Virtue and Contingent History

Some philosophers of science suggest that a narrow calculus of rationality—the axioms of probability calculus and the rule of conditionalization—suffices to characterize the epistemic aspect of science, including the phenomena of scientific knowledge and empirical justification. But what if a rationality constricted to a narrow calculus is a rationality inhibited in its pursuit of epistemic aims key to science? This chapter uses virtue as Aristotle understands it to develop a broader picture of rationality, a picture that likens some varieties of rationality to second-nature capacities. It discusses not only the epistemic aims that might be advanced by the exercise of epistemic second natures in the sciences but also the social conditions promoting this advancement.

The Fraternal Birth-Order Effect as Statistical Artefact: Convergent Evidence from Probability Calculus, Simulated Data, and Multiverse Meta- Analysis

For a quarter of a century researchers investigating the origins of sexual orientation have largely ascribed to the fraternal birth order effect (FBOE) as a fact, holding that older brothers increase the odds of homosexual orientation among men through an immunoreactivity process. Here, we triangulate the empirical foundations of the FBOE from three distinct, informative perspectives: First, drawing on basic probability calculus, we deduce mathematically that the body of statistical evidence of the FBOE rests on the false assumptions that effects of family size should be controlled for and that this could be achieved through the use of ratio variables. Second, using a data-simulation approach, we demonstrate that by using ratio variables, researchers are bound to falsely declare corroborating evidence of an excess of older brothers at a rate of up to 100%, and that valid approaches attempting to quantify a potential excess of older brothers among homosexual men must control for the confounding effects of the number of older siblings. And third, we re-examine the empirical evidence of the FBOE by using a novel specification-curve and multiverse approach to meta-analysis. This yielded highly inconsistent and moreover similarly-sized effects across 64 male and 17 female samples (N = 2,778,998), compatible with an excess as well as with a lack of older brothers in both groups, thus, suggesting that almost no variation in the number of older brothers in men is attributable to sexual orientation.

The Epistemic Use of ‘Ought’

A good deal of Dorothy Edgington’s work has involved fruitful applications of the probability calculus to philosophical subject matters—notably, conditionals and vagueness. This chapter forms part of a project of exploring the relevance of probability to various epistemic phenomena, including knowledge and epistemic modality. Its focus here is on certain epistemic uses of ‘ought’ and ‘should’. The chapter argues against flat-footed ways of grounding those concepts in the ideology of probability, although it makes room for certain other, less reductive, structural relationships between the two. The discussion involves various idealizations and simplifications. Nevertheless, it argues that flattened ordering sources are a useful tool for developing a broadly Kratzer-style treatment of least some uses of ‘ought’.

Probability and Decision Theory

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.

“Till at last there remain nothing”

In A Treatise of Human Nature, David Hume presents an argument according to which all knowledge reduces to probability, and all probability reduces to nothing. Many have criticized this argument, while others find nothing wrong with it. In this paper we explain that the argument is invalid as it stands, but for different reasons than have been hitherto acknowledged. Once the argument is repaired, it becomes clear that there is indeed something that reduces to nothing, but it is something other than what, according to many, Hume had in mind. Thus two views emerge of what exactly it is that reduces. We surmise that Hume failed to distinguish the two, because he lacked the formal means to differentiate between a rendering of his argument that is in accordance with the probability calculus, and one that is not.

Probabilism, Assertion, and Higher-Order Vagueness

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.