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Hace 4 días · Analysis, probability, and astronomical stability. Laplace's early published work in 1771 started with differential equations and finite differences but he was already starting to think about the mathematical and philosophical concepts of probability and statistics.
2 de jul. de 2024 · Probability is the study of randomness. It has a mathematical aspect and a philosophical aspect. The mathematical aspect is described in Chapter 17, Probability: Axioms and Fundaments.
21 de jun. de 2024 · In 1814 Laplace published a popular work for the general reader, Essai philosophique sur les probabilités (A Philosophical Essay on Probability).
23 de jun. de 2024 · It makes sense that the (epistemic) probability of a position conditioned on evidence which entails it is 1—but from that it doesn't seem to follow that P(B) cannot be greater than P(A). What if, for example, B occurs if A occurs or if C occurs, while A and C can occur independently of one another.
12 de jun. de 2024 · In 1814, in his Philosophical Essay on Probabilities, Pierre-Simon Laplace first described an intelligence, now known as Laplace’s demon, that could predict these outcomes: We ought to regard the present state of the universe as the effect of its antecedent state and as the cause of the state that is to follow.
21 de jun. de 2024 · I would argue that there is little difference between outcomes if the effect on the observer and the reaction by the observer are the same. This eventually leads to many philosophical questions relating to probability, which is a larger topic that I don't have the time or energy to share my complete thoughts on.
28 de jun. de 2024 · I use John Conway's surreal numbers to capture these pre-theoretic judgements about the relative probabilities of Al's, Betty's, and Carl's claims. Surreal-valued probabilities also allow us to calculate precise numerical values for those claims.
