The famous de Moivre’s Laplace limit theorem proved the probability density function of Gaussian distribution from binomial probability mass function under specified conditions. De Moivre’s Laplace approach is cumbe...The famous de Moivre’s Laplace limit theorem proved the probability density function of Gaussian distribution from binomial probability mass function under specified conditions. De Moivre’s Laplace approach is cumbersome as it relies heavily on many lemmas and theorems. This paper invented an alternative and less rigorous method of deriving Gaussian distribution from basic random experiment conditional on some assumptions.展开更多
Empirical, formal, and speculative understandings of logic as identified by Hegel will be formalized. Being formalized the propositions will be deduced from how probabilities can be used to make decisions by appropria...Empirical, formal, and speculative understandings of logic as identified by Hegel will be formalized. Being formalized the propositions will be deduced from how probabilities can be used to make decisions by appropriating Hegel＇s concept of being two-sided for inferences. This will work for what I will call grounded as opposed to ungrounded probability functions. The domain of their values will be decided by a three-valued modal relation of the binomial probability function. Keynes （1920, Ch. IV ~17） and Popper＇s （1959, Ch. 59） solution to the problem of unknown proportions will be challenged by an understanding of logic that puts the content of what the axioms mean for making rational decisions before their mere being. What is true for the different types inferences will then work for the principle of the dialectic in contrast to the two proposed by Hume and the one proposed by David Lewis. In this way, it will be demonstrated that Hegel＇s understanding of logic is still more advanced than one that fails to recognize it falls within the scope of the dialectic. Dialectic as such will be a principle where the different understandings of a predicated logic will have a modal value within a higher standpoint of system.展开更多
文摘The famous de Moivre’s Laplace limit theorem proved the probability density function of Gaussian distribution from binomial probability mass function under specified conditions. De Moivre’s Laplace approach is cumbersome as it relies heavily on many lemmas and theorems. This paper invented an alternative and less rigorous method of deriving Gaussian distribution from basic random experiment conditional on some assumptions.
文摘Empirical, formal, and speculative understandings of logic as identified by Hegel will be formalized. Being formalized the propositions will be deduced from how probabilities can be used to make decisions by appropriating Hegel＇s concept of being two-sided for inferences. This will work for what I will call grounded as opposed to ungrounded probability functions. The domain of their values will be decided by a three-valued modal relation of the binomial probability function. Keynes （1920, Ch. IV ~17） and Popper＇s （1959, Ch. 59） solution to the problem of unknown proportions will be challenged by an understanding of logic that puts the content of what the axioms mean for making rational decisions before their mere being. What is true for the different types inferences will then work for the principle of the dialectic in contrast to the two proposed by Hume and the one proposed by David Lewis. In this way, it will be demonstrated that Hegel＇s understanding of logic is still more advanced than one that fails to recognize it falls within the scope of the dialectic. Dialectic as such will be a principle where the different understandings of a predicated logic will have a modal value within a higher standpoint of system.
