"The word ‘chance’ then expresses only our ignorance of the causes of the phenomena that we observe to occur and to succeed one another in no apparent order. Probability is relative in part to this ignorance, and in part to our knowledge.” (Pierre-Simon Laplace, "Mémoire sur les Approximations des Formules qui sont Fonctions de Très Grands Nombres", 1783)
"[It] may be laid down as a general rule that, if the result of a long series of precise observations approximates a simple relation so closely that the remaining difference is undetectable by observation and may be attributed to the errors to which they are liable, then this relation is probably that of nature.” (Pierre-Simon Laplace, "Mémoire sur les Inégalites Séculaires des Planètes et des Satellites”, 1787)
"The algebraic analysis soon makes us forget the main object [of our researches] by focusing our attention on abstract combinations and it is only at the end that we return to the original objective. But in abandoning oneself to the operations of analysis, one is led to the generality of this method and the inestimable advantage of transforming the reasoning by mechanical procedures to results often inaccessible by geometry. Such is the fecundity of the analysis that it suffices to translate into this universal language particular truths In order to see emerge from their very expression a multitude of new and unexpected truths. No other language has the capacity for the elegance that arises from a long sequence of expressions linked one to the other and all stemming from one fundamental idea. Therefore the geometers [mathematicians] of this century convinced of its superiority have applied themselves primarily to extending Its and pushing back its bounds." (Pierre-Simon Laplace, "Exposition du system du monde" ["Explanation on the solar system"], 1796)
"Surrounded as we are by an infinite variety of phenomena, which continually succeed each other in the heavens and on the earth, philosophers have succeeded in recognizing the small number of general laws to which matter is subject in its motions. To them, all nature is obedient; and everything is as necessarily derived from them, as the return of the seasons; so that the curve which is described by the lightest atom that seems to be driven at random by the winds, is regulated by laws as certain as those which confine the planets to their orbits." (Pierre-Simon Laplace, "System of the World" Vol. 1, 1809)
"If we seek a cause wherever we perceive symmetry, it is not that we regard a symmetrical event as less possible than the others, but, since this event ought to be the effect of a regular cause or that of chance, the first of these suppositions is more probable than the second.” (Pierre-Simon de Laplace, "Philosophical Essay on Probabilities”, 1812)
"The most important questions of life are indeed, for the most part, really only problems of probability.” (Pierre-Simon Laplace, "Analytical Theory of Probability, 1812)
"The theory of probabilities is at bottom nothing but common sense reduced to calculus; it enables us to appreciate with exactness that which accurate minds feel with a sort of instinct for which of times they are unable to account.” (Pierre-Simon Laplace, "Analytical Theory of Probability, 1812)
"If we seek a cause wherever we perceive symmetry, it is not that we regard a symmetrical event as less possible than the others, but, since this event ought to be the effect of a regular cause or that of chance, the first of these suppositions is more probable than the second.” (Pierre-Simon de Laplace, "Philosophical Essay on Probabilities”, 1812)
"The most important questions of life are indeed, for the most part, really only problems of probability.” (Pierre-Simon Laplace, "Analytical Theory of Probability, 1812)
"The theory of probabilities is at bottom nothing but common sense reduced to calculus; it enables us to appreciate with exactness that which accurate minds feel with a sort of instinct for which of times they are unable to account.” (Pierre-Simon Laplace, "Analytical Theory of Probability, 1812)
"Analysis and natural philosophy owe their most important discoveries to this fruitful means, which is called induction. Newton was indebted to it for his theorem of the binomial and the principle of universal gravity." (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)
"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)
"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)
"In the game of heads and tails, if head comes up a hundred times in a row then this appears to us extraordinary, because after dividing the nearly infinite number of combinations that can arise in a hundred throws into regular sequences, or those in which we observe a rule that is easy to grasp, and into irregular sequences, the latter are incomparably more numerous." (Pierre-Simon Laplace, "A Philosophical Essay on Probability Theories", 1951)
"[…] we must not measure the simplicity of the laws of nature by our facility of conception; but when those which appear to us the most simple, accord perfectly with observations of the phenomena, we are justified in supposing them rigorously exact.” (Pierre-Simon Laplace)
"All the effects of nature are only mathematical results of a small number of immutable laws." (Pierre-Simon de Laplace)
"Such is the advantage of a well-constructed language that its simplified notation often becomes the source of profound theories.” (Pierre-Simon Laplace)
"The present state of the system of nature is evidently a consequence of what is in the preceding moment, and if we conceive of an intelligence which at a given instant knew all the forces acting in nature and the position of every object in the universe - if endowed with a brain sufficiently vast to make all necessary calculations - could describe with a single formula the motions of the largest astronomical bodies and those of the smallest atoms. To such an intelligence, nothing would be uncertain; the future, like the past, would be an open book." (Pierre-Simon Laplace)
"All the effects of nature are only mathematical results of a small number of immutable laws." (Pierre-Simon de Laplace)
"Such is the advantage of a well-constructed language that its simplified notation often becomes the source of profound theories.” (Pierre-Simon Laplace)
"The present state of the system of nature is evidently a consequence of what is in the preceding moment, and if we conceive of an intelligence which at a given instant knew all the forces acting in nature and the position of every object in the universe - if endowed with a brain sufficiently vast to make all necessary calculations - could describe with a single formula the motions of the largest astronomical bodies and those of the smallest atoms. To such an intelligence, nothing would be uncertain; the future, like the past, would be an open book." (Pierre-Simon Laplace)
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