We improve results of Marczewski, Frankiewicz, Brown, and others comparing the $\sigma$-ideals of measure zero, meager, Marczewski measure zero, and completely Ramsey null sets; in particular, we remove CH from the hypothesis of many of Brown's constructions of sets lying in some of these ideals but not in others. We improve upon work of Marczewski by constructing, without CH, a nonmeasurable Marczewski measure zero set lacking the property of Baire. We extend our analysis of $\sigma$-ideals to include the completely Ramsey (...) null sets relative to a Ramsey ultrafilter and obtain all 32 possible examples of sets in some ideals and not others, some under the assumption of MA, but most in ZFC alone. We also improve upon the known constructions of a Marczewski measure zero set which is not Ramsey by using a set theoretic hypothesis which is weaker than those used by other authors. We give several consistency proofs: one concerning the relative sizes of the covering numbers for the meager sets and the completely Ramsey null sets; another concerning the size of non; and a third concerning the size of add$. We also study those classes of perfect sets which are bases for the class of always first category sets. (shrink)

In this paper we introduce the Wholeness Axiom , which asserts that there is a nontrivial elementary embedding from V to itself. We formalize the axiom in the language {∈, j } , adding to the usual axioms of ZFC all instances of Separation, but no instance of Replacement, for j -formulas, as well as axioms that ensure that j is a nontrivial elementary embedding from the universe to itself. We show that WA has consistency strength strictly between I 3 (...) and the existence of a cardinal that is super- n -huge for every n . ZFC + WA is used as a background theory for studying generalizations of Laver sequences. We define the notion of Laver sequence for general classes E consisting of elementary embeddings of the form i :V β → M , where M is transitive, and use five globally defined large cardinal notions – strong, supercompact, extendible, super-almost-huge, superhuge – for examples and special cases of the main results. Assuming WA at the beginning, and eventually refining the hypothesis as far as possible, we prove the existence of a strong form of Laver sequence for a broad range of classes E that include the five large cardinal types mentioned. We show that if κ is globally superstrong, if E is Laver-closed at beth fixed points, and if there are superstrong embeddings i with critical point κ and arbitrarily large targets such that E is weakly compatible with i , then our standard constructions are E -Laver at κ . , there is an extendible Laver sequence at κ .) In addition, in most cases our Laver sequences can be made special if E is upward λ -closed for sufficiently many λ. (shrink)

Versions of Laver sequences are known to exist for supercompact and strong cardinals. Assuming very strong axioms of infinity, Laver sequences can be constructed for virtually any globally defined large cardinal not weaker than a strong cardinal; indeed, under strong hypotheses, Laver sequences can be constructed for virtually any regular class of embeddings. We show here that if there is a regular class of embeddings with critical point κ, and there is an inaccessible above κ, then it is consistent for (...) there to be a regular class that admits no Laver sequence. We also show that extendible cardinals are Laver-generating, i.e., that assuming only that κ is extendible, there is an extendible Laver sequence at κ. We use the method of proof to answer a question about Laver-closure of extendible cardinals at inaccessibles. Finally, we consider Laver sequences for super-almost-huge cardinals. Assuming slightly more than super-almost-hugeness, we show that there are super-almost-huge Laver sequences, improving the previously known upper bound for such Laver sequences. We also describe conditions under which the canonical construction of a Laver sequence fails for super-almost-huge cardinals. (shrink)

In 1970, K. Kunen, working in the context of Kelley–Morse set theory, showed that the existence of a nontrivial elementary embedding j:V→V is inconsistent. In this paper, we give a finer analysis of the implications of his result for embeddings V→V relative to models of ZFC. We do this by working in the extended language , using as axioms all the usual axioms of ZFC , along with an axiom schema that asserts that j is a nontrivial elementary embedding. Without (...) additional axiomatic assumptions on j, we show that that the resulting theory is weaker than an ω-Erdös cardinal, but stronger than n-ineffables. We show that natural models of ZFC+BTEE give rise to Schindler’s remarkable cardinals. The approach to inconsistency from ZFC+BTEE forks into two paths: extensions of ZFC+BTEE+Cofinal Axiom and ZFC+BTEE+¬Cofinal Axiom, where Cofinal Axiom asserts that the critical sequence is cofinal in the ordinals. We describe near-minimal inconsistent extensions of each of these theories. The path toward inconsistency from ZFC+BTEE+¬Cofinal Axiom is paved with a sequence of theories of increasing large cardinal strength. Indeed, the extensions of the theory ZFC +“j is a nontrivial elementary embedding” form a hierarchy of axioms, ranging in strength from Con to the existence of a cardinal that is super-n-huge for every n, to inconsistency. This hierarchy is parallel to the usual hierarchy of large cardinal axioms, and can be used in the same way. We also isolate several intermediate-strength axioms which, when added to ZFC+BTEE, produce theories having strengths in the vicinity of a measurable cardinal of high Mitchell order, a strong cardinal, ω Woodin cardinals, and n-huge cardinals. We also determine precisely which combinations of axioms, of the form result in inconsistency. (shrink)

