Some principles weaker than Markov’s principle.Makoto Fujiwara,Hajime Ishihara &Takako Nemoto -2015 -Archive for Mathematical Logic 54 (7-8):861-870.detailsWe 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 Formalization of Model-Theoretic Proofs of Gödel's Theorems.Makoto Kikuchi &Kazuyuki Tanaka -1994 -Notre Dame Journal of Formal Logic 35 (3):403-412.detailsWithin 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.
Shōnin to jiyū: Hēgeru jissen tetsugaku no saikōsei.Makoto Takada -1994 - Tōkyō: Miraisha.details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。.
A strategic justification of the constrained equal awards rule through a procedurally fair multilateral bargaining game.Makoto Hagiwara &Shunsuke Hanato -2020 -Theory and Decision 90 (2):233-243.detailsWe 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.
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Prenex normal form theorems in semi-classical arithmetic.Makoto Fujiwara &Taishi Kurahashi -2021 -Journal of Symbolic Logic 86 (3):1124-1153.detailsAkama 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)
Weak vs. strong Readings of donkey sentences and monotonicity inference in a dynamic setting.Makoto Kanazawa -1994 -Linguistics and Philosophy 17 (2):109 - 158.detailsIn 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)
Religion and the State from Tanabe’s Dialectical Perspective.Makoto Ozaki -2018 -Proceedings of the XXIII World Congress of Philosophy 61:129-133.detailsTanabe 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)
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A Note on Boolos' Proof of the Incompleteness Theorem.Makoto Kikuchi -1994 -Mathematical Logic Quarterly 40 (4):528-532.detailsWe 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.
The Lambek calculus enriched with additional connectives.Makoto Kanazawa -1992 -Journal of Logic, Language and Information 1 (2):141-171.detailsSome 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.
König's lemma, weak König's lemma, and the decidable fan theorem.Makoto Fujiwara -2021 -Mathematical Logic Quarterly 67 (2):241-257.detailsWe 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)
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Conservation Theorems on Semi-Classical Arithmetic.Makoto Fujiwara &Taishi Kurahashi -2023 -Journal of Symbolic Logic 88 (4):1469-1496.detailsWe 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)
Generalizations of gödel’s incompleteness theorems for ∑N-definable theories of arithmetic.Makoto Kikuchi &Taishi Kurahashi -2017 -Review of Symbolic Logic 10 (4):603-616.detailsIt 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)
Relation Dynamique entre Image et Forme dans la Pensée de Platon.Makoto Sekimura -2008 -Proceedings of the Xxii World Congress of Philosophy 12:71-77.detailsOn 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)
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They Ought to Do This, But They Can’t.Makoto Suzuki -2008 -Proceedings of the Xxii World Congress of Philosophy 10:409-417.detailsWe tend to think every ought statement implies that an actual agent can comply. However, our uses of “ought” suggest that some ought statements fail to have this implication: it is possible that the actual agent ought to do something she has no chance of accomplishing even if she intends to do so. Rather they imply that if the agent and her circumstances were defect-free, she could and would perform the prescribed action. There are two types of evaluation for ought (...) statements. One type of evaluation addresses the question of what to do given the agent’s peculiar capacity and condition. The point of this evaluation is giving personalized action guidance, and so recommends only what the actual agent can do under the actual condition. Another type of evaluation addresses a different question, that of what to do as a type of agents. The point of this evaluation is the coordination of individuals by selecting a shared norm for them: the standard that prescribes all of them to perform the same action and classifies for all of them the same traits as defect. This is why it endorses the ought statements that some actual agents cannot comply with, but that a normal agent could and would do so under normal conditions. (shrink)
Bushidō kō: kenka, katakiuchi, bureiuchi = Hinc omne principivm.ShinkoTaniguchi -2007 - Tōkyō: Hatsubaimoto Kadokawa Gurūpu Paburisshingu.details江戸時代、喧嘩をした者は、喧嘩両成敗法により両成敗になったという通念は、従来「理非を論ぜず」を「理由の如何を問わず」と解釈されてきたことによる。しかし、実際の裁判記録では、理不尽な実力行使に対する自己 防衛の場合は無罪とされることも多く、異なる身分の喧嘩では武士により重い罰が与えられていた。一方、百姓・町人に対する武士の横暴として見られがちな無礼討ちは、武士にとっては名誉と身分秩序を守るための義務で あった。武士による喧嘩・敵討・無礼討ちの豊富な事例を通して、近世社会の身分秩序意識、「家」の名誉、武士が考える武士道を再考する。.
Retroactive Justice: Trials for Human Rights Violations Under a Prior Regime.Makoto Usami -2001 - In Burton M. Leiser & Tom Campbell,Human Rights in Philosophy & Practice. Ashgate Publishing. pp. 423--442.detailsIn the transition from a repressive to a democratic society, the successor government faces the problem of how to deal with grave human rights violations such as killings and torture committed under its predecessor. This paper analyzes the dilemma a new government may encounter when it attempts to prosecute and punish those found responsible. On one hand, trials of chargeable officers may be able to prevent human rights abuses in the future and to facilitate instituting or restoring democracy. On the (...) other, in the case that there were no legal rules definitively prohibiting the abuses committed by these officers, the trials require ex post facto laws, which breach the principle of nulla poena sine lege, and more generally violate the rule of law. These retroactive laws not only break legal predictability but treat individuals unfairly. After identifying both the need for, and the legal and political losses incurred by such criminal trials, the author examines the claims that international law resolves the dilemma of retroactive justice or that prosecution is justified as a fulfillment of international obligation. Then the author refers to this dilemma as “dirty hands” to characterize a circumstance in which one cannot avoid using the wrong means to obtain the best ends. Such characterization has normative implications for three aspects of trials: the process of enacting retroactive laws and the process of conducting the trials; the choice of other possible legal remedies; and the principles related to reactions in the international community. (shrink)
On the strength of marriage theorems and uniformity.Makoto Fujiwara,Kojiro Higuchi &Takayuki Kihara -2014 -Mathematical Logic Quarterly 60 (3):136-153.detailsKierstead showed that every computable marriage problem has a computable matching under the assumption of computable expanding Hall condition and computable local finiteness for boys and girls. The strength of the marriage theorem reaches or if computable expanding Hall condition or computable local finiteness for girls is weakened. In contrast, the provability of the marriage theorem is maintained in even if local finiteness for boys is completely removed. Using these conditions, we classify the strength of variants of marriage theorems in (...) the context of reverse mathematics. Furthermore, we introduce another condition that also makes the marriage theorem provable in, and investigate the sequential and Weihrauch strength of marriage theorems under that condition. (shrink)
Refining the arithmetical hierarchy of classical principles.Makoto Fujiwara &Taishi Kurahashi -2022 -Mathematical Logic Quarterly 68 (3):318-345.detailsWe 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.