The boy-emperor Leo II has bequeathed us more than his share of chronological puzzles. He was only seven years old when he died in 474 but he had possessed imperial authority for nearly half his short life. There is uncertainty about the date of his birth, and most of his career as emperor with his grandfather Leo I. If we still had the chronicle of Nestorianos which actually terminated at the death of Leo II we would probably be fully informed (...) on these matters. Instead, several of the relevant documents have been consistently misconstrued, that is, they have been made to fit a predetermined interpretation or order of events. Moreover, one important text has been ignored altogether. The chronology of the boy-emperor's career depends on Seeck's Regesten which has inevitably shaped the coverage in the standard accounts of Bury and Stein. The authority of Seeck also underpins the entry in the Prosopography of the Later Roman Empire which sets out the following chronology of Leo's brief life and imperial career: 467 – birth; 473 – elevated to Caesar by Leo I, October; 474 – elevated to Augustus by Leo I, before 18 January; 474 – death, November. This investigation is designed to show that the multiple phases in the imperial rule of Leo II have never been properly disentangled. To do so not only brings greater precision to the sequence of events, and to Leo's short career, but also casts light on the wider context of these turbulent few years. (shrink)

Among the many codices carried by Cassiodorus when he returned to Italy from Constantinople in the early 550s was a copy of the chronicle of Marcellinus, an Illyrian who had lived for many years in Constantinople before writing his chronicle in A.D. 518/519. The chronicle covered events from 379 to the death of Anastasius and was later continued by Marcellinus to 534.1 That the chronicle is preserved at all is due partly to the fact that Cassiodorus recommended it in his (...) reading guide for monks, the Institutiones, where it is included under the heading ‘Christian Historians’. If you want to know which chroniclers to read, says Cassiodorus, then begin with Jerome's translation of Eusebius and his own continuation of Eusebius to 378. Of all the continuators of Jerome Cassiodorus recommends Marcellinus and Prosper, but in mentioning Marcellinus he digresses slightly to include some valuable and unique information which he had picked up while in Constantinople on Marcellinus' public career. (shrink)

The development of “smart stadia”, i.e. the use of “smart technologies” in the way sports stadia are designed and managed, promises to enhance the experience of attending a live match through innovative and improved services for the audience, as well as for the players, vendors and other stadium stakeholders. These developments offer us a timely opportunity to reflect on the ethical implications of the use of smart technologies and the emerging Internet of Things (IoT). The IoT has the potential to (...) radically transform society and is representative of the ways that novel technologies will alter human life. We use Dublin’s Croke Park stadium smart project as a case study for examining the development of smart stadia. (shrink)

The development of “smart stadia”, i.e. the use of “smart technologies” in the way sports stadia are designed and managed, promises to enhance the experience of attending a live match through innovative and improved services for the audience, as well as for the players, vendors and other stadium stakeholders. These developments offer us a timely opportunity to reflect on the ethical implications of the use of smart technologies and the emerging Internet of Things. The IoT has the potential to radically (...) transform society and is representative of the ways that novel technologies will alter human life. We use Dublin’s Croke Park stadium smart project as a case study for examining the development of smart stadia. (shrink)

Let wF, wC+, and wC– be three distinct worlds, each of which contains only a single point-sized material particle, and in each of which spacetime is: uniformly flat, constantly positively curved, and constantly negatively curved, respectively. By the relationist’s lights, these worlds seem to be qualitatively identical. Nevertheless, for each world, there are propositions concerning possible arrangements of material points that are true in that world, but false in the other two. I argue that, surprisingly, the relationist can ground these (...) differences in the distinct non-modal and intrinsic relations that are instantiated in each of wF, wC+, and wC–. (shrink)

Way-finding (WF) is the ability to move around efficiently and find the way from a starting point to a destination. It is a component of spatial navigation, a coordinate and goal-directed movement of one’s self through the environment. In the present study, the relationship between WF tasks (route tracing and shortcut finding) and individual factors were explored with the hypothesis that WF tasks would be predicted by different types of cognitive, affective, motivational variables and personality factors. A group of 116 (...) university students (88 F.) was conducted along a route in a virtual environment and then asked first to trace the same route again, and then to find a shortcut between the start and end points. Several instruments assessing visuospatial working memory, mental rotation ability, self-efficacy, spatial anxiety, positive attitude to exploring, and personality traits were administered. The results showed that a latent spatial ability factor (measured with the visuospatial working memory and mental rotations tests) - controlled for gender - predicted route-tracing performance, while self-report measures of anxiety, efficacy, and pleasure in exploring, and some personality traits were more likely to predict shortcut-finding performance. We concluded that both personality and cognitive abilities affect WF performance, but differently, depending on the requirements of the task. (shrink)

