ProbPropCond · Probabilities, Propensities, and Conditionals: Implications for Logic and Empirical Science

Probabilities, Propensities, and Conditionals: Implications for Logic and Empirical Science

Probabilistic thinking has of course been a hallmark of European theory and practice ever since the inception of the so-called “probabilistic revolution” (Kruger et al. 1987). It is typical to distinguish subjective or epistemic probabilities, on the one hand, and objective or physical ones, on the other (Hacking, 1990). The present project focuses on objective probability, and its overall aim is to develop a framework to map the conceptual and empirical connections that obtain between probabilities, propensities, and conditionals. Subsequently the aim is to bring to bear this framework on a number of issues of current interest in logic and the philosophy of logic, probability and statistics, and in particular in the conceptual foundations of the empirical sciences, particularly physics. This is a research area that has received considerable interest recently. For instance, the last few years have seen a number of significant colletions of essays, published in some of the leading houses (Beisbart and Hartmann, eds., 2011; Ben Menahem and Hemmo, eds., 2012; Suárez, ed., 2011). There have also been many conferences, seminar series, and workshops, including those organized by the Principal Investigator within the framework of the current research project. Although the emphases differ, these volumes and public events point to a strong revival of research interest in the foundations and applications of probability within philosophy of science. Further afield, statisticians and practicing scientists have been making use of the related notions of propensity and propensity scores. The project was set up to explore and exploit some of these new avenues of research, as well as the intellectual, institutional, and methodological synergies that open up in the wake of these and other significant recent scientific publications. Propensities first appeared as part of the notorious propensity interpretation of probability, which was popular in the 1960’s and 1970’s (Popper, 1959; see Gillies, 2000, for a review). However, the particular emphasis on the generation conditions of probability distributions out of propensity ascriptions is a very recent development in the field that is only now beginning to receive the attention it deserves from philosophers and physicists alike (Mumford and Anjum, 2011; Thompson, 2011). The most prominent objection to the identification simpliciter of propensities with probabilities is known as Humphrey’s paradox (Humphreys, 1985, 2004). An important part of the research undertaken during the two years of the project concerns the nature of this objection, with an eye on the development of a radical solution to this problem (as outlined in Suárez, 2013). An important focus of research during this year was devoted to developing an account of propensities in statistical modelling. The researcher undertook in depth training in statistics, pursing some of the modules in the MSc and postgraduate Diploma in Statistics offered at Birkbeck during 2014-15. He went on to develop a new line of research defending a three tier account of probabilistic modelling which he presented at several important conferences and invited venues. Other problems that received considerable attention during the first year concern Adams’ thesis (Adams, 1975), which asserts roughly that an indicative conditional A → B may be understood as a conditional probability Prob (B / A). Some of the work during the first year addressed the question whether there remains a defensible version of Adam’s thesis. The thesis received less attention during the second year, since it was concluded that whatever versions of Adam’s thesis remain are unlikely to be helpful in formulating new propensity notions. Instead efforts redoubled on accounts of chance in metaphysics, in particular those deriving from David Lewis’ Principal Principle (PP). On a Lewisian understanding of chance, propensity ascriptions can only be understood as entailed by the compete theory of chance detailing every history-of-the-world-to-chance conditional. So propensities are in some sense to be defined in relation to conditionals, although this is clearly not the sense of Adam’s thesis. Thus the Lewisian account provides a contemporary alternative to propensities as dispositional properties of object systems. A reading group was conducted during the first year to review the extensive literature on this topic, and to map out the different options. In the second year, this work continued towards an edited volume on the topic with contributions from some of the invited speakers in the seminar series. As part of the project, a website was designed that provides up to date information on all the outcomes, deliverables, both submitted and in progress, and other hallmarks of the project, including logos and so on. It may be accessed at: http://probpropcond.blogs.sas.ac.uk The fellow has now returned to his position in Spain, and may be reached at: msuarez@filos.ucm.es. His personal website may be consulted at: https://www.ucm.es/dpto_logica/mauricio_suarez

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