Within a weak subsystem of second-order arithmetic , that is -conservative over , we reformulate Kreisel's proof of the Second Incompleteness Theorem and Boolos' proof of the First Incompleteness Theorem.

N'ayant pas réussi à joindre Masato Goda, nous publions ce magnifique texte sans son autorisation. Nous espérons qu'il nous en excusera. It has been more than thirty years since I discovered the texts of Emmanuel Levinas. Before publishing the Japanese translations of Totality and Infinite and Otherwise than being, I published an anthology of Levinas' work that included texts such as ‘‘Il y a'', ‘‘Reality and its shadow'' and so on. While I translated these texts, I noticed the importance (...) - Philosophie – Nouvel article. (shrink)

専門的な予備知識は仮定せずに完全性定理や計算可能性から論じ、第一および第二不完全性定理、Rosserの定理、Hilbertのプログラム、G ̈odelの加速定理、算術の超準モデル、Kolmogorov複雑性などを紹介して、不完全性定理の数学的意義と、その根源にある哲学的問題を説く。.

明治時代、人々は狐憑きやコックリさんなどの怪現象に右往左往していた。若き哲学者の井上圓了は、それらに合理的な道筋をつけることこそが哲学普及につながると信じて奔走。柳田國男からは見地の違いから「井上圓了 君には徹頭徹尾反対」と言われながらも、開学した「哲学館」(現東洋大学)で「妖怪学」の講義を行い、日本各地で膨大な怪異談を収集した。妖怪学者であり、哲学者、宗教改革者であった隠れた偉人、初の評伝。.

In this note we show that groups with definable generics in a separably closed valued field K of finite imperfection degree can be embedded into groups definable in the algebraic closure of K.

We define and investigate a uniformly locally o-minimal structure of the second kind in this paper. All uniformly locally o-minimal structures of the second kind have local monotonicity, which is a local version of monotonicity theorem of o-minimal structures. We also demonstrate a local definable cell decomposition theorem for definably complete uniformly locally o-minimal structures of the second kind. We define dimension of a definable set and investigate its basic properties when the given structure is a locally o-minimal structure which (...) admits local definable cell decomposition. (shrink)

Consider a definably complete uniformly locally o-minimal expansion of the second kind of a densely linearly ordered abelian group. Let $f:X \rightarrow R^n$ be a definable map, where X is a definable set and R is the universe of the structure. We demonstrate the inequality $\dim ) \leq \dim $ in this paper. As a corollary, we get that the set of the points at which f is discontinuous is of dimension smaller than $\dim $. We also show that the (...) structure is definably Baire in the course of the proof of the inequality. (shrink)

This study contributes to the emerging literature on the negative effects over consumption that social media users may develop as a consequence of being engaged on social media platforms. The authors tested materialism’s direct and indirect impacts on compulsive, conspicuous, and impulsive buying, adding two novel mediators: attitudes toward social media content and social media intensity. The study uses a convenience sample of 400 Thai social media users analyzed using structural equation modeling. The results confirmed the well-established positive relationships between (...) materialism and each of the three-negative consumption behaviors also in the social media domain. A novel finding showed the important role played by SMI which was found to be a strong predictor of each of the three negative consumption behaviors and it was also found to significantly mediate the relationship between materialism and the three-negative consumption behaviors. An additional contribution of the study was found on the role of attitudes which, contrary to what is commonly believed, were often not significant in predicting any negative behavior. (shrink)

We consider locally o-minimal structures possessing tame topological properties shared by models of DCTC and uniformly locally o-minimal expansions of the second kind of densely linearly ordered abelian groups. We derive basic properties of dimension of a set definable in the structures including the addition property, which is the dimension equality for definable maps whose fibers are equi-dimensional. A decomposition theorem into quasi-special submanifolds is also demonstrated.

