Gentzen's three consistency proofs for elementary number theory have a common aim that originates from Hilbert's Program, namely, the aim to justify the application of classical reasoning to quantified propositions in elementary number theory. In addition to this common aim, Gentzen gave a “finitist” interpretation to every number-theoretic proposition with his 1935 and 1936 consistency proofs. In the present paper, we investigate the relationship of this interpretation with intuitionism in terms of the debate between the Hilbert School and the Brouwer (...) School over the significance of consistency proofs. First, we argue that the interpretation had the role of responding to a Brouwer-style objection against the significance of consistency proofs. Second, we propose a way of understanding Gentzen's response to this objection from an intuitionist perspective. (shrink)

The motor modules during human walking are identified using non-negative matrix factorization from surface electromyography signals. The extraction of motor modules in healthy participants is affected by the change in pre-processing of EMG signals, such as low-pass filters ; however, the effect of different pre-processing methods, such as the number of necessary gait cycles in post-stroke patients with varying steps, remains unknown. We aimed to specify that the number of GCs influenced the motor modules extracted in the consideration of LPFs (...) in post-stroke patients. In total, 10 chronic post-stroke patients walked at a self-selected speed on an overground walkway, while EMG signals were recorded from the eight muscles of paretic lower limb. To verify the number of GCs, five GC conditions were set, namely, 25, 20, 15, 10, and 5 gate cycles with three LPFs. First, the number of modules, variability accounted for, and muscle weightings extracted by the NNMF algorithm were compared between the conditions. Next, a modified NNMF algorithm, in which the activation timing profiles among different GCs were unified, was performed to compare the muscle weightings more robustly between GCs. The number of motor modules was not significantly different, regardless of the GCs. The difference in VAF and muscle weightings in the different GCs decreased with the LPF of 4 Hz. Muscle weightings in 15 GCs or less were significantly different from those in 25 GCs using the modified NNMF. Therefore, we concluded that the variability extracted motor modules by different GCs was suppressed with lower LPFs; however, 20 GCs were needed for more representative extraction of motor modules during walking in post-stroke patients. (shrink)

Aphasia is a language disorder that occurs after a stroke and impairs listening, speaking, reading, writing, and calculation skills. Patients with post-stroke aphasia in Japan are increasing due to population aging and the advancement of medical treatment. Opportunities for adequate speech therapy in chronic stroke are limited due to time constraints. Recent studies have reported that intensive speech therapy for a short period of time or continuous speech therapy using high-tech equipment, including speech applications (apps, can improve aphasia even in (...) the chronic stage. However, its underlying mechanism for improving language function and its effect on other cognitive functions remains unclear. In the present study, we investigated whether intensive speech therapy using a newly developed speech support app could improve aphasia and other cognitive functions in patients with chronic stroke. Furthermore, we examined whether it can alter the brain network related to language and other cortical areas. Thus, we conducted a prospective, single-comparison study to examine the effects of a new speech support app on language and cognitive functions and used resting state functional MRI (rs-fMRI) regions of interest (ROI) to ROI analysis to determine changes in the related brain network. Two patients with chronic stroke participated in this study. They used the independent speech therapy system to perform eight sets of 20 randomly presented words/time (taking approximately 20 min), for 8 consecutive weeks. Their language, higher cognitive functions including attention function, and rs-fMRI, were evaluated before and after the rehabilitation intervention using the speech support app. Both patients had improved pronunciation, daily conversational situations, and attention. The rs-fMRI analysis showed increased functional connectivity of brain regions associated with language and attention related areas. Our results show that intensive speech therapy using this speech support app can improve language and attention functions even in the chronic stage of stroke, and may be a useful tool for patients with aphasia. In the future, we will conduct longitudinal studies with larger numbers of patients, which we hope will continue the trends seen in the current study, and provide even stronger evidence for the usefulness of this new speech support app. (shrink)

Extracellular ATP released from necrotic cells in inflamed tissues activates the P2X7 receptor, stimulates the exposure of phosphatidylserine, and causes cell lysis. Recent findings indicated that XK, a paralogue of XKR8 lipid scramblase, forms a complex with VPS13A at the plasma membrane of T cells. Upon engagement by ATP, an unidentified signal(s) from the P2X7 receptor activates the XK‐VPS13A complex to scramble phospholipids, followed by necrotic cell death. P2X7 is expressed highly in CD25+CD4+ T cells but weakly in CD8+ T (...) cells, suggesting a role of this system in the activation of the immune system to prevent infection. On the other hand, a loss‐of‐function mutation in XK or VPS13A causes neuroacanthocytosis, indicating the crucial involvement of XK‐VPS13A‐mediated phospholipid scrambling at plasma membranes in the maintenance of homeostasis in the nervous and red blood cell systems. (shrink)

