‘More than a swineherd’

Abstract

This article suggests that alongside the strongly biblical defence of the royal supremacy, which was common in Elizabethan England, there can be found a distinctive line of argument; it stresses the roots of the magistrate’s ‘cura religionis’ in natural and human law, rather than simply divine law. This argument is often identified with Richard Hooker, who is taken to be innovative at this point. This study argues, however, that many of the same philosophical and theological points can be found in Peter Martyr Vermigli, who may have influenced Hooker. Elements of Vermigli’s Aristotelian political theory are traceable on a reading of his Commentary on Aristotle’s Nicomachean Ethics, and the application of these concepts in his biblical commentaries is noticeable.     

ON THE BUDDHIST TRUTHS AND THE PARADOXES IN POPULATION ETHICS

Starting point The starting point of this paper is the following citation concerning the state of contemporary population ethics:

Most discussion in population ethics has concentrated on how to evaluate populations in regard to their goodness, that is, how to order populations by the relations ‘is better than’ and ‘is as good as’. This field has been riddled with paradoxes which purport to show that our considered beliefs are inconsistent in cases where the number of people and their welfare varies. (Arrhenius 2004, 201)

Type of problem The best known and most discussed example shattering our intuitions is Parfit's Mere Addition Paradox. This paper explores the potential of the Buddhist Truths to answer the following questions: What is at the source of the Mere Addition Paradox? and Why are paradoxes unavoidable in population ethics?

Results The comparison of classical utilitarian and Buddhist intuitions demonstrates the close tie between intuitions and interests. The perplexing Buddhist intuition about non-existence can be explained (except for metaphysical reasons) by a radically different priority given to survival. The method of measuring the quality of life is not decisive for the existence of paradoxes; the Buddhist axiology changes but does not remove counter-intuitive combinations. If the conflict of interest (quantity versus quality) is described within a two-parameter model, it causes conflicting intuitions; in axiologies that favour quantity (utilitarianism) or quality (perfectionism), the conflicting intuitions inevitably lead to paradoxes. In order to find a compromise, one would have to find a universal interest and a corresponding universal intuition; the obvious candidate to meet this request is sympathy but, since there is no universal consensus on the desirable degree of sympathy, the normative force of such an approach is limited. Breaking out of the two-parameter model and accepting the incommensurability of certain qualities threatens the normative claim of population ethics.     

Using Relational Cultural Theory as a Pedagogical Approach for Counselor Education

ABSTRACT

In the article the authors will discuss core concepts of RCT in greater detail while relating these concepts to the counselor education classroom setting. There are many aspects of the counseling process that are open-ended due to the necessity of counselors needing to be responsive to the client’s needs in the moment. It is the assertion of the authors that using RCT in the classroom as a pedagogical framework may be beneficial to the growth of CITs. Through creating and maintaining an environment that supports growth fostering relationships, mutual empathy, authenticity, recognition and healing of disconnection, identification of central relational paradoxes, and processing relational images can all lead to developing relational competence in the CITs who will become the next generation of counselors. Additionally, the authors provide examples of the core concepts in action that are grounded in their experiences, blending RCT into their instructional delivery in their course.     

悖论的自指性与循环性

本文使用语义网分析悖论与自指性和循环性。主要结论是证明了有穷悖论都是自指的,同时其矛盾性必定基于循环性。我们还证明存在非自指但基于循环性的(无穷)悖论,比如亚布鲁悖论及其一般变形;又证明了存在自指但不基于循环性的(无穷)悖论,比如超穷赫兹伯格悖论和麦基悖论。这表明自指性与循环性对悖论而言是两个不同的概念。     

Hilbert's Programs and Beyond

Pour résoudre les paradoxes bien connus de la mécanique quantique, on propose une interprétation par ramification (ou univers parallèles) analogue à celle d’Everett, mais avec des différences: (i) on propose une infinité continue de branches, dont les poids (o[ugrave] probabilités) se calculent par intégrale; (ii) les branches sont séparées par des ramifieurs qui se propagent à la vitesse de la lumière. Lorsqu’est négligeable la composante d’énergie négative de la fonction d’onde, le poids de chaque branche en un point donné u est égal au flux du quadrivecteur (courant-densité de présence), soit à travers l'élément d’écran antérieur à u sur lequel l'impact est perçu, soit à travers le cône passé de u si aucun impact n’est perçu.

