On defining necessity in terms of entailment

In their book Entailment, Anderson and Belnap investigate the consequences of defining Lp (it is necessary that p) in system E as (pp)p. Since not all theorems are equivalent in E, this raises the question of whether there are reasonable alternative definitions of necessity in E. In this paper, it is shown that a definition of necessity in E satisfies the conditions { _E Lpp, _EL(pq)(LpLq), _E pLp} if and only if its has the form C ₁.C₂ .... C_np, where each C _iis equivalent in E to either pp or ((pp)p)p.     

Once More into the Breach of Self-Ownership: Reply to Narveson and Brenkert

In reply to Narveson, I distinguish his no-proviso argument from his liberty argument, and I show that both fail. I also argue that interference lacks the strategic status he assigns to it, because it cannot be appropriately distinguished, conceptually and morally, from prevention; that natural resources do enjoy the importance he denies they have; that laissez-faire economies lack the superiority he attributes to them; that ownership can indeed be a reflexive relation; that anti-paternalism does not entail libertarianism; and that he misrepresents the doctrines of a number of philosophers, including John Locke, Ronald Dworkin, and myself. In reply to Brenkert, I show that he seriously misconstrues my view of the nature of freedom, and of its relationship to self-ownership. I then refute his criticisms of my treatment of the contrasts between self-ownership, on the one hand, and autonomy and non-slavery, on the other. I also show that his attempt to exorcize the demon of self-ownership is multiply flawed.     

Modal logic with names

We investigate an enrichment of the propositional modal language with a universal modality having semanticsx iff y(y ), and a countable set of names — a special kind of propositional variables ranging over singleton sets of worlds. The obtained language _c proves to have a great expressive power. It is equivalent with respect to modal definability to another enrichment () of, where is an additional modality with the semanticsx iff y(y x y ). Model-theoretic characterizations of modal definability in these languages are obtained. Further we consider deductive systems in _c. Strong completeness of the normal _c-logics is proved with respect to models in which all worlds are named. Every _c-logic axiomatized by formulae containing only names (but not propositional variables) is proved to be strongly frame-complete. Problems concerning transfer of properties ([in]completeness, filtration, finite model property etc.) from to _c are discussed. Finally, further perspectives for names in multimodal environment are briefly sketched.     

A New Representation Theorem for Contranegative Deontic Logic

The logic of an ought operator O is contranegative with respect to an underlying preference relation if it satisfies the property Op & (¬p)(¬q) Oq. Here the condition that is interpolative ((p (pq) q) (q (pq) p)) is shown to be necessary and sufficient for all -contranegative preference relations to satisfy the plausible deontic postulates agglomeration (Op & OqO(p&q)) and disjunctive division (O(p&q) Op Oq).     

On not knowing what or who one is: Reflections on the intelligibility of dualism

Beginning with Descartes' caution not imprudently to take some other object in place of myself, I consider first the problems of self-identification confronted by variousamnesiacs, both ordinary and Cartesian. Noting thatcogitationes as such do not individuate, I proceed to examine conclusions drawn from certain sorts of body-switching thought experiments. This, in turn, gives rise to a general critique of psychological connectedness or unity of consciousness as a candidate criterion of personal identity. I conclude that our ability to apply any notion of personal identity is parasitic upon the existence of a conceptual apparatus for individuating, identifying, and reidentifying objects. Finally, I argue that, if person is a proper sortal predicate to begin with, Descartes'res cogitans cannot be understood as a species of the (metaphysical) genusres, distinct fromres extensa and only problematically in interaction with it. Cartesian dualism is a multiply untenable doctrine.     

On a certain class ofm-address machines

Conclusion It follows from the proved theorems that ifM =Q, (whereQ={0,q ₁,q ₂,...,q }) is a machine of the classM _F then there exist machinesM _i such thatM _i(1,c)=M (q _i,c) andQ _i={0, 1, 2, ..., +1} (i=1, 2, ..., ).And thus, if the way in which to an initial function of content of memorycC a machine assigns a final onecC is regarded as the only essential property of the machine then we can deal with the machines of the formM ={0, 1, 2, ..., }, and processes (t) (wheret=1,c,cC) only.Such approach can simplify the problem of defining particular machines of the classM _F , composing and simplifying them.Allatum est die 19 Januarii 1970     

Depression and Anxiety in Persons with Parkinson's Disease With and Without “On–Off” Phenomena

On–off phenomena in Parkinson's disease (PD) are unpredictable motor fluctuations associated with long-term levodopa use. Mood fluctuations have been found to coincide with the motor fluctuations in that depression and anxiety increase while the person with PD is in the off state. What has been relatively unexplored is whether those persons with PD who have on–off phenomena differ psychologically in fundamental ways from those who do not have on–off phenomena. In the present study, depression and anxiety symptoms were assessed in 36 persons with PD (n = 14 with on–off phenomena, n = 22 without on–off phenomena). All those with on–off phenomena were assessed in their on state. Those persons with PD with on–off phenomena had significantly higher levels of anxiety than those without on–off phenomena. However, both groups, regardless of on–off status, were mildly depressed. Neurobiological interpretations of the results implicate the locus coeruleus in the pathogenesis of both on–off phenomena and anxiety, whereas psychological interpretations of the results involve the issues of learned helplessness and control over health symptoms in PD.     