The Wholeness Axiom (WA) is an axiom schema that can be added to the axioms of ZFC in an extended language $\{\in,j\}$ , and that asserts the existence of a nontrivial elementary embedding $j:V\to V$ . The well-known inconsistency proofs are avoided by omitting from the schema all instances of Replacement for j-formulas. We show that the theory ZFC + V = HOD + WA is consistent relative to the existence of an $I_1$ embedding. This answers a question about the (...) existence of Laver sequences for regular classes of set embeddings: Assuming there is an $I_1$ -embedding, there is a transitive model of ZFC +WA + “there is a regular class of embeddings that admits no Laver sequence.”. (shrink)

We suggest a new approach for addressing the problem of establishing an axiomatic foundation for large cardinals. An axiom asserting the existence of a large cardinal can naturally be viewed as a strong Axiom of Infinity. However, it has not been clear on the basis of our knowledge of ω itself, or of generally agreed upon intuitions about the true nature of the mathematical universe, what the right strengthening of the Axiom of Infinity is—which large cardinals ought to be derivable? (...) It was shown in the 1960s by Lawvere that the existence of an infinite set is equivalent to the existence of a certain kind of structure-preserving transformation from V to itself, not isomorphic to the identity. We use Lawvere's transformation, rather than ω, as a starting point for a reasonably natural sequence of strengthenings and refinements, leading to a proposed strong Axiom of Infinity. A first refinement was discussed in later work by Trnková—Blass, showing that if the preservation properties of Lawvere's tranformation are strengthened to the point of requiring it to be an exact functor , such a transformation is provably equivalent to the existence of a measurable cardinal. We propose to push the preservation properties as far as possible, short of inconsistency. The resulting transformation V→V is strong enough to account for virtually all large cardinals, but is at the same time a natural generalization of an assertion about transformations V→V known to be equivalent to the Axiom of Infinity. (shrink)

We describe a fairly general procedure for preserving I3 embeddings j: Vλ → Vλ via λ-stage reverse Easton iterated forcings. We use this method to prove that, assuming the consistency of an I3 embedding, V = HOD is consistent with the theory ZFC + WA where WA is an axiom schema in the language {∈, j} asserting a strong but not inconsistent form of “there is an elementary embedding V → V”. This improves upon an earlier result in which consistency (...) was established assuming an I1 embedding. (shrink)

We improve results of Marczewski, Frankiewicz, Brown, and others comparing the σ-ideals of measure zero, meager, Marczewski measure zero, and completely Ramsey null sets; in particular, we remove CH from the hypothesis of many of Brown's constructions of sets lying in some of these ideals but not in others. We improve upon work of Marczewski by constructing, without CH, a nonmeasurable Marczewski measure zero set lacking the property of Baire. We extend our analysis of σ-ideals to include the completely Ramsey (...) null sets relative to a Ramsey ultrafilter and obtain all 32 possible examples of sets in some ideals and not others, some under the assumption of MA, but most in ZFC alone. We also improve upon the known constructions of a Marczewski measure zero set which is not Ramsey by using a set theoretic hypothesis which is weaker than those used by other authors. We give several consistency proofs: one concerning the relative sizes of the covering numbers for the meager sets and the completely Ramsey null sets; another concerning the size of non(CRU 0); and a third concerning the size of add(CRU 0). We also study those classes of perfect sets which are bases for the class of always first category sets. (shrink)

We describe a fairly general procedure for preserving I3 embeddings j: V λ → V λ via λ-stage reverse Easton iterated forcings. We use this method to prove that, assuming the consistency of an I3 embedding, V = HOD is consistent with the theory ZFC + WA where WA is an axiom schema in the language {∈, j} asserting a strong but not inconsistent form of “there is an elementary embedding V → V”. This improves upon an earlier result in (...) which consistency was established assuming an I1 embedding. (shrink)

This self-contained treatise, originally published in 1947 by Holt, Rinehart and Winston, examines fundamental features of nature in order to lay the groundwork for providing a solution to the major problems of ethics.

