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.

Velina Hasu Houston’s theatrical representations focus on exploring cultural collision and coalescence in transnational communities. With her biographical and cultural background deeply influenced by her Japanese mother’s way of life and sense of values, Houston has been open-minded in creating a new viewpoint through which to look at Japan, the United States and the world. Calligraphy is quite challenging in that it looks at her mother’s aging from both Japanese and American perspectives. It sheds new light on not only understanding (...) the beauty in the aging process but also women’s memories that have value beyond the personal. Since she wrote Tea based on her mother’s life as a war bride, Houston has presented a pioneering, in-depth exploration of Asian women’s memories that have been historically ignored in the United States. This paper examines how Houston’s insight into transnationalism through the transformative nature of cultural identity and change inspires her to re-envision women’s writing and highlights the need for a re-examination of the power of love and beauty. (shrink)

Previous studies have suggested that auditory hallucination is closely related to thought insertion. In this study, we investigated the relationship between the external misattribution of thought and auditory hallucination-like experiences. We used the AHES-17, which measures auditory hallucination-like experiences in normal, healthy people, and the Deese–Roediger–McDermott paradigm, in which false alarms of critical lure are regarded as spontaneous external misattribution of thought. We found that critical lures elicited increased the number of false alarms as AHES-17 scores increased and that scores (...) of AHES-17 predicted the rate of false memory of critical lures. Furthermore, we revealed that the relationship between AHES-17 scores and the rates of false alarms to critical lures was strictly linear. Therefore, it might be said that individual differences in auditory hallucination-like experiences are highly related to the external misattribution of thought. We discussed these results from the perspective of the sense of agency over thought. (shrink)

We investigated output-monitoring errors over speech based on findings in the research on the sense of agency. Several words were presented one-by-one, and we asked participants to say the word aloud, mouth the word, or imagine saying the word aloud. Later, participants were asked whether each word was said aloud. We found that the “said aloud” response was higher for generated words than that for observed words; it was decreased when the pitch of the feedback was lowered but still higher (...) than when no feedback was received, and it was the same when no feedback was received and when feedback was replaced by another’s voice. Furthermore, we found that the “said aloud” response did not decrease even when the altered feedback was received with a short delay. These results were discussed according to the sense of agency and agency memory. (shrink)

By using a provability predicate of PA, we define ThmPA(M) as the set of theorems of PA in a modelMof PA. We say a modelMof PA is (1) illusory if ThmPA(M) ⊈ ThmPA(ℕ), (2) heterodox if ThmPA(M) ⊈ TA, (3) sane ifM⊨ ConPA, and insane if it is not sane, (4) maximally sane if it is sane and ThmPA(M) ⊆ ThmPA(N) implies ThmPA(M) = ThmPA(N) for every sane modelNof PA. We firstly show thatMis heterodox if and only if it is (...) illusory, and that ThmPA(M) ∩ TA ≠ ThmPA(ℕ) for any illusory modelM. Then we show that there exists a maximally sane model, every maximally sane model satisfies ¬ConPA+ConPA, and there exists a sane model of ¬ConPA+ConPAwhich is not maximally sane. We define that an insane model is (5) illusory by nature if its every initial segment being a nonstandard model of PA is illusory, and (6) going insane suddenly if its every initial segment being a sane model of PA is not illusory. We show that there exists a model of PA which is illusory by nature, and we prove the existence of a model of PA which is going insane suddenly. (shrink)

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 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.

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)

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)

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)

To preserve postoperative brain function, it is important for neurosurgeons to fully understand the brain's structure, vasculature, and function. Intraoperative high-frequency electrical stimulation during awake craniotomy is the gold standard for mapping the function of the cortices and white matter; however, this method can only map the “focal” functions and cannot monitor large-scale cortical networks in real-time. Recently, an in vivo electrophysiological method using cortico-cortical evoked potentials induced by single-pulse electrical cortical stimulation has been developed in an extraoperative setting. By (...) using the CCEP connectivity pattern intraoperatively, mapping and real-time monitoring of the dorsal language pathway is available. This intraoperative CCEP method also allows for mapping of the frontal aslant tract, another language pathway, and detection of connectivity between the primary and supplementary motor areas in the frontal lobe network. Intraoperative CCEP mapping has also demonstrated connectivity between the frontal and temporal lobes, likely via the ventral language pathway. Establishing intraoperative electrophysiological monitoring is clinically useful for preserving brain function, even under general anesthesia. This CCEP technique demonstrates potential clinical applications for mapping and monitoring large-scale cortical networks. (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)

We shall prove the second incompleteness theorem via Kolmogorov complexity.

