ON AN APPLICATION OF REGULAR VARIATION IN PROBABILITY THEORY

The reference considers probability theory in two main domains: fuzzy set theory, and quantum models. Readers will learn about the Kolmogorov probability theory and its implications in these two areas. Other topics covered include intuitionistic fuzzy sets (IF-set) limit theorems, individual ergodic theorem and relevant statistical applications (examples from correlation theory and factor analysis in Atanassov intuitionistic fuzzy sets systems, the individual ergodic theorem and the Poincaré recurrence theorem). This book is a useful resource for mathematics students and researchers seeking information about fuzzy sets in quantum spaces.

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Arguments from Providence and from Miracles

10.1093/oso/9780190842215.003.0021 ◽

2018 ◽

Author(s):

Timothy McGrew

Keyword(s):

Probability Theory ◽

20Th Century ◽

Probabilistic Analysis ◽

Interdisciplinary Collaboration ◽

Formal Analysis ◽

Empirical Science ◽

The Subject

The mid-20th century consensus regarding Hume’s critique of reported miracles has broken down dramatically in recent years thanks to the application of probabilistic analysis to the issue and the rediscovery of its history. Progress from this point forward is likely to be made along one or more of three fronts. There is wide room for interdisciplinary collaboration, work that will bring together scholars with expertise in religion, psychology, philosophy, and empirical science. There is a great deal of work still to be done in formal analysis, making use of the tools of modern probability theory to model questions about testimony and inference. And the recovery and study of earlier works on the subject—works that should never have been forgotten—can significantly enrich our understanding of the underlying issues.

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The Non-Causal Character of Renormalization Group Explanations

10.1093/oso/9780198777946.003.0011 ◽

2018 ◽

Author(s):

Margaret Morrison

Keyword(s):

Probability Theory ◽

Renormalization Group ◽

Dynamical Systems ◽

Recent Literature ◽

Mathematical Explanation ◽

Causal Status ◽

Physical Information ◽

The Relationship ◽

Structural Aspects

After reviewing some of the recent literature on non-causal and mathematical explanation, this chapter develops an argument as to why renormalization group (RG) methods should be seen as providing non-causal, yet physical, information about certain kinds of systems/phenomena. The argument centres on the structural character of RG explanations and the relationship between RG and probability theory. These features are crucial for the claim that the non-causal status of RG explanations involves something different from simply ignoring or “averaging over” microphysical details—the kind of explanations common to statistical mechanics. The chapter concludes with a discussion of the role of RG in treating dynamical systems and how that role exemplifies the structural aspects of RG explanations which in turn exemplifies the non-causal features.

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