Cut-free tableau calculi for some propositional normal modal logics

We give sound and complete tableau and sequent calculi for the prepositional normal modal logics S4.04, K4B and G ⁰(these logics are the smallest normal modal logics containing K and the schemata A A, A A and A ( A); A A and AA; A A and ((A A) A) A resp.) with the following properties: the calculi for S4.04 and G ⁰are cut-free and have the interpolation property, the calculus for K4B contains a restricted version of the cut-rule, the so-called analytical cut-rule.In addition we show that G ⁰is not compact (and therefore not canonical), and we proof with the tableau-method that G ⁰is characterised by the class of all finite, (transitive) trees of degenerate or simple clusters of worlds; therefore G ⁰is decidable and also characterised by the class of all frames for G ⁰.Research supported by Fonds zur Förderung der wissenschaftlichen Forschung, project number P8495-PHY.Presented by W. Rautenberg     

The group member's view of inner and outer reality: The Janus phenomenon applied to the group

This paper surveys some theoretical aspects of psychodynamic group treatment from the vantage point of the Janus phenomenon. This focus may provide some clarification in understanding how group therapy facilitates growth, especially in the relationships between inner realities and the realities of the external world. The paper explores and seeks bridges and connections between the dynamics of the group and intrapsychic dynamics. The inner view may be understood as intimately connected with intrapsychic concerns, whereas the issues for patients in groups do, to a degree, concern interpersonal processes in and projections onto the external world. The paper concludes that, thus far, we must accept less than perfect integration of theory and settle for limited domain reasoning (Scheidlinger, 1982). Erlebnis is the term coined by Paul Federn (1952) to refer to subjective experience of the self.     

Is “some-other-time” sometimes better than “sometime” for proving partial correctness of programs?

The main result of this paper belongs to the field of the comparative study of program verification methods as well as to the field called nonstandard logics of programs. We compare the program verifying powers of various well-known temporal logics of programs, one of which is the Intermittent Assertions Method, denoted as Bur. Bur is based on one of the simplest modal logics called S5 or sometime-logic. We will see that the minor change in this background modal logic increases the program verifying power of Bur. The change can be described either technically as replacing the reflexive version of S5 with an irreflexive version, or intuitively as using the modality some-other-time instead of sometime. Some insights into the nature of computational induction and its variants are also obtained.This project was supported by the Hungarian National Foundation for Scientific Research, Grant No. 1810.     

The Self Psychology of Heinz Kohut: What's It All About Theologically?

As a psychoanalytic thinker who offered by means of his self psychology a new paradigm of psychological development and functioning, Heinz Kohut was also a theologian manqué. With the help of the method of interpretation devised by Paul Tillich and David Tracy, Kohut's limit-concepts of tragic man, the self-object, and empathy, all set within his theory of narcissism, are elucidated as theological constructs. These are critiqued for adequacy from a Christian perspective. The conclusion is that Kohut's understanding of the human dilemma and of the way of salvation correlates well with Christianity, while his view of empathy as the means of salvation has created some confusion. Kohut has thus left an unfinished, profoundly important, agenda for theologians and clinicians.     

On superintuitionistic logics as fragments of proof logic extensions

Coming fromI andCl, i.e. from intuitionistic and classical propositional calculi with the substitution rule postulated, and using the sign to add a new connective there have been considered here: Grzegorozyk's logicGrz, the proof logicG and the proof-intuitionistic logicI set up correspondingly by the calculiFor any calculus we denote by the set of all formulae of the calculus and by the lattice of all logics that are the extensions of the logic of the calculus, i.e. sets of formulae containing the axioms of and closed with respect to its rules of inference. In the logiclG the sign is decoded as follows: A = (A & A). The result of placing in the formulaA before each of its subformula is denoted byTrA. The maps are defined (in the definitions of x and the decoding of is meant), by virtue of which the diagram is constructedIn this diagram the maps, x and are isomorphisms, thereforex ^–1 = ; and the maps and are the semilattice epimorphisms that are not commutative with lattice operation +. Besides, the given diagram is commutative, and the next equalities take place: ^–1 = ^–1 and = ^–1 x. The latter implies in particular that any superintuitionistic logic is a superintuitionistic fragment of some proof logic extension.     