While people are still alive, we owe them respect. Yet what, if anything, do we owe the newly dead? This question is an urgent practical concern for aged societies, because older people die at higher rates than any other age group. One novel way in which Japan, the frontrunner of aged societies, meets its need to accommodate high numbers of newly dead is itai hoteru or corpse hotels. Itai hoteru offer families a way to wait for space in over‐crowded crematoriums (...) while affording an environment conducive to grieving. Drawing on conversations with itai hoteru employees, we delineate the values this contemporary death practice expresses and show how these values comprise part of the broader idea of a good death. A good death implies duties on both sides of death's divide: to both the dying and the newly dead. (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.

We present a version of Herbelin’s image-calculus in the call-by-name setting to study the precise correspondence between normalization and cut-elimination in classical logic. Our translation of λμ-terms into a set of terms in the calculus does not involve any administrative redexes, in particular η-expansion on μ-abstraction. The isomorphism preserves β,μ-reduction, which is simulated by a local-step cut-elimination procedure in the typed case, where the reduction system strictly follows the “ cut=redex” paradigm. We show that the underlying untyped calculus is confluent (...) and enjoys the PSN property for the isomorphic image of λμ-calculus, which in turn yields a confluent and strongly normalizing local-step cut-elimination procedure for classical logic. (shrink)

We define a liar-type paradox as a consistent proposition in propositional modal logic which is obtained by attaching boxes to several subformulas of an inconsistent proposition in classical propositional logic, and show several famous paradoxes are liar-type. Then we show that we can generate a liar-type paradox from any inconsistent proposition in classical propositional logic and that undecidable sentences in arithmetic can be obtained from the existence of a liar-type paradox. We extend these results to predicate logic and discuss Yablo’s (...) Paradox in this framework. Furthermore, we define explicit and implicit self-reference in paradoxes in the incompleteness phenomena. (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。.

サンデルや現代コミュニタリアンは、なぜ今、古代からの西洋政治思想「共通善」を改めて説くのか。新たな実践哲学が、ここから始まる。.

On applique ici la méthode de l’analyse de réseau pour comprendre les temporalités de la construction de l’imprimerie, comme activité économique associant des hommes de lettres et des acteurs économiques. À partir des informations contenues dans l’Incunabula Short Title Catalogue, deux types de réseaux sont construits pour les éditions imprimées à Venise entre 1469 et 1500. Le premier permet d’observer le vivier des noms d’auteurs présents dans les éditions. Le second permet d’aller plus loin dans les notions de centralité et (...) d’autorité dans le réseau. Les presses vénitiennes se sont construites par l’utilisation réciproque des ateliers et des grands noms lettrés, dont le prestige légitimait les grandes entreprises typographiques. Avec le développement de l’imprimerie, les noms d’auteurs contemporains se font plus nombreux. Pour l’ensemble des lettrés impliqués dans l’imprimerie, cela se traduit par un rapport de force en leur défaveur. Les imprimeurs organisent eux-mêmes leurs collaborations en choisissant dans un vivier qui ne fait que s’accroître. Le prestige des auteurs est plus diffus et se nourrit de l’association de plusieurs noms dans une édition. Mais certains ont su particulièrement bien en jouer, comme le montre l’exemple d’Antonio Mancinelli. Ces réseaux éditoriaux, analysés dans leur épaisseur chronologique, permettent ainsi de redonner une vraie dimension temporelle à la construction d’une nouvelle industrie culturelle. (shrink)

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。.

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)

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)

We introduce a dual-context style sequent calculus which is complete with respectto Kripke semantics where implication is interpreted as strict implication in the modal logic K. The cut-elimination theorem for this calculus is proved by a variant of Gentzen's method.

We introduce a Gentzen style formulation of Basic Propositional Calculus(BPC), the logic that is interpreted in Kripke models similarly tointuitionistic logic except that the accessibility relation of eachmodel is not necessarily reflexive. The formulation is presented as adual-context style system, in which the left hand side of a sequent isdivided into two parts. Giving an interpretation of the sequents inKripke models, we show the soundness and completeness of the system withrespect to the class of Kripke models. The cut-elimination theorem isproved (...) in a syntactic way by modifying Gentzen's method. Thisdual-context style system exemplifies the effectiveness of dual-contextformulation in formalizing various non-classical logics. (shrink)