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)

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)

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)

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)

The Wheeler-Feynman (WF) relativistic theory of interacting point particles, generalized by acceptance of an arbitrary spacelike interaction, is shown to possess a privileged status, reminiscent of the “central force” interactions occurring in Newtonian mechanics. This scheme is shown to be isomorphic to the classical one of the statics of interacting flexible current-carrying wires obeying the Ampère-Laplace (AL) formulas: to the tensionT (T 2 =const) of the wire corresponds the momentum-energy pi (pipi=−c2m2) of the particle; to the Laplace linear force density (...) −iH×dr corresponds the Lorentz force QHij drj; to the Laplace potential ir−1 dr corresponds the WF potential Qδ(r2) dri, etc. Among the differences, there is self-action in the AL scheme and no self-action in the WF scheme. A stationary energy principle in the AL scheme is isomorphic to Fokker's stationary action principle in the WF scheme. (shrink)

We show that there are continuum many different extensions of SCI (the basic theory of non-Fregean propositional logic) that lie below WF (the Fregean extension) and are closed under substitution. Moreover, continuum many of them are independent from WB (the Boolean extension), continuum many lie above WB and are independent from WH (the Boolean extension with only two values for the equality relation), and only countably many lie between WH and WF.

Recently, Brass and Dix showed 143–165) that the well founded semantics WFS can be defined as a confluent calculus of transformation rules. This led not only to a simple extension to disjunctive programs 167–213), but also to a new computation of the well-founded semantics which is linear for a broad class of programs. We take this approach as a starting point and generalize it considerably by developing a general theory of Confluent LP-systems CS . Such a system CS is a (...) rewriting system on the set of all logic programs over a fixed signature L and it induces in a natural way a canonical semantics. Moreover, we show four important applications of this theory: most of the well-known semantics are induced by confluent LP-systems , there are many more transformation rules that lead to confluent LP-systems , semantics induced by such systems can be used to model aggregation , the new systems can be used to construct interesting counterexamples to some conjectures about the space of well-behaved semantics. (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)

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)

Standard unary modal logic and binary modal logic, i.e. modal logic with one binary operator, are shown to be definitional extensions of one another when an additional axiom |$U$| is added to the basic axiomatization of the binary side. This is a strengthening of our previous results. It follows that all unary modal logics extending Classical Modal Logic, in other words all unary modal logics with a neighborhood semantics, can equivalently be seen as binary modal logics. This in particular applies (...) to standard modal logics, which can be given simple natural axiomatizations in binary form. We illustrate this in the logic K. We call such logics binary expansions of the unary modal logics. There are many more such binary expansions than the ones given by the axiom |$U$|⁠. We initiate an investigation of the properties of these expansions and in particular of the maximal binary expansions of a logic. Our results directly imply that all sub- and superintuitionistic logics with a standard modal companion also have binary modal companions. The latter also applies to the weak subintuitionistic logic WF of our previous papers. This logic doesn’t seem to have a unary modal companion. (shrink)