Some modifications of Scott's theorem on injective spaces

D. Scott in his paper [5] on the mathematical models for the Church-Curry -calculus proved the following theorem.A topological space X. is an absolute extensor for the category of all topological spaces iff a contraction of X. is a topological space of Scott's open sets in a continuous lattice.In this paper we prove a generalization of this theorem for the category of , -closure spaces. The main theorem says that, for some cardinal numbers , , absolute extensors for the category of , -closure spaces are exactly , -closure spaces of , -filters in , >-semidistributive lattices (Theorem 3.5).If = and = we obtain Scott's Theorem (Corollary 2.1). If = 0 and = we obtain a characterization of closure spaces of filters in a complete Heyting lattice (Corollary 3.4). If = 0 and = we obtain a characterization of closure space of all principial filters in a completely distributive complete lattice (Corollary 3.3).     

Interpretations of the first-order theory of diagonalizable algebras in peano arithmetic

For every sequence |p _n } _n of formulas of Peano ArithmeticPA with, every formulaA of the first-order theory diagonalizable algebras, we associate a formula ⁰ A, called the value ofA inPA with respect to the interpretation. We show that, ifA is true in every diagonalizable algebra, then, for every, ⁰ A is a theorem ofPA.     

Six-year-old children's understanding of sentences adjoined with time adverbs

The adjoining of clauses with temporal links is the basis for many sentences that convey sequence of events. The present study attempts to delineate 6-year-old children's (N=30) understanding of the meaning sequences imparted by sentences adjoined with after, before, and until. Their performance of the meaning sequence for each of 24 carefully constructed sentences is compared to an adult model. Analysis of the results (using a Wilcoxon Matched Pairs Signed Rank Test) indicated that: (1)Ss understood sentences adjoined with after according to an adult model more frequently than before adjoined sentences (P<0.01); (b) Until adjoined sentences with a negative marker in the main clause were understood according to an adult model more often than until adjoined sentences with no such negative element, but the difference was not significant at a=0.01; (3)Ss understood before adjoined sentences according to an adult model more often than until adjoined sentences, but the difference was not significant at a=0.01. In general, the results indicated that 6-year-olds have not yet completed development of an adult grammar with respect to adjoining clauses with temporal links, after, before, and until.     

