Probabilism, Assertion, and Higher-Order Vagueness

2018 ◽  
Author(s):  
Andrew Bacon
Keyword(s):  
Probability Theory ◽  
Higher Order ◽  
Dutch Book ◽  
Probability Calculus ◽  
Hartry Field ◽  
Standard Probability

Hartry Field has recently suggested that a non-standard probability calculus better represents our beliefs about vague matters. His theory has two notable features: (i) that your attitude to P when you are certain that P is higher-order borderline ought to be the same as your attitude when you are certain that P is simply borderline, and (ii) that when you are certain that P is borderline you should have no credence in P and no credence in ~. This chapter rejects both elements of this view and advocates instead for the view that when you are in possession of all the possible evidence, and it is borderline whether P is borderline, it is borderline whether you should believe P. Secondly, it argues for probabilism: the view that your credences ought to conform to the probability calculus. To get a handle on these issues, the chapter looks at Dutch book arguments and comparative axiomatizations of probability theory.

The Oxford Handbook of Probability and Philosophy

2017 ◽  
Keyword(s):  
Social Sciences ◽  
Probability Theory ◽  
Philosophy Of Science ◽  
Significant Role ◽  
Philosophy Of Religion ◽  
Social Philosophy ◽  
The State ◽  
Science Ethics ◽  
Probabilistic Judgment ◽  
Standard Probability

Probability theory is a key tool of the physical, mathematical, and social sciences. It has also been playing an increasingly significant role in philosophy: in epistemology, philosophy of science, ethics, social philosophy, philosophy of religion, and elsewhere. This Handbook encapsulates and furthers the influence of philosophy on probability, and of probability on philosophy. Nearly forty articles summarize the state of play and present new insights in various areas of research at the intersection of these two fields. The volume begins with a primer on those parts of probability theory that we believe are most important for philosophers to know, and the rest is divided into seven main sections: history; formalism; alternatives to standard probability theory; interpretations and interpretive issues; probabilistic judgment and its applications; applications of probability: science; and applications of probability: philosophy.

scholarly journals Ratio of two random variables

2006 ◽  
Vol 3 (1) ◽  
Author(s):  
Anton Cedilnik ◽  
Katarina Košmelj ◽  
Andrej Blejec
Keyword(s):  
Probability Theory ◽  
Statistical Inference ◽  
Additional Assumption ◽  
Existence Theorems ◽  
Random Variables ◽  
Specific Behaviour ◽  
Standard Probability

To enable correct statistical inference, the knowledge about the existence of moments is crucial. The objective of this paper is to study the existence of the moments for the ratio \(Z = X/Y\) , where \(X\) and \(Y\) are arbitrary random variables with the additional assumption \(P(Y = 0) = 0\). We present three existence theorems showing that specific behaviour of the distribution of \(Y\) in the neighbourhood of zero is essential. Simple consequences of these theorems give evidence to the existence of the moments for particular random variables; some of these results are well known from standard probability theory. However, we obtain them in a simple way.

Probability and Decision Theory

2020 ◽  
pp. 6-41
Author(s):  
Juan Comesaña
Keyword(s):  
Decision Theory ◽  
Conditional Probability ◽  
Expected Utility ◽  
Utility Maximization ◽  
Measure Theory ◽  
Dutch Book ◽  
Logical Omniscience ◽  
Probability Calculus ◽  
Expected Utility Maximization ◽  
Truth Tables

This chapter introduces the mathematics of probability and decision theory. The probability calculus is introduced in both a set-theoretic and a propositional context. Probability is also related to measure theory, and stochastic truth-tables are presented. Problems with conditional probability are examined. Two interpretations of the probability calculus are introduced: physical and normative probabilities. The problem of logical omniscience for normative probabilities is discussed. Dutch Book arguments and accuracy-based arguments for Probabilism (the claim that our credences must satisfy the probability axioms) are examined and rejected. Different interpretations of the “idealization” reply to the problem of logical omniscience are considered, and one of them is tentatively endorsed. The expected utility maximization conception of decision theory is introduced, and representation arguments are considered (and rejected) as another reply to the problem of logical omniscience.

Upshots for Other Debates

2021 ◽  
pp. 281-314
Author(s):  
Alex Worsnip
Keyword(s):  
Rational Choice ◽  
Rational Choice Theory ◽  
Choice Theory ◽  
Higher Order ◽  
Dutch Book ◽  
Philosophical Literature ◽  
Normativity Of Logic ◽  
Money Pump ◽  
Higher Order Evidence

This chapter explores and draws out the consequences of both the dualist view of rationality defended in Part I and the theory of structural rationality defended in Part II for a series of standing debates in (meta)ethics and epistemology—including debates about moral rationalism, rational choice theory, higher-order evidence, the normativity of logic, epistemic permissivism, and conditionalization. It also considers and criticizes some popular ways of trying to account for the existence and force of coherence requirements in the formally inclined philosophical literature—namely, Dutch book and money pump arguments and accuracy dominance arguments.

Introduction

2017 ◽  
Author(s):  
Alan Hájek ◽  
Christopher Hitchcock
Keyword(s):  
Probability Theory ◽  
Current Debate ◽  
Probabilistic Judgment ◽  
Exciting Time ◽  
Standard Probability

This is an exciting time for the philosophy of probability, and probability theory’s value to philosophy has never been as appreciated as it is nowadays. The introduction to this Handbook sets out the context of the current debate in this area and provides a primer on those parts of probability theory that are most important for philosophers to know. It then goes on to introduce the seven main sections of the handbook: History; Formalism; Alternatives to Standard Probability Theory; Interpretations and Interpretive Issues; Probabilistic Judgment and Its Applications; Applications of Probability: Science; and Applications of Probability: Philosophy.

Let us not put the probabilistic cart before the uncertainty bull

2009 ◽  
Vol 32 (1) ◽  
pp. 100-101 ◽  
Author(s):  
Guy Politzer ◽  
Jean-François Bonnefon
Keyword(s):  
Probabilistic Framework ◽  
Probability Calculus ◽  
The Past ◽  
Standard Probability

AbstractAlthough we endorse the primacy of uncertainty in reasoning, we argue that a probabilistic framework cannot model the fundamental skill of proof administration. Furthermore, we are skeptical about the assumption that standard probability calculus is the appropriate formalism to represent human uncertainty. There are other models up to this task, so let us not repeat the excesses of the past.

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