating in his own past, but nothing in their separate pasts causes them to meet each other there. The coincidence is, therefore, an uncaused or a chance event.
While we are dealing with caused and chance events, let us spend a moment on the Aristotelian theory of the four causes -- the material cause is the nature of the materials on which the artist operates, the formal cause is the productive idea in the artist's mind. The final cause is the end or purpose that motivates the artist to produce the work of art, and the efficient cause is the action of the artist's hands and tools. But when we depart from the sphere of artistic production, final causes do not operate. What happens naturally happens without any purpose or end to be served.
The critics of Aristotle in modern times who denied teleology or purpose in the physical world were correct in dismissing final causes, but they were incorrect in dismissing the operation of material, formal, and efficient cause in the works of nature, corresponding to those in works of art.
In human activity, free choice as well as physical cause operate. Freedom of choice is present when in deciding on any activity, the individual could have chosen otherwise. His action is, therefore, causally determined by the exercise of his willpower rather than by the kind of causes that operate in nature.
It is, therefore, incorrect to think that there is an irresolute conflict between free will and causal determinism. The freely chosen decision is causally determined, but not in the same way that events in the physical world are causally determined.
Adler's Philosophical Dictionary (1995)
Great Ideas from the Great Books (1963)
by Mortimer J. Adler