In this paper, I show that the availability of what some authors have called the weak reading and the strong reading of donkey sentences with relative clauses is systematically related to monotonicity properties of the determiner. The correlation is different from what has been observed in the literature in that it concerns not only right monotonicity, but also left monotonicity (persistence/antipersistence). I claim that the reading selected by a donkey sentence with a double monotone determiner is in fact the one (...) that validates inference based on the left monotonicity of the determiner. This accounts for the lack of strong reading in donkey sentences with MON determiners, which have been neglected in the literature. I consider the relevance of other natural forms of inference as well, but also suggest how monotonicity inference might play a central role in the actual process of interpretation. The formal theory is couched in dynamic predicate logic with generalized quantifiers. (shrink)

没後20年、いま必要な歴史に裏打ちされた予見力、現実政治に提言する率直さ、道義性と理想主義。.

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。.

Tanabe Hajime, the Kyoto School philosopher of modern Japan, proposes a new idea of the relationship between religion and politics in terms of the triadic logic of species that is motivated by the religious moment of repentance. Even the state existence has the inherently radical evil as in the case of the individual person, due to its duality of the species level of being. This means that the state existence is on the way of actualization of the genus like universality, (...) while always involving in the regression into the past substrative being which prevents it from realizing its own universality. In other words, the state existence is not absolute as such but rather a balanced being between ideality and reality, absolute and relative. This entails that politics is in need of perpetual reformation in connection with the religious act of repentance for sin and evil deeply lurked in human beings from time immemorial. Tanabe’s Logic of Species as the dialectic elucidates the negative mediation of politics and religion from the metanoetic perspective and sheds a new light on the relation of world religion and politics today. (shrink)

ヘーゲル哲学研究の新しい領域として注目されつつある〈承認〉の概念をめぐって、独自の視角から検討をすすめてきた著者の成果を書き下ろす。.

Some formal properties of enriched systems of Lambek calculus with analogues of conjunction and disjunction are investigated. In particular, it is proved that the class of languages recognizable by the Lambek calculus with added intersective conjunction properly includes the class of finite intersections of context-free languages.

A critical examination of Japanese literary and art theories.

We propose a new game to strategically justify the constrained equal awards rule in claims problems. Our game is “procedurally fair” and “multilateral”. In addition, even if claimants cannot reach an agreement in any period, they can renegotiate in the next period. We show that, for each claims problem, the awards vector chosen by the constrained equal awards rule achieved at period 1 is the unique subgame perfect equilibrium outcome of the game.

It is proved that for any k, the class of classical categorial grammars that assign at most k types to each symbol in the alphabet is learnable, in the Gold (1967) sense of identification in the limit from positive data. The proof crucially relies on the fact that the concept known as finite elasticity in the inductive inference literature is preserved under the inverse image of a finite-valued relation. The learning algorithm presented here incorporates Buszkowski and Penn's (1990) algorithm for (...) determining categorial grammars from input consisting of functor-argument structures. (shrink)

Akama et al. [1] systematically studied an arithmetical hierarchy of the law of excluded middle and related principles in the context of first-order arithmetic. In that paper, they first provide a prenex normal form theorem as a justification of their semi-classical principles restricted to prenex formulas. However, there are some errors in their proof. In this paper, we provide a simple counterexample of their prenex normal form theorem [1, Theorem 2.7], then modify it in an appropriate way which still serves (...) to largely justify the arithmetical hierarchy. In addition, we characterize a variety of prenex normal form theorems by logical principles in the arithmetical hierarchy. The characterization results reveal that our prenex normal form theorems are optimal. For the characterization results, we establish a new conservation theorem on semi-classical arithmetic. The theorem generalizes a well-known fact that classical arithmetic is $\Pi _2$ -conservative over intuitionistic arithmetic. (shrink)

