A Humean Guide to Spielraum Probabilities

Abstract

The most promising accounts of ontic probability include the Spielraum conception of probabilities, which can be traced back to J. v. Kries and H. Poincaré, and the best system account by D. Lewis. This paper aims at comparing both accounts and at combining them to obtain the best of both worlds. The extensions of both Spielraum and best system probabilities do not coincide because the former only apply to systems with a special dynamics. Conversely, Spielraum probabilities may not be part of the best system, e.g. if a broad class of random devices is not often used. Spielraum probabilities have the potential to provide illuminating explanations of frequencies with which outcomes of trials on gambling devices arise. They ultimately fail to account for such frequencies though because they are compatible with frequencies that grossly differ from the values of the respective probabilities. I thus follow recent proposals by M. Strevens and M. Abrams and strengthen the definition of Spielraum probabilities by adding a further condition that restricts some actual frequencies. The resulting account remains limited in scope, but stands objections raised against it in the recent literature: It is neither circular nor based upon arbitrary choices of a measure or of physical variables. Nor does it lack any explanatory power.

Understanding quantum mechanics: a review and synthesis in precise language

“…-The epistemic sense of probability can be viewed as one or more of subjective, logical (determined by the information available) [103, § 4], personalist (varying from person to person) [103, § 2], or pluralist (common to groups of people, or intersubjective) [104]. -The ontological sense can be viewed in terms of frequencies [105,106], stochastic or deterministic dynamics [105,107], the Humean mosaic (facts in the world) [105][106][107], propensities (single-case or longrun) [105,106], or features of theories [106,108].…”

A subjectivist’s guide to deterministic chance

“…For those individuals may not have 33 Rosenthal (2010Rosenthal ( , 2012Rosenthal ( , 2016. 34 Strevens (2003Strevens ( , 2011, Abrams (2012), and Beisbart (2016). 35 Albert (2000Albert ( , 2015, Loewer (2001Loewer ( , 2004Loewer ( , 2007, and Roberts (2016) (though Roberts is not committed to a 'best systems' account of laws).…”

“… See Rosenthal (2010. 10 SeeStrevens (2003Strevens ( , 2011,Abrams (2012), andBeisbart (2016). 11 SeeAlbert (2000Albert ( , 2015,Loewer (2001Loewer ( , 2004Loewer ( , 2007, andRoberts (2016).12 This puts me in the company ofSavage (1971) andMyrvold (2012).13 von Kries (1886) scooped Poincaré by several years, though he left the mathematical details rather vague.…”