Related papers: Yablo's paradox and forcing
We give a forcing construction of the square principle on omega_1 using forcing with conditions whose domain is finite.
In the Zermelo--Fraenkel set theory with the Axiom of Choice a forcing notion is "$\kappa$-distributive" if and only if it is "$\kappa$-sequential". We show that without the Axiom of Choice this equivalence fails, even if we include a weak…
We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…
We isolate a combinatorial property of capacities leading to a construction of proper forcings. Then we show that many classical capacities such as the Newtonian capacity satisfy the property.
We present a formal measure of argument strength, which combines the ideas that conclusions of strong arguments are (i) highly probable and (ii) their uncertainty is relatively precise. Likewise, arguments are weak when their conclusion…
The 1961 Ellsberg paradox is typically seen as an empirical challenge to the subjective expected utility framework. Experiments based on Ellsberg's design have spawned a variety of new approaches, culminating in a new paradigm represented…
We develop a forcing framework based on the idea of amalgamating language fragments into a theory with a canonical term model. We then demonstrate the usefulness of this framework by applying it to variants of the extended Namba problem, as…
We present two different paradoxes related to the length contraction in special relativity and explain their resolution.
A bilateralist take on proof-theoretic semantics can be understood as demanding of a proof system to display not only rules giving the connectives' provability conditions but also their refutability conditions. On such a view, then, a…
The foundations of forcing theory are reworked to streamline the presentation and to show how the most basic results are applicable in very general contexts.
We give a counterexample to a recently conjectured variant of the Penrose inequality.
Towards combining "compactness" and "hugeness" properties at $\omega_2$, we investigate the relevance of side-conditions forcing. We reduce the upper bound on the consistency strength of the weak Chang's Conjecture at $\omega_2$ using…
This paper is concerned with the well known Jeffreys-Lindley paradox. In a Bayesian set up, the so-called paradox arises when a point null hypothesis is tested and an objective prior is sought for the alternative hypothesis. In particular,…
The aim of these lectures is to give a short introduction to forcing. We will avoid metamathematical issues as much as possible and similarly we will avoid performing the actual construction of forcing. We assume familiarity with basic…
Following F. William Lawvere, we show that many self-referential paradoxes, incompleteness theorems and fixed point theorems fall out of the same simple scheme. We demonstrate these similarities by showing how this simple scheme encompasses…
Some such as Dean (2014) suggest that Montague's paradox requires the necessitation rule, and that the use of the rule in such a context is contentious. But here, I show that the paradox arises independently of the necessitation rule. A…
Demonstrations of quantum entanglement which confirm the violation of Bell's inequality indicate that under certain conditions action at a distance is possible. This consequence seems to contradict the relativistic principle of causality,…
In this paper, we introduce a translation that combines the $j$-translation with Kripke forcing in the internal logic of an elementary topos. First, we show that our translation is sound for intuitionistic first-order logic and Heyting…
The Parrondo's paradox is a counterintuitive phenomenon where individually-losing strategies can be combined in producing a winning expectation. In this paper, the issues surrounding the Parrondo's paradox are investigated. The focus is…
In this note we study the effect of adding fixed points to justification logics. We introduce two extensions of justification logics: extensions by fixed point (or diagonal) operators, and extensions by least fixed points. The former is a…