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 identify bar recursion on moduli of continuity as a fundamental notion of constructive mathematics. We show that continuous functions from the Baire space \ to the natural numbers \ which have moduli of continuity with bar recursors are exactly those functions induced by Brouwer operations. The connection between Brouwer operations and bar induction allows us to formulate several continuity principles on the Baire space stated in terms of bar recursion on continuous moduli which naturally characterise some variants of bar (...) induction. These principles state that a certain kind of continuous function from \ to \ admits a modulus of continuity with a bar recursor. The results for the Baire space are recast in the setting of the Cantor space \ using the notion of fan recursor, a bar recursor for binary trees. This yields characterisations of uniformly continuous functions on the Cantor space and fan theorem in terms of fan recursors. The results for the Cantor space hold over the extensional version of intuitionistic arithmetic in all finite types ), and those for the Baire space hold over \ extended with the type for Brouwer operations. Our work places Spector’s bar recursion in a proper context of Brouwer’s intuitionistic mathematics and clarifies the connection between bar recursion and bar induction. (shrink)

Along the line of Hirst‐Mummert and Dorais, we analyze the relationship between the classical provability of uniform versions Uni(S) of Π2‐statements S with respect to higher order reverse mathematics and the intuitionistic provability of S. Our main theorem states that (in particular) for every Π2‐statement S of some syntactical form, if its uniform version derives the uniform variant of over a classical system of arithmetic in all finite types with weak extensionality, then S is not provable in strong semi‐intuitionistic systems (...) including bar induction in all finite types but also nonconstructive principles such as Kőnig's lemma and uniform weak Kőnig's lemma. Our result is applicable to many mathematical principles whose sequential versions imply. (shrink)

Estrogen receptor α (ERα) is a ligand‐dependent transcription factor that regulates the expression of estrogen‐responsive genes. Approximately 70% of patients with breast cancer are ERα positive. Estrogen stimulates cancer cell proliferation and contributes to tumor progression. Endocrine therapies, which suppress the ERα signaling pathway, significantly improve the prognosis of patients with breast cancer. However, the development of de novo or acquired endocrine therapy resistance remains a barrier to breast cancer treatment. Therefore, understanding the regulatory mechanisms of ERα is essential to (...) overcome the resistance to treatment. This review focuses on the regulation of ERα expression, including copy number variation, epigenetic regulation, transcriptional regulation, and stability, as well as functions from the point of view post‐translational modifications. (shrink)

We investigate stationarity of types over models in simple theories. In particular, we show that in simple theories with finite SU-rank, any complete type over a model having Cantor-Bendixson rank is stationary.

Poppe r e nt i e nde l a r a c i ona l i da d e ntérminos de nuestra actitud intelectual.Nuestra racionalidad no es una facultad ni un don intelectual.No es al go dado a un i ndi vi duo, deacuerdo con él. Es una actitud que hemosadquirido de nuestra relación intelectualcon otros. Popper no usa “racionalismo”como un término filosófico que significaintelectualismo en oposición a empirismo.El artículo muestra claramente que Popperent i ende el r aci onal i (...) smo no como l agr a nde z a de l a r a z ón, s i no c omo l acomprensión de uno del límite de la razón.Sin embargo, surge una pregunta; ¿qué tanbien ha comprendido tal racionalista ellímite de su propio racionalismo? ¿Cómodebemos entender este límite? Popperafi rma que un raci onal i sta ha notadoel límite del racionalismo al prever elcarácter auto-destructivo del racionalismoc ompr e he ns i vo. A f i n de ha c e r má scomprensible su afirmación tenemos queexplicar el racionalismo comprehensiveque Popper aprehendió.Popper understands the rationality interms of our intellectual attitude. Ourrationality is neithera faculty nor an intellectual gift. It isnot something given to an individual,according to him. It is an attitude thatwe have acquired from our intellectualintercourse with others. Popper does notuse “rationalism” as a philosophical termthat means intellectualism in oppositionto empiricism.This paper clearly shows that Popperunde r s t a nds r a t i o na l i s m no t a s t heal mi ght i nes s of r eas on, but as one’ srealization of the limit of reason. However,there arises a question; how has such arationalist realized the limit of his ownrationalism? How we should understandthis limit? Popper asserts that a rationalisthas noticed the limit of rationalism byenvisaging the self-defeating character ofthe comprehensive rationalism. In order tomake more understandable his assertion,we must at first explain the comprehensiverationalism apprehended by Popper. (shrink)