We first show that the projection image of a discrete definable set is again discrete for an arbitrary definably complete locally o‐minimal structure. This fact together with the results in a previous paper implies a tame dimension theory and a decomposition theorem into good‐shaped definable subsets called quasi‐special submanifolds. Using this fact, we investigate definably complete locally o‐minimal expansions of ordered groups when the restriction of multiplication to an arbitrary bounded open box is definable. Similarly to o‐minimal expansions of ordered (...) fields, Łojasiewicz's inequality, Tietze's extension theorem and affiness of pseudo‐definable spaces hold true for such structures under the extra assumption that the domains of definition and the pseudo‐definable spaces are definably compact. Here, a pseudo‐definable space is a topological space having finite definable atlases. We also demonstrate Michael's selection theorem for definable set‐valued functions with definably compact domains of definition. (shrink)

Recently, Edwards and Liaschenko questioned the validity of an argument put forward by Dr Søren Holm and Joseph Dunne concerning the impossibility of a theory of nursing. Taking into consideration the premises of the argument, I describe how Maritain's conception of philosophy allows for the possibility of a theory of nursing conceived as a philosophy of nursing art that is both practical and propositional in nature. As well, I identify how the philosophy of nursing art guides nursing art in developing (...) and applying other kinds of artistic practical nursing knowledge: artistic nursing rules and artistic prudential nursing judgements. Finally, the relationship of ethical knowledge to artistic practical nursing knowledge is set down. (shrink)

Continuing Pfeiffer 1972, Pfeiffer 2018 examines inherited Dravidian etyma of Kurux, one of the most northerly Dravidian languages. After an overview of the book, we discuss problems involved in Pfeiffer’s arguments, methods, and materials. Then we try to narrow down the conditions of some of the sound changes Pfeiffer proposes, in conformity with the Neogrammarian hypothesis of regularity. We also point out that closer study of word-final phonology would answer some of the pending questions of Kurux-Malto morphology. Finally, we argue (...) that phonological and morphological reconstruction can unveil more features to help revise the subgrouping of Kurux-Malto in the Dravidian family. (shrink)

Recently, a concern has been raised about a particular kind of behaviour that is adversely affecting the quality of nursing theoretical discourse. With the behaviour being attributed to nurses’ tendency to think in binary terms, it has been proposed that nurses replace their binary way of thinking with thinking that is inclusive and expansive and is based on an epistemology of contradiction. While agreeing that the behaviour of concern is indeed unscholarly, I disagree that the culprit is the binary. In (...) this commentary, I argue that the culprit is sophistical argumentation involving a binary (real or not) and that, by not making room for legitimate binaries, we run the danger of ‘throwing out the baby with the bathwater’. Further, I argue that the proffered solution is illusory. Its epistemological basis prohibits the deliverance of that which is promised. (shrink)

This paper introduces sequent systems for Visser's two propositional logics: Basic Propositional Logic (BPL) and Formal Propositional Logic (FPL). It is shown through semantical completeness that the cut rule is admissible in each system. The relationships with Hilbert-style axiomatizations and with other sequent formulations are discussed. The cut-elimination theorems are also demonstrated by syntactical methods.

By formalizing Berry's paradox, Vopěnka, Chaitin, Boolos and others proved the incompleteness theorems without using the diagonal argument. In this paper, we shall examine these proofs closely and show their relationships. Firstly, we shall show that we can use the diagonal argument for proofs of the incompleteness theorems based on Berry's paradox. Then, we shall show that an extension of Boolos' proof can be considered as a special case of Chaitin's proof by defining a suitable Kolmogorov complexity. We shall show (...) also that Vopěnka's proof can be reformulated in arithmetic by using the arithmetized completeness theorem. (shrink)

We give a proof of Gödel's first incompleteness theorem based on Berry's paradox, and from it we also derive the second incompleteness theorem model-theoretically.

The present study examined the effect of residential mobility on impression formation. In the study, participants were first engaged in a residential mobility priming task where they were asked to imagine and describe either frequent moving life or less frequent moving life. They then evaluated their attitudes toward four types of target persons: competent vs. incompetent and warm vs. cold. As a result, in the high-mobility condition, the effect of competence was observed only when participants evaluated a warm person, whereas (...) in the low-mobility condition, it appeared only when participants evaluated a cold person. The potential influence of individual residential mobility on the relationship formation is also discussed. (shrink)

This study explored representations of self-injury in Japanese manga. A content analysis of fifteen slice-of-life manga published between 2000-2017 was conducted, focusing on forty scenes that depict eighteen characters engaging in self-injury. Most depictions of self-injury reflect a stereotypical perception of “self-injurer,” a young girl cutting herself to cope with negative emotion. Characters receive informal support from friends and partners, while parents are portrayed as unsupportive and even triggering. An emergent trend was observed among manga targeting male readers to label (...) self-injuring women as “menhera” - mentally vulnerable damsels in distress - inviting a fetishistic gaze on the self-injuring female bodies. (shrink)

We study definably complete locally o‐minimal expansions of ordered groups. We propose a notion of special submanifolds with tubular neighborhoods and show that any definable set is decomposed into finitely many special submanifolds with tubular neighborhoods.

