Proof-Theoretic Modal PA-Completeness I: A System-Sequent Metric

This paper is the first of a series of three articles that present the syntactic proof of the PA-completeness of the modal system G, by introducing suitable proof-theoretic objects, which also have an independent interest. We start from the syntactic PA-completeness of modal system GL-LIN, previously obtained in [7], [8], and so we assume to be working on modal sequents S which are GL-LIN-theorems. If S is not a G-theorem we define here a notion of syntactic metric d(S, G): we calculate a canonical characteristic fomula H of S (char(S)) so that _G H (S) and _GL-LIN H, and the complexity of H gives the distance d(S, G) of S from G. Then, in order to produce the whole completeness proof as an induction on this d(S, G), we introduce the tree-interpretation of a modal sequent Q into PA, that sends the letters of Q into PA-formulas describing the properties of a GL-LIN-proof P of Q: It is also a d(*, G)-metric linked interpretation, since it will be applied to a proof-tree T of H with H = char(S) and ( H) = d(S, G).     

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.     

Death and the “life review” in Halakhah

Coping with old age involves resolving the task of integrity versus despair, which demands a nondefensive confrontation with the inevitability of death. Halakhah (Jewish ethics) also considered this task critical in later years of life, spoke of death's inevitability, and attempted to discourage denial of death. The Jewish approach seems compatible with Butler's concept of life review as a reconciliation with death and a reintegration of one's identity that occurs throughout later years. While the Eriksonian goal is confronting old age with a certain capacity for wisdom, the rabbis maintained that such wisdom must culminate in the creative act of repentance.     

On the logic of conscious belief

In this paper we are discussing a version of propositional belief logic, denoted by LB, in which so-called axioms of introspection (B BB and B B B) are added to the usual ones. LB is proved to be sound and complete with respect to Boolean algebras equipped with proper filters (Theorem 5). Interpretations in classical theories (Theorem 4) are also considered. A few modifications of LB are further dealt with, one of which turns out to be S5.     

Variations in use of the term “or”

Two studies showed that adults' responses to questions involving the term or varied markedly depending upon the type of question presented. When presented with various objects (A's and B's) and asked to circle all things which are A or B subjects tended to circle A's as well as B's, whereas when asked to circle all the A's or B's subjects showed a relatively stronger tendency to circle one or the other. Moreover the nature of the sets of objects (As and Bs) influenced behavior as well. There was also evidence that the effects due to question wording or set type transferred.     

The endorsement of irrational beliefs in a general clinical population

Burgess' Attitude and Belief Scale, a measure of Ellis' irrational beliefs, was administered to a large sample of outpatients. All 13 subscales demonstrate very adequate internal consistency. A factor analysis yielded one factor accounting for 83% of the variance, which was labeled irrationality. Clients endorsed focused items more than overgeneralized items, self-referential items more than non-self-referential items, and preferential items more than irrational items. Clients also received higher scores on the irrational process of demandingness than they did on the irrational process of awfulizing, self-worth and low frustration tolerance. The results were consistent with new formulations in Rational-Emotive theory. Suggestions were made for the construction of measures of irrational beliefs.     

The liar: What paradox?

Most philosophers believe that the Liar Paradox is semantical in character, and arises from difficulties in the predicate true. The author argues that the paradox is pragmatic, not semantic, and arises from violations of essential conditions that define statement-making speech acts. The author shows that his solution to the paradox will not only handle the classical Liar sentences that are necessarily or intrinsically paradoxical, but also sets of Kripke-sentences that are contingently paradoxical.     

Making noises in counterpoint or chorus: Putnam''s rejection of relativism

Putnam's internal realism entails the simultaneous rejection of metaphysical realism and (anything goes or total or cultural) relativism. Putnam argues, in some places, that relativism is self-contradictory, and in others, that it is self-refuting. This paper attempts the exegetical task of explicating these challenging arguments, and the critical task of suggesting that a full-blown epistemological relativism may be capable of surviving the Putnam attack.     

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).     

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.     

Modifying Violent Communities by Enhancing Altruism: A Vision of Possibilities

A model for diagnosing and treating violent communities is outlined. The treatment consists of enhancing a form of pragmatic altruism by building relationships and mutual understanding between community leaders who are derived from task groups called community stabilizing systems, defined as groups essential for peaceful, creative stability in a community. Two examples of an intervention derived from this theory are described.     

