How do we ascribe subjective probability? In decision theory, this question is often addressed by representation theorems, going back to Ramsey (1926), which tell us how to define or measure subjective probability by observable preferences. However, standard representation theorems make strong rationality assumptions, in particular expected utility maximization. How do we ascribe subjective probability to agents which do not satisfy these strong rationality assumptions? I present a representation theorem with weak rationality assumptions which can be used to define or measure (...) subjective probability for partly irrational agents. (shrink)

I argue that we should solve the Lottery Paradox by denying that rational belief is closed under classical logic. To reach this conclusion, I build on my previous result that (a slight variant of) McGee’s election scenario is a lottery scenario (see Lissia 2019). Indeed, this result implies that the sensible ways to deal with McGee’s scenario are the same as the sensible ways to deal with the lottery scenario: we should either reject the Lockean Thesis or Belief Closure. After (...) recalling my argument to this conclusion, I demonstrate that a McGee-like example (which is just, in fact, Carroll’s barbershop paradox) can be provided in which the Lockean Thesis plays no role: this proves that denying Belief Closure is the right way to deal with both McGee’s scenario and the Lottery Paradox. A straightforward consequence of my approach is that Carroll’s puzzle is solved, too. (shrink)

Vann McGee has presented a putative counterexample to modus ponens. I show that (a slightly modified version of) McGee’s election scenario has the same structure as a famous lottery scenario by Kyburg. More specifically, McGee’s election story can be taken to show that, if the Lockean Thesis holds, rational belief is not closed under classical logic, including classical-logic modus ponens. This conclusion defies the existing accounts of McGee’s puzzle.

This paper develops a trivalent semantics for the truth conditions and the probability of the natural language indicative conditional. Our framework rests on trivalent truth conditions first proposed by Cooper (1968) and Belnap (1973) and it yields two logics of conditional reasoning: (i) a logic C of certainty-preserving inference; and (ii) a logic U for uncertain reasoning that preserves the probability of the premises. We show systematic correspondences between trivalent and probabilistic representations of inferences in either framework, and we use (...) the distinction between the two systems to cast light on the validity of inferences such as Modus Ponens, Or-To-If, and Conditional Excluded Middle. Specifically, the conditional behaves monotonically in C, but non-monotonically in U; Modus Ponens is valid in C, but valid in U only for non-nested conditionals. The result is a unified account of the semantics and epistemology of indicative conditionals that can be fruitfully applied to analyzing the validity of conditional inferences. (shrink)

This paper presents an analysis of inquisitive rising declaratives (Gunlogson 2001, Jeong 2018) within the Table model (Farkas & Bruce 2010). On this account, intonational tunes are modifiers of context update functions: rising intonation removes the speaker commitment component of a context update. This delivers a compositional account of the contributions of sentence type and intonational tune to the illocutionary mood of an utterance, showing how the semantic type of declarative sentences, the rising intonational tune, and a general-purpose utterance function (...) (Farkas & Roelofsen 2017) conspire to derive the basic discourse effect of rising declaratives without any construction-specific stipulations. The account makes use of only the most fundamental representational primitives independently necessary to model assertions and neutral questions, showing that rising declaratives can be accounted for without recourse to projected commitments, metalinguistic issues, or explicit marking of commitment strength, evidence source, or epistemic bias (cf. Gunlogson 2008, Northrup 2014, Malamud & Stephenson 2015, Farkas & Roelofsen 2017). Inferences of bias generated by rising declaratives are accounted for with a novel pragmatics for the Table model, formalizing what is implicit in discussions of the role played in the model by speaker commitments and projected Common Grounds. (shrink)