Sustained peripheral somatosensory stimulations, such as high-frequency repetitive somatosensory stimulation (HF-RSS) and vibrated stimulation, are effective in altering the balance between excitation and inhibition in the somatosensory cortex (S1) and motor cortex (M1). A recent study reported that whole-hand water flow (WF) stimulation induced neural disinhibition in the M1. Based on previous results, we hypothesized that whole-hand WF stimulation would lead to neural disinhibition in the S1 because there is a strong neural connection between M1 and S1 and aimed to (...) examine whether whole-hand WF stimulation would change the neural balance between excitation and inhibition in the S1. Nineteen healthy volunteers were studied by measuring excitation and inhibition in the S1 before and after each of the four 15-min interventions. The excitation and inhibition in the S1 were assessed using somatosensory evoked potentials (SEPs) and paired-pulse inhibition (PPI) induced by single- and paired-pulse stimulations, respectively. The four interventions were as follows: control, whole-hand water immersion, whole-hand WF, and HF-RSS. The results showed no significant changes in SEPs and PPI following any intervention. However, changes in PPI with an interstimulus interval (ISI) of 30 ms were significantly correlated with the baseline value before whole-hand WF. Thus, the present findings indicated that the whole-hand WF stimulation had a greater decreased neural inhibition in participants with higher neural inhibition in the S1 at baseline. Considering previous results on M1, the present results possibly show that S1 has lower plasticity than M1 and that the duration (15 min) of each intervention may not have been enough to alter the balance of excitation and inhibition in the S1. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:98 HISTORY OF PHILOSOPHY quoted in great numbers. The other is Kern's philosophical competence and his skill in handling complex problems. The book is divided into two parts. Part I gives the reader a brief historical survey of Husserl's changing attitudes toward Kant and the neo-Kantians (especially Natorp and ttickert). Indicating the influences which shaped Husserl's thinking during the years of his studies at the universities of Berlin and (...) Vienna, Kern traces Husserl's development throughout his career as a thinker and a writer. But this survey (pp. 1-50) provides merely the general framework within which the intensive and detailed analyses of Part II (pp. 51-424) must be viewed. Two appendices, an extensive bibliography, and a name index complete the work. The detailed discussions of Part II are, of course, the really important contributions to our understanding of Husserl's relation to Kant and the Kantians. As was to be expected, Husserl found in Kant's works formulations of problems and profound insights that he regarded as crucial to any philosophy. At times, however, Husserl was sure that because of mistaken assumptions, insufficiently clarified presuppositions, and methodological deficiencies Kant himself had not fully realized his intentions. Still, it is evident that, in time, Husserl found himself increasingly in sympathy with Kant's postion. In fact, in the end he used Kant's term "transcendental idealism" to designate his own philosophy. In the course of this development, however, Husserl's thinking underwent various changes and reversals. The detailed analyses of them make fascinating reading and are most revelatory of Husserl's own struggles with obtrnsive problems. In Chapter z of Part II (pp. 55-134), the author discusses Husserl's criticism of Kant's positionwKant's conception of the apriori, his strict separation of "sensibility" and "understanding," his presupposition of a "natural world view," his failure to ask sufficiently radical questions concerning the foundations of knowledge, his lack of a proper method of analysis, and his "psychologism." In the course of his own development, however, Husserl modified and, in some respects, even reversed his criticisms of Kant. Chapters ~, m, re and v of Part II, dealing with problems of formal and transcendental logic, with the possibihty of metaphysics on Kantian principles, and with the complex problems of subjectivity, bear witness to the fact that Huseerl often changed his opinion of Kant's work. Of special interest, however, is Chapter vz. It is devoted to a comparison of Husserl's and Kant's "transcendental idealism" and reveals most strikingly the similarities of the two positions. The chapter dealing with Husserl's relation to l~atorp and Rickert, interesting in its own way, is essentially only a footnote, as it were, to the rest of the hook; but it completes the survey. As I said before, this book gives us not only a remarkable insight into the various phases of development in Husserl's thinking and is therefore indispensable to a real understanding of Husserl's intentions and achievements; it also lets us see Kant's philosophy in a new and revealing perspective--both as to its value and it deficiencies. Only a detailed study can do justice to this book. W. H. WF~mMF~STZR Florida State University Ludwig Wittgenstein. Zettel. Edited by G. E. M. Anscombe and G. H. von Wright. Translated by G. E. M. Anscombe. (University of California Press and Basil Blackwell, 1967. Pp. v + 124 [German and English on facing pages]. $6.95.) The paragraphs in this volume, the editors tell us, were collected in a box-file by Wittgenstein from a period beginning in 1929,though the bulk of them come from typescripts dictated between 1945 and 1948. The editors credit Peter Geach with the major work of arrangement. Whoever is responsible did a superlative job, a remark that holds as well for Miss Anscombe's translation. The editors and Mr. Geach have performed an invaluable service to those interested BOOK REVIEWS 99 in Wittgenstein and--quite apart from Wittgensteinian exegesis--in the problems treated in these pages. The philosophical topics are those of the Investigations (PI) and The Remarks on the Foundations o] Mathematir~ (RFM)---e.g., the attack on... (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)

Pain has not only sensory, but also emotional and cognitive, components. Some studies have explored the effect of pain on time perception, but the results remain controversial. Whether individual pain-related emotional and cognitive factors play roles in this process should also be explored. In this study, we investigated the effect of electrical stimulation–induced pain on interval timing using a temporal bisection task. During each task session, subjects received one of five types of stimulation randomly: no stimulus and 100 and 300 (...) ms of non-painful and painful stimulation. Pain-related emotional and cognitive factors were measured using a series of questionnaires. The proportion of “long” judgments of a 1,200-ms visual stimulus duration was significantly smaller with 300 ms painful stimulation than with no stimulus and 100 ms and 300 ms non-painful stimulation. The point of subjective equality did not differ among sessions, but the average Weber fraction was higher for painful sessions than for no-stimulus session. The pain fear score correlated positively with the PSE under 100 ms non-painful and painful and 300 ms painful stimulation. Pain catastrophizing and pain anxiety scores correlated significantly with the WF under no stimulus and 100 ms non-painful stimulation, respectively. These results suggest that electrical stimulation–induced pain affects temporal sensitivity, and that pain-related emotional and cognitive factors are associated with the processing of time perception. (shrink)