Related papers: Montague's Paradox without Necessitation
In this paper we have resolved the apparent paradox of different mechanical equations for force and torque governing the motion of a charged particle in different inertial frames. The same paradox arises in all usual ``explanations'' of the…
Distributive laws of a monad T over a functor F are categorical tools for specifying algebra-coalgebra interaction. They proved to be important for solving systems of corecursive equations, for the specification of well-behaved structural…
For which (first-order complete, usually countable) $T$ do there exist non-isomorphic models of $T$ which become isomorphic after forcing with a forcing notion $\mathbb{P}$? Necessarily, $\mathbb{P}$ is non-trivial; i.e.~it adds some new…
The independence of the continuum hypothesis is a result of broad impact: it settles a basic question regarding the nature of N and R, two of the most familiar mathematical structures; it introduces the method of forcing that has become the…
Conditional independence and Markov properties are powerful tools allowing expression of multidimensional probability distributions by means of low-dimensional ones. As multidimensional possibilistic models have been studied for several…
In this paper, we argue that while the concept of a set-theoretic paradox (or paradoxical set) can be relatively well-defined within a formal setting, the concept of a set-theoretic hypodox (or hypodoxical set) remains significantly less…
When a proposition has no proof in an inference system, it is sometimes useful to build a counter-proof explaining, step by step, the reason of this non-provability. In general, this counter-proof is a (possibly) infinite co-inductive proof…
Taking symmetric extensions can be considered as a generalisation of forcing, which produces a richer multiverse of models with and without the axiom of choice. We can study the structure of this multiverse using modal logic. In particular,…
By adding the total time derivatives of all the constraints to the Lagrangian step by step, we achieve the further work of the Dirac conjecture left by Dirac. Hitherto, the Dirac conjecture is proved completely. It is worth noticing that…
The Donald-Flanigan conjecture asserts that any group algebra of a finite group has a separable deformation. We apply an inductive method to deform group algebras from deformations of normal subgroup algebras, establishing an infinite…
Paradoxes are a very frequent phenomenon in processes of thought which strive towards the intelectual and cognitive shifts. They occur in all areas of human spiritual activites. What we are interested here in, are the paradoxes in physics.…
Simpson's paradox and collapsibility are two closely related concepts in the context of data analysis. While the knowledge about the occurrence of Simpson's paradox helps a statistician to draw correct and meaningful conclusions, the…
A model is constructed and a paradox concerning the proper direction and magnitude of the external force to maintain the equilibrium state of a parallel plate capacitor system is raised. By a thorough study of the model using different…
If a higher derivative theory arises from a transformation of variables that involves time derivatives, a tailor-made Hamiltonian formulation is shown to exist. The details and advantages of this elegant Hamiltonian formulation, which…
While Fourier's law is empirically confirmed for many substances and over an extremely wide range of thermodynamic parameters, a convincing microscopic derivation still poses difficulties. With current machines the solution of Newton's…
We present a few charge distributions for which the application of Gauss' law in its integral form, as typically outlined in standard textbooks, results in a contradiction. We identify the root cause of such contradictions and put forward a…
When aggregating logically interconnected judgments from $n$ agents, the result might be inconsistent with the logical connection. This inconsistency is known as the doctrinal paradox, which plays a central role in the field of judgment…
In a previous article [1] we presented an argument to obtain (or rather infer) Born's rule, based on a simple set of axioms named "Contexts, Systems and Modalities" (CSM). In this approach there is no "emergence", but the structure of…
Defeasible logic is a rule-based nonmonotonic logic, with both strict and defeasible rules, and a priority relation on rules. We show that inference in the propositional form of the logic can be performed in linear time. This contrasts…
In the infinite-horizon and discrete-time framework we establish maximum principles of Pontryagin under assumptions which weaker than these ones of existing results. We avoid several assumptions of continuity and of…