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.     

In and behind a Lenneberg paradigm

Lenneberg suggested that a chimpanzee's linguistic ability could be tested by presenting sentences containing two prepositional phrases joined by a conjunction. This would involve joining two semantic propositions, and thus represents a more complex test of chimpanzee syntactic competence than previously attempted. Jane, a five year-old language trained chimpanzee, was tested on her ability to both produce and comprehend sentences involving a preposition (in or behind) and a conjunction (and). The results from production and comprehension were substantially the same. Jane showed the ability to appropriately deploy and, behind and in, but displayed very little flexibility in their use. It is suggested that a chimpanzee may be able to learn some rules of syntax but is not able to be creative with that syntax.     

Partially-Ordered (Branching) Generalized Quantifiers: A General Definition

Following Henkins discovery of partially-ordered (branching) quantification (POQ) with standard quantifiers in 1959, philosophers of language have attempted to extend his definition to POQ with generalized quantifiers. In this paper I propose a general definition of POQ with 1-place generalized quantifiers of the simplest kind: namely, predicative, or cardinality quantifiers, e.g., most, few, finitely many, exactly , where is any cardinal, etc. The definition is obtained in a series of generalizations, extending the original, Henkin definition first to a general definition of monotone-increasing (M) POQ and then to a general definition of generalized POQ, regardless of monotonicity. The extension is based on (i) Barwises 1979 analysis of the basic case of M POQ and (ii) my 1990 analysis of the basic case of generalized POQ. POQ is a non-compositional 1st-order structure, hence the problem of extending the definition of the basic case to a general definition is not trivial. The paper concludes with a sample of applications to natural and mathematical languages.     

Computer content analysis of sex differences in the language of children

This study presents empirical procedures for the collection and content analysis of the oral language of kindergarten children. The analysis technique used material and machines available to most researchers. The results of the analysis of language samples of 144 randomly selected children from the entire kindergarten class of the Ithaca, New York, school system showed that boys produced significantly more language than did the girls as well as significantly more references to aggression, self, time, space, quantity, fears, good, act of oral communication, negation, and affirmation, and asked more questions of the examiner than did the girls. The girls made significantly more female references than did the boys. Implications for future research are discussed.     

The elimination of de re formulas

It is shown that de re formulas are eliminable in the modal logic S5 extended with the axiom scheme x x.     

Involuntary retrieval in alphabet-arithmetic tasks: Task-mixing and task-switching costs

This study explores the effects of memory retrieval in task switching. To this end, item-specific stimulus-to-task mappings were manipulated in two alphabet-arithmetic experiments. Letter-stimuli were presented and the responses were verbal letter names. The task was either to name the next letter in the alphabet, (e.g., C D, task plus), or to name the preceding letter (e.g., C B, task minus). The mapping of individual stimuli to the two tasks (and thus to responses) was either consistent (CM) or varied (VM). In Experiment 1, performance was worse for VM items relative to CM items, indicating item-specific task-mapping effects. These task-mapping effects also contributed to mixing costs (i.e., worse performance in mixed-task blocks than in pure-task blocks) but not to switch costs (worse performance in task-switch trials than in repeat trials within mixed blocks). Experiment 2 manipulated pure and mixed tasks between-participants, and the data again showed differential effects of the task-mapping manipulation on mixing costs and switch costs. This suggests that, in these memory-dependent, alphabet-arithmetic tasks, interference due to involuntary task (and/or response) retrieval primarily increases general multi-task effects, such as maintaining activation of the current task.     

“Girl,” “woman,” “guy,” “man”: The effects of sexist labeling

An experiment was conducted to investigate the effects of sexist labeling. Sixty males and 60 females were asked to evaluate an artist and a series of paintings on a variety of cognitive and affective measures. For half the subjects, the artist was identified as a male with either a high status label (man), a low status label (guy), or a neutral label (person); for the other half of the subjects, the artist was identified as a female with either a high status label (woman), a low status label (girl), or a neutral label (person). The findings indicated that for the female artist, the low and high status labels had an equally negative effect on subjects' judgments; for the male artist, the low and high status labels had an equally positive effect on subjects' judgments. There were no significant differences between male and female subjects. The social and psychological implications of the findings are discussed.The present study is based in part on a paper presented at the meetings of the Western Psychological Association held in San Diego, California, April 1979, in collaboration with Ms. Julie Horowitz.     

A Translation of Intuitionistic Predicate Logic into Basic Predicate Logic

Basic Predicate Logic, BQC, is a proper subsystem of Intuitionistic Predicate Logic, IQC. For every formula in the language {, , , , , , }, we associate two sequences of formulas 0,1,... and 0,1,... in the same language. We prove that for every sequent , there are natural numbers m, n, such that IQC , iff BQC n m. Some applications of this translation are mentioned.     

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.     

Treating the “Wise Baby”

In a previous examination of Ferenczis concept of the Wise Baby (1996), I had noted both its applications and its limitations in the analytic treatment of an unusually intelligent adult. Ferenczis concepts of the origin of intellect in trauma and of the wise baby have often left the indistinct impression of being interrelated phenomena. In this paper, I regard as arguable the notion that very high intelligence is pathological when it is precocious. This return visit to the territory of the wise baby extends Ferenczis ideas about the origin and use of the intellect to include a consideration of what may constitute effective treatment for those who suffer from giftedness.Judith E. Vida, M.D. edits On the Arts for this journal. She is a Founding Member and Faculty of the Institute of Contemporary Psychoanalysis in Los Angeles, CA, a member of both American and International Psychoanalytic Associations, and of the Sándor Ferenczi Society of Budapest. Her private practice is in Pasadena, CA.Address correspondence to Judith E. Vida, 301 S. Fair Oaks Ave., Suite 406A, Pasadena, CA 91105, USA; e-mail: jvida@spence.net     

