The central problem in the quantum theory of measurement, how to describe the process of state reduction in terms of the quantum mechanical formalism, is solved on the basis of the relativity of quantal states, which implies that once the apparatus is detected in a well-defined state, the object state must reduce to a corresponding one. This is a process termed by Schrödinger disentanglement. Here, it is essential to observe that Renninger's negative result does constitute an actual measurement process. From (...) this point of view, Heisenberg's interpretation of his microscope experiment and the Einstein-Podolsky-Rosen arguments are reinvestigated. Satisfactory discussions are given to various experimental situations, such as the Stern-Gerlach-type experiment, successive measurements, macroscopic measurements, and Schrödinger's cat. Finally it is proposed to regard a state vector in quantum mechanics as an irreducible physical construct, in Margenau's sense, that is not further analyzable both mathematically and conceptually. (shrink)

Akama et al. [1] systematically studied an arithmetical hierarchy of the law of excluded middle and related principles in the context of first-order arithmetic. In that paper, they first provide a prenex normal form theorem as a justification of their semi-classical principles restricted to prenex formulas. However, there are some errors in their proof. In this paper, we provide a simple counterexample of their prenex normal form theorem [1, Theorem 2.7], then modify it in an appropriate way which still serves (...) to largely justify the arithmetical hierarchy. In addition, we characterize a variety of prenex normal form theorems by logical principles in the arithmetical hierarchy. The characterization results reveal that our prenex normal form theorems are optimal. For the characterization results, we establish a new conservation theorem on semi-classical arithmetic. The theorem generalizes a well-known fact that classical arithmetic is $\Pi _2$ -conservative over intuitionistic arithmetic. (shrink)

We provide a fine‐grained analysis on the relation between König's lemma, weak König's lemma, and the decidable fan theorem in the context of constructive reverse mathematics. In particular, we show that double negated variants of König's lemma and weak König's lemma are equivalent to double negated variants of the general decidable fan theorem and the binary decidable fan theorem, respectively, over a nearly intuitionistic system containing a weak countable choice only. This implies that the general decidable fan theorem is not (...) equivalent to the binary decidable fan theorem in the absence of a strong countable choice. In addition, we introduce a principle which fills the gap between König's lemma and weak König's lemma, and show that König's lemma is equivalent to weak König's lemma plus this principle. We also solve several problems arising from the investigation. (shrink)

We systematically study conservation theorems on theories of semi-classical arithmetic, which lie in-between classical arithmetic $\mathsf {PA}$ and intuitionistic arithmetic $\mathsf {HA}$. Using a generalized negative translation, we first provide a structured proof of the fact that $\mathsf {PA}$ is $\Pi _{k+2}$ -conservative over $\mathsf {HA} + {\Sigma _k}\text {-}\mathrm {LEM}$ where ${\Sigma _k}\text {-}\mathrm {LEM}$ is the axiom scheme of the law-of-excluded-middle restricted to formulas in $\Sigma _k$. In addition, we show that this conservation theorem is optimal in the (...) sense that for any semi-classical arithmetic T, if $\mathsf {PA}$ is $\Pi _{k+2}$ -conservative over T, then ${T}$ proves ${\Sigma _k}\text {-}\mathrm {LEM}$. In the same manner, we also characterize conservation theorems for other well-studied classes of formulas by fragments of classical axioms or rules. This reveals the entire structure of conservation theorems with respect to the arithmetical hierarchy of classical principles. (shrink)

We systematically study several principles and give a principle which is weaker than disjunctive Markov’s principle. We also show that the principle is underivable and strictly weaker than MP∨ in certain extensions of the system EL of elementary analysis.

We refine the arithmetical hierarchy of various classical principles by finely investigating the derivability relations between these principles over Heyting arithmetic. We mainly investigate some restricted versions of the law of excluded middle, De Morgan's law, the double negation elimination, the collection principle and the constant domain axiom.

