PhD Student Session: Simon Knutson & Joe Roussos

Simon Knutson (Stockholm). “Many-valued logic as a reply to sequence arguments in value theory”

Abstract: Some find it plausible that a sufficiently long duration of torture is worse than any duration of mild headaches. Similarly, it has been claimed that a million people living great lives is better than any number of worm-like creatures feeling a few seconds of pleasure each. Some have related bad things to good things along the same line. For example, one may hold that a future in which a sufficient number of beings experience a lifetime of torture is bad, regardless of what else that future contains, while holding that minor bad things, such as slight unpleasantness, can always be counterbalanced by enough good things. Among the most common objections to such ideas are sequence arguments. I investigate many-valued logic as a reply to sequence arguments, and I focus on an important many-valued logic called Łukasiewicz logic. I show that if one accepts that ‘at least as bad as’ is a complete and transitive relation, then when replying to sequence arguments, it does not help to assume Łukasiewicz logic at the object-level and classical logic at the meta-level. Still, one could, for example, try to reply to sequence arguments by assuming Łukasiewicz logic while holding that it is less than maximally true that ‘at least as bad as’ is complete. There are also other many-valued logics that remain to be analysed that may be good replies to sequence arguments.

Joe Roussos (LSE) “Modelling in formal epistemology: the case of probabilism”

Abstract: It is increasingly common to claim that modelling is a useful method for philosophy; Williamson, Hartmann, Leitgeb, and Titelbaum have all made versions of this claim for epistemology in particular. This paper shows what it means to take that idea seriously, by applying the philosophy of scientific modelling to work in formal epistemology. I begin with a quick characteristic argument that formal epistemologists are indeed in the business of modelling. I illustrate this in detail for a probabilistic model of partial belief. The fact that these are models (in the scientific sense) makes problematic certain common inferential moves: realist inferences about model-constitutuents, rebuttals from counter-intuitions, and counter-examples more generally. Reflecting on the debate over Precise vs. Imprecise Probabilism, I argue that it can be construed as a (misguided) disagreement over modelling choices. I close with a discussion of the implications of model pluralism for epistemology.