On an influential line of thinking tracing back to Ramsey, conditionals are closely linked to the attitude of supposition. When applied to counterfactuals, this view suggests a subjunctive version of the so-called Ramsey test: the probability of a counterfactual If A, would B ought to be equivalent to the probability of B, under the subjunctive supposition that A. I present a collapse result for any view that endorses the subjunctive version of the Ramsey test. Starting from plausible assumptions, the result (...) shows that one’s rational credence in a would-counterfactual and in the corresponding might-counterfactual have to be identical. (shrink)

According to Stalnaker’s Thesis, the probability of a conditional is the conditional probability. Under some mild conditions, the thesis trivialises probabilities and conditionals, as initially shown by David Lewis. This article asks the following question: does still lead to triviality, if the probability function in is replaced by a probability-like function? The article considers plausibility functions, in the sense of Friedman and Halpern, which additionally mimic probabilistic additivity and conditionalisation. These quasi probabilities comprise Friedman–Halpern’s conditional plausibility spaces, as well as (...) other known representations of conditional doxastic states. The paper proves Lewis’ triviality for quasi probabilities and discusses how this has implications for three other prominent strategies to avoid Lewis’ triviality: Adams’ thesis, where the probability function on the left in is replaced by a probability-like function, abandoning conditionalisation, where probability conditionalisation on the right in is replaced by another propositional update procedure and the approximation thesis, where equality in is replaced by approximation. The paper also shows that Lewis’ triviality result is really about ‘additiveness’ and ‘conditionality’. (shrink)

In this paper, I propose and defend a pair of necessary conditions on evidence-based knowledge which bear resemblance to the troubled sensitivity principles defended in the philosophical literature. We can think of the traditional principles as simple but inaccurate approximations of the new proposals. Insofar as the old principles are intuitive and used in scientific and philosophical contexts, but are plausibly false, there’s a real need to develop precise and correct formulations. These new renditions turned out to be more cautious, (...) so they won’t be able to do everything the old principled promised they could. For example, they respect closure for knowledge. But these sober formulations, or something like them, might be the best that we can do with respect to sensitivity. And there’s value in understanding the limits to these types of principles. (shrink)

Williamson proposes that a "suppositional procedure" is a central heuristic we use to evaluate the truth of conditionals, though he also argues that this method often leads us astray. An alternative approach to the link between supposition and conditionals is to claim that we are guided by our antecedent conditional judgements in our supposing, and in particular in our determining which things follow from an initial supposition. This alternative explanation of the close link between conditionals and supposition is developed and (...) compared to Williamson's proposal. (shrink)

ABSTRACT A trivalent theory of indicative conditionals automatically enforces Stalnaker's thesis – the equation between probabilities of conditionals and conditional probabilities. This result holds because the trivalent semantics requires, for principled reasons, a modification of the ratio definition of conditional probability in order to accommodate the possibility of undefinedness. I explain how this modification is motivated and how it allows the trivalent semantics to avoid a number of well-known triviality results, in the process clarifying why these results hold for many (...) bivalent theories. In short, the slew of triviality results published in the last 40-odd years need not be viewed as an argument against Stalnaker's thesis: it can be construed instead as an argument for abandoning the bivalent requirement that indicative conditionals somehow be assigned a truth-value in worlds in which their antecedents are false. (shrink)

– We offer a new motivation for imprecise probabilities. We argue that there are propositions to which precise probability cannot be assigned, but to which imprecise probability can be assigned. In such cases the alternative to imprecise probability is not precise probability, but no probability at all. And an imprecise probability is substantially better than no probability at all. Our argument is based on the mathematical phenomenon of non-measurable sets. Non-measurable propositions cannot receive precise probabilities, but there is a natural (...) way for them to receive imprecise probabilities. The mathematics of non-measurable sets is arcane, but its epistemological import is far-reaching; even apparently mundane propositions are liable to be affected by non-measurability. The phenomenon of non-measurability dramatically reshapes the dialectic between critics and proponents of imprecise credence. Non-measurability offers natural rejoinders to prominent critics of imprecise credence. Non-measurability even reverses some of the critics’ arguments—by the very lights that have been used to argue against imprecise credences, imprecise credences are better than precise credences. (shrink)

Most meanings we express belong to large families of variant meanings, among which it would be implausible to suppose that some are much more apt for being expressed than others. This abundance of candidate meanings creates pressure to think that the proposition attributing any particular meaning to an expression is modally plastic: its truth depends very sensitively on the exact microphysical state of the world. However, such plasticity seems to threaten ordinary counterfactuals whose consequents contain speech reports, since it is (...) hard to see how we could reasonably be confident in a counterfactual whose consequent can be true only if a certain very finely tuned microphysical configuration obtains. This essay develops the foregoing puzzle and explores several possible solutions. (shrink)

The problem of probabilities of conditionals is one of the long-standing puzzles in philosophy of language. We defend and update Adams' solution to the puzzle: the probability of an epistemic conditional is not the probability of a proposition, but a probability under a supposition. -/- Close inspection of how a triviality result unfolds in a concrete scenario does not provide counterexamples to the view that probabilities of conditionals are conditional probabilities: instead, it supports the conclusion that probabilities of conditionals violate (...) standard probability theory. -/- This does not call into question probability theory per se; rather, it calls for a more careful understanding of its role: probability theory is a theory of probabilities of propositions; but as conditionals do not express propositions, their probabilities are not subject to the standard laws. -/- We argue that both conditional probabilities and probabilities of conditionals are best understood in terms of the dynamics of supposing, modeled as a restriction operation on a probability space. This version of the suppositionalist view allows us to connect Adams' Thesis to the widely held restrictor view of the semantics of conditionals. -/- We address two common objections to Adams' view: that the relevant probabilities are ‘probabilities only in name’, and that giving up conditional propositions puts us at a disadvantage when it comes to interpreting compounds. -/- Finally, we argue that some putative counterexamples to Adams' Thesis can be diagnosed as fallacies of probabilistic reasoning: they arise from applying to conditionals laws of standard probability theory which are invalid for them. (shrink)

Intellectual progress involves forming a more accurate picture of the world. But it also figuring out which concepts to use for theorizing about the world. Bayesian epistemology has had much to say about the former aspect of our cognitive lives, but little if at all about the latter. I outline a framework for formulating questions about conceptual change in a broadly Bayesian framework. By enriching the resources of Epistemic Utility Theory with a more expansive conception of epistemic value, I offer (...) a picture of our cognitive economy on which adopting new conceptual tools can sometimes be epistemically rational. (shrink)