On sait que Platon fait grand cas des êtres intelligibles en instaurant la théorie des Idées. Mais il n’est pas approprié de le considérer comme penseur qui néglige le rôle de l’apparence sensible. Ce philosophe demeure très sensible à la modalité par laquelle les phénomènes apparaissent dans le champ de notreperception. En distinguant deux types d’apparence : image et simulacre, il donne à l’image le rôle d’intermédiaire actif entre le sensible et l’intelligible. L’examen des modalités des actions humaines qui reçoivent (...) et créent des images, nous aide à voir comment Platon intègre la fonction des images dans la structure de sa philosophie. La réception et la création des images sont étroitement reliées et synthétisées pour former le système original de Platon, système dans lequel le fondement de la théorie des Idées relève d’un certain dynamisme de l’action humaine. Dans la recherche relative à la modalité de réception et de création des images, je porte mon attention sur l’usage platonicien du terme tupos qui exprime le principe de la conformité de l’image et de son modèle.Notamment dans la théorie de la formation des futurs gardiens de la cité idéale, le tupos fonctionne, comme un principe qui réglemente et oriente à plusieurs niveaux les activités de la mimèsis et de la poièsis qui portent sur les images. La réflexion sur cette fonction conductrice. (shrink)

A minimal formula is a formula which is minimal in provable formulas with respect to the substitution relation. This paper shows the following: (1) A β-normal proof of a minimal formula of depth 2 is unique in NJ. (2) There exists a minimal formula of depth 3 whose βη-normal proof is not unique in NJ. (3) There exists a minimal formula of depth 3 whose βη-normal proof is not unique in NK.

We shall prove the second incompleteness theorem via Kolmogorov complexity.

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.

As Hegel suggests, there is no philosophy apart from the history of philosophy. Each philosophy represents the spirit peculiar to its own period. Heidegger, too, holds that every philosophy is the sound of Being, and the history of philosophy is the history of Being. This is true for the Kyoto School philosophy of modern Japan represented by Kitaro Nishida, Hajime Tanabe, and Tetsuro Watsuji, who made to endeavor to construct a new synthesis of Western and Eastern philosophy in the critical, (...) confrontational, and creative ways in the given historical contexts. In particular, Tanabe attempts at the dialectical unification of Christianity and Buddhism in the last resort from the standpoint of Absolute Nothingness. As, in Whitehead’s conception of process, actuality is composed of the past objective being as the given data and the present subjective act of becoming, so it might be highly significant to analyze the constitutive elements of Tanabe’s system of thought from the historical and comparative contexts. (shrink)

Robots that incorporate the function of apologizing have emerged in recent years. This paper examines the moral permissibility of making robots apologize. First, I characterize the nature of apology based on analyses conducted in multiple scholarly domains. Next, I present a prima facie argument that robot apologies are not permissible because they may harm human societies by inducing the misattribution of responsibility. Subsequently, I respond to a possible response to the prima facie objection based on the interpretation that attributing responsibility (...) to a robot is analogous to having an attitude toward fiction. Then, I demonstrate that there are cases of robot apologies where the prima facie objection does not apply, by considering the following two points: (1) apology-related practices found in our human-to-human apologies, and (2) a difference in the degree of harm caused by robot failures and the resulting apologies. Finally, given the current norms governing our apology-related practices, I argue that some instances of making robots apologize are permissible, and I propose conducting critical robotics research questioning the validity of such norms. (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)