We elaborate Weiermann-style phase transitions for well-partial-orderings (wpo) determined by iterated finite sequences under Higman-Friedman style embedding with Gordeev’s symmetric gap condition. For every d-times iterated wpo \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\left({\rm S}\text{\textsc{eq}}^{d}, \trianglelefteq _{d}\right)}$$\end{document} in question, d > 1, we fix a natural extension of Peano Arithmetic, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T \supseteq \sf{PA}}$$\end{document}, that proves the corresponding second-order sentence \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sf{WPO}\left({\rm (...) S}{\textsc{eq}}^{d}, \trianglelefteq _{d}\right) }$$\end{document}. Having this we consider the following parametrized first-order slow well-partial-ordering sentence \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sf{SWP}\left({\rm S}\text{\textsc{eq}}^{d}, \trianglelefteq _{d}, r\right):}$$\end{document}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( \forall K > 0 \right) \left( \exists M > 0\right) \left( \forall x_{0},\ldots,x_{M}\in {\rm S}\text{\textsc{eq}}^{d}\right)$$\end{document}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( \left( \forall i\leq M\right) \left( \left| x_{i}\right| 1}$$\end{document} then \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sf{SWP}\left({\rm S}\text{\textsc{eq}}^{d}, \trianglelefteq _{d},r \right) }$$\end{document} is not provable in T.Moreover, by the well-known proof theoretic equivalences we can just as well replace T by PA or ACA0 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta _{1}^{1}\sf{CA}}$$\end{document}, if d = 2 and d = 3, respectively.In the limit case d → ∞ we replaceEFA-provably computable reals r by EFA-provably computable functions \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${f: \mathbb{N} \rightarrow \mathbb{R}_{+}}$$\end{document} and prove analogous theorems. (In the sequel we denote by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{R}_{+}}$$\end{document} the set of EFA-provably computable positive reals). In the basic case T = PA we strengthen the basic phase transition result by adding the following static threshold clause\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sf{SWP}\left({\rm S}\text{\textsc{eq}}^{2}, \trianglelefteq _{2}, 1\right)}$$\end{document} is still provable in T = PA (actually in EFA). Furthermore we prove the following dynamic threshold clauses which, loosely speaking are obtained by replacing the static threshold t by slowly growing functions 1α given by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${1_{\alpha }\left( i\right)\,{:=}\,1+\frac{1}{H_{\alpha }^{-1}\left(i\right) }, H_{\alpha}}$$\end{document} being the familiar fast growing Hardy function and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${H_{\alpha }^{-1}\left( i\right)\,{:=}\,\rm min \left\{ j \mid H_{\alpha } \left ( j\right) \geq i \right\}}$$\end{document} the corresponding slowly growing inversion. If \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\alpha < \varepsilon _{0}}$$\end{document}, then \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sf{SWP}\left({\rm S}\text{\textsc{eq}}^{2}, \trianglelefteq _{2}, 1_{\alpha}\right)}$$\end{document} is provable in T = PA. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sf{SWP}\left( {\rm S}\text{\textsc{eq}}^{2}, \trianglelefteq _{2},1_{\varepsilon _{0}}\right)}$$\end{document} is not provable in T = PA. We conjecture that this pattern is characteristic for all \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T\supseteq \sf{PA}}$$\end{document} under consideration and their proof-theoretical ordinals o (T ), instead of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varepsilon _{0}}$$\end{document}. (shrink)

It might seem that there are two separate questions about universals, the question of what they are and the question why we should believe that there are such things, and that the former question should be taken first; it might seem that until you know what they are it cannot be sensible to ask whether one should believe in them. How, for example, could one know whether it was sensible or even possible to believe in Father Christmas until one knew (...) who or what he was supposed to be? But appearances could be deceptive. In the case of universals the position is different. What happened was that philosophers found themselves faced with certain problems of which they were inclined to say: this problem is insoluble unless there are some entities which have certain characteristics, the characteristics which would enable the problem to be solved. The things which, if they existed, would solve their problems they called forms or universals. So universals are things which have whatever properties they need to have to solve certain problems. This being so, it is clearly sensible to approach the theory of universals from the problems which led to philosophers postulating their existence. (shrink)

The essays in this volume explore current work in central areas of philosophy, work unified by attention to salient questions of human action and human agency. They ask what it is for humans to act knowledgeably, to use language, to be friends, to act heroically, to be mortally fortunate, and to produce as well as to appreciate art. The volume is dedicated to J. O. Urmson, in recognition of his inspirational contributions to these areas. All the essays but one have (...) been specially written for this volume. (shrink)

The many worlds interpretation of quantum mechanics (MWI) states that the world we live in is just one among many parallel worlds. It is widely believed that because of this commitment to parallel worlds, the MWI violates common sense. Some go so far as to reject the MWI on this basis. This is despite its myriad of advantages to physics (e.g. consistency with relativity theory, mathematical simplicity, realism, determinism, etc.). Here, we make the case that common sense in fact favors (...) the MWI. We argue that causal explanations are commonsensical only when they are local causal explanations. We present several quantum mechanical experiments that seem to exhibit nonlocal “action at a distance”. Under the assumption that only one world exists, these experiments seem immune to local causal explanation. However, we show that the MWI, by taking all worlds together, can provide local causal explanations of the experiments. The MWI therefore restores common sense to physical explanation. (shrink)