The following two assertions are equivalent for an o-minimal expansion of an ordered group $$\mathcal M=(M,<,+,0,\ldots )$$. There exists a definable bijection between a bounded interval and an unbounded interval. Any definable continuous function $$f:A \rightarrow M$$ defined on a definable closed subset of $$M^n$$ has a definable continuous extension $$F:M^n \rightarrow M$$.

We define a discrete closure operator for definably complete locally o‐minimal structures. The pair of the underlying set of and the discrete closure operator forms a pregeometry. We define the rank of a definable set over a set of parameters using this fact and call it ‐dimension. A definable set X is of dimension equal to the ‐dimension of X. The structure is simultaneously a first‐order topological structure. The dimension rank of a set definable in the first‐order topological structure also (...) coincides with its dimension. (shrink)

This paper discusses sufficient conditions for a definably complete expansion of a densely linearly ordered abelian group to have uniformly locally o‐minimal open cores of the first/second kind and strongly locally o‐minimal open core, respectively.

In his essay on Herman Melville, Gilles Deleuze writes about an affirmation of the world as process and as archipelago. What does this mode of affirmation mean not only for the philosophy of Deleuze, but also for us all who live in this world today? This is the principal issue which I try to take up in my paper. Already in his text on David Hume, the young Deleuze was obliged to confront the problematics of the becoming-system of collection, which (...) would accompany him throughout his life. This essay discusses the ways in which Deleuze's central concepts including ‘transcendental empiricism', ‘difference/repetition', ‘schizophrenia’, ‘chaosmos', ‘thousand plateaus', ‘and’ and ‘line of flight’ are interconnected within his notion of archipelagic system. (shrink)

We consider a set-theoretic version of mereology based on the inclusion relation ⊆ and analyze how well it might serve as a foundation of mathematics. After establishing the non-definability of ∈ from ⊆, we identify the natural axioms for ⊆-based mereology, which constitute a finitely axiomatizable, complete, decidable theory. Ultimately, for these reasons, we conclude that this form of set-theoretic mereology cannot by itself serve as a foundation of mathematics. Meanwhile, augmented forms of set-theoretic mereology, such as that obtained by (...) adding the singleton operator, are foundationally robust. (shrink)

It is well known that Gödel’s incompleteness theorems hold for ∑1-definable theories containing Peano arithmetic. We generalize Gödel’s incompleteness theorems for arithmetically definable theories. First, we prove that every ∑n+1-definable ∑n-sound theory is incomplete. Secondly, we generalize and improve Jeroslow and Hájek’s results. That is, we prove that every consistent theory having ∏n+1set of theorems has a true but unprovable ∏nsentence. Lastly, we prove that no ∑n+1-definable ∑n-sound theory can prove its own ∑n-soundness. These three results are generalizations of Rosser’s (...) improvement of the first incompleteness theorem, Gödel’s first incompleteness theorem, and the second incompleteness theorem, respectively. (shrink)

In contrast to temporal asymmetry stressed in process philosophy, symmetry prevails in Mahayana Buddhism and East Asian philosophy formed under its influence. The paper clarifies the meaning of symmetry from the perspectives of Kitaro Nishida and Dogen, it explores similar or overlapping ideas in Whitehead’s philosophy oforganism, and it suggests that the differences among them are much smaller than commonly believed.

Following a science and ontology conference in Barbizon, France, Layla Raïd and Karim Belabas published an article on Peirce and Quine that focuses on truth considered as the convergence of opinions or theories. 2 The article is a productive collaboration between a philosopher and mathematician, identifying two problems that Quine poses: first, the use of numerical analogy in Peirce’s account of truth, and second, the uniqueness of the final opinion, which can presumably be defeated or undermined by arguments from underdetermination (...) of theories. 3 I accept their interpretation insofar as these two problems are considered to constitute main issues for those—including myself—who wish to advocate Peirce’s view, but.. (shrink)