Philosophy Of Probability

Objective Probability in Everettian Quantum Mechanics

by Alastair Wilson

Forthcoming in British Journal for Philosophy of Science.

David Wallace has given a decision-theoretic argument for the Born Rule in the context of Everettian quantum mechanics... more David Wallace has given a decision-theoretic argument for the Born Rule in the context of Everettian quantum mechanics (EQM). This approach promises to resolve some long-standing problems with probability in EQM, but it has faced plenty of resistance. One kind of objection (the ‘Incoherence problem’) charges that the requisite notion of decision-theoretic uncertainty is unavailable in the Everettian picture, so that the argument cannot gain any traction; another kind of objection grants the proof’s applicability and targets the premises. In this paper I propose some novel principles connecting the physics of EQM with the metaphysics of modality, and argue that in the resulting framework the Incoherence problem does not arise. These principles also help to justify one of the most controversial premises of Wallace’s argument, ‘branching indifference’. Absent any  a priori reason to align the metaphysics with the physics in some other way, we can adopt the proposed principles on grounds of theoretical utility. The upshot is that Everettians can, after all, make clear sense of objective probability.

Discovery Reconceived: Product Before Process (FLM 2012)

by Dor Abrahamson

Abrahamson, D. (2012). Discovery reconceived: product before process. For the Learning of Mathematics, 32(1), 8-15.

FOREWORD: In this paper, I reflect on epistemological issues germane to the practice of pedagogical design. What does it mean to know a mathematical concept? What is a concept grounded in? How can it have meaning at all? What does this imply for education? I contextualize these questions in a couple of empirical episodes selected from previous design-based research studies. One is a probability design building on tacit perception of statistical representativeness, the other is a design for proportion that builds on tacit perception of geometrical similitude (or, perhaps, object constancy). So these designs are both of what I call the "perception-based" ilk. My more recent design is of the "action-based" ilk.

ABSTRACT: Motivated by the question, "What exactly about a mathematical concept should students discover, when... more ABSTRACT: Motivated by the question, "What exactly about a mathematical concept should students discover, when they study it via discovery learning?", I present and demonstrate an interpretation of discovery pedagogy that attempts to address its criticism. My approach hinges on decoupling the solution process from its resultant product. Whereas theories of learning often focus on process as the site of discovery, I propose to focus instead on product. Specifically, I view student discovery of mathematical concepts as their guided heuristic–semiotic aligning of the product of analysis process with informal inference from naively seeing situations. I support my thesis with two vignettes.

PROPENSITIES AND PRAGMATISM_final

by Mauricio Suárez

Forthcoming in Journal of Philosophy, 2012

This paper outlines a genuinely pragmatist conception of propensity, and defends it against common objections
to... more This paper outlines a genuinely pragmatist conception of propensity, and defends it against common objections
to the propensity interpretation of probability, prominently Humphreys’ paradox. The paper reviews the paradox and identifies one of its key assumptions, the identity thesis, according to which propensities are probabilities (under a suitable interpretation of Kolmogorov’s axioms). The identity thesis is also involved in empiricist propensity interpretations deriving from Popper’s influential original proposal, and makes such interpretations untenable. As an alternative, I urge a
return to Charles Peirce’s original insights on probabilistic dispositions, and offer a reconstructed version of his pragmatist conception, which rejects the identity thesis.

Probability and Prodigality

by Daniel Greco

Forthcoming in Oxford Studies in Epistemology, Volume 4

I present a straightforward objection to the view that what we know has epistemic probability 1: when combined with... more I present a straightforward objection to the view that what we know has epistemic probability 1: when combined with orthodox decision theory, the view seems to entail implausible conclusions concerning rational choice. I consider and reject three responses. The first holds that the fault is with decision theory, rather than the view that knowledge has probability 1. The second two try to reconcile the claim that knowledge has probability 1 with decision theory by appealing to contextualism and sensitive invariantism, respectively. I argue that each response fails, and that we can hold on to much of what was attractive in the responses while denying that what we know has probability 1.

Review of Hugh Mellor's Probability (Routledge, 2005)

by Mauricio Suárez

Published in Theoria, 70 (January 2011), pp. 99-103.

Concepts of Probability in Radiocarbon Analysis.

by Olaf Jöris

Weninger et al. 2011: B. Weninger / K. Edinborough / L. Clare / O. Jöris, Concepts of Probability in Radiocarbon Analysis. Documenta Prehistorcia XXXVIII, 1-20.
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ABSTRACT – In this paper, we explore the meaning of the word probability, not in general terms, but restricted to the... more ABSTRACT – In this paper, we explore the meaning of the word probability, not in general terms, but restricted to the field of Radiocarbon dating, where it has the meaning of ‘dating probability assigned to calibrated 14C-ages’. The intention of our study is to improve our understanding of certain properties of radiocarbon dates which – although mathematically abstract – are fundamental both for the construction of age models in prehistoric archaeology, as well as for an adequate interpretation
of their reliability.

