Special Issue "Logic, Inference, Probability and Paradox"

A special issue of Philosophies (ISSN 2409-9287).

Deadline for manuscript submissions: 30 November 2017

Special Issue Editors

Guest Editor
Prof. Dr. Julio Stern

Department of Applied Mathematics, Institute of Mathematics and Statistics, University of São Paulo, Rua do Matão 1010 – Cidade Universitária, CEP 05508-900 São Paulo, SP, Brazil
Website | E-Mail
Interests: Bayesian inference; foundations of statistics; significance measures; evidence; logic and epistemology of significance measures
Guest Editor
Prof. Dr. Walter Carnielli

Centre for Logic, Epistemology and the History of Science, State University of Campinas, Cidade Universitária Zeferino Vaz - Barão Geraldo, Campinas - SP, 13083-970, Brazil
Website | E-Mail
Interests: logic foundations of probability and posibility; probabilistic reasoning; philosophy of probability; combinatorics and probability
Guest Editor
Dr. Juliana Bueno-Soler

FT - School of Technology, State University of Campinas, Campus Limeira, Limeira - SP, 13484-332, Brazil
Website | E-Mail
Interests: Bayesian inference; probabilistic reasoning; logic foundations of probability; interpretations of probability; statistical models

Special Issue Information

Dear Colleagues,

Reasoning with uncertain knowledge is a growing area of interest, involving several tendencies, such as reasoning with non-standard theories of probability (e.g., theories of probability based on non-classical logics) and combining argumentation systems, is more qualitative in nature, with probabilities or probabilistic semantics. All such tendencies and areas of investigation are naturally generalized to possibility systems and other credal calculi. This poses new and intriguing questions on the philosophy of probability and credal calculi in general, amplifying the discussions around the correct formal theories of probability and on the interpretations of probability, among the classical, logical, frequentist, propensity, and subjectivist (and possibly others). Dilemmas and paradoxes in probabilities and credal calculi are also a relevant area of research. This Special Issue intends to contribute to the state-of-the-art of such research topics by gathering together the contribution of authors in interconnected areas including logical, mathematical and conceptual aspects.

Prof. Dr. Julio Michael Stern
Prof. Dr. Walter Alexandre Carnielli
Dr. Juliana Bueno-Soler
Guest Editors

Manuscript Submission Information

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Keywords

  • interpretations of probability, possibility and other credal calculi
  • philosophy of probability, possibility and other credal calculi
  • probabilistic and possibilistic argumentation and inference
  • probability, possibility and uncertain reasoning
  • paradoxes in probability, possibility and other credal calculi

Published Papers (2 papers)

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Research

Open AccessArticle The Interpretation of Probability: Still an Open Issue? 1
Philosophies 2017, 2(3), 20; doi:10.3390/philosophies2030020
Received: 19 July 2017 / Revised: 18 August 2017 / Accepted: 19 August 2017 / Published: 29 August 2017
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Abstract
Probability as understood today, namely as a quantitative notion expressible by means of a function ranging in the interval between 0–1, took shape in the mid-17th century, and presents both a mathematical and a philosophical aspect. Of these two sides, the second is
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Probability as understood today, namely as a quantitative notion expressible by means of a function ranging in the interval between 0–1, took shape in the mid-17th century, and presents both a mathematical and a philosophical aspect. Of these two sides, the second is by far the most controversial, and fuels a heated debate, still ongoing. After a short historical sketch of the birth and developments of probability, its major interpretations are outlined, by referring to the work of their most prominent representatives. The final section addresses the question of whether any of such interpretations can presently be considered predominant, which is answered in the negative. Full article
(This article belongs to the Special Issue Logic, Inference, Probability and Paradox)
Open AccessArticle Entrance Fees and a Bayesian Approach to the St. Petersburg Paradox
Philosophies 2017, 2(2), 11; doi:10.3390/philosophies2020011
Received: 16 February 2017 / Revised: 2 May 2017 / Accepted: 4 May 2017 / Published: 10 May 2017
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Abstract
In An Introduction to Probability Theory and its Applications, W. Feller established a way of ending the St. Petersburg paradox by the introduction of an entrance fee, and provided it for the case in which the game is played with a fair
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In An Introduction to Probability Theory and its Applications, W. Feller established a way of ending the St. Petersburg paradox by the introduction of an entrance fee, and provided it for the case in which the game is played with a fair coin. A natural generalization of his method is to establish the entrance fee for the case in which the probability of heads is θ ( 0 < θ < 1 / 2 ) . The deduction of those fees is the main result of Section 2. We then propose a Bayesian approach to the problem. When the probability of heads is θ ( 1 / 2 < θ < 1 ) the expected gain of the St. Petersburg game is finite, therefore there is no paradox. However, if one takes θ as a random variable assuming values in ( 1 / 2 , 1 ) the paradox may hold, which is counter-intuitive. In Section 3 we determine necessary conditions for the absence of paradox in the Bayesian approach and in Section 4 we establish the entrance fee for the case in which θ is uniformly distributed in ( 1 / 2 , 1 ) , for in this case there is a paradox. Full article
(This article belongs to the Special Issue Logic, Inference, Probability and Paradox)
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