Probabilities in Science and Philosophy (The First Jerusalem-MCMP Workshop in the Philosophy of Science)
Idea and Motivation
The notion of ‘probability’ refers to a host of formal systems and to a host of ways of interpreting them. It is used in a host of various fields including Bayesian epistemology, decision theory, statistical considerations in social and natural sciences, and as part of the theories of physics, and more. In this workshop we shall address this intriguing notion from a variety of viewpoints and in a variety of context, with the hope that this interdisciplinary exchanges will yield deeper understanding and novel insights as to the meaning and use of probability in each of the different domains.
Day 1 (Thursday, 19 May 2016)
|09:30 – 10:00||Gathering and Refreshments|
|10:00 – 10:10||Opening|
|10:10 – 11:10||Stephan Hartmann: “Learning Causal Conditionals“|
|11:10 – 12:10||Ittay Nissan-Rozen: “The Ramsey Test, the Principal Principle and Admissible Propositions“|
|12:10 – 14:00||Lunch Break|
|14:00 – 15:00||Erik Curiel: “What Is Generic and What Is Special about the Universe?“|
|15:00 – 16:00||Orly Shenker: “Probability and Typicality in Statistical Mechanics“|
|16:00 – 16:20||Coffee Break|
|16:20 – 17:20||Meir Hemmo: “Probability and Typicality in Everett’s Approach to Quantum Mechanics“|
Day 2 (Friday, 20 May 2016)
|10:00 – 11:00||Seamus Bradley: “A Survey of Imprecise Probability with an Ulterior Motive“|
|11:00 – 12:00||Malte Doehne: “From Actor Characteristics to Actor Configurations: Predicting Relations between Entities“|
|12:00 – 12:20||Coffee Break|
|12:20 – 13:20||Danny November: “Ontological Implications of the Probability Space“|
|Afternoon tour for participants|
The Imprecise Probability (IP) model of rational belief has been gaining momentum in recent years. The core idea is that the standard Bayesian picture of partial belief needs some modification, and that using sets of probability functions, rather than single such functions, provides a good generalization of the standard view. This paper surveys the arguments and counterarguments for and against IP. However, the real goal is not to survey the extant literature, but rather to articulate a view on the methodology of formal epistemology that emerges from the dialectic of critically assessing the status of the debate on IP.top
Some of the deepest questions in cosmology concern what features of our universe are generic and what are special. Was the highly homogeneous state of the very early universe special in some sense (and so seemingly requiring explanation)? Do spacetimes such as ours generically possess singularities? To attempt to formulate such questions precisely and then address them requires probabilistic concepts and reasoning. Because of the peculiar and complex nature of the probability spaces involved – generally, infinite-dimensional manifolds – standard forms of probabilistic concepts and reasoning do not apply. I discuss the problems such questions pose, and consider some possibilities for addressing them. Along the way, I explicate the role the topology of a probability space plays in these sorts of problems, and its relation to possible probability measures on the space, an issue not adequately recognized in the literature on probabilistic reasoning. I state and sketch the proof of a theorem whose natural interpretation is that there is, at present, no satisfactory framework for posing and addressing such questions in even a somewhat precise and rigorous sense. I conclude by discussing the consequences for how we should assess the strength of standard forms of argument in sciences such as cosmology that would attempt to reason probabilistically about entities living in infinite-dimensional spaces.top
Malte Doehne (MCMP/LMU Munich): From Actor Characteristics to Actor Configurations: Predicting Relations between Entities
Much of empirical social science is concerned with predicting how particular actor characteristics affect the probability of observing specific behaviors being exhibited by mutually independent actors. In recent years, this received view of empirical social science is being supplanted by a battery of novel methods and approaches that shift attention from the characteristics of trait-bearing entities to the relations that are observed or assumed to be in place between them. Agent-based Modeling and Social Network Analysis are prominent examples. In this presentation, I draw upon an ongoing empirical research project at LMU Munich that is concerned with identifying antecedents to aggressive behavior among adolescents to discuss implications of this present ‘relational turn’ in the social sciences.top
Modeling how to learn an indicative conditional (“if A then B”) has been a major challenge for Bayesian epistemologists. One proposal to meet this challenge is to construct the posterior probability distribution by minimizing the Kullback-Leibler divergence between the posterior probability distribution and the prior probability distribution, taking the learned information as a constraint (expressed as a conditional probability statement) into account. This proposal has been criticized in the literature based on several clever examples. In this talk, I will revisit four of these examples and show that one obtains intuitively correct results for the posterior probability distribution if the underlying probabilistic models reflect the causal structure of the scenarios in question.top
