We give an extender characterization of a very strong elementary embedding between transitive models of set theory, whose existence is known as the axiom I2. As an application, we show that the positive solution of a partition problem raised by Magidor would refute it.

A change of gaze behavior at a small mistake moment is a natural response that reveals our own mistakes and suggests an apology to others with whom we are working or interacting. In this paper we investigate how robot gaze behaviors at small mistake moments change the impressions of others. To prepare gaze behaviors for a robot, first, we identified by questionnaires how human gaze behaviors change in such situations and extracted three kinds: looking at the other, looking down, and (...) looking away. We prepared each gaze behavior, added a no-gaze behavior, and investigated how a robot’s gaze behavior at a small mistake moment changes the impressions of the interacting people in a simple cooperative task. Experiment results show that the ‘looking at the other’ gaze behavior outperforms the other gaze behaviors and indicates the degrees of perceived apologeticness and friendliness. Keywords: Communication robots; gaze; mistake; mitigation. (shrink)

We introduce the Easton collapse and show that the two-stage iteration of Easton collapses gives a model in which the successor of a regular cardinal carries a strongly saturated filter. This allows one to get a model in which many successor cardinals carry saturated filters just by iterating Easton collapses.

Determining the relationship between the entire brain structure and individual differences is important in extending healthy life expectancy, which can be affected by brain atrophy. The entire brain structure has been gradually known to be correlated not only with age but also with individual differences, such as quality of life, general intelligence, and lifestyle. However, little attention has been paid to the relationship between the entire brain structure and personal traits. We herein focused on one personal trait, namely spiritual growth, (...) and examined its relationship with the entire brain structure using two neuroimaging-derived measures, namely the gray matter Brain Healthcare Quotient, a measure of GM volume, and the fractional anisotropy Brain Healthcare Quotient, a measure of white matter integrity, in 229 healthy participants. The results indicated no significant relationship between the GM-BHQ and spiritual growth, but there was a significant positive correlation between the FA-BHQ and spiritual growth after controlling for age, sex, and body mass index with partial correlation analysis. Furthermore, multiple regression analysis revealed a significant positive correlation between the FA-BHQ and spiritual growth after controlling for physical characteristics, such as age, sex, and BMI, as well as other variables related to lifestyle that were collected using the Health-Promoting Lifestyle Profile. These results support the idea that there is a relationship between the entire WM brain structure and spiritual growth. Further studies are required to clarify the causal relationship between the entire WM brain structure and spiritual growth with some interventions to improve spiritual growth. Such studies will help extend healthy life expectancy from a new perspective of personal trait. (shrink)

The Abhidharmakosabha'ya, preserved at the Ethnographic Museum in Stockholm, is the second longest Abhidharma text in Uighur. The important Buddhist text was written in Sanskrit by Vasubandhu and translated into Chinese by Zhen Di (499-569 AD) and Xuan Zang (602-664 AD). Later during the Yuan Dynasty the text was translated from Chinese to Uighur on the basis of Xuan Zang's version of the original Sanskrit text. Masahiro Shogaito examines the Uighur version of the Abhidharmakosabha'ya and provides the Uighur text (...) in transcription and the English translation with the corresponding Chinese text on opposite pages. The volume contains additional commentaries, a glossary and the original manuscripts as facsimiles. (shrink)

We show that every MALL proof-structure [9] satisfies the property of softness, originally a categorical notion introduced by Joyal. Furthermore, we show that the notion of hereditary softness precisely captures Girard’s algebraic restriction of the technical condition on proof-structures. Relying on this characterization, we prove a MALL+Mix sequentialization theorem by a proof-theoretical method, using Girard’s notion of jump. Our MALL+Mix correctness criterion subsumes the Danos/Fleury-Retoré criterion [6] for MLL+Mix.

