some arguments against infinite regress in islamic philosophy such as applied proof or argument of ones and thousands are based on the mathematical foundations and preliminaries. extraction and analysis of these preliminaries exposes mathematical nature of these arguments and shows that besides philosophical approach to these arguments should also look at them from perspective of mathematics. a...

When I studied microeconomics forty years ago, I was first taught how optimizing firms and consumers would behave, and then taught the nature of the economic equilibrium which would result from such behavior. Let me refer to this as part one and part two of my microeconomics course. My work on portfolio theory considers how an optimizing investor would behave, whereas the work by Sharpe and Lin...

Information has become the most precious resource of society. At the same time, there is no consensus on the meaning of the term " information, " and many researchers have considered problems of information definition. This results in a quantity of contradictions, misconceptions, and paradoxes related to the world of information. To remedy the situation, a new approach in information theory, wh...

This paper states necessary and sufficient conditions for the existence, uniqueness, and updating according to Bayes’ rule, of subjective probabilities representing individuals’ beliefs. The approach is preference based, and the result is an axiomatic subjective expected utility model of Bayesian decision making under uncertainty with statedependent preferences. The theory provides foundations ...

Consider a cofibrantly generated model category S, a small category C and a subcategory D of C. We endow the category S C of functors from C to S with a model structure, defining weak equivalences and fibrations ob-jectwise but only on D. Our first concern is the effect of moving C, D and S. The main notion introduced here is the " D-codescent " property for objects in S C. Our long-term progra...