Meir Hemmo (Department of Philosophy, Haifa University): Probability and Typicality in Everett’s Approach to Quantum Mechanics
Everett’s approach to quantum mechanics takes the quantum state of the universe and its Schroedinger evolution to be all there is, and aims to explain how the probabilistic Born rule explains the observed relative frequencies, and how it emerges from the underlying deterministic picture. A claim often made in standard attempts to justify the Everettian picture is that the Born rule is explained by the empirical experience in ‘typical’ histories or branches. In this talk we shall try to explain this notion of typicality. We will present similarities between the notion of typicality and its role in the Everettian approach and the notion of typicality in classical statistical mechanics, and also point out some dissimilarities. Together, this analysis will yield to questioning the soundness and completeness of this approach to quantum mechanics.top
Danny November (Edelstein Center, Hebrew University of Jerusalem): Ontological Implications of the Probability Space
‘Probability’ and ‘event’ are the two main notions of probability theory. They have different definitions depending on the interpretation of probability theory. Despite having these radically different (informal) definitions, these two notions are commonly formalized mathematically in the same way. The mathematical structure that is commonly used to formally define them is Kolmogorov’s probability space. In my talk I will analyze the ontological implications of accepting Kolmogorov’s probability space as a correct formalization of ‘probability’ and ‘event’. I will claim that by accepting the probability space as an appropriate formalization of these notions, one is committed to much more than just a mathematical definition of them. In my view, an acceptance of the formalization carries with it a commitment to a distinction between different types of existence. This ontological commitment seems to be in tension with the main interpretations of probability theory as they are commonly presented. A tension which might call for a revision of the informal definitions of the notions ‘probability’ and ‘event’ in light of this commitment. Therefore I claim that this commitment should be addressed within each interpretation so that the notions ‘probability’ and ‘event’ would be clarified.top
Ittay Nissan-Rozen (Hebrew University of Jerusalem): The Ramsey Test, the Principal Principle and Admissible Propositions
Several authors have proposed in recent years accounts of chance that allow special sciences to have chances that are autonomous from those of physics. I demonstrate how the debate between these authors to authors who reject such accounts is linked to a theoretical choice between two versions of the Principal Principle, a version that refers to conditional chances and makes use of no admissibility clause and a version that refers to unconditional chances but does make use of an admissibility clause. I then examine the debate from the perspective of a recent suggestion regarding the connection between the Principal Principle and the probability of conditionals, made by Richard Bradley.
Orly Shenker (Edelstein Center, Hebrew University of Jerusalem): Probability and Typicality in Statistical Mechanics
Mechanics is compatible with a world in which entropy remains low and even decreases, giving rise to Maxwellian Demons (as in Hemmo and Shenker The Road to Maxwell’s Demon, CUP 2012). Why, then, isn’t our world like that? Why does the Second Law of Thermodynamics seem to hold in our universe? A prevalent answer is that the possible initial conditions of the universe that give rise to thermodynamic worlds, namely those that satisfy the Second Law, are typical. In this talk we shall discuss this notion of typicality, and how it relates to the notion of probability, and will argue that typicality arguments are question begging and are therefore not explanatory. We will then explain how an empirically significant and explanatory notion of probability can emerge out of a fundamental deterministic theory such as classical mechanics. In doing so we will outline the foundation of statistical mechanics, in which the notion of probability is based on an interplay between macrivariables and macrostates on the one hand and the details of the dynamics on the other hand, and show in what sense the notion of probability distribution over initial conditions can be made coherent and empirically meaningful.
Edelstein Center for History and Philosophy of Science, Technology and Medicine,
Levi Building, Safra Campus
The Hebrew University of Jerusalem.
The conference is supported by The Sydney M. Edelstein Center for History and Philosophy of Science, Technology and Medicine and the Alexander von Humboldt Foundation through an Alexander von Humboldt Professorship.