In order to solve well-known paradoxes in quantum mechanics, we propose a reworking of Everett's interpretation with ramified branches (or many worlds), yet somewhat different: (i) branches form an infinity continuum and each weight (probability) is defined by an integral; (ii) branches are separated by ramifiers which propagate themselves with the velocity of light. Assuming we can neglect the negative-energy component in the wave function, then the weight of each branch at a given point u is equal to the flux of the quadrivector (current-presence density), either through the screen element where the impact occurs, or through the past light-cone of u if no impact occurs.     

A Berry and A Russell Without Self-Reference

In this paper I present two new paradoxes, a definability paradox (related to the paradoxes of Berry, Richard and König), and a paradox about extensions (related to Russell’s paradox). However, unlike the familiar definability paradoxes and Russell’s paradox, these new paradoxes involve no self-reference or circularity.     

Infinity in Mathematics and Theology

Abstract

“Infinity” and its derivatives are frequently used in mathematics and theology. Do these expressions denote the same thing in those distinct areas of scholarship? In this article the uses of “infinity” in mathematics and its uses in theology are examined and compared. One conclusion is that quite different concepts go under the heading of “infinity.” Although they must not be confused, there are some relations between mathematical and theological senses of infinity.     

Modal Expansionism

There are various well-known paradoxes of modal recombination. This paper offers a solution to a variety of such paradoxes in the form of a new conception of metaphysical modality. On the proposed conception, metaphysical modality exhibits a type of indefinite extensibility. Indeed, for any objective modality there will always be some further, broader objective modality; in other terms, modal space will always be open to expansion.

     

Six Groups of Paradoxes in Ancient China From the Perspective of Comparative Philosophy

This paper divides the sophisms and paradoxes put forth by Chinese thinkers of the pre-Qin period of China (before 221 BCE) into six groups: paradoxes of motion and infinity, paradoxes of class membership, semantic paradoxes, epistemic paradoxes, paradoxes of relativization, other logical contradictions. It focuses on the comparison between the Chinese items and the counterparts of ancient Greek and even of contemporary Western philosophy, and concludes that there turn out to be many similar elements of philosophy and logic at the beginnings of Chinese and Greek civilizations.     

The Groundedness Approach to Class Theory

Abstract

Kripke showed how to restrict Tarski’s schema to grounded sentences. I examine the prospects for an analogous approach to the paradoxes of naive class comprehension. I present new methods to obtain theories of grounded classes and test them against antecedently motivated desiderata. My findings cast doubt on whether a theory of grounded classes can accommodate both the extensionality of classes and allow for class definition in terms of identity.     

Spiritual Maturity and Meaning-Filled Relationships: A Sociological Perspective

SUMMARY

The process of self-development, spiritual maturity and the construction of new meaning-filled relationships in late life are analyzed through the actions and interactions observed in the biographical case history of Sarah-Patton Boyle. Atchley's four stages in the process of retirement applied to the case of Sarah-Patton Boyle identifies the changes in her social roles and relationships and the struggle to maintain a positive self-view in the midst of socio-environmental changes. The struggle to continue “spiritual self” identity and ties with the church are discussed.     

Russell's Schema,Not Priest's Inclosure

On investigating a theorem that Russell used in discussing paradoxes of classes, Graham Priest distills a schema and then extends it to form an Inclosure Schema, which he argues is the common structure underlying both class-theoretical paradoxes (such as that of Russell, Cantor, Burali-Forti) and the paradoxes of ‘definability’ (offered by Richard, König-Dixon and Berry). This article shows that Russell's theorem is not Priest's schema and questions the application of Priest's Inclosure Schema to the paradoxes of ‘definability’.1 ^1?Special thanks to Francesco Orilia for criticisms of an early draft of this article.      

Motor Behavior Concepts in the Study of Balance: A Scoping Review

Abstract

Previous research suggests that using Fitts’ law; attentional focus or challenge point framework (CPF) is beneficial in balance control studies. A scoping review was conducted to examine studies that utilized these motor behavior concepts during balance control tasks. An extensive literature search was performed up to January 2018. Two independent reviewers conducted a study selection process followed by data extraction of the search results. Forty-six studies were identified, with 2 studies related to CPF, 12 studies related to Fitts’ law and 32 studies related to focus of attention. The CPF appears to be a useful method for designing a progressive therapeutic program. Fitts’ law can be used as a tool for controlling the difficulty of motor tasks. Focus of attention studies indicate that adopting an external focus of attention improves task performance. Overall, studies included in this review report benefit when using the selected motor behavior concepts. However, the majority (>80%) of studies included in the review involved healthy populations, with only three clinical trials. In order to ascertain the benefits of the selected motor behavior concepts in clinical settings, future research should focus on using these concepts for clinical trials to examine balance control among people with balance impairments.     

