Proof-theoretical notions and techniques, developed on the basis of sentential/symbolic representations of formal proofs, are applied to Euler diagrams. A translation of an Euler diagrammatic system into a natural deduction system is given, and the soundness and faithfulness of the translation are proved. Some consequences of the translation are discussed in view of the notion of free ride, which is mainly discussed in the literature of cognitive science as an account of inferential efficacy of diagrams. The translation enables us to (...) formalize and analyze free ride in terms of proof theory. The notion of normal form of Euler diagrammatic proofs is investigated, and a normalization theorem is proved. Some consequences of the theorem are further discussed: in particular, an analysis of the structure of normal diagrammatic proofs; a diagrammatic counterpart of the usual subformula property; and a characterization of diagrammatic proofs compared with natural deduction proofs. (shrink)

One of the traditional applications of Euler diagrams is as a representation or counterpart of the usual set-theoretical models of given sentences. However, Euler diagrams have recently been investigated as the counterparts of logical formulas, which constitute formal proofs. Euler diagrams are rigorously defined as syntactic objects, and their inference systems, which are equivalent to some symbolic logical systems, are formalized. Based on this observation, we investigate both counter-model construction and proof-construction in the framework of Euler diagrams. We introduce the (...) notion of “counter-diagrammatic proof”, which shows the invalidity of a given inference, and which is defined as a syntactic manipulation of diagrams of the same sort as inference rules to construct proofs. Thus, in our Euler diagrammatic framework, the completeness theorem can be formalized in terms of the existence of a diagrammatic proof or a counter-diagrammatic proof. (shrink)

To investigate the relationship between logical reasoning and majority voting, we introduce logic with groups Lg in the style of Gentzen’s sequent calculus, where every sequent is indexed by a group of individuals. We also introduce the set-theoretical semantics of Lg, where every formula is interpreted as a certain closed set of groups whose members accept that formula. We present the cut-elimination theorem, and the soundness and semantic completeness theorems of Lg. Then, introducing an inference rule representing majority voting to (...) Lg, we introduce logic with majority voting Lv. Formalizing the discursive paradox in judgment aggregation theory, we show that Lv is inconsistent. Based on the premise-based and conclusion-based approaches to avoid the paradox, we introduce logic with majority voting for axioms Lva, where majority voting is applied only to non-logical axioms as premises to construct a proof in Lg, and logic with majority voting for conclusions Lvc, where majority voting is applied only to the conclusion of a proof in Lg. We show that both Lva and Lvc are syntactically complete and consistent, and we construct collective judgments based on the provability in Lva and Lvc, respectively. Then, we discuss how these systems avoid the discursive paradox. (shrink)

We extend natural deduction for first-order logic (FOL) by introducing diagrams as components of formal proofs. From the viewpoint of FOL, we regard a diagram as a deductively closed conjunction of certain FOL formulas. On the basis of this observation, we first investigate basic heterogeneous logic (HL) wherein heterogeneous inference rules are defined in the styles of conjunction introduction and elimination rules of FOL. By examining what is a detour in our heterogeneous proofs, we discuss that an elimination-introduction pair of (...) rules constitutes a redex in our HL, which is opposite the usual redex in FOL. In terms of the notion of a redex, we prove the normalization theorem for HL, and we give a characterization of the structure of heterogeneous proofs. Every normal proof in our HL consists of applications of introduction rules followed by applications of elimination rules, which is also opposite the usual form of normal proofs in FOL. Thereafter, we extend the basic HL by extending the heterogeneous rule in the style of general elimination rules to include a wider range of heterogeneous systems. (shrink)

Proof-theory has traditionally been developed based on linguistic (symbolic) representations of logical proofs. Recently, however, logical reasoning based on diagrammatic or graphical representations has been investigated by logicians. Euler diagrams were introduced in the eighteenth century. But it is quite recent (more precisely, in the 1990s) that logicians started to study them from a formal logical viewpoint. We propose a novel approach to the formalization of Euler diagrammatic reasoning, in which diagrams are defined not in terms of regions as in (...) the standard approach, but in terms of topological relations between diagrammatic objects. We formalize the unification rule, which plays a central role in Euler diagrammatic reasoning, in a style of natural deduction. We prove the soundness and completeness theorems with respect to a formal set-theoretical semantics. We also investigate structure of diagrammatic proofs and prove a normal form theorem. (shrink)