ABSTRACT Let wF, wC+, and wC− be three distinct worlds, each of which contains only a single point-sized material particle, and in each of which spacetime is: uniformly flat, constantly positively curved, and constantly negatively curved, respectively. By the relationist’s lights, these worlds seem to be qualitatively identical. Nevertheless, for each world, there are propositions concerning possible arrangements of material points that are true in that world, but false in the other two. I argue that, surprisingly, the relationist can ground (...) these differences in the distinct non-modal and intrinsic relations that are instantiated in each of wF, wC+, and wC–. (shrink)

We highlight that the connection of well-foundedness and recursive definitions is more than just convenience. While the consequences of making well-foundedness a sufficient condition for the existence of hierarchies have been extensively studied, we point out that well-foundedness is a necessary condition for the existence of hierarchies e.g. that even in an intuitionistic setting α⊢wfwhereα\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${_\alpha \vdash \mathsf{wf}\, {\rm where}\, _\alpha}$$\end{document} stands for the iteration of Π10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} (...) \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Pi^0_1}$$\end{document} comprehension along some ordinal α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\alpha}$$\end{document} and wf\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{wf}}$$\end{document} stands for the well-foundedness of α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\alpha}$$\end{document}. (shrink)

We study the extension 123) of the theory S21 by instances of the dual weak pigeonhole principle for p-time functions, dWPHPx2x. We propose a natural framework for formalization of randomized algorithms in bounded arithmetic, and use it to provide a strengthening of Wilkie's witnessing theorem for S21+dWPHP. We construct a propositional proof system WF , which captures the Π1b-consequences of S21+dWPHP. We also show that WF p-simulates the Unstructured Extended Nullstellensatz proof system of Buss et al. 256). We prove that (...) dWPHP is equivalent to a statement asserting the existence of a family of Boolean functions with exponential circuit complexity. Building on this result, we formalize the Nisan–Wigderson construction in a conservative extension of S21+dWPHP. (shrink)

A version of Bradley's regress can be endorsed in an effort to address the problem of the unity of states of affairs or facts, thereby arriving at a doctrine that I have called fact infinitism . A consequence of it is the denial of the thesis, WF, that all chains of ontological dependence are well-founded or grounded. Cameron has recently rejected fact infinitism by arguing that WF, albeit not necessarily true, is however contingently true. Here fact infinitism is supported by (...) showing that Cameron's argument for the contingent truth of WF is unsuccessful. (shrink)

Abstract.As an undergraduate at Cambridge, Newton entered into his ‘Waste Book’ an assumption that we have named the Equivalence Assumption (The Younger): ‘‘ If a body move progressively in some crooked line [about a center of motion]..., [then this] crooked line may bee conceived to consist of an infinite number of streight lines. Or else in any point of the croked line the motion may bee conceived to be on in the tangent.’’ In this assumption, Newton somewhat imprecisely describes two (...) mathematical models, a ‘‘polygonal limit model’’ and a ‘‘tangent deflected model,’’ for ‘‘one-body motion,’’ that is, for the motion of a ‘‘body in orbit about a fixed center,’’ and then claims that these two models are equivalent. In the first part of this paper, we study the Principia to determine how the elder Newton would more carefully describe the polygonal limit and tangent deflected models. From these more careful descriptions, we then create Equivalence Assumption (The Elder), a precise interpretation of Equivalence Assumption (The Younger) as it might have been restated by Newton, after say 1687. We then review certain portions of the Waste Book and the Principia to make the case that, although Newton never restates nor even alludes to the Equivalence Assumption after his youthful Waste Book entry, still the polygonal limit and tangent deflected models, as well as an unspoken belief in their equivalence, infuse Newton’s work on orbital motion. In particular, we show that the persuasiveness of the argument for the Area Property in Proposition 1 of the Principia depends crucially on the validity of Equivalence Assumption (The Elder). After this case is made, we present the mathematical analysis required to establish the validity of the Equivalence Assumption (The Elder). Finally, to illustrate the fundamental nature of the resulting theorem, the Equivalence Theorem as we call it, we present three significant applications: we use the Equivalence Theorem first to clarify and resolve questions related to Leibniz’s ‘‘polygonal model’’ of one-body motion; then to repair Newton’s argument for the Area Property in Proposition 1; and finally to clarify and resolve questions related to the transition from impulsive to continuous forces in ‘‘De motu’’ and the Principia. (shrink)

