"The calculation of probabilities is of the utmost value, […] but in statistical inquiries there is need not so much of mathematical subtlety as of a precise statement of all the circumstances. The possible contingencies are too numerous to be covered by a finite number of experiments, and exact calculation is, therefore, out of the question. Although nature has her habits, due to the recurrence of causes, they are general, not invariable. Yet empirical calculation, although it is inexact, may be adequate in affairs of practice." (Gottfried W Leibniz [letter to Bernoulli], 1703)
"We define the art of conjecture, or stochastic art, as the art of evaluating as exactly as possible the probabilities of things, so that in our judgments and actions we can always base ourselves on what has been found to be the best, the most appropriate, the most certain, the best advised; this is the only object of the wisdom of the philosopher and the prudence of the statesman." (Jacob Bernoulli, "Ars Conjectandi", 1713)
"Probability is a degree of certainty and it differs from certainty as a part from a whole." (Jacob Bernoulli, "Ars Conjectandi", 1713)
"The probability of an Event is greater, or less, according to the number of Chances by which it may Happen, compar’d with the number of all the Chances, by which it may either Happen or Fail. […] Therefore, if the Probability of Happening and Failing are added together, the Sum will always be equal to Unit." (Abraham De Moivre, "The Doctrine of Chances", 1718)
"Probable evidence, in its very nature, affords but an imperfect kind of information, and is to be considered as relative only to beings of limited capacities. For nothing which is the possible object of knowledge, whether past, present, or future, can be probable to an infinite Intelligence; […] to us, probability is the very guide of life." (Joseph Butler, "The Analogy of Religion, Natural and Revealed, to the Constitution and Course of Nature", 1736)
"Do not expect to arrive at certainty in every subject which you pursue. There are a hundred things wherein we mortals […] must be content with probability, where our best light and reasoning will reach no farther." (Isaac Watts," The Improvement of the Mind", 1741)
No comments:
Post a Comment