In this paper I shall focus on Castaneda's notion of quasi-indicators and I shall defend the following theses: (i) Essential indexicals (‘I’, ‘here’ and ‘now’) are intrinsically perspectival mechanisms of reference and, as such, they are not reducible to any other mechanism reference...

v. 1. 1955-1960.--v. 2. 1960-1964.--v. 3. March-November 1964.--v. 4. November 26, 1964-September 2, 1965.--v. 5. September 3, 1965-August 27, 1968.--v. 6. August 28, 1968-May 22, 1971.--v. 7. April 13, 1975-June 21, 1976.--v. 7, pt. 2. September 17, 1977-February 26, 1978.--v. 8. April 28, 1978-July 28, 1980 -- v. 9. August 16, 1980-March 15, 1984 -- v. 11. January 19, 1986-May 27, 1987.

The options in a decision problem generally have outcomes with common features. Putting aside the common features simplifies deliberations, but the simplification requires a philosophical justification that this book provides.

We defend the view that an indexical uttered by an actor works on the model of deferred reference. If it defers to a character which does not exist, it is an empty term, just as‘Hamlet’and‘Ophelia’are. The utterance in which it appears does not express a proposition and thus lacks a truth value. We advocate an ontologically parsimonious, anti‐realist, position. We show how the notion of truth in our use and understanding of indexicals as they appear within a fiction is not (...) a central issue. We claim that our use and understanding of indexicals rests on the fact that their cognitive contribution is not exhausted by their semantic contribution. (shrink)

According to proponents of the continuity hypothesis, metaphors represent one end of a spectrum of linguistic phenomena, which includes various forms of loosening/broadening, such as category extensions and approximations, as well as hyperbolic interpretations. The continuity hypothesis is used to establish that the inferences derived from the set of linguistic expressions mentioned above result from the same or nearly similar pragmatic processes. In this paper, we want to challenge that particular aspect of the continuity hypothesis. We do so based on (...) considerations and analysis of an understudied linguistic phenomenon that we call the metaphorical uses of proper names (MPNs). We first explain how MPNs represent a unique linguistic class distinguishable from, for example, nicknames. In addition, we offer some remarks on how MPNs can be understood against the background of current debates between referentialists and predicativists about names. Our discussion leads us to conclude that MPNs are categorically different from literal interpretations of proper names. We spell out the consequences that the results of our analysis have for the continuity hypothesis. (shrink)

Feyerabrend argues that intellectual progress relies on the creativity of the scientist, against the authority of science.

Zusammenfassungen der Referate in französischer Sprache.

In the first part of this paper some general theses concerning the difference between logic and mathematics are defended. In the second part four different views for a possible demarcation between logic and mathematics are stated.

An agent often does not have precise probabilities or utilities to guide resolution of a decision problem. I advance a principle of rationality for making decisions in such cases. To begin, I represent the doxastic and conative state of an agent with a set of pairs of a probability assignment and a utility assignment. Then I support a decision principle that allows any act that maximizes expected utility according to some pair of assignments in the set. Assuming that computation of (...) an option's expected utility uses comprehensive possible outcomes that include the option's risk, no consideration supports a stricter requirement. (shrink)

Schelling und Hegel benutzen in ihren philosophischen Texten mathematische und naturwissenschaftliche Modelle wie Unendlichkeit oder Gleichgewicht. Die Strukturen dieser Begriffe liefern einen Massstab fur den Vergleich der Positionen Schellings und Hegels, der fur Schellings Identitatsphilosophie und Hegels erste Jenaer Schriften durchgefuhrt wird. Als wichtigstes Resultat kann eine grundlegende Differenz zwischen beiden Positionen bereits um 1801 nachgewiesen und gezeigt werden, dass diese auf einer unterschiedlichen Auffassung der Rolle des Absoluten beruht.

