A note on the ω-incompleteness formalization

The paper studies two formal schemes related to -completeness.LetS be a suitable formal theory containing primitive recursive arithmetic and letT be a formal extension ofS. Denoted by (a), (b) and (c), respectively, are the following three propositions (where (x) is a formula with the only free variable x): (a) (for anyn) ( _T (n)), (b) _{T x} Pr _T (^–(x)^–) and (c) _T x(x) (the notational conventions are those of Smoryski [3]). The aim of this paper is to examine the meaning of the schemes which result from the formalizations, over the base theoryS, of the implications (b) (c) and (a) (b), where ranges over all formulae. The analysis yields two results overS : 1. the schema corresponding to (b) (c) is equivalent to ¬Cons _T and 2. the schema corresponding to (a) (b) is not consistent with 1-CON _T. The former result follows from a simple adaptation of the -incompleteness proof; the second is new and is based on a particular application of the diagonalization lemma.Presented byMelvin Fitting     

Yablo’s Paradox and ω-Inconsistency

It is argued that Yablo’s Paradox is not strictly paradoxical, but rather ‘ω-paradoxical’. Under a natural formalization, the list of Yablo sentences may be constructed using a diagonalization argument and can be shown to be ω-inconsistent, but nonetheless consistent. The derivation of an inconsistency requires a uniform fixed-point construction. Moreover, the truth-theoretic disquotational principle required is also uniform, rather than the local disquotational T-scheme. The theory with the local disquotation T-scheme applied to individual sentences from the Yablo list is also consistent.     

Topological representations of Post algebras of order ω+ and open theories based on ω+-valued Post logic

Post algebras of order ⁺ as a semantic foundation for ⁺-valued predicate calculi were examined in [5]. In this paper Post spaces of order ⁺ being a modification of Post spaces of order n2 (cf. Traczyk [8], Dwinger [1], Rasiowa [6]) are introduced and Post fields of order ⁺ are defined. A representation theorem for Post algebras of order ⁺ as Post fields of sets is proved. Moreover necessary and sufficient conditions for the existence of representations preserving a given set of infinite joins and infinite meets are established and applied to Lindenbaum-Tarski algebras of elementary theories based on ⁺-valued predicate calculi in order to obtain a topological characterization of open theories.     

The Error In ‘The Error In The Error Theory’

In his paper ‘The Error in the Error Theory’[this journal, 2008], Stephen Finlay attempts to show that the moral error theorist has not only failed to prove his case, but that the error theory is in fact false. This paper rebuts Finlay's arguments, criticizes his positive theory, and clarifies the error-theoretic position.     

The Critical Reception of Michelangelo's ‘The Last Judgement': The Theological Context

Abstract

Considered here will be the question of how the hostility of the clerical elite in sixteenth-century Italy to Michelangelo's Sistine Chapel ‘Last Judgment’ may be explained. The problem arose from the many nude figures that the fresco contained. Why was nudity in Church so unpopular with the clerical elite in 1541 and for sixty years afterwards, bearing in mind that it had not raised an outcry in roughly similar circumstances earlier in the century? No real answers to these questions are to be found either in the Trent Decree on sacred images, or in the work of such sixteenth-century critics as Gilio da Fabriano. This study aims to shed more light on the matter. Some help is forthcoming from modern writers like Romeo de Maio and Bernardine Barnes. They emphasize the leading role of the ‘Theatine’ prelates, but without exposing the basic assumptions on which the ‘Theatine’ attitude depends. These basic assumptions can be probed to assess whether the objection was only to nudity in sacred spaces or to nudity tout court, and with particular reference to the argument of one theologian—Catharinus—who opted for comprehensive restrictions. In an argument directed against the Erasmian view of marriage, Catharinus identified Erasmus as a Pelagian and summarized the Augustinian argument against the Pelagians. His emphasis is on the fundamental depravity of all human beings after the Fall, a depravity that involved the stigmatization of the body and particularly of the sexual organs, since sin is a sexually transmitted disease. The upshot is that much of the human body is only presentable when veiled. In other words, nude art—'pagan art'—is not compatible with the Christian ethos.     

The White–Jung Friendship: The Untold Story

For decades Jung searched in vain for a theologian with whom he could deeply and openly converse about his new vision of Christianity. Only very late in his life did he find and form a deep friendship with Victor White, a Dominican theology professor, whose own psychic life was saved by Jung's teachings. Jung saw White as the first theologian he had met who truly understood his psychology. Jung wanted to use White's expertise in Catholic theology in his pioneering efforts to transform Christianity, through his psychology, into a living, breathing, vital faith in the divine. For his part, White wanted to resuscitate Thomistic theology by infusing its dry, cerebral character with the emotional vitality of the original Thomas Aquinas by using his newly discovered Jungian teachings combined with some of the original teachings of Aquinas. In the process of their work together, Jung and White became close, trusting friends. However, White was pushed beyond the limits of his psychological resources by political events within his order, whose superiors destroyed his career as a theologian and sent him into exile. In his scathing review of Answer to Job, White displaced his anger/rage onto Jung instead of the appropriate objects. This attack wounded their friendship deeply, and it was only toward the end of their lives that a partial reconciliation was possible. And yet, Jung's friendship with White was perhaps the closest and most trusting relationship he had with a man during his lifetime. Finally, I suggest that White's mission in this life was to resuscitate Thomism rather than help Jung achieve his purposes, and that White achieved his mission.     