Hobson’s Conception of Definable Numbers

In this paper, I explore an intriguing view of definable numbers proposed by a Cambridge mathematician Ernest Hobson, and his solution to the paradoxes of definability. Reflecting on König’s paradox and Richard’s paradox, Hobson argues that an unacceptable consequence of the paradoxes of definability is that there are numbers that are inherently incapable of finite definition. Contrast to other interpreters, Hobson analyses the problem of the paradoxes of definability lies in a dichotomy between finitely definable numbers and not finitely definable numbers. To bypass this predicament, Hobson proposes a language dependent analysis of definable numbers, where the diagonal argument is employed as a means to generate more and more definable numbers. This paper examines Hobson’s work in its historical context, and articulates his argument in detail. It concludes with a remark on Hobson’s analysis of definability and Alan Turing’s analysis of computability.     

Fichte’s method of moral justification

ABSTRACT

While Kant’s claim that the moral law discloses our freedom to us has been extensively discussed in recent decades, the reactions to this claim among Kant’s immediate successors have gone largely overlooked by scholars. Reinhold, Creuzer, and Maimon were among three prominent thinkers of the era unwilling to follow Kant in making the moral law the condition for knowing our freedom. Maimon went so far as to reject Kant’s method of appealing to our everyday awareness of duty on the grounds that common human understanding is susceptible to error and illusion. In this paper I shall examine how these skeptical reactions to Kant’s position shaped the background for Fichte’s method of moral justification, leading up to his own deduction of the moral law in the System of Ethics (1798). By way of conclusion, I shall propose a new interpretation of how consciousness of the moral law serves as an entry-point to Fichte’s form of idealism.     

Descartes and More on the infinity of the world

ABSTRACT

In this paper, I address the controversy between Henry More and René Descartes on the indefinite extension of the world. I provide a new reading of Descartes’ famous final answer of 15 April 1649. I read the entire debate in the terms of a disagreement concerning the epistemological status of the necessity of our judgement about the extension of the universe. Accordingly, the disagreement on the infinity of the world constitutes a case of a more general disagreement on the nature of the necessity of the theorems of Cartesian Physics. In particular, as concerns Descartes’ last reply, I argue that his assertion that a finite world is contradictory should be interpreted as a reply to More’s claim that the thesis of the infinity of the world, in so far as it cannot be grounded on the identity between matter and extension, does not express a logical necessity. Descartes’ assertion of the logical impossibility of a finite world, far from being, as it has always been read, a concession he made under the pressure of More’s objections, expresses the more radical element of the entire debate about the extension of the universe.     

Radical views on cognition and the dynamics of scientific change

Radical views on cognition are generally defined by a cluster of features including non-representationalism and vehicle-externalism. In this paper, I concentrate on the way radical views on cognition define themselves as revolutionary theories in cognitive science. These theories often use the Kuhnian concepts of “paradigm” and “paradigm shift” for describing their ambitions and the current situation in cognitive science. I examine whether the use of Kuhn’s theory of science is appropriate here. There might be good reasons to think that cognitive science is in a situation of foundational crisis, but that does not entail that the classical paradigm (computationalism) is currently displaced to the benefit of a new paradigm. Larry Laudan’s theory of research traditions is more enlightening than Kuhn’s theory for describing the scope and ambitions of radical views on cognition, and their relations with an anti-intellectualist tradition in philosophy.

     

A neglected response to the paradoxes of confirmation

Hempel's paradox of the ravens, and his take on it, are meant to be understood as being restricted to situations where we have no additional background information. According to him, in the absence of any such information, observations of FGs confirm the hypothesis that all Fs are G. In this paper I argue against this principle by way of considering two other paradoxes of confirmation, Goodman’s “grue” paradox and the “tacking” (or “irrelevant conjunct”) paradox. What these paradoxes reveal, I argue, is that a presumption of causal realism is required to ground any confirmation; but once we grant causal realism, we have no reason to accept the central principles giving rise to the paradoxes.     

Definability and the Structure of Logical Paradoxes

Graham Priest 2002 argues that all logical paradoxes that include set-theoretic paradoxes and semantic paradoxes share a common structure, the Inclosure Schema, so they should be treated as one family. Through a discussion of Berry's Paradox and the semantic notion ‘definable’, I argue that (i) the Inclosure Schema is not fine-grained enough to capture the essential features of semantic paradoxes, and (ii) the traditional separation of the two groups of logical paradoxes should be retained.