Die MISCELLANEA MEDIAEVALIA präsentieren seit ihrer Gründung durch Paul Wilpert im Jahre 1962 Arbeiten des Thomas-Instituts der Universität zu Köln. Das Kernstück der Publikationsreihe bilden die Akten der im zweijährigen Rhythmus stattfindenden Kölner Mediaevistentagungen, die vor über 50 Jahren von Josef Koch, dem Gründungsdirektor des Instituts, ins Leben gerufen wurden. Der interdisziplinäre Charakter dieser Kongresse prägt auch die Tagungsakten: Die MISCELLANEA MEDIAEVALIA versammeln Beiträge aus allen mediävistischen Disziplinen - die mittelalterliche Geschichte, die Philosophie, die Theologie sowie die Kunst- und (...) Literaturwissenschaften sind Teile einer Gesamtbetrachtung des Mittelalters. (shrink)

Summary The present work focuses on the transformations of the psychotherapeutic field through the relationship dynamics which occur within it. The first part of this article starts with a brief outline of the Gestalt psychological understanding of the field concept, also in its application to the psychotherapeutic situation, followed by a brief review of the introduction of the field concept into the psychoanalytic theory formation. After this, the first author first presents the theoretical concept underlying a new approach he has (...) developed for observing the relationship dynamics in psychotherapy. Mirroring a formation of both psychoanalytic and Gestalt theory of the main author, this new approach is based on the combination of psychoanalytic and Gestalt psychological concepts. According to the clinical experience and insights of the author, the phenomenological and relational approach of Gestalt theory fits well with the psychoanalytic approach; on this basis, a criterion for recording the progress of therapy can be developed. This criterion is the phenomenology of the development of the qualities of the relationships of the client, as they become visible in his dream narrations and the subsequent associations in the analysis room and continue to develop during the session and the further course of therapy. The relationship dynamics in the dream narration is thus compared with those which develop in the course of the subsequent associations. This is demonstrated and further elaborated in the second part of this article on the basis of a clinical case. The clinical example shows how the relationship dynamics develop in this sense in the individual therapy sessions and over a longer course of therapy. The associated transformations of the therapeutic field give a good indication of the progress of therapy. The main author gained such insights into the transformations of the therapeutic field and the progression of therapy, which are visible in the course of therapy, from the careful application of the criterion “MDAC of relational dynamics”. In the specific case, there was also a high degree of correspondence between the results of the application of this phenomenological criterion and the empirical evidence of the symptom questionnaire, a self-report measure requested by the patient himself during the course of the therapy. (shrink)

The first book-length study of a leading tenth-century Ismaili theoretician Abu Ya'qub al-Sijistani.

Summary The present work focuses on the transformations of the psychotherapeutic field through the relationship dynamics that occur within it. The first part of this article starts with a brief outline of the Gestalt psychological understanding of the field concept, also in its application to the psychotherapeutic situation, followed by a brief review of the introduction of the field concept into the psychoanalytic theory formation. After this, the first author first presents the theoretical concept underlying a new approach he has (...) developed for observing the relationship dynamics in psychotherapy. Mirroring a formation both psychoanalytic and gestaltic of the main author, this new approach is based on the combination of psychoanalytic and Gestalt psychological concepts. According to the clinical experience and insights of the author, the phenomenological and relational approach of Gestalt theory fits well with the psychoanalytic approach; on this basis, a criterion for recording the progress of therapy can be developed. This criterion is the phenomenology of the development of the qualities of the relationships of the client, as they become visible in his dream narrations and the subsequent associations in the analysis room, and continue to develop during the session and the further course of therapy. The relationship dynamics in the dream narration is thus compared with those that develop in the course of the subsequent associations. This is demonstrated and further elaborated in the second part of this paper on the basis of a clinical case. The clinical example shows how the relationship dynamics develop in this sense in the individual therapy sessions and over a longer course of therapy. The associated transformations of the therapeutic field give a good indication of the progress of therapy. The main author gained such insights into the transformations of the therapeutic field and the progression of therapy, which are visible in the course of therapy, from the careful application of the criterion “manifest dream/associations comparison of relational dynamics”. In the specific case, there was also a high degree of correspondence between the results of the application of this phenomenological criterion and the empirical evidence of the symptom questionnaire, a self-report measure requested by the patient himself during the course of the therapy. (shrink)

The present article shows that there are consistent and decidable manyvalued systems of propositional logic which satisfy two or all the three criteria for non-trivial inconsistent theories by da Costa . The weaker one of these paraconsistent system is also able to avoid a series of paradoxes which come up when classical logic is applied to empirical sciences. These paraconsistent systems are based on a 6-valued system of propositional logic for avoiding difficulties in several domains of empirical science ).