Are The Statue and The Clay Mutual Parts?

Are a material object, such as a statue, and its constituting matter, the clay, parts of one another? One wouldn't have thought so, and yet a number of philosophers have argued that they are. I review the arguments for this surprising claim showing how they all fail. I then consider two arguments against the view concluding that there are both pre‐theoretical and theoretical considerations for denying that the statue and the clay are mutual parts.     

“The primary process”: The vicissitude of a concept

Abstract

During the first twenty years that Freud spent creating his theory, he assumed that most of the functions responsible for creating mental-thought structures were organized according to two different forms or principles of thought. He called these forms “primary process” and “secondary process”. The “secondary process” is identified with rational thinking and the ego, and it is easy to follow the changes that this concept underwent in the works of Freud that followed. The concept of “primary process”, on the other hand, disappeared from his later works with no explanation. This article traces the changes that the “primary process” underwent in Freud's thinking and examines the connection between his analytical technique and his research method. A close study of the changes that the “primary process” underwent reveals that Freud's developmental thought process included concepts whose directional changes may be termed “regressive”.     

Finding The “Self” in Self-Regulation: The Identity-Value Model

Many psychological theories suggest a link between self-regulation and identity, but, until now, a mechanistic account that suggests ways to improve self-regulation has not been put forth. The identity-value model (IVM) connects the idea from social psychology that aspects of identity such as core values and group affiliations hold positive subjective value to the process-focused account from decision making and behavioral economics that self-regulation is driven by a dynamic value integration across a range of choice attributes. Together, these ideas imply that goal-directed behaviors that are identity relevant are more likely to be enacted because they have greater subjective value than identity-irrelevant behaviors. A central hypothesis, therefore, is that interventions that increase the degree to which a target behavior is perceived as self-relevant will improve self-regulation. In addition, identity-based changes in self-regulation are expected to be mediated by changes in subjective value and its underlying neural systems. In this article we define the key constructs relevant to the IVM, explicate the model and delineate its boundary conditions, and describe how it fits with related theories. We also review disparate results in the research literature that might share identity-related value as a common underlying mechanism of action. We close by discussing questions about the model, the answers to which could advance the study of self-regulation.     

The Family and Political Justice – The Case for Political Liberalisms

This paper examines two central arguments raised byfeminist theorists against the coherence andconsistency of political liberalisms, a recentrecasting of liberal theories of justice. They arguethat due to political liberalisms' uncritical relianceon a political/personal distinction, they permit theinstitution of the family to take sexist and illiberalforms thus undermining its own aims and politicalproject. Political liberalisms' tolerance of a widerange of family forms result in two fatalinconsistences. Firstly, it retards or completelyprevents women from developing the necessary politicalsense of self required for citizenship, and secondly,it prevents children from acquiring the requisitepolitical virtues and sense of justice necessary forthe viability and long-term stability of such asociety. In the paper, I argue that despite theirinitial appeal these feminist criticisms are notcompelling. Firstly, they misunderstand what politicalliberalisms mean by unjust family forms, secondly,they trade on a misunderstanding of thepolitical/personal distinction and, finally, they makequestionable empirical claims about the effects of theilliberal family on a viable political conception ofjustice.     

The Life of Spirit: The Self and Sanctification in Søren Kierkegaard's The Sickness unto Death

Danish theologian and philosopher Søren Kierkegaard is often overlooked as an author in the Christian spiritual tradition. This paper answers Christopher Barnett's call to investigate themes of Christian spirituality in Kierkegaard's writing. In this paper, I argue that we can construct of vision of sanctification from Kierkegaard's The Sickness unto Death. While Kierkegaard does not directly deal with themes of sanctification in The Sickness unto Death, Kierkegaard's pseudonym Anti-Climacus does demonstrate the ‘spiritless’ life of despair. The ‘spiritless’ life, as Anti-Climacus defines it, is a life that is not truly a ‘self’. Anti-Climacus systematically demonstrates four categories of despair, and all people not living in faith, whether they realise it or not, fit into one of these categories of ‘spiritless’ existence. I argue that by constructing the opposites of Kierkegaard's categories of despair I demonstrate that a ‘spirit-filled’ life exemplifies a vibrant Christian life of sanctification.     

The ‘workshy’

Abstract

This article is an attempt to apply the Kleinian ‘positions’ to long-term unemployment and to use them to suggest an alternative to punitive concepts such as ‘workshy’, while discussing the paradox in which a sincere attempt to find work exists alongside behaviour which seems designed to sabotage it. Such sabotaging behaviour not only offers secondary gains but affords channels for projections which mitigate unresolved aggression. While effective in coping with long-term unemployment, these mechanisms inhibit development and ‘benign cycles’ are gridlocked. Change and growth are seen as threats and aggression cannot be worked through and must be projected. Persecutory anxieties and a lack of enrichment by ‘otherness’ results and is reinforced by the reality of chronic unemployment. No opportunity for reparative work exists, so ‘concern’ and a sense of responsibility are inhibited. Narcissistic omnipotence and grandiosity is a feature. Long-term unemployment and homelessness show similar revolving door patterns connected to similar coping mechanisms.