The uniform continuity theorem states that every pointwise continuous real‐valued function on the unit interval is uniformly continuous. In constructive mathematics, is strictly stronger than the decidable fan theorem, but Loeb [17] has shown that the two principles become equivalent by encoding continuous real‐valued functions as type‐one functions. However, the precise relation between such type‐one functions and continuous real‐valued functions (usually described as type‐two objects) has been unknown. In this paper, we introduce an appropriate notion of continuity for a modulus (...) of a continuous real‐valued function on [0, 1], and show that real‐valued functions with continuous moduli are exactly those functions induced by Loeb's codes. Our characterisation relies on two assumptions: (1) real numbers are represented by regular sequences (equivalently Cauchy sequences with explicitly given moduli); (2) the continuity of a modulus is defined with respect to the product metric on the regular sequences inherited from the Baire space. Our result implies that is equivalent to the statement that every pointwise continuous real‐valued function on [0, 1] with a continuous modulus is uniformly continuous. We also show that is equivalent to a similar principle for real‐valued functions on the Cantor space. These results extend Berger's [2] characterisation of for integer‐valued functions on and unify some characterisations of in terms of functions having continuous moduli. (shrink)

Kierstead showed that every computable marriage problem has a computable matching under the assumption of computable expanding Hall condition and computable local finiteness for boys and girls. The strength of the marriage theorem reaches or if computable expanding Hall condition or computable local finiteness for girls is weakened. In contrast, the provability of the marriage theorem is maintained in even if local finiteness for boys is completely removed. Using these conditions, we classify the strength of variants of marriage theorems in (...) the context of reverse mathematics. Furthermore, we introduce another condition that also makes the marriage theorem provable in, and investigate the sequential and Weihrauch strength of marriage theorems under that condition. (shrink)

RESUMO O presente artigo pretende restituir o exame ontofenomenológico da ipseidade e da temporalidade em “L’être et le néant” a partir de dois momentos, quais sejam: fenomenologia das três dimensões temporais e ontologia da temporalidade. Este duplo exame não poderá ser pensado sem uma definição prévia do para-si como ipse temporal que falta de... para..., isto é, como ser que, enquanto nada de ser, é uma falta de ser que busca, em vão, preenchê-la. A impossibilidade deste preenchimento, como buscaremos evidenciar, (...) é ontologicamente necessária para que a temporalização do serpara-si não se deixe infestar com a inércia típica do ser-em-si. ABSTRACT The present article intends to restore, from the Sartrean work L'être et le néant, the ontophenomenological examination of ipseity and temporality, understanding this examination in two moments: phenomenology of the three temporal dimensions and ontology of temporality. This double exam could not be thought without a previous definition of for-itself’s as temporal ipseas lack of from… to…, that is, as a for-itself which, while nothingness of being, is a lack of being that constantly seeks to fill it. The impossibility of this fill-up, as we shall see, is ontologically necessary so that the temporality of the being-for-itself does not let itself infest with the typical inertia of the being-in-itself. (shrink)

Neste artigo pretendemos analisar a maneia pela qual o filósofo francês Jean-Paul Sartre modaliza, a partir da psicanálise existencial elaborada em L’être et le néant, sua biografia existencial sobre o poeta Charles Baudelaire. Em Baudelaire, seremos capazes de localizar os prolegômenos a toda biografia existencial sartreana futura, isto é, o modus operandi de investigação/escrita biográfica de Sartre.

We aim at developing a systematic method of separating omniscience principles by constructing Kripke models for intuitionistic predicate logic $\mathbf {IQC}$ and first-order arithmetic $\mathbf {HA}$ from a Kripke model for intuitionistic propositional logic $\mathbf {IPC}$. To this end, we introduce the notion of an extended frame, and show that each IPC-Kripke model generates an extended frame. By using the extended frame generated by an IPC-Kripke model, we give a separation theorem of a schema from a set of schemata in (...) $\mathbf {IQC}$ and a separation theorem of a sentence from a set of schemata in $\mathbf {HA}$. We see several examples which give us separations among omniscience principles. (shrink)

Erdelyi distinguishes between cognitive and emotional forms of repression, but argues that they use the same general mechanism. His discussion of experimental memory findings, on the one hand, and clinical examples, on the other, does indeed indicate considerable overlap. As an in-between level of evidence, research findings on emotion in neuroscience, as well as experimental and social/personality psychology, further support his argument.

