Forthcoming in Social Choice and Welfare Abstract. Many groups make decisions over multiple interconnected propositions. The “doctrinal paradox” or “discursive dilemma” shows that propositionwise majority voting can generate inconsistent collective sets of judgments, even when individual sets of judgments are all consistent. I develop a simple model for determining the probability of the parado...

Topological semantics appears to be the first semantics suggested for modal logic in 1938 by Tsao-Chen [9]. Picking up from Tsao-Chen’s work, McKinsey (later with Tarski) incorporated various other algebraic and topological tools into modal logic, always remaining within the limits of classical logic [4, 6, 5, 7]. However, the strength of topological semantics arguably comes from its versatilit...

The Barrett and Arntzenius (1999) decision paradox involves unbounded wealth, the relationship between period-wise and sequence-wise dominance, and an infinite-period split-minute setting. A version of their paradox involving bounded (in fact, constant) wealth decisions is presented, along with a version involving no decisions at all. The common source of paradox in Barrett– Arntzenius and thes...

As organizational environments become more global, dynamic, and competitive, contradictory demands intensify. To understand and explain such tensions, academics and practitioners are increasingly adopting a paradox lens. We review the paradox literature, categorizing types and highlighting fundamental debates. We then present a dynamic equilibrium model of organizing, which depicts how cyclical...

A variation of Fitch's Paradox is given, where no special rules of inference are assumed, only axioms. These axioms follow from the familiar assumptions which involve rules of inference. We show (by constructing a model) that by allowing that possibly the knower doesn't know his own soundness (while still requiring he be sound), Fitch's Paradox is avoided. Provided one is willing to admit that ...

Recently the following understanding of epistemological skepticism has become widely accepted: skepticism about our knowledge of the world is not a thesis to be accepted or refuted; the philosophical problem skepticism presents is nothing but a paradox to be solved, a paradox given rise to by some apparently forceful arguments for skepticism. Call this the paradox view of skepticism. The parado...

Stefan Banach and Alfred Tarski introduced the phrase: “a pea can be chopped up and reassembled into the Sun,” a seemingly impossible concept. Using this theorem as motivation, this paper will explore the existence of non-measurable sets and paradoxical decompositions as well as provide a sketch of the proof of the paradox.