PROBABILITY, CERTAINTY, AND FACTS IN FRANCIS BACON'S NATURAL HISTORIES. A DOUBLE ATTITUDE TOWARDS SKEPTICISM

by Silvia Manzo

Infinite populations and counterfactual frequencies in evolutionary theory

by Marshall Abrams

Infinite Populations and Counterfactual Frequencies in Evolutionary Theory, Studies in History and Philosophy of Biological and Biomedical Sciences, 37(2), June 2006

One finds intertwined with ideas at the core of evolutionary theory claims about frequencies in counterfactual and... more One finds intertwined with ideas at the core of evolutionary theory claims about frequencies in counterfactual and infinitely large populations of organisms, as well as in sets of populations of organisms. One also finds claims about frequencies in counterfactual and infinitely large populations--of events--at the core of an answer to a question concerning the foundations of evolutionary theory. The question is this: To what do the numerical probabilities found throughout evolutionary theory correspond? The answer in question says that evolutionary probabilities are "hypothetical frequencies" (including what are sometimes called "long-run frequencies" and "long-run propensities"). In this paper, I review two arguments against hypothetical frequencies. The arguments have implications for the interpretation of evolutionary probabilities, but more importantly, they seem to raise problems for biologists' claims about frequencies in counterfactual or infinite populations of organisms and sets of populations of organisms. I argue that when properly understood, claims about frequencies in large and infinite populations of organisms and sets of populations are not threatened by the arguments. Seeing why gives us a clearer understanding of the nature of counterfactual and infinite population claims and probability in evolutionary theory.

Mechanistic Probability

by Marshall Abrams

Forthcoming in Synthese.  (PDF available by request, or at the journal's site: http://www.springerlink.com/content/kn133p8611p48qg2/ .

I describe a realist, ontologically objective interpretation of probability, "far-flung frequency (FFF)... more I describe a realist, ontologically objective interpretation of probability, "far-flung frequency (FFF) mechanistic probability".  FFF mechanistic probability is defined in terms of facts about the causal structure of devices and certain sets of frequencies in the actual world.  Though defined partly in terms of frequencies, FFF mechanistic probability avoids many drawbacks of well-known frequency theories and helps causally explain stable frequencies, which will usually be close to the values of mechanistic probabilities.  I also argue that it's a virtue rather than a failing of FFF mechanistic probability that it does not define single-case chances, and compare some aspects of my interpretation to a recent interpretation proposed by Strevens.

"Mechanistic Social Probability: How Individual Choices and Varying Circumstances Produce Stable Social Patterns"

by Marshall Abrams

Forthcoming in the Oxford Handbook of the Philosophy of the Social Sciences

"When Do I Get My Money?" A Probabilistic Theory Of Knowledge. PhD thesis 2011

by Jonny Blamey

PhD thesis KCL 2011. Examiners Jon Williamson and Luc Bovens, final supervisor David Papineau.

The important claim in this thesis is that it is rational to vary your degree of belief relative to what is at stake.... more The important claim in this thesis is that it is rational to vary your degree of belief relative to what is at stake. This allows a probabilistic theory of knowledge that can answer scepticism and avoid Gettier problems. It provides a decision theory that explains the Allais paradox, the Ellsberg paradox and gives an empirically adequate account of decisions under risk, whilst providing a probability measure that conforms to the Kolmogorov axioms. The probabilistic theory of knowledge thus vindicates the intuition that the same evidence can yeild knowledge at low stakes but not at high stakes.
At the heart of the theory is the Stake Size variation principle. This is a development of Ramseys theory of probability. The Stake Size Variation Principle give a measure of evidential support that is commensurable with measures for good. This allows a two dimensional account of evidential strength in terms of the point probability and the evidential value. The evidential value then determines how resilient the point probability is in the face of changes in stake size, as well as changes in evidence. The SSVP thus equates knowledge with value via the expectation principle.
There are two main arguments for the SSVP.
Firstly there is the contextualist argument that the scope of alternatives that need to be eliminated by the evidence can expand with an expansion of the stakes. In otherwords, it is wise to consider more possibilities when the stakes are high before settling in certainty.
Secondly there is the information theoretic argument based on the work of Kelly Jnr, which shows the inevitability of a downward drift and eventual ruin if one bets at the objective probability. This is due to the logarhythmic nature of growth.
The thesis concludes with a discussion of inductive certainty, showing how the SSVP can give an adequate account of how inductive certainty is possible.     

Objective probability-like things with and without objective indeterminism

by László E. Szabó

Quantum structures do not exist in reality

by László E. Szabó

Bruno de Finetti, l'origine de son subjectivisme

by Simona Morini

In this paper, I study the philosophical origins of Bruno de Finetti’s subjectivist theses in his interpretation ofmore In this paper, I study the philosophical origins of Bruno de Finetti’s subjectivist theses in his interpretation of
probabilities.

"Probability and Economy in Newman's Theory of Knowledge"

by Dwight Lindley

Newman Studies Journal (Spring 2010)