Akama et al. [1] introduced a hierarchical classification of first-order formulas for a hierarchical prenex normal form theorem in semi-classical arithmetic. In this paper, we give a justification for the hierarchical classification in a general context of first-order theories. To this end, we first formalize the standard transformation procedure for prenex normalization. Then we show that the classes $$\textrm{E}_k$$ and $$\textrm{U}_k$$ introduced in [1] are exactly the classes induced by $$\Sigma _k$$ and $$\Pi _k$$ respectively via the transformation procedure in (...) any first-order theory. (shrink)

We systematically study the interrelations between all possible variations of \(\Delta ^0_1\) variants of the law of excluded middle and related principles in the context of intuitionistic arithmetic and analysis.

O presente artigo perscruta o modo dialético pelo qual Sartre, desde os anos 1960, aclimata a vida psíquica e o vivido. Para esta lida, realizaremos uma incursão investigativa sustentada por um conjunto de escritos sartreanos deste período, dando especial enfoque sobretudo ao ensaio Questões de método (1957) e à conferência que nosso autor profere em 1961, e cujo título, Marxismo e subjetividade, é revelador da sua tentativa de conciliar o existencialismo e o materialismo histórico à luz de uma dialética existencial. (...) Na sequência, mostramos como a dialetização da vida psíquica, que pressupõe uma antinomia dialética (presença a si e ausência de si), enseja, por parte do filósofo, uma crítica pontual à psicanálise freudiana. (shrink)

Este artigo pretende restituir a leitura que Heidegger e Sartre realizam da filosofia de Descartes, desvelando, a partir disso, as diferentes posições interpretativas que ambos os filósofos tomam em relação ao pensamento cartesiano. Observar-se-á que o tratamento dado por Heidegger à metafísica cartesiana explicita um anti-humanismo contrário ao humanismo sartreano. A partir dessa diferença, seremos capazes de assinalar um distanciamento teórico entre Heidegger e Sartre, distanciamento que poderá revelar, por conseguinte, a maneira peculiar pela qual Sartre opera com os conceitos (...) hedeggerianos em L’être et le néant. Palavras-chave: humanismo; anti-humanismo; fenomenologia; liberdade; metafísica.: This article aims to replace the Hedeigger’s and Sartre’s read from Descarte’s philosophy unveiling, from that, the different interpretive positions that both philosophers take in relation to the Cartesian thought. We will observe that the treatment given by Heidegger to the Cartesian metaphysics reveals an anti-humanism contrary from Sartre’s humanism. From this difference, we will be able to point out a theoretical detachment between Heidegger and Sartre, detachment that may reveal, meanwhile, the peculiar way by which Sartre deals with the Heidegger’s concepts in L’être et le néant. Keywords: humanism; anti-humanism; phenomenology; freedom; metaphysics. (shrink)

We identify bar recursion on moduli of continuity as a fundamental notion of constructive mathematics. We show that continuous functions from the Baire space \ to the natural numbers \ which have moduli of continuity with bar recursors are exactly those functions induced by Brouwer operations. The connection between Brouwer operations and bar induction allows us to formulate several continuity principles on the Baire space stated in terms of bar recursion on continuous moduli which naturally characterise some variants of bar (...) induction. These principles state that a certain kind of continuous function from \ to \ admits a modulus of continuity with a bar recursor. The results for the Baire space are recast in the setting of the Cantor space \ using the notion of fan recursor, a bar recursor for binary trees. This yields characterisations of uniformly continuous functions on the Cantor space and fan theorem in terms of fan recursors. The results for the Cantor space hold over the extensional version of intuitionistic arithmetic in all finite types ), and those for the Baire space hold over \ extended with the type for Brouwer operations. Our work places Spector’s bar recursion in a proper context of Brouwer’s intuitionistic mathematics and clarifies the connection between bar recursion and bar induction. (shrink)

Along the line of Hirst‐Mummert and Dorais, we analyze the relationship between the classical provability of uniform versions Uni(S) of Π2‐statements S with respect to higher order reverse mathematics and the intuitionistic provability of S. Our main theorem states that (in particular) for every Π2‐statement S of some syntactical form, if its uniform version derives the uniform variant of over a classical system of arithmetic in all finite types with weak extensionality, then S is not provable in strong semi‐intuitionistic systems (...) including bar induction in all finite types but also nonconstructive principles such as Kőnig's lemma and uniform weak Kőnig's lemma. Our result is applicable to many mathematical principles whose sequential versions imply. (shrink)

This book tracks the emergence of the modern Japanese nation in the nineteenth century through the history of some of its local aspirants. It explores how kokugaku (Japan studies) scholars envisioned their place within Japan and the globe, while living in a castle town and domain far north of the political capital.