We first note that Gentzen's proof-reduction for his consistency proof of PA can be directly interpreted as moves of Kirby-Paris' Hydra Game, which implies a direct independence proof of the game . Buchholz's Hydra Game for labeled hydras is known to be much stronger than PA. However, we show that the one-dimensional version of Buchholz's Game can be exactly identified to Kirby-Paris' Game , by a simple and natural interpretation . Jervell proposed another type of a combinatorial game, by abstracting (...) Gentzen's proof-reductions and showed that his game is independent of PA. We show that this Jervell's game is actually much stronger than PA, by showing that the critical ordinal of Jervell's game is φω = ϵ0) in the Veblen hierarchy of ordinals. (shrink)

現代における重要テーマをめぐって重ねてきた言葉たちを結晶化した対談集。対談者:戸谷洋志、小松原織香、山口尚、永井玲衣.

In our former works, for a given concept of reduction, we study the following hypothesis: “For a random oracle A, with probability one, the degree of the one-query tautologies with respect to A is strictly higher than the degree of A.” In our former works (Suzuki in Kobe J. Math. 15, 91–102, 1998; in Inf. Comput. 176, 66–87, 2002; in Arch. Math. Logic 44, 751–762), the following three results are shown: The hypothesis for p-T (polynomial-time Turing) reduction is equivalent to (...) the assertion that the probabilistic complexity class R is not equal to NP; The hypothesis for p-tt (polynomial-time truth-table) reduction implies that P is not NP; The hypothesis holds for each of the following: disjunctive reduction, conjunctive reduction, and p-btt (polynomial-time bounded-truth-table) reduction. In this paper, we show the following three results: (1) Let c be a positive real number. We consider a concept of truth-table reduction whose norm is at most c times size of input, where for a relativized propositional formula F, the size of F denotes the total number of occurrences of propositional variables, constants and propositional connectives. Then, our main result is that the hypothesis holds for such tt-reduction, provided that c is small enough. How small c can we take so that the above holds? It depends on our syntactic convention on one-query tautologies. In our setting, the statement holds for all c < 1. (2) The hypothesis holds for monotone truth-table reduction (also called positive reduction). (3) Dowd (in Inf. Comput. 96, 65–76, 1992) shows a polynomial upper bound for the minimum sizes of forcing conditions associated with a random oracle. We apply the above result (1), and get a linear lower bound for the sizes. (shrink)

The theory of the appearance of the Absolute is the last theme of Fichte’s Science of Knowledge. Since he lectured the theory of appearance with that of truth in his Systemconcept of the Transcendentalphilosophy in 1804, he said that the Absolute exists, and that the Absolute appears. In the lecture in 1812, he explains the necessity of appearance, criticizing Spinoza’s Monismus. It is denied by the fact that a concept exists outside the only one substance, while the latter is thought (...) about. There is a Nonabsolute outside the Absolute. Fichte names it ›appearance‹, which is synonym with ›image‹ and ›scheme‹ of the Absolute. The appearance has a life to appear to itself. Because it is a concept and knowledge of the Absolute, it knows itself as such. Between two appearances is a difference, through which the manifold springs. The earlier question against Schelling’s philosophy of identity, how the finite can be deduced from the infinite or the Absolute, is solved here. Fichte calls the self-appearance of the appearance ›Seeing‹ and ›reflection‹. Also the ego as subject-object is born in it. The task of Science of Knowledge is to analyze it, through which the appearance appears to itself not only as appearing to itself, but also as appearing to itself as appearing to itself. Fichte calls this the formula of Science of Knowledge. In the appearance is a reflexibility, whose ground is the visibility of the Absolute, the absolute evidence or the light. Even the image-making act of ego is in fact that of the Absolute. The Absolute intuits itself. Ego, as a representant of it, should stand under the law of the Absolute and devote its freedom and will to this. Standing upon the will to obey the law Science of Knowledge can gain the total scope of knowledge and open the way to God and the morality.Die Lehre der Erscheinung des Absoluten ist der letzte Schritt der Entwicklung der Wissenschaftslehre bei Fichte. Nachdem er in seinem Systementwurf von 1804 die Erscheinungslehre neben die Wahrheitslehre gestellt hat, äußerte Fichte, »Das Absolute existiert« und »Das Absolute erscheint«. Im Vortrag von 1812 erklärt er die Notwendigkeit der Erscheinung des Absoluten in der Auseinandersetzung mit Spinozas Monismus. Dieser sei schon widerlegt, weil das Denken der Substanz als das Sein außerhalb derselben ist. Dies Nicht-Absolute heißt ›Erscheinung‹, welche als Bild oder Schema des Absoluten genommen wird. Die Erscheinung hat das Leben, sich selbst zu erscheinen. Da sie der Begriff oder das Wissen vom Absoluten ist, weiß sie zugleich sich selbst als solches. Zwischen zwei Erscheinungen ist eine Disjunktion, womit das Entspringen des Mannigfaltigen erklärt wird. Die früher gegen Schellings Identitätsphilosophie gerichtete Frage, wie aus dem Absoluten das Endliche abgeleitet werden könne, wird hier aufgelöst. Das Sicherscheinen der Erscheinung nennt Fichte ›Sehen‹ und ›Reflexion‹, und sieht die Aufgabe der Wissenschaftslehre in dessen Analyse. Dabei gehört diese selbst der Erscheinung an. In ihr erscheint die Erscheinung sich selbst als sich selbst erscheinend. Außerdem erscheint sie sich selbst als sich selbst erscheinend als sich selbst erscheinend, welches die Formel der Wissenschaftslehre ist. In ihr liegt die Reflexibilität, wodurch eben das Ich als Subjekt-Objekt entsteht. Dahinter aber ist die Sichtbarkeit des Absoluten, die absolute Evidenz oder das Licht. Die Bildungskraft des Ich ist in Wahrheit die des Absoluten. Das Absolute selbst schaut sich selbst an, und das Ich ist bloß sein Repräsentant. Es soll unter dem Gesetz des Absoluten stehen und seine Freiheit und den Willen diesem übertragen. Die Wissenschaftslehre macht den ganzen Umkreis des Wissens klar und öffnet den Weg zu Gott und zur Sittlichkeit, indem sie auf dem Willen als ihrem Standpunkt steht. (shrink)