The Schrodinger's Cat and Wigner's Friend thought experiments, which logically follow from the universality of quantum mechanics at all scales, have been repeatedly characterized as possible in principle, if perhaps difficult or impossible for all practical purposes. I show in this paper why these experiments, and interesting macroscopic superpositions in general, are actually impossible in principle. First, no macroscopic superposition can be created via the slow process of natural quantum packet dispersion because all macroscopic objects are inundated with decohering interactions (...) that constantly localize them. Second, the SC/WF thought experiments depend on von Neumann-style amplification to achieve quickly what quantum dispersion achieves slowly. Finally, I show why such amplification cannot produce a macroscopic quantum superposition of an object relative to an external observer, no matter how well isolated the object from the observer, because: the object and observer are already well correlated to each other; and reducing their correlations to allow the object to achieve a macroscopic superposition relative to the observer is equally impossible, in principle, as creating a macroscopic superposition via the process of natural quantum dispersion. (shrink)

A version of Bradley's regress can be endorsed in an effort to address the problem of the unity of states of affairs or facts, thereby arriving at a doctrine that I have called fact infinitism. A consequence of it is the denial of the thesis, WF, that all chains of ontological dependence are well‐founded or grounded. Cameron has recently rejected fact infinitism by arguing that WF, albeit not necessarily true, is however contingently true. Here fact infinitism is supported by showing (...) that Cameron's argument for the contingent truth of WF is unsuccessful. (shrink)

Let A be an infinite Δ₂⁰ set and let K be creative: we show that K≤Q A if and only if K≤Q₁ A. (Here ≤Q denotes Q-reducibility, and ≤Q₁ is the subreducibility of ≤Q obtained by requesting that Q-reducibility be provided by a computable function f such that Wf(x)∩ Wf(y)=∅, if x \not= y.) Using this result we prove that A is hyperhyperimmune if and only if no Δ⁰₂ subset B of A is s-complete, i.e., there is no Δ⁰₂ subset (...) B of A such that \overline{K}≤s B, where ≤s denotes s-reducibility, and \overline{K} denotes the complement of K. (shrink)

This paper examines the legal justification for water fluoridation (WF) in the United Kingdom. While current legislation clearly permits WF, there is a degree of obfuscation concerning whether the practice amounts to medication, and were it to be acknowledged that fluoridated water constitutes a medicine, the legality of the practice would not be so obvious. It is concluded that an accurate and honest interpretation of the law would result in the conclusion that fluoridation does constitute medication, as it seeks to (...) improve health by the addition of a chemical. (shrink)

By a classical theorem of Harvey Friedman, every countable nonstandard model $\mathcal {M}$ of a sufficiently strong fragment of ZF has a proper rank-initial self-embedding j, i.e., j is a self-embedding of $\mathcal {M}$ such that $j[\mathcal {M}]\subsetneq \mathcal {M}$, and the ordinal rank of each member of $j[\mathcal {M}]$ is less than the ordinal rank of each element of $\mathcal {M}\setminus j[\mathcal {M}]$. Here, we investigate the larger family of proper initial-embeddings j of models $\mathcal {M}$ of fragments of (...) set theory, where the image of j is a transitive submodel of $\mathcal {M}$. Our results include the following three theorems. In what follows, $\mathrm {ZF}^-$ is $\mathrm {ZF}$ without the power set axiom; $\mathrm {WO}$ is the axiom stating that every set can be well-ordered; $\mathrm {WF}$ is the well-founded part of $\mathcal {M}$ ; and $\Pi ^1_\infty \text{-}\mathrm {DC}_\alpha $ is the full scheme of dependent choice of length $\alpha $.Theorem A.There is an $\omega $ -standard countable nonstandard model $\mathcal {M}$ of $\mathrm {ZF}^-+\mathrm {WO}$ that carries no initial self-embedding $j:\mathcal {M} \longrightarrow \mathcal {M}$ other than the identity embedding.Theorem B.Every countable $\omega $ -nonstandard model $\mathcal {M}$ of $\ \mathrm {ZF}$ is isomorphic to a transitive submodel of the hereditarily countable sets of its own constructible universe $L^{\mathcal {M}}$.Theorem C.The following three conditions are equivalent for a countable nonstandard model $\mathcal {M}$ of $\mathrm {ZF}^{-}+\mathrm {WO}+\forall \alpha \ \Pi ^1_\infty \text{-}\mathrm {DC}_\alpha $. There is a cardinal in $\mathcal {M}$ that is a strict upper bound for the cardinality of each member of $\mathrm {WF}$. $\mathrm {WF}$ satisfies the powerset axiom.For all $n \in \omega $ and for all $b \in M$, there exists a proper initial self-embedding $j: \mathcal {M} \longrightarrow \mathcal {M}$ such that $b \in \mathrm {rng}$ and $j[\mathcal {M}] \prec _n \mathcal {M}$. (shrink)