“Anchor-range” results with “same” and “different” responses and similar and dissimilar stimuli

Summary Blocks of pairs of dissimilar (anchor-like) circles were unexpectedly followed by single pairs of similar circles and vice versa. The dissimilar circles were 3 and 10 mm in diameter, and the similar circles were 3 and 5 mm, 5 and 7 mm, and 7 and 10 mm in diameter. In a second experiment, the dissimilar and similar circles did not overlap in size (e.g., they were 1.5 and 5 mm and 7 and 10 mm, respectively). The same responses to the unexpected same pairs of similar circles were faster than the same responses to the identical pairs in the blocks. In contrast, the different responses to the unexpected different pairs of similar circles were slower than the different responses to the identical pairs in the blocks. Similar stimuli accelerate same responses and slow down different responses. So the time results (and the error results as well) suggest that the context of the block dissimilar circles increased the perceived similarity of the unexpected similar circles. These anchor-range results are not explained by Thurstonian theories, which are based on the absolute properties of stimuli. Instead, they imply that the relation between the similar circles in the context of the relation between the dissimilar circles affected performance.     

Quantum Logic as a Fragment of Independence-Friendly Logic

The working assumption of this paper is that noncommuting variables are irreducibly interdependent. The logic of such dependence relations is the author's independence-friendly (IF) logic, extended by adding to it sentence-initial contradictory negation ¬ over and above the dual (strong) negation . Then in a Hilbert space turns out to express orthocomplementation. This can be extended to any logical space, which makes it possible to define the dimension of a logical space. The received Birkhoff and von Neumann quantum logic can be interpreted by taking their disjunction to be ¬(A & B). Their logic can thus be mapped into a Boolean structure to which an additional operator has been added.     

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.     

Poetry in Existential Psychotherapy with Couples and Families

The use of poetry during the process of existential psychotherapy with couples and families is described and illustrated. In this approach, poems can be utilized to help the couple and/or family notice meaning potentials in the future, actualize and make use of such meaning potentials in the here and now, and re-collect and honor meanings previously actualized and deposited in the past.     

Modal Logics of Succession for 2-Dimensional Integral Spacetime

We consider the problem of axiomatizing various natural successor logics for 2-dimensional integral spacetime. We provide axiomatizations in monomodal and multimodal languages, and prove completeness theorems. We also establish that the irreflexive successor logic in the standard modal language (i.e. the language containing and ) is not finitely axiomatizable.     

Is the holocaust relevant to sociobiology?

Sociobiologists have emphasized that altruism and benevolent behavior are part of the genetic repertoire of most animals and certainly of man. They have constructed a theory of ethics as a biological phenomenon without reference to the concept of evil. It is concluded here however, that holocaust behavior is not equivalent to the natural manifestation of an incompletely tamed animal flashing its teeth. Biologists have been too rigid in trying to equate ethical behavior with social behavior. The added dimension of ethical behavior is a special kind of sensitivity to the needs of others, just as evil is the total lack of it. The evolution of this moral sense may itself have important selective value for the human species, whose survival depends on creating maximal diversity in its gene pool.     

Die Rechtsansichten der Eurasier -- Rechtsordnung oder Wertordnung?

In their juridical doctrines, the members of the Evrazijstvo movement advocated the idea of a Russian special path criticizing at the same time the formalism and coldness of the western conception of law, based principally on Roman law. Their views are characterized by an evident priority accorded to justice over law, to the order of values over legal order.     

On the relation between recent neurobiological data on perception (and action) and the Husserlian theory of constitution

The phenomenological theory of constitution promises a solution for the problem of consciousness insofar as it changes the traditional terms of this problem by systematically correlating subject and object in the unifying context of intentional acts. I argue that embodied constitution must depend upon the role of kinesthesia as a constitutive operator. In pursuing the path of intentionality in its descent from an idealistic level of pure constitution to this fully embodied kinesthetic constitution, we are able to gain access to different ontological regions such as physical thing, owned body and shared world. Neuroscience brings to light the somatological correlates of noemata. Bridging the gap between incarnation and naturalisation represents the best way of realizing the foundational program of transcendental phenomenology.