"Probability has reference partly to our ignorance, partly to our knowledge [..] The theory of chance consists in reducing all the events of the same kind to a certain number of cases equally possible, that is to say, to such as we may be equally undecided about in regard to their existence, and in determining the number of cases favorable to the event whose probability is sought. The ratio of this number to that of all cases possible is the measure of this probability, which is thus simply a fraction whose number is the number of favorable cases and whose denominator is the number of all cases possible." (Pierre-Simon Laplace, "Philosophical Essay on Probabilities", 1814)
"One may even say, strictly speaking, that almost all our knowledge is only probable; and in the small number of things that we are able to know with certainty, in the mathematical sciences themselves, the principal means of arriving at the truth - induction and analogy - are based on probabilities, so that the whole system of human knowledge is tied up with the theory set out in this essay." (Pierre-Simon Laplace, "Philosophical Essay on Probabilities", 1814)
"One of the great advantages of the calculus of probabilities is to teach us to distrust first opinions." (Pierre-Simon Laplace, "Philosophical Essay on Probabilities", 1814)
"In all speculations on the origin, or agents that have produced the changes on this globe, it is probable that we ought to keep within the boundaries of the probable effects resulting from the regular operations of the great laws of nature which our experience and observation have brought within the sphere of our knowledge. When we overleap those limits, and suppose a total change in nature's laws, we embark on the sea of uncertainty, where one conjecture is perhaps as probable as another; for none of them can have any support, or derive any authority from the practical facts wherewith our experience has brought us acquainted." (William Maclure, "Observations on the Geology of the United States of America", 1817)
"From the foregoing we see that the two justifications each leave something to be desired. The first depends entirely on the hypothetical form of the probability of the error; as soon as that form is rejected, the values of the unknowns produced by the method of least squares are no more the most probable values than is the arithmetic mean in the simplest case mentioned above. The second justification leaves us entirely in the dark about what to do when the number of observations is not large. In this case the method of least squares no longer has the status of a law ordained by the probability calculus but has only the simplicity of the operations it entails to recommend it." (Carl Friedrich Gauss, "Anzeige: Theoria combinationis observationum erroribus minimis obnoxiae: Pars prior", Göttingische gelehrte Anzeigen, 1821)
"The calculus of probability is equally applicable to things of all kinds, moral and physical and, if only in each case observations provide the necessary numerical data, it does not at all depend on their nature." (Siméon-Denis Poisson, "Researches into the Probabilities of Judgements in Criminal and Civil Cases", 1837)
"The probability of an event is our reason to believe that it will occur or occurred. [...] Probability depends on our knowledge about an event; for the same event it can differ for different persons. Thus, if a person only knows that an urn contains white and black balls, whereas another person alsoknows that there are more white balls than black ones, the latter has more grounds to believe in the extraction of a white ball. In other words, for him, that event has a higher probability than for the former." (Siméon-Denis Poisson, "Règles générales des probabilités", 1837)
"The measure of the probability of an event is the ratio of the number of cases favourable to that event, to the total number of cases favourable or contrary, and all equally possible' (equally like to happen)." (Siméon-Denis Poisson, "'Règles générales des probabilités", 1837)
"I consider the world probability as meaning the state of mind with respect to an assertion, a coming event, or any other matter on which absolute knowledge does not exist." (Augustus De Morgan, "Essay on Probability", 1838)
"By degree of probability we really mean, or ought to mean, degree of belief [...] Probability then, refers to and implies belief, more or less, and belief is but another name for imperfect knowledge, or it may be, expresses the mind in a state of imperfect knowledge. (Augustus De Morgan, "Formal Logic: Or, The Calculus of Inference, Necessary and Probable", 1847)
"Without doubt, matter is unlimited in extent, and, in this sense, infinite; and the forces of Nature mould it into an innumerable number of worlds. Would it be at all astonishing if, from the universal dice-box, out of an innumberable number of throws, there should be thrown out one world infinitely perfect? Nay, does not the calculus of probabilities prove to us that one such world out of an infinite number, must be produced of necessity? (Philippe Buchez & William B Greene, "Remarks on the Science of History: Followed by an a priori autobiography", 1849)
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