We introduce a simple inference system based on two primitive relations between terms, namely, inclusion and exclusion relations. We present a normalization theorem, and then provide a characterization of the structure of normal proofs. Based on this, inferences in a syllogistic fragment of natural language are reconstructed within our system. We also show that our system can be embedded into a fragment of propositional minimal logic.

This paper presents a polarized phase semantics, with respect to which the linear fragment of second order polarized linear logic of Laurent [15] is complete. This is done by adding a topological structure to Girard's phase semantics [9]. The topological structure results naturally from the categorical construction developed by Hamano—Scott [12]. The polarity shifting operator ↓ (resp. ↑) is interpreted as an interior (resp. closure) operator in such a manner that positive (resp. negative) formulas correspond to open (resp. closed) facts. (...) By accommodating the exponentials of linear logic, our model is extended to the polarized fragment of the second order linear logic. Strong forms of completeness theorems are given to yield cut-eliminations for the both second order systems. As an application of our semantics, the first order conservativity of linear logic is studied over its polarized fragment of Laurent [16]. Using a counter model construction, the extension of this conservativity is shown to fail into the second order, whose solution is posed as an open problem in [16]. After this negative result, a second order conservativity theorem is proved for an eta expanded fragment of the second order linear logic, which fragment retains a focalized sequent property of [3]. (shrink)

Girard introduced phase semantics as a complete set-theoretic semantics of linear logic, and Okada modified phase-semantic completeness proofs to obtain normal-form theorems. On the basis of these works, Okada and Takemura reformulated Girard’s phase semantics so that it became phase semantics for proof-terms, i.e., lambda-terms. They formulated phase semantics for proof-terms of Laird’s dual affine/intuitionistic lambda-calculus and proved the normal-form theorem for Laird’s calculus via a completeness theorem. Their semantics was obtained by an application of computability predicates. In this (...) paper, we first formulate phase semantics for proof-terms of second-order intuitionistic propositional logic by modifying Tait-Girard’s saturated sets method. Next, we prove the completeness theorem with respect to this semantics, which implies a strong normalization theorem. (shrink)

One influential positive argument for moral realism is the Explanatory Indispensability Argument. A crucial premise of this argument is the explanatory relevance of moral properties. On this premise, moral properties, such as wrongness, rightness, courage, and cowardice, are explanatorily indispensable to some empirical phenomena. Although there has been a lively debate on this premise, one crucial challenge to this thesis, what I call the Scientific Standard Challenge, has not been properly discussed. After explaining this challenge and a related concern, I (...) argue that in response to this central challenge, the proponents of the argument should take what I call the localist turn to defend the explanatory indispensability of moral properties. The localist turn encourages the defenders of moral explanations to be more sensitive to the nature of each moral explanation. For instance, some moral explanations are explanations of social matters, so the standards they need to meet are provided by relevant branches of the social sciences. On the other hand, some other moral explanations are about our psychology, so the theoretical standards those explanations need to meet should come from psychology. I illustrate how this localist project can be conducted in the case of the moral explanation that appeals to injustice. I argue that the field of comparative politics provides the theoretical standards moral explanations of institutional change need to meet. I shall then illustrate how a sophisticated moral explanation can meet those theoretical standards and how this moral explanation can be strong evidence of injustice’s explanatory indispensability. (shrink)

