The Logic of Conditional Belief

The logic of indicative conditionals remains the topic of deep and intractable philosophical disagreement. I show that two influential epistemic norms—the Lockean theory of belief and the Ramsey test for conditional belief—are jointly sufficient to ground a powerful new argument for a particular conception of the logic of indicative conditionals. Specifically, the argument demonstrates, contrary to the received historical narrative, that there is a real sense in which Stalnaker’s semantics for the indicative did succeed in capturing the logic of the Ramseyan indicative conditional

Towards a Paraconsistent Quantum Set Theory

In this paper, we will attempt to establish a connection between quantum set theory, as developed by Ozawa, Takeuti and Titani, and topos quantum theory, as developed by Isham, Butterfield and Doring, amongst others. Towards this end, we will study algebraic valued set-theoretic structures whose truth values correspond to the clopen subobjects of the spectral presheaf of an orthomodular lattice of projections onto a given Hilbert space. In particular, we will attempt to recreate, in these new structures, Takeuti's original isomorphism between the set of all Dedekind real numbers in a suitably constructed model of set theory and the set of all self adjoint operators on a chosen Hilbert space.Comment: In Proceedings QPL 2015, arXiv:1511.0118

Antireductionist Interventionism

Kim’s causal exclusion argument purports to demonstrate that the non-reductive physicalist must treat mental properties (and macro-level properties in general) as causally inert. A number of authors have attempted to resist Kim’s conclusion by utilizing the conceptual resources of Woodward’s (2005) interventionist conception of causation. The viability of these responses has been challenged by Gebharter (2017a), who argues that the causal exclusion argument is vindicated by the theory of causal Bayesian networks (CBNs). Since the interventionist conception of causation relies crucially on CBNs for its foundations, Gebharter’s argument appears to cast significant doubt on interventionism’s antireductionist credentials. In the present article, we both (1) demonstrate that Gebharter’s CBN-theoretic formulation of the exclusion argument relies on some unmotivated and philosophically significant assumptions (especially regarding the relationship between CBNs and the metaphysics of causal relevance), and (2) use Bayesian networks to develop a general theory of causal inference for multi-level systems that can serve as the foundation for an antireductionist interventionist account of causation

Principles of Indifference

The principle of indifference states that in the absence of any relevant evidence, a rational agent will distribute their credence equally among all the possible outcomes under consideration. Despite its intuitive plausibility, PI famously falls prey to paradox, and so is widely rejected as a principle of ideal rationality. In this article, I present a novel rehabilitation of PI in terms of the epistemology of comparative confidence judgments. In particular, I consider two natural comparative reformulations of PI and argue that while one of them prescribes the adoption of patently irrational epistemic states, the other provides a consistent formulation of PI that overcomes the most salient limitations of existing formulations

Principles of Indifference

The principle of indifference (PI) states that in the absence of any relevant evidence, a rational agent will distribute their credence (or `degrees of belief') equally amongst all the possible outcomes under consideration. Despite its intuitive plausibility, PI famously falls prey to paradox, and so is widely rejected as a principle of ideal rationality. Some authors have attempted to show that by conceiving of the epistemic states of agents in terms of imprecise credences, it is possible to overcome these paradoxes and thus to achieve a consistent rehabilitation of PI. In this article, I present an alternative rehabilitation of PI in terms of the epistemology of comparative confidence judgements of the form `I am more confident in the truth of p than I am in the truth q' or `I am equally confident in the truth of p and q'. In particular, I consider two natural comparative reformulations of PI, and argue that while one of them prescribes the adoption of patently irrational epistemic states, the other (which is only available when we drop the standard but controversial `Opinionation' assumption from the comparative confidence framework) provides a consistent formulation of PI that overcomes the fundamental limitations of all existing formulations

Principles of Indifference

The principle of indifference (PI) states that in the absence of any relevant evidence, a rational agent will distribute their credence (or `degrees of belief') equally amongst all the possible outcomes under consideration. Despite its intuitive plausibility, PI famously falls prey to paradox, and so is widely rejected as a principle of ideal rationality. Some authors have attempted to show that by conceiving of the epistemic states of agents in terms of imprecise credences, it is possible to overcome these paradoxes and thus to achieve a consistent rehabilitation of PI. In this article, I present an alternative rehabilitation of PI in terms of the epistemology of comparative confidence judgements of the form `I am more confident in the truth of p than I am in the truth q' or `I am equally confident in the truth of p and q'. In particular, I consider two natural comparative reformulations of PI, and argue that while one of them prescribes the adoption of patently irrational epistemic states, the other (which is only available when we drop the standard but controversial `Opinionation' assumption from the comparative confidence framework) provides a consistent formulation of PI that overcomes the fundamental limitations of all existing formulations

Bayesian Argumentation and the Value of Logical Validity

According to the Bayesian paradigm in the psychology of reasoning, the norms by which everyday human cognition is best evaluated are probabilistic rather than logical in character. Recently, the Bayesian paradigm has been applied to the domain of argumentation, where the fundamental norms are traditionally assumed to be logical. Here, we present a major generalisation of extant Bayesian approaches to argumentation that (i)utilizes a new class of Bayesian learning methods that are better suited to modelling dynamic and conditional inferences than standard Bayesian conditionalization, (ii) is able to characterise the special value of logically valid argument schemes in uncertain reasoning contexts, (iii) greatly extends the range of inferences and argumentative phenomena that can be adequately described in a Bayesian framework, and (iv) undermines some influential theoretical motivations for dual function models of human cognition. We conclude that the probabilistic norms given by the Bayesian approach to rationality are not necessarily at odds with the norms given by classical logic. Rather, the Bayesian theory of argumentation can be seen as justifying and enriching the argumentative norms of classical logic

Causal Explanatory Power

Schupbach and Sprenger (2011) introduce a novel probabilistic approach to measuring the explanatory power that a given explanans exerts over a corresponding explanandum. Though we are sympathetic to their general approach, we argue that it does not (without revision) adequately capture the way in which the causal explanatory power that c exerts on e varies with background knowledge. We then amend their approach so that it does capture this variance. Though our account of explanatory power is less ambitious than Schupbach and Sprenger's in the sense that it is limited to causal explanatory power, it is also more ambitious because we do not limit its domain to cases where c genuinely explains e. Instead, we claim that c causally explains e if and only if our account says that c explains e with some positive amount of causal explanatory power

Causal Explanatory Power

Schupbach and Sprenger (2011) introduce a novel probabilistic approach to measuring the explanatory power that a given explanans exerts over a corresponding explanandum. Though we are sympathetic to their general approach, we argue that it does not (without revision) adequately capture the way in which the causal explanatory power that c exerts on e varies with background knowledge. We then amend their approach so that it does capture this variance. Though our account of explanatory power is less ambitious than Schupbach and Sprenger's in the sense that it is limited to causal explanatory power, it is also more ambitious because we do not limit its domain to cases where c genuinely explains e. Instead, we claim that c causally explains e if and only if our account says that c explains e with some positive amount of causal explanatory power