A Philosophical Essay on Probabilities (Google eBook)

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Cosimo, Inc., Apr 1, 2007 - Mathematics - 208 pages
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In this, his most famous work, Pierre-Simon, Marquis de Laplace lays out a system for reasoning based on probability. The single most famous piece introduced in this work is the rule of succession, which calculates the probability that a trial will be a success based on the number of times it has succeeded in the past. Students of mathematics will find A Philosophical Essay on Probabilities an essential read for understanding this complex field of study and applying its truths to their lives. French mathematician PIERRE-SIMON, MARQUIS DE LAPLACE (1749-1827) was essential in the formation of mathematical physics. He spent much of his life working on mathematical astronomy and even suggested the existence of black holes. Laplace is also known for his work on probability.
  

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on page 177: (This simplicity of ratios will not appear astonishing if we consider that) all the effects of nature are only mathematical results of a small number of immutable laws.

Contents

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Page 4 - Given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective situation of the beings who compose it — an intelligence sufficiently vast to submit these data to analysis — it would embrace in the same formula the movements of the greatest bodies of the universe and those of the lightest atom; for it, nothing would be uncertain and the future, as the past, would be present to its eyes.
Page 7 - 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 the cases possible...
Page 4 - Given, for one instant, an intelligence which could comprehend all the forces by which nature is animated and the respective situation of the beings who compose it — an intelligence sufficiently vast to submit these data to analysis — it would embrace in the same formula the movements of the greatest bodies of the universe and those of the lightest atom. For it, nothing would be uncertain and the future, as the past, would be present to its eyes.
Page 15 - C; it would change to certainty if a black ball had been drawn from the same urn. We will determine this influence by means of the following principle, which is a corollary of the preceding one. Fifth Principle. — If we calculate a priori the probability of the occurred event and the probability of an event composed of that one and a second one which is expected, the second probability divided by the first will be the probability of the event expected, drawn from the observed event. Here is presented...
Page 1 - ... only problems of probability. Strictly speaking it may even be said that nearly all our knowledge is problematical; and in the small number of things which we are able to know with certainty, even in the mathematical sciences themselves, the principal means of ascertaining truth — induction, and analogy — are based on probabilities; so that the entire system of human knowledge is connected with the theory set forth in this essay.
Page 13 - We cannot better compare this diminution of the probability than with the extinction of the light of objects by the interposition of several pieces of glass. A relatively small number of pieces suffices to take away the view of an object that a single piece allows us to perceive in a distinct manner. The historians do not appear to have paid sufficient attention to this degradation of the probability of events when seen across a great number of successive generations; many historical events reputed...
Page 4 - Its discoveries in mechanics and geometry, added to that of universal gravity, have enabled it to comprehend in the same analytical expressions the past and future states of the system of the world. Applying the same method to some other objects of its knowledge, it has succeeded in referring to general laws observed phenomena and in foreseeing those which given circumstances ought to produce. All these efforts in the search for truth tend to lead it back continually to the vast intelligence which...
Page 6 - has reference partly to our ignorance, partly to our knowledge. We know that among three or more events, one, and only one, must happen ; but there is nothing leading us to believe that any one of them will happen rather than the others. In this state of indecision, it is impossible for us to pronounce with certainty on their occurrence. It is, however, probable that any one of these events, selected at pleasure, will not take place ; because we perceive several cases, all equally possible, which...

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