The second edition of Aquinas, _On Law, Morality, and Politics _ retains the selection of texts presented in the first edition but offers them in new translations by Richard J. Regan--including that of his Aquinas, _Treatise on Law_. A revised Introduction and glossary, an updated select bibliography, and the inclusion of summarizing headnotes for each of the units--Conscience, Law, Justice, Property, War and Killing, Obedience and Rebellion, and Practical Wisdom and Statecraft—further enhance its usefulness.

_God and Creation_ is a new translation of St. Thomas Aquinas's treatment of these subjects in the _Summa Theologiae_, with introductory and explanatory material provided to assist the reader's understanding of the texts. The selected questions and articles fall within the area of what is described as natural theology or the study of truth about God that are accessible to human reason without the aid of divine revelation.

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 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)

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 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 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)

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)

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)

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)

We prove that there exists a function f which reduces a given Π1 1 subset P of an internal set X of an ω1-saturated nonstandard universe to the set WF of well-founded trees possessing properties similar to those possessed by the standard part map. We use f to define the Lusin-Sierpinski index of points in X, and prove the basic properties of that index using the classical properties of the Lusin-Sierpinski index. An example of a Π1 1 but not Σ1 (...) 1 set is given. (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)

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)

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.

Let A be an infinite $\Delta _{2}^{0}$ 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 ≠ y.) Using this result we prove that A is hyperhyperimmune if and only if no $\Delta _{2}^{0}$ subset B of A is (...) s-complete. i.e., there is no $\Delta _{2}^{0}$ subset B of A such that K̄ ≤s B, where ≤s denotes s-reducibility, and K̄ 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)

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)

Adaptive optics are techniques used for processing the spatial resolution of astronomical images taken from large ground-based telescopes. In this work, computational results are presented for a modified curvature sensor, the tomographic pupil image wavefront sensor, which measures the turbulence of the atmosphere, expressed in terms of an expansion over Zernike polynomials. Convolutional neural networks are presented as an alternative to the TPI-WFS reconstruction. This technique is a machine learning model of the family of artificial neural networks, which are widely (...) known for its performance as modeling and prediction technique in complex systems. Results obtained from the reconstruction of the networks are compared with the TPI-WFS reconstruction by estimating errors and optical measurements. The reconstructed wavefronts from both techniques are compared for wavefronts of 153 Zernike modes. For this case, a detailed comparison and grid search to find the most suitable neural network is performed, searching between multi-layer perceptron, CNN and recurrent networks topologies. In general, the best network was a CNN trained for TPI-WFS reconstruction, achieving better performance than the reconstruction software from TPI-WFS in most of the turbulent profiles, but the most significant improvements were found for higher turbulent profiles that have the lowest r0 values. (shrink)

Die Dissertation von G. Gentzen enthält einen Wf-beweis der reinen Zahlentheorie ohne vollständige Induktion, der auf dem folgenden Grundgedanken beruht: jede herleitbare Sequenz muß sich auch ohne...

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)

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)