Conversational exculpature is a pragmatic process whereby information is subtracted from, rather than added to, what the speaker literally says. This pragmatic content subtraction explains why we can say "Rob is six feet tall" without implying that Rob is between 5'11.99" and 6'0.01" tall, and why we can say "Ellen has a hat like the one Sherlock Holmes always wears" without implying Holmes exists or has a hat. This paper presents a simple formalism for understanding this pragmatic mechanism, specifying how, in context, the result of such subtractions is determined. And it shows how the resulting theory of conversational Conversational Exculpature / 3 38 nearest inch, p 1 is not wholly relevant because it specifies his height to a greater degree of precision than the interests of the conversational participants require. Exculpature repairs such discrepancies. Simons (2005Simons ( , 2013 calls the contextual presupposition of an utterance: roughly, these are presuppositions that connect an utterance's literal content to the question under discussion. It is these presuppositions, like q 1 and q 2 above, that are subtracted from the literal content in exculpature. Below we will see how an utterance's literal content p, the underlying contextual presupposition q, and the question under discussion S jointly determine a unique, wholly relevant remainder r. The prediction is that only this relevant remainder r, and not p or q, is seriously endorsed and added to the conversational common ground. Accordingly, it involves what MandyIt is worth stressing that, following Yablo (2014, ch. 11-12), the notion of content subtraction presented here extends beyond cases where the equality p = (pq) ∧ q holds: that is to say, content subtraction is not just an inverse of content addition or conjunction. For example, (2)'s literal content p 2 is not equivalent to (p 2q 2 ) ∧ q 2 : since p 2 is true in worlds where Holmes and Ellen both wear a sombrero, it fails to entail both the subtracted proposition q 2 and the remainder (p 2q 2 ). The truth in the vicinity is that p ∧ q = (pq) ∧ q, wherever (pq) is defined. Thus conversational exculpature is a retrenchment from the speaker's overall commitments p ∧ q (literal content + contextual presupposition), but the resulting message (pq) need not be entailed by p alone, as (2) illustrates. Consequently, pragmatic subtraction does not always lead to weakening of the literal content. In some cases, like (1), exculpature yields a message that is entailed by the literal content. But in cases like (2), the intended message is logically independent of the literal content, and in still other cases it is logically stronger.As we will shortly see, this feature of the account is central to its empirical success relative to competing accounts, which wrongly treat loose talk as a form of pragmatic weakening.The introduction of the novel term "exculpature" may suggest an exaggerated claim to originality, so let me take a moment to cancel that implicature. This paper's primary contribution is to synthesi...

Choices confront us with questions. How we act depends on our answers to those questions. So the way our beliefs guide our choices is not just a function of their informational content, but also depends systematically on the questions those beliefs address. This paper gives a precise account of the interplay between choices, questions and beliefs, and harnesses this account to obtain a principled approach to the problem of deduction. The result is a novel theory of belief-guided action that explains and predicts the decisions of agents who, like ourselves, fail to be logically omniscient: that is, of agents whose beliefs may not be deductively closed, or even consistent.

Models of collective deliberation often assume that the chief aim of a deliberative exchange is the sharing of information. In this paper, we argue that an equally important role of deliberation is to draw participants’ attention to pertinent questions, which can aid the assembly and processing of distributed information by drawing deliberators’ attention to new issues. The assumption of logical omniscience renders classical models of agents' informational states unsuitable for modelling this role of deliberation. Building on recent insights from psychology, linguistics and philosophy about the role of questions in speech and thought, we propose a different model in which beliefs are treated as answers directed at specific questions. Here, questions are formally represented as partitions of the space of possibilities and individuals’ information states as sets of and corresponding partial answers to them. The state of conversation is then characterised by individuals’ information together with the questions under discussion, which can be steered by various deliberative inputs. Using this model, deliberation is then shown to shape collective decisions in ways that classical models cannot capture, allowing for novel explanations of how group consensus is achieved.

Using Riemann's Rearrangement Theorem, Øystein Linnebo (2020) argues that, if it were possible to apply an infinite positive weight and an infinite negative weight to a working scale, the resulting net weight could end up being any real number, depending on the procedure by which these weights are applied. Appealing to the First Postulate of Archimedes' treatise on balance, I argue instead that the scale would always read 0 kg. Along the way, we stop to consider an infinitely jittery flea, an infinitely protracted border conflict, and an infinitely electric glass rod.Annexia. The final area of Annexia is a function of the particular regions that end up under Annexian control. Within the given parameters, Annexia could end up with 0.69 mi 2 of additional territory: this happens if the trades involve an ever-shrinking border region between the two nations, so that almost every location has a final claimant. But that optimal outcome is not at all guaranteed. If the swaps are more disparate, there could be large areas that are traded back and forth indefinitely, without a final claimant. Suppose ownership of those areas remains unsettled. Then, far from gaining any land, Annexia could be left without a settled claim to any territory at all, provided its neighbour is strategic enough to organise the swaps in a suitable way.The Rod. The positive charge of the rod is generated by the electron deficit in the rod (or, if you prefer, by the proton surplus). After the first step, the rod has an electron deficit of 1 coulomb. That deficit is subsequently compensated in part by electrons added later in the process. But how many of those compensating electrons last until the end? Assuming it makes sense to re-identify token electrons (cf. Huggett 1999), the answer depends on which individual electrons are removed at each step. For suppose the electrons exit the rod in the same order as they entered. Then each electron that enters the rod during this supertask will be removed at some later step. Consequently, the charge in the rod will then be 1 coulomb or greater at the end of the task, since nothing remains to compensate the initial deficit. Alternatively, it could be that some number of newly added electrons do stick around, which could lead to any intermediate outcome between 0.69 and 1 coulomb.

This paper presents and defends an argument that the continuum hypothesis is false, based on considerations about objective chance and an old theorem due to Banach and Kuratowski. More specifically, I argue that the probabilistic inductive methods standardly used in science presuppose that every proposition about the outcome of a chancy process has a certain chance between 0 and 1. I also argue in favour of the standard view that chances are countably additive. Since it is possible to randomly pick out a point on a continuum, for instance using a roulette wheel or by flipping a countable infinity of fair coins, it follows, given the axioms of ZFC, that there are many different cardinalities between countable infinity and the cardinality of the continuum. Quine told us that there are no islands in science, and that even our mathematical beliefs have to face the tribunal of experience. The examples usually adduced in support of his view are non-Euclidean geometry and quantum probability, mathematical theories whose development was in part inspired by physical discoveries. But in those cases, it is unclear whether our beliefs about the mathematics itself were revised, or just our beliefs about the applicability of certain mathematical theories. In this