Girard introduced phase semantics as a complete set-theoretic semantics of linear logic, and Okada modified phase-semantic completeness proofs to obtain normal-form theorems. On the basis of these works, Okada and Takemura reformulated Girard’s phase semantics so that it became phase semantics for proof-terms, i.e., lambda-terms. They formulated phase semantics for proof-terms of Laird’s dual affine/intuitionistic lambda-calculus and proved the normal-form theorem for Laird’s calculus via a completeness theorem. Their semantics was obtained by an application of computability predicates. In this paper, (...) we first formulate phase semantics for proof-terms of second-order intuitionistic propositional logic by modifying Tait-Girard’s saturated sets method. Next, we prove the completeness theorem with respect to this semantics, which implies a strong normalization theorem. (shrink)

In this paper, I will argue from a historical perspective that Gentzen’s 1935 consistency proof of 1st order Peano Arithmetic PA principally aimed to give a finitist interpretation of implication and this aspect of the 1935 proof emerged as the attempt to cope with the non-finiteness in BHK-interpretation of implication. My argument consists of two parts. First, I will explain that the fundamental idea of the 1935 proof is to show the soundness of PA on some finitist interpretation and Gentzen (...) had attempted to use BHK-interpretation as such an interpretation. It is claimed that he eventually thought that there is a ‘circularity’ which is due to the non-finiteness of BHK-interpretation of implication, so it cannot be used as a finitist interpretation. Secondly, I will argue that the principal aim of the 1935 proof is to give his own finitist interpretation of implication which avoids such a ‘circularity’. Finally, this paper’s conclusion and an open question are presented. (shrink)

It is increasingly argued that polymathy—vocational and avocational pursuits in multiple domains—is deeply associated with creativity and innovation, and that its development enables the creation of important bridges between otherwise fragmented, dispersed sets of knowledge. Nevertheless, the dominant culture in both industry and academia is still that of narrow specialization. In this paper, we argue that in the context of COVID-19 crisis, with its wicked and transdisciplinary nature, the disciplinary approach of specialization is ill-suited to solve our increasingly complex problems, (...) and that polymathic thinking can be a crucial asset in this regard. Drawing on different literature strands, we first examine the interplay between polymathy and other well-developed constructs in personality and temperament research. We then advance theoretical predictions regarding the relationship between trait polymathy and resilience in the COVID-19 crisis. After that, we discuss learnable strategies that can be used in complex, uncertain and adverse situations, which are associated with development of a more polymathic set of knowledge. Later, we discuss how it may be possible to better capitalize on the key features of polymathic thinking at the societal level. Finally, we conclude with a reflection on the adequacy of our current institutions for dealing with complex problems, and we underscore the crucial role of polymathic thinking in an increasingly complex and interrelated world. (shrink)

The commutativity of the 1-dimensional XY-h type Hamiltonian and the transfer matrix of a 2-dimensional spin-lattice model constructed from an R-matrix is studied by Sutherland's method. We generalize Krinsky's result to more general Hamiltonians and more general R matrices, and we obtain a generic condition on their parameters for the commutativity, which defines an irreducible algebraic manifold in the parameter space.

We study the finite frame property of some extensions of Fitting, Marek, and Truszczyński’s pure logic of necessitation $$\textbf{N}$$ N. For any natural numbers m, n, we introduce the logic $$\textbf{N}^+\textbf{A}_{m,n}$$ N + A m, n by adding the single axiom scheme $$\Box ^n \varphi \rightarrow \Box ^m \varphi$$ □ n φ → □ m φ and the rule $$\dfrac{\lnot \Box \varphi }{\lnot \Box \Box \varphi }$$ ¬ □ φ ¬ □ □ φ ($${\text {Ros}}^\Box$$ Ros □ ) (...) into $$\textbf{N}$$ N. We prove the finite frame property of $$\textbf{N}^+\textbf{A}_{m, n}$$ N + A m, n with respect to Fitting, Marek, and Truszczyński’s relational semantics. We also prove that for $$n \ge 2$$ n ≥ 2, the logic obtained by removing the rule $${\text {Ros}}^\Box$$ Ros □ from $$\textbf{N}^+\textbf{A}_{0, n}$$ N + A 0, n is incomplete with respect to that semantics. (shrink)

Kei Yoshida’s recent book Philosophy of the Social Sciences: An Introduction is the first introductory textbook on the philosophy of the social sciences written in Japanese. It concisely expounds on a wide range of topics in the discipline, while its explication of those topics is not impartial or neutral as the author himself says. This paper gives a critical review of the book. The first half of it briefly overviews and assesses the book as a whole. The latter half of (...) the paper reconstructs the gist of the author’s exposition of the naturalism/interpretivism debate and criticizes it. (shrink)