Autism spectrum disorders (ASD) are heterogeneous neurodevelopmental disorders that are reportedly characterized by aberrant neural networks. Recently developed multiscale entropy analysis (MSE) can characterize the complexity inherent in EEG dynamics over multiple temporal scales in the dynamics of neural networks. We encountered an 18-year-old man with ASD whose refractory catatonic obsessive–compulsive symptoms were improved dramatically after electroconvulsive therapy (ECT). In this clinical case study, we strove to clarify the neurophysiological mechanism of ECT in ASD by assessing EEG complexity using MSE. (...) Along with ECT, the frontocentral region showed decreased EEG complexity at higher temporal scales, whereas the occipital region expressed an increase at lower temporal scales. Furthermore, these changes were associated with clinical improvement associated with the elevation of brain-derived neurotrophic factor, which is a molecular hypothesis of ECT, playing key roles in ASD pathogenesis. Changes in EEG complexity in a region-specific and temporal scale-specific manner we found might reflect atypical EEG dynamics in ASD. Although MSE is not a direct approach to measuring neural connectivity and the results are from only a single case, they might reflect specific aberrant neural network activity and the therapeutic neurophysiological mechanism of ECT in ASD. (shrink)

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)

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)

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)

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)

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)

In this paper we introduce a paradigm of experiment which, we believe, is of interest both in psychology and philosophy. There the subject wears an HMD (head-mount display), and a camera is set up at the upper corner of the room, in which the subject is. As a result, the subject observes his own body through the HMD. We will mainly focus on the philosophical relevance of this experiment, especially to the thesis of so-called 'immunity to error through misidentification relative (...) to the first-person pronoun'. We will argue that one experiment conducted in this setting, which we call the bodily illusion experiment, provides a counterexample to that thesis. (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.

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)

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.

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.

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)

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.

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)