Resumo: Este artigo pretende investigar a maneira pela qual o filósofo francês Jean-Paul Sartre enquadra, em sua psicologia fenomenológica da imaginação, a problemática acerca do irreal normal e do irreal patológico. Estruturando psicofenomenologicamente a atividade da consciência imaginante, será possível ver que a imagem difere radicalmente da percepção, mas ambas permanecem, contudo, consciência intencional. Nessa toada, cabe a indagação: se toda consciência imaginante é consciência intencional, como enquadrar as experiências alucinatórias?: The aim of the present article is to investigate how (...) the French philosopher Jean-Paul Sartre understood, in his phenomenological psychology of the imagination, the problematic of the "normal unreal" and the "pathological unreal". By psycho-phenomenologically structuring the activity of the imaginative consciousness, we can see that the image differs radically from perception, but both remain intentional consciousness. In this context, it is necessary to ask the following question: if all imaginative consciousness is intentional consciousness, how can we frame hallucinatory experiences? (shrink)

This volume investigates how the phenomenology of religion was accepted and developed in different national contexts. It consists of interviews with senior scholars, who are experts on the development of the phenomenology of religion in their countries, along with commentary and analysis.

We investigate the novel problem of what happens in special relativity and in relativistic field theories whenthree-dimensional space is quantized. First we examine the equation for elastic waves on a linear chain, the simplest example of a quantized medium, and propose, on its analogy, a nonlinearp-k relationp=ħk(sinhkl)/kl for light and material waves. Here,kl is a new variable which represents the space-quantization effect on the plane wave of wave numberk=|k|. (Note thatkl=0 givesp=ħk.) This relation makes the light velocity in vacuum dependent (...) onkl. We postulate, however, that the phase and group velocities of each individual light wave are still invariant, and try to generalize special relativity to the case ofkl ≠ 0. This can be simply done if the invariance ofkl is assumed. Our results suggest that “localization” might be a relative concept. One interesting consequence of our proposal is that relativistic field theories become automatically finite. This comes out without violating unitarity or causality. A precise measurement of velocities of high-energy photons or massive particles is desirable for checking our proposal. (shrink)

Pretendemos analisar neste artigo o fundamento ontofenomenológico do conhecimento em L’être et le néant. Como veremos, o conhecimento será concebido a partir de uma negação de tipo interna definida como relação ontológica fundamental entre ser-para-si e ser-em-si. Todavia, caso almejemos compreender o estatuto profundo de uma tal relação, teremos que escrutinar as definições sartreanas de ser do fenômeno e fenômeno de ser, ser transfenomenal, ser-em-si, ser-para-si e estrutura reflexo-refletidora do cogito. Recuperando tais definições, mostraremos que a identidade do ser do (...) para-si e do conhecimento, antes de sinalizar que o conhecimento seja a medida do ser, desponta de um registro ontofenomenológico no qual o para-si, enquanto nada de ser, anuncia a si mesmo a partir do em-si. (shrink)

Este artigo visa analisar a categoria do mágico em duas obras fenomenológicas do filósofo francês Jean-Paul Sartre, quais sejam: La transcendance de l’Ego e Esquisse d’une théorie des émotions. Em ambos os textos, o expediente do mágico é recorrente e assinala, por sua vez, uma certa experiência da consciência que poderíamos nomear como anti-fenomenológica. Ademais, este registro do mágico constitui para Sartre um modo, digamos, privilegiado no que tange à análise da ininteligibilidade da relação da consciência com o mundo, com (...) os outros e consigo mesma. (shrink)

O presente artigo objetiva uma análise crítica da aproximação de Sartre com o marxismo. Para tanto, são analisados alguns conceitos fundamentais de Questions de Méthode (1957). Como buscaremos evidencia aqui, o filósofo, apesar de incorporar o social em suas análises, parece insistir em um subjetivismo que traz consequências paradoxais para esta sua nova fase filosófica.

Este artigo pretende elucidar alguns aspectos da biografia existencial de Sartre sobre o poeta e romancista Jean Genet. Elucidando a estrutura da obra, veremos que a presente biografia faz emergir o sentido e o peso do social nas análises sartreanas acerca da liberdade.