We defend the many-worlds interpretation of quantum mechanics against the objection that it cannot explain why measurement outcomes are predicted by the Born probability rule. We understand quantum probabilities in terms of an observer's self-location probabilities. We formulate a probability postulate for the MWI: the probability of self-location in a world with a given set of outcomes is the absolute square of that world's amplitude. We provide a proof of this postulate, which assumes the quantum formalism and two principles concerning (...) symmetry and locality. We also show how a structurally similar proof of the Born rule is available for collapse theories. We conclude by comparing our account to the recent account offered by Sebens and Carroll. (shrink)

J.O. Urmson's The Greek Philosophical Vocabulary contains some five hundred alphabetically arranged entries, each aiming to provide useful information on a particular word used by Greek philosophers. The book includes a wealth of quotations ranging from the fifth century BC to the sixth century AD.

Aristotle's doctrine of the mean is not a counsel to perform mean or moderate actions. It states that excellence of character is a mean state with regard to the having and displaying of emotions. All emotions are morally neutral; character is shown by displaying emotions on the right occasions, Not too often or too rarely, Not too strongly or too weakly, For sufficient and only sufficient reasons, Etc. The difficulties for such a view presented by justice and such bad emotions (...) as envy are discussed. The conclusion is that basically aristotle's theory can resist critical scrutiny. (shrink)

The influence of J. L. Austin on contemporary philosophy was substantial during his lifetime, and has grown greatly since his death, at the height of his powers, in 1960. Philosophical Papers, first published in 1961, was the first of three volumes of Austin's work to be edited by J. O. Urmson and G. J. Warnock. Together with Sense and Sensibilia and How to do things with Words, it has extended Austin's influence far beyond the circle who knew him or read (...) the handful of papers he published in journals. (shrink)

J. O. Urmson; VIII*—A Defence of Intuitionism, Proceedings of the Aristotelian Society, Volume 75, Issue 1, 1 June 1975, Pages 111–120, https://doi.org/10.1093/.

Title: BerkeleyPublisher: Oxford University PressISBN: 0192875469Author: J.O. UrmsonTitle: KantPublisher: Oxford University Press ISBN: 0192801996Author: Roger Scruton.

"This volume offers a new translation of the Neoplatonist philosopher Simplicius' commentary on the chapters concerning place and time in Aristotle's Physics, Book Four. Written after the closing of the Athenian Neoplatonist school in A.D. 529, the commentary clarifies the structure and meaning of Aristotle's arguments and provides a rich account of 800 years of interpretation." "Surprisingly, in the first five chapters of Book Four Aristotle shows place as two-dimensional: one's place is the two-dimensional inner surface of one's surroundings. He (...) also suggests that the upward motion of air and fire and the downward motion of earth and water are partly explained by the natural places to which they tend. Place thus has power (dunamis) of its own. In his last five chapters, Aristotle argues that if time did not entail change its passage would be undetectable, and that time, by definition countable, requires the existence of conscious beings to do the counting. Among the many relevant views that Simplicius records are those of Galen, who attacks this claim, and of Eudemus, who rebuts the Pythagorean theory that history will repeat itself exactly. J. O. Urmson's translation serves as a companion to his earlier translation of the Corollaries on Place and Time, in which Simplicius sets forth his own views as distinct from those of Aristotle." "A major sourcebook for the interpretation of Aristotle, this volume will be welcomed by scholars and students in the fields of classics, ancient philosophy, ancient history, and medieval studies."--BOOK JACKET.Title Summary field provided by Blackwell North America, Inc. All Rights Reserved. (shrink)

J. O. Urmson; VIII*—A Defence of Intuitionism, Proceedings of the Aristotelian Society, Volume 75, Issue 1, 1 June 1975, Pages 111–120, https://doi.org/10.1093/.

An ecumenical effort, sensitive to both the scriptural and dogmatic issues, and directed at laying open the often overlooked, historical and doctrinal affinities underlying Protestant and Catholic Marian theology. As O'Meara correctly points out, while Luther and Calvin did indeed remove Mary from some aspects of the Church, it was some of their later followers who removed her entirely from any essential involvement with the mystery of Christ and the Church. But as in all ecumenical discussions worthy of that name, (...) genuine difficulties are not glossed over. In particular O'Meara questions the prevailing, either/or tendency in Protestant theology not to admit the possibility of a middle range of worship, i.e., hyperdulia, as falling between latria and dulia. While the treatment is for the most part scrupulously fair, O'Meara's defense of the traditional Catholic exegesis of the "I know not man" passage, which is crucial for the Catholic teaching on the virginity of Mary, seems to place an unfair burden of proof on the Protestant interpretation, which is prima facie the more obvious one.—J. J. O. (shrink)