Turing Impossibility Properties for Stack Machine Programming

The strong, intermediate, and weak Turing impossibility properties are introduced. Some facts concerning Turing impossibility for stack machine programming are trivially adapted from previous work. Several intriguing questions are raised about the Turing impossibility properties concerning different method interfaces for stack machine programming.Comment: arXiv admin note: substantial text overlap with arXiv:0910.556

The impossibility of sympathy

Copyright © 2010 University of Pennsylvania Press. All rights reserved. Except for brief quotations used for purposes of scholarly citation, none of this work may be reproduced in any form by any means without written permission from the publisher. For information address the University of Pennsylvania Press, 3905 Spruce Street, Philadelphia, Pennsylvania 19104-4112.This article questions the status of sympathy in eighteenth century studies. It argues that sympathy can be seen as an economy of two persistent idealizations: the untouchable—that touches everything. Tracing the genealogy of fellow feeling as a militant Puritan concept of exclusion that is still marked by its theological and political past, the sympathy advocated by Hutcheson, Hume and Smith appears as an idealization confronted by its own impossibility. The eighteenth century is a century in search of an absent and insufficient sympathy, a sympathy that is already preoccupied with its own limitations and excesses: a meta-discourse on sympathy still eludes us

Impossibility and Impossible Worlds

Possible worlds have found many applications in contemporary philosophy: from theories of possibility and necessity, to accounts of conditionals, to theories of mental and linguistic content, to understanding supervenience relationships, to theories of properties and propositions, among many other applications. Almost as soon as possible worlds started to be used in formal theories in logic, philosophy of language, philosophy of mind, metaphysics, and elsewhere, theorists started to wonder whether impossible worlds should be postulated as well. In many applications, possible worlds face limitations that can be dealt with through postulating impossible worlds as well. This chapter examines some of the uses of impossible worlds, and philosophical challenges theories of impossible worlds face

Impossibility of Gathering, a Certification

Recent advances in Distributed Computing highlight models and algorithms for autonomous swarms of mobile robots that self-organise and cooperate to solve global objectives. The overwhelming majority of works so far considers handmade algorithms and proofs of correctness. This paper builds upon a previously proposed formal framework to certify the correctness of impossibility results regarding distributed algorithms that are dedicated to autonomous mobile robots evolving in a continuous space. As a case study, we consider the problem of gathering all robots at a particular location, not known beforehand. A fundamental (but not yet formally certified) result, due to Suzuki and Yamashita, states that this simple task is impossible for two robots executing deterministic code and initially located at distinct positions. Not only do we obtain a certified proof of the original impossibility result, we also get the more general impossibility of gathering with an even number of robots, when any two robots are possibly initially at the same exact location.Comment: 10

Two Kinds of Logical Impossibility

In this paper, we argue that a distinction ought to be drawn between two ways in which a given world might be logically impossible. First, a world w might be impossible because the laws that hold at w are different from those that hold at some other world (say the actual world). Second, a world w might be impossible because the laws of logic that hold in some world (say the actual world) are violated at w. We develop a novel way of modelling logical possibility that makes room for both kinds of logical impossibility. Doing so has interesting implications for the relationship between logical possibility and other kinds of possibility (for example, metaphysical possibility) and implications for the necessity or contingency of the laws of logic

Characterizing quantum theory in terms of information-theoretic constraints

We show that three fundamental information-theoretic constraints--the impossibility of superluminal information transfer between two physical systems by performing measurements on one of them, the impossibility of broadcasting the information contained in an unknown physical state, and the impossibility of unconditionally secure bit commitment--suffice to entail that the observables and state space of a physical theory are quantum-mechanical. We demonstrate the converse derivation in part, and consider the implications of alternative answers to a remaining open question about nonlocality and bit commitment.Comment: 25 pages, LaTe

A Unifying Impossibility Theorem

This paper considers social choice correspondences assigning a choice set to each non-empty subset of social alternatives. We impose three requirements on these correspondences: unanimity, independence of preferences over infeasible alternatives and choice consistency with respect to choices out of all possible alternatives. With more than three social alternatives and the universal preference domain, any social choice correspondence that satisfies our requirements is serially dictatorial. A number of known impossibility theorems — including Arrow’s Impossibility Theorem, the Muller-Satterthwaite Theorem and the impossibility theorem under strategic candidacy — follow as corollaries. Our new proof highlights the common logical underpinnings behind these theorems.