Distribution of the feature [+animate] in the lexicon of the child

Piaget suggests that animistic thinking is a pervasive feature of children's cognition. To test this notion, 4- to 8-year-old children were shown several inanimate objects and asked to pick those which perform activities characteristic of living organisms. These activities were typified by six verbs: eat, sleep, breathe, grow, die,, and be alive. Fifty percent of the younger children responded animistically, by misattributing life processes to inanimate objects, but only 18% of their total responses were animistic. Twenty percent of the older children responded animistically, but only 20% of their responses were animistic. In Experiment II, children were shown drawings singly and asked if the object could perform activities named by one of the six verbs. Results were similar to those of Experiment I but with somewhat less animism. Experiment III required children to spontaneously name things that are alive. There were no animistic responses. It was concluded that animistic thinking is not a genuine phenomenon but linguistic confusion elicited by novel objects and unfamiliar words.This work was supported by NSF Grant GB 23083.A portion of the data of Experiment I constituted a Bachelor Honors Thesis conducted by the first author under the direction of the second and submitted to Florida State University. These data were presented at the meeting of the Southeastern Psychological Association, New Orleans, April 1973.     

On the relation provable equivalence and on partitions in effectively inseparable sets

We generalize a well-knownSmullyan's result, by showing that any two sets of the kindC _a = {x/ xa} andC _b = {x/ xb} are effectively inseparable (if I b). Then we investigate logical and recursive consequences of this fact (see Introduction).     

Richard Zaner’s Phenomenology of the Clinical Encounter

The clinical ethics propounded by Richard Zaner is unique. Partly because of his phenomenological orientation and partly because of his own daily practice as a clinical ethicist in a large university hospital, Zaner focuses on the particular concrete situations in which patients and their families confront illness and injury and struggle toward workable ways for dealing with them. He locates ethical reality in the clinical encounter. This encounter encompasses not only patient and physician but also the patients family and friends and indeed the entire lifeworld in which the patient is still striving to live. In order to illuminate the central moral constituents of such human predicaments, Zaner discusses the often-overlooked features of disruption and crisis, the changed self, the patients dependence and the physicians power, the violation of personal boundaries and their necessary reconfiguring, and the art of listening.     

Critical Psychologies of Religious Matters: A Late Modern Enterprise

Drawing upon illustrations of research in psychology and religion, this essay sketches a historical account of twentieth century scholarship in terms of three phases. In the early modern phase research was problem-centered: scholars customarily drew upon expertise in cognate areas of inquiry in solving a problem. In the modern phase research is specialization-based: scholars develop competence in the perspectives, concepts, and methods peculiar to their subfield. In the late modern phase research is interdisciplinary and multidisciplinary: scholars achieve proficiency in cognate subfields and acquire fluency in coordinating the assumptions, concepts, and methods of those subfields. This historical account provides the context and warrant for formulating an enterprise expressing the spirit of the late modern phase: critical psychologies of religious matters.     

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.     

A note on syntactical and semantical functions

We say that a semantical function is correlated with a syntactical function F iff for any structure A and any sentence we have A F A .It is proved that for a syntactical function F there is a semantical function correlated with F iff F preserves propositional connectives up to logical equivalence. For a semantical function there is a syntactical function F correlated with iff for any finitely axiomatizable class X the class ^–1X is also finitely axiomatizable (i.e. iff is continuous in model class topology).     

Endogenous Ketamine-Like Compounds and the NDE: If So, So What?

This commentary on Karl Jansen's ketamine model for the near-death experience expands upon and raises additional questions about several issues and hypotheses: self-experimentation as a source of data; ketamine's similarities to and differences from classical hallucinogens; the need for quantification of unusual subjective states; clinical research and toxicological implications of this model; drugs as gateways to religious states; and evolutionary versus religious significance of naturally occurring compounds released in the near-death state. I suggest future research that could help explicate several of these areas.Formerly Associate Professor of Psychiatry at the University of New Mexico School of Medicine     

Interpolation and amalgamation properties in varieties of equivalential algebras

Important positive as well as negative results on interpolation property in fragments of the intuitionistic propositional logic (INT) were obtained by J. I. Zucker in [6]. He proved that the interpolation theorem holds in purely implicational fragment of INT. He also gave an example of a fragment of INT for which interpolation fails. This fragment is determined by the constant falsum (), well known connectives: implication () and conjunction (), and by a ternary connective defined as follows: (p, q, r)= ^df (pq)(pr).Extending this result of J. I. Zucker, G. R. Renardel de Lavalette proved in [5] that there are continuously many fragments of INT without the interpolation property.This paper is meant to continue the research mentioned above. To be more precise, its aim is to answer questions concerning interpolation and amalgamation properties in varieties of equivalential algebras, particularly in the variety determined by the purely equivalential fragment of INT.     

Логистическая система, исходными связками которой являются эквивалентность и дизъюнкция

- Allatum est die 5 Martii 1970     

Rational choices in wason's selection task

Sixty-eight subjects were asked to solve a series of six Wason selection problems by physically turning relevant cards over until they could say whether the rule was correct or false. In the first experiment most of the subjects misunderstood the rule they were asked to verify, different subjects misunderstanding in different ways, but commonly reading (a) top/underneath for one side/other side and (b) a dual conditional for if..., then.... However, a majority of subjects thereafter responded in complete logical consistency with the rule as they understood it to be. When the misunderstandings revealed in the first experiment were themselves presented as rules to be verified in a second experiment, performance was much more logical than is usually reported. It is concluded that the illogicality commonly associated with Wason's selection task is only apparent.