This paper shows that the inhabitation problem in the lambda calculus with negation, product, polymorphic, and existential types is decidable, where the inhabitation problem asks whether there exists some term that belongs to a given type. In order to do that, this paper proves the decidability of the provability in the logical system defined from the second-order natural deduction by removing implication and disjunction. This is proved by showing the quantifier elimination theorem and reducing the problem to the provability in (...) propositional logic. The magic formulas are used for quantifier elimination such that they replace quantifiers. As a byproduct, this paper also shows the second-order witness theorem which states that a quantifier followed by negation can be replaced by a witness obtained only from the formula. As a corollary of the main results, this paper also shows Glivenko’s theorem, Double Negation Shift, and conservativity for antecedent-empty sequents between the logical system and its classical version. (shrink)

This article aims to discuss how Lucretius arranges the four ‘roots’ at the end of successive lines of verse in the De rerum natura (henceforth, DRN) (1.5–8). In this passage Lucretius, alluding to Empedocles, puts the words in such an order that one can see the layers of the world by a vertical reading. In the same passage, Lucretius imitates the very beginning of Homer's ecphrasis (Il. 18.478–85), which the allegorical tradition will explain as an image of the world, related (...) to Empedoclean theory. The article also discusses the allusion to Daedalus by means of the adjective daedalus in DRN 1.7 (daedala tellus), which could be related to both Empedocles and Homer. This adjective is a keyword for discussing the image produced by the words on the written page. (shrink)

環境問題が生じる存在論的根拠とは―。本書は、環境問題を存在論的問題として捉え、空間、時間、言語論の観点から、そして労働と環境の関連、環境倫理の存在論的根拠について論じる。.

A proof is given for the theorem that at least one bound state exists in a one-dimensional attractive potential however weak it may be. The proof is constructive in that it provides a method to explicitly solve the eigenvalue problem for the eigenvalues as well as the eigenfunctions. The method is well suited to precise numerical calculations.

In this paper we will study a formal system of intuitionistic modal predicate logic. The main result is its semantic completeness theorem with respect to algebraic structures. At the end of the paper we will also present a brief consideration of its syntactic relationships with some similar systems.

Minami–Sakai :883–898, 2016) investigated the cofinal types of the Katětov and the Katětov–Blass orders on the family of all \ ideals. In this paper we discuss these orders on analytic P-ideals and Borel ideals. We prove the following:The family of all analytic P-ideals has the largest element with respect to the Katětov and the Katětov–Blass orders.The family of all Borel ideals is countably upward directed with respect to the Katětov and the Katětov–Blass orders. In the course of the proof of (...) the latter result, we also prove that for any analytic ideal \ there is a Borel ideal \ with \. (shrink)

We investigate how weak square principles are denied by Chang’s Conjecture and its generalizations. Among other things we prove that Chang’s Conjecture does not imply the failure of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square_{\omega_1, 2}}$$\end{document}, i.e. Chang’s Conjecture is consistent with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square_{\omega_1, 2}}$$\end{document}.

This book explores the contributions of East Asian traditions, particularly Buddhism and (Euro)Daoism, to environmental philosophy. It critically examines the conceptions of human responsibility toward nature and across time presented within these traditions as well as in European philosophy. The volume rethinks human relationships to the natural world by focusing on three main themes: Daoist and Eurodaoist perspectives on nature, human responsibility toward nature, and Buddhist perspectives on life and nature. By way of discussing East Asian traditions and European thinkers, (...) this collection reveals that the impact of humanity on the environment is shaped not only by distinctive modes of economic production, but also by cultural beliefs and practices. Representing a unique constellation of environmental and intercultural philosophy, the contributions present systematic approaches to the global need for cultivating environmental responsibility across cultures and generations to address the political, ethical, and aesthetic challenges arising from humanity’s transformative impact on the natural world. (shrink)

The primary objective of this anthology is to make intergenerational justice an issue for intercultural philosophy, and, conversely, to allow the latter to enrich the former. In times of large-scale environmental destabilization, fair- ness between generations is an urgent issue of justice across time, but it is also a global issue of justice across geographical and nation-state borders. This means that the future generations envisioned by the currently living also cross these borders. Thus, different philosophical cultures and traditions of thought (...) should converse to re ect on what is fair to future people. In the remainder of this introduction, we will detail these claims and give an overview of the volume’s chapters. (shrink)

We study the relationship between the semistationary reflection principle and stationary reflection principles. We show that for all regular cardinals Λ ≥ ω₂ the semistationary reflection principle in the space [Λ](1) implies that every stationary subset of $E_{\omega}^{\lambda}\coloneq \{\alpha \in \lambda \,|\,{\rm cf}(\alpha)=\omega \}$ reflects. We also show that for all cardinals Λ ≥ ω₃ the semistationary reflection principle in [Λ](1) does not imply the stationary reflection principle in [Λ](1).