Savant syndrome and prime numbers Oliver Sacks reported that a pair of autistic twins had extraordinary number abilities and that they spontaneously generated huge prime numbers. Such abilities could contradict our understanding of human abilities. Sacks' report attracted widespread attention, and several researchers speculated theoretically. Unfortunately, most of the explanations in the literature are wrong. Here a correct explanation on prime number identification is provided. Fermat's little theorem is implemented in spreadsheet. Also, twenty years after the report, questionable aspects were (...) found in it. Extreme abilities became dubious. One possibility for the less extreme abilities is incomplete trial division. (shrink)

Das Problem der Intersubjektivitiit Intersubjektivität ist Husserl schon seit der Darstellung der Ideen I in Zusammenhang mit dem Problem der phiinomenologischen phänomenologischen Reduk tion sehr stark bewusst und wird, wie die neue VerOffentlichung Veröffentlichung 'Zur Phänome Phiinome nologie der Intersubjektivität'l Intersubjektivitiit'l ausdrücklich ausdrucklich zeigt, zeit seines Lebens in seinem Denken mit mehr oder weniger Intensitiit Intensität behandelt. Bekanntlich hat Husserl Hussed die Einfühlungslehre EinfUhlungslehre in seinem spiiten späten Versuch mit der 'Selbstobjektivation' 'Selbstobjektivation',, 'Selbstauslegung' des absoluten, anonymen, transzen 2 dentalen ego (...) erkliirt. erklärt. Gerade auf diesen Punkt konzentriert sich zutreffende Kritik und zeigt die Unvermeidbarkeit des transzendentalen Solipsismus; was als Grund für fUr echte echte Intersubjektivitiit Intersubjektivität gesucht gesucht wird, wird, niimlich nämlich die die Gleichursprunglich Gleichursprünglich keit keit von von Subjekten, Subjekten, fUhrt führt schliesslich schliesslich auf auf den den Weg der Radikalisierung der trans zendentalen Reduktion und der Erklärung Erkliirung mit der immanenten Zeitigung des transzendentalen ego in die 'einseitige Verlagerung des Gewichts auf ein konsti tuierendes Ur-Ich, dem kein ebenso ursprungliches ursprüngliches Du gegenübersteht, gegeniibersteht,...'3. (shrink)

A critical examination of Japanese literary and art theories.

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。.

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.

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)

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.

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)

We provide a fine‐grained analysis on the relation between König's lemma, weak König's lemma, and the decidable fan theorem in the context of constructive reverse mathematics. In particular, we show that double negated variants of König's lemma and weak König's lemma are equivalent to double negated variants of the general decidable fan theorem and the binary decidable fan theorem, respectively, over a nearly intuitionistic system containing a weak countable choice only. This implies that the general decidable fan theorem is not (...) equivalent to the binary decidable fan theorem in the absence of a strong countable choice. In addition, we introduce a principle which fills the gap between König's lemma and weak König's lemma, and show that König's lemma is equivalent to weak König's lemma plus this principle. We also solve several problems arising from the investigation. (shrink)

We systematically study several principles and give a principle which is weaker than disjunctive Markov’s principle. We also show that the principle is underivable and strictly weaker than MP∨ in certain extensions of the system EL of elementary analysis.

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)

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 refine the arithmetical hierarchy of various classical principles by finely investigating the derivability relations between these principles over Heyting arithmetic. We mainly investigate some restricted versions of the law of excluded middle, De Morgan's law, the double negation elimination, the collection principle and the constant domain axiom.

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)

We systematically study conservation theorems on theories of semi-classical arithmetic, which lie in-between classical arithmetic $\mathsf {PA}$ and intuitionistic arithmetic $\mathsf {HA}$. Using a generalized negative translation, we first provide a structured proof of the fact that $\mathsf {PA}$ is $\Pi _{k+2}$ -conservative over $\mathsf {HA} + {\Sigma _k}\text {-}\mathrm {LEM}$ where ${\Sigma _k}\text {-}\mathrm {LEM}$ is the axiom scheme of the law-of-excluded-middle restricted to formulas in $\Sigma _k$. In addition, we show that this conservation theorem is optimal in the (...) sense that for any semi-classical arithmetic T, if $\mathsf {PA}$ is $\Pi _{k+2}$ -conservative over T, then ${T}$ proves ${\Sigma _k}\text {-}\mathrm {LEM}$. In the same manner, we also characterize conservation theorems for other well-studied classes of formulas by fragments of classical axioms or rules. This reveals the entire structure of conservation theorems with respect to the arithmetical hierarchy of classical principles. (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.

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.

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)

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)