A. A. Markov's work on probability

Communicated by H. Freudenthal     

P.S. Laplace's work on probability

Taken together with my previous articles [77], [80] devoted to the history of finite random sums and to Laplace's theory of errors, this paper sheds sufficient light on the whole work of Laplace in probability. Laplace's theory of probability is subdivided into theory of probability proper, limit theorems and mathematical statistics (not yet distinguished as a separate entity). I maintain that in its very design Laplace's theory of probability is a discipline pertaining to natural science rather than to mathematics. I maintain also the idea that the so-called Laplacian determinism was no hindrance to applications of his theory of probability to natural science and that one of his utterances in this connection could have well been made by Maxwell's contemporaries.Two possible reasons why the theory of probability stagnated after Laplace's work are singled out: the absence of new fields of application and, also, the insufficient level of mathematical abstraction used by Laplace. For all his achievements, I reach the general conclusion that he did not originate the theory of probability as it is now known. Dedicated to the memory of my Father, Boris A. Sheynin (1898–1975), the first generation of the Russian revolution Cette inégalité [Lunaire] quoique indiquée par les observations, était négligée par le plus grand nombre des astronomes, parce qu'elle ne paraissait pas résulter de la théorie de la pesanteur universelle. Mais, ayant soumis son existence au Calcul des Probabilités, elle me parut indiqués avec une probabilité si forte, que je crus devoir en rechercher la cause.(P. S. Laplace (Théor. anal. prob., p. 361))     

H. Poincaré's work on probability

Communicated by O. Pedersen     

Newton and the classical theory of probability

Summary Probabilistic ideas and methods from Newton's writings are discussed in § 1: Newton's ideas pertaining to the definition of probability, his probabilistic method in chronology, his probabilistic ideas and method in the theory of errors and his probabilistic reasonings on the system of the world. Newton's predecessors and his influence upon subsequent scholars are dealt with in §2: beginning with his predecessors the discussion continues with his contemporaries Arbuthnot and De Moiver, then Bentley. The section ends with Laplace, whose determinism is seen as a development of the Newtonian determinism.An addendum is devoted to Lambert's reasoning on randomness and to the influence of Darwin on statistics. A synopsis is attached at the end of the article.Abbreviations PT abridged Philosophical Transactions of the Royal Society 1665–1800 abridged. London, 1809 - Todhunter I. Todhunter, History of the mathematical theory of probability, Cambridge, 1865 To the memory of my mother, Sophia Sheynin (1900–1970)     

Chebyshev's lectures on the theory of probability

Communicated by B. Bru     

Chance,determinism and the classical theory of probability

This paper situates the metaphysical antinomy between chance and determinism in the historical context of some of the earliest developments in the mathematical theory of probability. Since Hacking's seminal work on the subject, it has been a widely held view that the classical theorists of probability were guilty of an unwitting equivocation between a subjective, or epistemic, interpretation of probability, on the one hand, and an objective, or statistical, interpretation, on the other. While there is some truth to this account, I argue that the tension at the heart of the classical theory of probability is not best understood in terms of the duality between subjective and objective interpretations of probability. Rather, the apparent paradox of chance and determinism, when viewed through the lens of the classical theory of probability, manifests itself in a much deeper ambivalence on the part of the classical probabilists as to the rational commensurability of causal and probabilistic reasoning.     

On the structure of Carnot's theory of heat

A simple connection is pointed out between the theory of heat formulated in Sadi Carnot's: Réflexions sur la puissance motrice du feu (1824) and the later Kelvin-Clausius thermodynamics. In both theories two well-defined quantities, a heat function and a work function, exist and can be calculated by integrating along a reversible path. In thermodynamics the work function (energy) is conserved, whereas the heat function (entropy) increases by irreversible processes. In Carnot's theory the heat function is conserved, whereas the work function decreases, so that in this theory the irreversible process is characterized by a loss of work.