The drive for meaning in William James' analysis of religious experience

Summary Now that we have looked at the characteristics of mystical experience, we are ready to discuss the assumption made in this paper that mystical experience can be translated into an understanding of integration or the drive for meaning which Fingarette pursues in a much more analytic fashion. Reviewing the conversion process as an integration process we have seen that for the sick-souled, beset with the meaninglessness or melancholy which paralyzes his will, his own awareness of wrong in his situation prevents him from opening up to larger views of reality. But, as James has described, at the same time as the subject is attending so strongly to his own sense of worthlessness, all the while the forces of mere organic ripening within him are going on towards their own prefigured result, and his conscious strainings are letting loose subconscious allies behind the scenes, which in their way work toward rearrangements. Yet the rearrangements can only come about by obeying the command of Chaung-Tse: Cease striving. The result is self-transformation in reconciling, unifying states. There is achieved a supersensuous meaning to the ordinary outward data of consciousness; facts already objectively before us fall into a new expressiveness and make a new connection with our active life.However, James cautions us to realize that the same incursions of the subconscious which produce such reconciling, unifying states can also produce pathological states, a diabolical mysticism, a sort of religious mysticism turned upside down. In such a state the meanings of events become dreadful and the ruling emotion is pessimism. To this possibility James applied the pragmatic test, By their fruits..., and concluded that the mystical experience which brings optimism to the individual is a genuine experience and one which brings truth. In our context then, we would say that real integration brings the subject away from the melancholy and meaninglessness he felt into the genuinely insightful resolution of which Fingarette speaks.Conversion, then, is a process in James's analysis of religious experience analogous to the process of integration and meaning-discovery while mysticism is analogous to the state in which integration or meaning-discovery is achieved. Conversion is climaxed by self-surrender; mysticism is characterized by new determination, self-transformation: two ways of describing an indivisible event. Furthermore, the four characteristics James applies to mysticism are indeed characteristic of the experience of integration.Two other points should be added here which are much in line with James's treatment of experience. In the first place, one of the basic principles of radical empiricism is that not only objects but relations between objects are the subject of experience. Such an experience of relationships, of wholeness, is exactly what characterizes integration. At the same time, the five senses are suspended, and the insight is experienced with such a strong immediacy that it is almost sensed. James refers to this quality of mystical states: The records show that even though the five senses be in abeyance in them, they are absolutely sensational in their epistemological quality, if I may be pardoned the barbarous expression, - that is, they are face to face presentations of what seems immediately to exist.I am not saying that every integration is a mystical experience. Rather I have been saying that James's discussion of religious experiences such as healthy-minded, sick-souled, melancholy, conversion, and mysticism provide analogues for better understanding the phenomenological processes and characteristics of the drive for meaning and integration which Fingarette analyzes. In fact, the very notion of religion itself for James bears not just an analogous resemblance but perhaps an identification with integration. For in his personal letters James had defined religious experience as Any moment of life that brings the reality of spiritual things more home to one. And in Varieties James defines religion as a man's total reaction upon life....; his attitude towards what he felt to be the primal truth.If we look upon this outlook of James toward religion as an exaggeration of the reality of integration, we can follow James to what he perceives as the importance of religion upon an individual's life. The man of religious feeling possesses the excitement of a higher kind of emotion, an enthusiastic temper of espousal in regions where morality strictly so called can at best but bow its head and acquiesce. So we are brought again to the area of creativity in which an individual has experienced the widening of the area of his immediate experience and is re-born in the karmic pattern, a valid pattern for both James and Fingarette. As Fingarette describes it, the converted individual creates values which the dead reality he had previously faced did not possess. The result of the achieved integration is explained by James when referring to religious experience as an excitement of the cheerful, expansive, dynamogenic order which, like any tonic, freshens our vital powers. This emotion overcomes temperamental melancholy [meaninglessness] and imparts endurances to the subject, or a zest, or a meaning, or an enchantment and glory to the common objects of life.We might sum up this discussion not by a criticism of the shortcomings of James's treatment of the religious life, such as his apparent insensitivity to the part played by institutions in the religious experience itself, but rather by underscoring the richness of the phenomenological analysis James has undertaken. James Edie acknowledges that James's studies of religious experience itself rather than of religion. ... are not only more sound phenomenologically than some of the studies which have, under the influence of Husserl, up to now explicitly invoked the phenomenological method, but they are also the first to establish any solid basis for a true phenomenology of religious experience.And John Wild has pointed out the parallel between James's concept of melancholy and Heidegger's concept of anxiety as the genesis of the process of becoming: beginning with the prospect of death and nothingness, the individual gropes toward new birth.As we have seen, then, James's analysis of the varieties of religious experience leads to a fruitful discussion of the psychological processes involved in melancholy and meaninglessness, rearrangement and integration. In all such experiences, a sense of inner unity is reached to which the following words of Fingarette would apply by analogy: The soul-racking death which leads to blissful rebirth is the death of the subjectively experienced, anxiety-generated self perception; it is the emergence into the freedom of introspective self-forgetfulness of the psychically unified self.     

The Deep Structure of Group Life: Unconscious Dimensions

There is a reconsideration and renaissance of interest in expanded conceptions of unconscious processes as they affect individuals and groups (Grotstein, 1999). Recent focus on social unconscious (Hopper, 1996) and cultural unconscious processes (Henderson, 1988) and the nature of intersubjectivity (Harwood and Pines, 1998) raise questions about the location of group analysis. This paper considers the deep structure of group life by examining four functions of the unconscious: repressive, conservative, creative, and mythopoetic (Ellenberger, 1970). On an individual level of analysis, these functions are equated respectively with formative ideas about the: personal–subjective, social–political, intersubjective–cultural and collective–objective unconscious. Group level analogs, as they develop and affect groups and their members, are explored as synthetic, shared, symbolicy and synchronous unconscious processes.     

Intuitionistic uniformity principles for propositions and some applications

This note deals with the prepositional uniformity principlep-UP: p x N A (p, x) x N p A (p, x) ( species of all propositions) in intuitionistic mathematics.p-UP is implied by WC and KS. But there are interestingp-UP-cases which require weak KS resp. WC only. UP for number species follows fromp-UP by extended bar-induction (ranging over propositions) and suitable weak continuity. As corollaries we have the disjunction property and the existential definability w.r.t. concrete objects. Other consequences are: there is no non-trivial countable partition of;id is the only injective function from to; there are no many-place injective prepositional functions; card () is incomparable with the cardinality of all metric spaces containing at least three elements.     

Hemingway's Aging Heroes and the Concept of Phronesis

This article explores the concept of phronesis (practical wisdom) in four aging protagonists in Ernest Hemingway's works ranging from the short story A Clean Well-Lighted Place to the novella The Old Man and the Sea. Phronesis represents an understanding of the ways of the world, an acute sensitivity to a critical logic of human existence that can be attained only through extensive experience and suffering. The four aging protagonists are examples of Hemingway's definition of aging productively and profitably by purchasing an inner peace that consists of an intuitive system of continuous adjustment to the exigencies of daily living.