This book is a collection of all the papers published in the special issue “Philosophy and Meaning in Life Vol.4: Selected Papers from the Pretoria Conference,” Journal of Philosophy of Life, Vol.12, No.1, 2022, pp.1-115. -/- Theorizing About Meaning in Life Cheshire Calhoun -/- Is It Possible to Say ‘Yes’ to Traumatic Experiences?: A Philosophical Approach to Human Suffering Masahiro Morioka -/- Why Beauvoir Is Not a Subjectivist about Meaning in Life Kiki Berk -/- Axiological Values Grounded in Basic (...) Motivational Dispositions: How to Be a Subjectivist about Meaning in Life Frank Martela -/- Pessimism, Political Critique, and the Contingently Bad Life Patrick O’Donnell -/- Reason, Luck, and Meaning: A Critique of the Moralist View of Meaning in Life Kazuki Watanabe. (shrink)

We shall give a direct proof of the independence result of a Buchholz style-Hydra Game on labeled finite trees. We shall show that Takeuti-Arai's cut-elimination procedure of $(\Pi^{1}_{1}-CA) + BI$ and of the iterated inductive definition systems can be directly expressed by the reduction rules of Buchholz's Hydra Game. As a direct corollary the independence result of the Hydra Game follows.

Let f ϵ Z [ X, Y ] be irreducible. We give a condition that there are only finitely many integers n ϵ Z such that f is reducible and we give a bound for such integers. We prove a similar result for polynomials with coefficients in polynomial rings. Both results are proved by, so-called, nonstandard arithmetic.

In this paper, we present a categorical model for Multiplicative Additive Polarized Linear Logic , which is the linear fragment of Olivier Laurent’s Polarized Linear Logic. Our model is based on an adjunction between reflective/coreflective full subcategories / of an ambient *-autonomous category . Similar structures were first introduced by M. Barr in the late 1970’s in abstract duality theory and more recently in work on game semantics for linear logic. The paper has two goals: to discuss concrete models and (...) to present various completeness theorems.As concrete examples, we present a hypercoherence model, using Ehrhard’s hereditary/anti-hereditary objects, a Chu-space model, a double gluing model over our categorical framework, and a model based on iterated double gluing over a *-autonomous category.For the multiplicative fragment of. (shrink)