Understanding the Brandenburger-Keisler Paradox

Adam Brandenburger and H. Jerome Keisler have recently discovered a two person Russell-style paradox. They show that the following configurations of beliefs is impossible: Ann believes that Bob assumes that Ann believes that Bob’s assumption is wrong. In [7] a modal logic interpretation of this paradox is proposed. The idea is to introduce two modal operators intended to represent the agents’ beliefs and assumptions. The goal of this paper is to take this analysis further and study this paradox from the point of view of a modal logician. In particular, we show that the paradox can be seen as a theorem of an appropriate hybrid logic. Special Issue Formal Epistemology II. Edited by Branden Fitelson     

Anti-luck epistemology

In this paper, I do three things. First, I offer an overview of an anti-luck epistemology, as set out in my book, Epistemic Luck (Oxford University Press, Oxford 2005). Second, I attempt to meet some of the main criticisms that one might level against the key theses that I propose in this work. And finally, third, I sketch some of the ways in which the strategy of anti-luck epistemology can be developed in new directions.     

A logical expression of reasoning

A non-monotonic logic, the Logic of Plausible Reasoning (LPR), capable of coping with the demands of what we call complex reasoning, is introduced. It is argued that creative complex reasoning is the way of reasoning required in many instances of scientific thought, professional practice and common life decision taking. For managing the simultaneous consideration of multiple scenarios inherent in these activities, two new modalities, weak and strong plausibility, are introduced as part of the Logic of Plausible Deduction (LPD), a deductive logic specially designed to serve as the monotonic support for LPR. Axiomatics and semantics for LPD, together with a completeness proof, are provided. Once LPD has been given, LPR may be defined via a concept of extension over LPD. Although the construction of LPR extensions is first presented in standard style, for the sake of comparison with existing non-monotonic formalisms, alternative more elegant and intuitive ways for constructing non-monotonic LPR extensions are also given and proofs of their equivalence are presented.     

An Axiomatisation for the Multi-modal Logic of Knowledge and Linear Time LTK

The paper aims at providing the multi-modal propositional logicLTK with a sound and complete axiomatisation. This logic combinestemporal and epistemic operators and focuses on m odeling thebehaviour of a set of agents operating in a system on the backgroundof a temporal framework. Time is represented as linear and discrete,whereas knowledge is modeled as an S₅-like modality. A furthermodal operator intended to represent environment knowledge isadded to the system in order to achieve the expressive powersufficient to describe the piece of information available tothe agents at each moment in the flow of time.     

Automatic verification of multi-agent systems by model checking via ordered binary decision diagrams

We present a methodology for the verification of multi-agent systems, whose properties are specified by means of a modal logic that includes a temporal, an epistemic, and a modal operator to reason about correct behaviour of agents. The verification technique relies on model checking via ordered binary decision diagrams. We present an implementation and report on experimental results for two scenarios: the bit transmission problem with faults and the protocol of the dining cryptographers.     

Cut-free common knowledge

Starting off from the infinitary system for common knowledge over multi-modal epistemic logic presented in [L. Alberucci, G. Jäger, About cut elimination for logics of common knowledge, Annals of Pure and Applied Logic 133 (2005) 73–99], we apply the finite model property to “finitize” this deductive system. The result is a cut-free, sound and complete sequent calculus for common knowledge.     

“Escape from Freedom”: Authoritarianism-related traits,political ideology,personality, and belief in free will/determinism

Philosophers have long speculated that authoritarianism and belief in determinism are functionally related. To evaluate this hypothesis, we assessed whether authoritarianism and allied personality and political variables predict varieties of belief in determinism in three community samples (N₁ = 566 to 20,010; N₂ = 500; N₃ = 419). Authoritarianism and allied variables manifested moderate to large positive correlations with both fatalistic and genetic determinism beliefs. Controlling for political conservatism did not meaningfully attenuate these relations. Further, openness was negatively related to fatalistic determinism beliefs and agreeableness was negatively related to genetic determinism beliefs. Taken together, our findings clarify the nature of relations between authoritarianism and general personality, on the one hand, and free will/determinism beliefs, on the other, and suggest intriguing intersections between worldviews and personality traits.     

The epistemic innocence of psychedelic states

One recent development in epistemology, the philosophical study of knowledge, is the notion of ‘epistemic innocence’ introduced by Bortolotti and colleagues. This concept expresses the idea that certain suboptimal cognitive processes may nonetheless have epistemic (knowledge-related) benefits. The idea that delusion or confabulation may have psychological benefits is familiar enough. What is novel and interesting is the idea that such conditions may also yield significant and otherwise unavailable epistemic benefits. I apply the notion of epistemic innocence to research on the transformative potential of psychedelic drugs. The popular epithet ‘hallucinogen’ exemplifies a view of these substances as fundamentally epistemically detrimental. I argue that the picture is more complicated and that some psychedelic states can be epistemically innocent. This conclusion is highly relevant to policy debates about psychedelic therapy. Moreover, analysing the case of psychedelics can shed further light on the concept of epistemic innocence itself.