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}.

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)

The weakly compact reflection principle\\) states that \ is a weakly compact cardinal and every weakly compact subset of \ has a weakly compact proper initial segment. The weakly compact reflection principle at \ implies that \ is an \-weakly compact cardinal. In this article we show that the weakly compact reflection principle does not imply that \ is \\)-weakly compact. Moreover, we show that if the weakly compact reflection principle holds at \ then there is a forcing extension preserving (...) this in which \ is the least \-weakly compact cardinal. Along the way we generalize the well-known result which states that if \ is a regular cardinal then in any forcing extension by \-c.c. forcing the nonstationary ideal equals the ideal generated by the ground model nonstationary ideal; our generalization states that if \ is a weakly compact cardinal then after forcing with a ‘typical’ Easton-support iteration of length \ the weakly compact ideal equals the ideal generated by the ground model weakly compact ideal. (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).

We give simple proofs of the Singular Cardinal Hypothesis from the Weak Reflection Principle and the Fodor-type Reflection Principle which do not use better scales.

It is known that there is a close relation between Prikry forcing and the iteration of ultrapowers: If U is a normal ultrafilter on a measurable cardinal κ and 〈Mn, jm,n | m ≤ n ≤ ω〉 is the iteration of ultrapowers of V by U, then the sequence of critical points 〈j0,n | n ∈ ω〉 is a Prikry generic sequence over Mω. In this paper we generalize this for normal precipitous filters.

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)

The forcing method is a powerful tool to prove the consistency of set-theoretic assertions relative to the consistency of the axioms of set theory. Laver’s theorem and Bukovský’s theorem assert that set-generic extensions of a given ground model constitute a quite reasonable and sufficiently general class of standard models of set-theory.In Sects. 2 and 3 of this note, we give a proof of Bukovsky’s theorem in a modern setting ). In Sect. 4 we check that the multiverse of set-generic extensions (...) can be treated as a collection of countable transitive models in a conservative extension of ZFC. The last section then deals with the problem of the existence of infinitely-many independent buttons, which arose in the modal-theoretic approach to the set-generic multiverse by Hamkins and Loewe :1793–1817, 2008). (shrink)

This note concerns the model theoretic properties of logics extending the first-order logic with monadic second-order variables equipped with the stationarity quantifier. The eight variations of the strong downward Löwenheim–Skolem Theorem down to <ℵ2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$<\aleph _2$$\end{document} for this logic with the interpretation of second-order variables as countable subsets of the structures are classified into four principles. The strongest of these four is shown to be equivalent to the conjunction of CH and the (...) Diagonal Reflection Principle for internally clubness of S. Cox. We show that a further strengthening of this SDLS and its variations follow from the Game Reflection Principle of B. König and its generalizations. (shrink)

Continuing, we study the Strong Downward Löwenheim–Skolem Theorems of the stationary logic and their variations. In Fuchino et al. it has been shown that the SDLS for the ordinary stationary logic with weak second-order parameters \. This SDLS is shown to be equivalent to an internal version of the Diagonal Reflection Principle down to an internally stationary set of size \. We also consider a version of the stationary logic and show that the SDLS for this logic in internal interpretation (...) \\) for reflection down to \ is consistent under the assumption of the consistency of ZFC \ “the existence of a supercompact cardinal” and this SDLS implies that the continuum is weakly Mahlo. These three “axioms” in terms of SDLS are consequences of three instances of a strengthening of generic supercompactness which we call Laver-generic supercompactness. Existence of a Laver-generic supercompact cardinal in each of these three instances also fixes the cardinality of the continuum to be \ or \ or very large respectively. We also show that the existence of one of these generic large cardinals implies the “\” version of the corresponding forcing axiom. (shrink)

『日本唯物論史』などで知られるわが国の唯物論哲学の開拓者・永田廣志の生涯をまとめ、その理論活動の意義を解明。哲学研究者と在野の郷土史家との共同研究が生み出した成果。本邦初公開の貴重な資料や秘蔵写真も多 数紹介。.

哲学者・古在由重がひとりの同時代人として、戦争に突き進み拡大する戦中、そして平和と民主主義を希求する戦後のなかで、何を学び、考え、仲間たちとどう交遊・談話し、どう生き、闘ったか。膨大な「古在由重文庫」 (藤沢市湘南大庭市民図書館所蔵)―古在の蔵書・著作はもちろん、原稿メモ、講義テープ、日記・手帳、書簡、新聞スクラップなど―ならびに関係者の著作・文章を渉猟し、さらに多数の人々の聞き取りなど六年をかけて 取材・執筆し、時代に正面から立ち向かった哲学者の実像に迫る力作。.

ウィトゲンシュタインの言語ゲームと龍樹の空思想を軸に、無明=実在論を反実在論に転ずれば、仏教思想は相貌を一変し、和辻哲郎の説く「縁起‐内‐存在」の倫理の哲学史的意義も鮮明になる。本書の透徹した言葉を熟 読玩味するときひらかれる新しい世界像にあなたは驚くに違いない。.

dai 1-kan. Ningen, kyōiku ga umarekawaru tame -- dai 2-kan. Ningen to no deai, kyōiku to no deai -- dai 3 kan. Ningenrashiku naru tedate -- dai 4-kan. Jinrui no kibō, osanago -- dai 5-kan. Shishū, ushinawareta kisetsu o motomete -- dai 6-kan. Aru mazushiki shōgai no kiroku -- [7] Kyōiku to kyōikugaku.

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.

敗戦、そして戸坂獄死から70年。1930年代、反戦運動が特高警察に根こそぎ弾圧されていくなかで、6年間にわたってしたたかに抵抗を続けた、世界に例のない文化組織「唯物論研究会」。戸坂潤をはじめ、この唯研 に集う若き知識人たちは、ファシズムが吹き荒れる下でも、人生を楽しみ、仲間と交わり、好戦イデオロギーに抗い続け、のちに戦後の民主主義運動の芽となっていった。.

現代を生き抜くための武器としての哲学を、西野カナ、ミスチル、いきものがかり等Jポップの歌詞を題材に、気鋭の哲学者が説く。.

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)

新しい社会科学の構築へ。来たるべき社会の基礎となる社会科学的方法論の課題を、第一線で活躍する十二名が「思想学」の観点から論じる。自由思想、啓蒙思想から神学、経済学まで多彩な視座より先哲の歩みを分析し、 思想研究の未来を探る充実の書。.

This article discusses what constituted Japan's conception of the world order, by analyzing political discourse of international order in modern Japan. It has been generally assumed that the Japanese vision of international order in the pre-World War II years was dominated by a belief in the supremacy of the sovereign state. Contrary to the conventional supposition, this paper will argue that modern Japan actually abounded in discourses of transnationalism, and that most of them cannot be seen as the product of (...) liberal ideas but rather the result of an unstable image of the sovereign state system. Surveying the historical development of political discourse of sovereignty and colonial administration in modern Japan, the way in which the ambivalence of Japanese transnationalism had affected the theoretical construction of the international order will be elucidated. Keeping in mind that previous studies on the genealogy of international relations have focused exclusively on the paradigmatic debate over the League of Nations, this article will also pay more attentions to the fact that rearrangement of empire had occupied the significant place in building the image of the world order. Based on the historical considerations mentioned above, the conclusion will offer generalized consideration of what constituteｄ Japan's conception of the world order. (shrink)

Abstract:Pedro Erber discusses with Naoki Sakai the history of Heidegger's influence on philosophy in Japan.