The centrality of death rituals has in anthropologically informed studies of Buddhism been little documented. The current volume brings together a range of perspectives on Buddhist death rituals including ethnographic, textual, historical and theoretically informed accounts, and presents the diversity of the Buddhist funeral cultures of mainland Southeast Asia and China. It arises out of the University of Bristol's Centre for Buddhist Studies research project Buddhist Death Rituals in Southeast Asia and China, funded by the United Kingdom's Arts and Humanities (...) Research Council. This project involved extensive new research in Thailand, Laos and China. Other items from that project included several public exhibitions, extensive stills photographs, and several video films. The project-team produced two 30 minutes films on the ghost festival in Laos and China, one on urban funerals in Chiang Mai (Thailand) and several shorter clips dealing with funeral cultures in Laos, Thailand and China. Most of this material (and an extensive bibliography on the topic) is available free of charge from the project website located at the webpage of the Department of Theology and Religious Studies (Centre for Buddhist Studies) at the University of Bristol. (shrink)

This article contends that the evolution toward interdisciplinary collaboration that we are witnessing in the sciences must also occur in the humanities to ensure their very survival. That is, humanists must be open to working with scientists and social scientists interested in similar research questions and vice versa. Digital humanities is a positive first step. Complexity science should be the next step. Even though much of the ground-breaking work in complexity science has been done in the natural sciences and mathematics, (...) it can, if critically adapted, provide the needed metaphor for a broad integration of disciplines, humanistic and otherwise. Given its almost a-disciplinary nature, a complexity approach to the research problems in the humanities necessarily breaks down silos. Moreover, it can restore and reframe the seamless intellectual fabric sought by researchers before the atomization of the various disciplines in the nineteenthcentury academy. (shrink)

Whilst it may seem strange to ask to whom “I” refers, we show that there are occasionswhen it is not always obvious. In demonstratingthis we challenge Kaplan's assumptionthat the utterer, agent and referent of “I” arealways the same person.We begin by presenting what weregard to be the received view about indexicalreference popularized by David Kaplan in hisinfluential 1972 “Demonstratives” before goingon, in section 2, to discuss Sidelle'sanswering machine paradox which may be thoughtto threaten this view, and his deferredutterance method of (...) resolving this puzzle. Insection 3 we introduce a novel version of theanswering machine paradox which suggests that,in certain cases, Kaplan's identification ofutterer, agent and referent of “I” breaks down.In the fourth section we go on to consider arecent revision of Kaplan's picture by Predelliwhich appeals to the intentions of the utterer,before arguing that this picture is committedto unacceptable consequences and, therefore,should be avoided if possible. Finally, insection 5, we present a new revision ofKaplan's account which retains much of thespirit of his original proposal whilst offeringa intuitively acceptable way to explain all ofthe apparently problematic data. In doing so,we also show how this picture is able toexplain the scenario which motivated Predelli'saccount without appealing to speakerintentions. (shrink)

Este ensaio tem como objetivo afirmar a leitura e a escrita enquanto processo ativo tradutório, por meio da reimaginação do Texto de Partida As cidades invisíveis, redigido em 1972 pelo autor italiano Ítalo Calvino. O ensaio é tecido mediante a noção de fragmentos, tal como entendido por Tavares, em que a escrita se constitui como uma experimentação do pensamento. Toma como ponto de partida as pistas deixadas pelo viajante Marco Polo, na obra de Calvino, a qual foi lida e reinventada (...) pelos acadêmicos do Curso de Pedagogia de uma Instituição de Ensino Superior localizada no interior do Rio Grande do Sul. Um Roteiro de Procedimentos Escrileitores – escritura e leitura – das Cidades de Calvino foi disponibilizado aos estudantes, tendo como proposição mostrar nove regras, cujo objetivo consistiu em servir à operação tradutório-inventiva. A partir delas, os estudantes arriscaram uma leitura ativa e uma escritura viva, ou seja, uma escritura tradutória, que não visa à recuperação literal do texto, mas privilegia uma escrileitura inventiva e traduções-reinvenções. Como aporte teórico, o texto aproxima-se do pensamento da diferença, de Roland Barthes, de Gilles Deleuze, além das teorizações da tradução literária propostas por Haroldo de Campos. Trata-se de experimentar a prática da leitura e o ensaio da escrita gerando novas interpretações ao Texto de Partida. Nesse sentido, ler-e-escrever configuram-se como uma prática aberta, jamais definitiva e tampouco estática. Em síntese, o texto propõe defender que os Textos de Partida são sempre fisgados pelos processos tradutórios e, por isso, novamente reinventados via leitura e escrita em Textos de Chegada. Palavras-chave: Tradução. Recriação. Pedagogia. Educação. (shrink)