This paper presents the way to make expansion for the next form function: to the numerical series. The most widely used methods to solve this problem are Newtons Binomial Theorem and Fundamental Theorem of Calculus (t...This paper presents the way to make expansion for the next form function: to the numerical series. The most widely used methods to solve this problem are Newtons Binomial Theorem and Fundamental Theorem of Calculus (that is, derivative and integral are inverse operators). The paper provides the other kind of solution, except above described theorems.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This paper presents the way to make expansion for the next form function: to the numerical series. The most widely used methods to solve this problem are Newtons Binomial Theorem and Fundamental Theorem of Calculus (that is, derivative and integral are inverse operators). The paper provides the other kind of solution, except above described theorems.
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.