This book provides an overview of behavioral decision theory and related research findings. In brief, behavioral decision theory is a general term for descriptive theories to explain the psychological knowledge related to decision-making behavior. It is called a theory, but actually it is a combination of various psychological theories, for which no axiomatic systems, such as the utility theory widely used in economics, have been established; it is often limited to qualitative knowledge. However, as suggested in the studies of H. (...) A. Simon, who won the Nobel Prize for Economics in 1978, and D. Kahneman, who won the prize in 2002, the psychological methodology and knowledge of behavioral decision theory have been applied widely in such fields as economics, business administration, and engineering, and are expected to become more useful in the future. This book explains various behavioral decision theories related to decision-making processes. Numerous models have been proposed to explain the psychological processes related to such a selection of decision strategies, and this book also introduces some new models that are useful to explain decision-making processes. The book concludes with speculation about the future of modern behavioral decision theories while referring to their relation to fields associated with neuroscience, such as neuroeconomics, that have been developed in recent years. In addition, each chapter includes a bibliography that can be referred to when studying more details related to behavioral decision theory. Reading this book requires no advanced expertise; nonetheless, an introductory knowledge of psychology, business administration, and economics, and approximately a high school graduate’s level of mathematics should facilitate the reader’s comprehension of the content. (shrink)

明治時代の“知と行動の巨人”の思想に迫る!東洋大学創立者、妖怪博士、近代仏教復興の立役者...と獅子奮迅の活躍を見せた井上円了。その業績を支えた独自の世界観・人生観を原典に基づきながら解明。.

仏教復興への情熱と行動の足跡を丹念にたどり、この偉大な先達が哲学的に究明した仏教思想の全貌をあきらかにする。画期的円了論。.

インド、中国そして日本。古代から近代へと、東洋思想の核心を求めて。この世界は、実体的存在などなく、あらゆるものが互いに関係し合って存在している。ではそこで自己とはいかなる存在で、どのようにあるべきなの か。唯識の事的世界観から華厳の事事無礙法界へ、さらに空海の人人無礙の曼荼羅、そして西田の「個物の哲学」へ。東洋の大地にそびえたつ哲学の連峰を縦横に踏破し、その叡智の真髄を未来に向けて照らし出す壮大な書 。.

Abstract“The wrongness of Albert's action causally explains why Jane judged that his action was wrong”. This type of causal moral explanation has been extensively discussed in the recent metaethical literature. This paper motivates the following claims about this type of moral explanation. First, a typical defence of this type of moral explanation suggested in the literature does not work because it predicts inaccurate modal information. Second, focusing on different aspects of the ways moral judgements are generated provides better chances for (...) the defender of this type of moral explanation. Third, the strategy mentioned in the previous point leads us to the following alternative evaluative explanation: The property of being a harmful action explains a recognisable pattern of moral judgements observed in the relevant empirical studies. One crucial implication the paper alludes to is a localist approach to the debates concerning moral realism: We should consider each moral property's ontological genuineness separately, referring to specific empirical findings that are particularly relevant to the target moral property in question. Such a localist approach can provide solid resources for realists to respond to various anti‐realist challenges, such as an influential evolutionary debunking argument. (shrink)

In this paper, using Mark Schroeder’s (2008a) expressivist semantic framework for normative language as a case study, I will identify difficulties that even an expressivist semantic theory capable of addressing the Frege-Geach problem will encounter in handling the logical possibility of moral dilemmas. To this end, I will draw on a classical puzzle formulated by McConnell (1978) that the logical possibility of moral dilemmas conflicts with some of the prima facie plausible axioms of the standard deontic logic, which include obligation (...) implies permission. On the tentative assumption that proponents of ethical expressivism should be generally committed to securing the logical possibility of moral dilemmas in their semantic theories, I will explore whether and how expressivists can successfully invalidate obligation implies permission within the framework developed by Schroeder. The case study eventually reveals that this can indeed be a hard task for expressivists. Generalizing from the case study, I will suggest that the source of the difficulty ultimately lies in the mentalist assumption of the expressivist semantic project that the logico-semantic relations exhibited by normative sentences should be modeled in terms of the psychological attitudes that speakers express by uttering them. My final goal will be to show that the difficulty expressivists face in dealing with the logical possibility of moral dilemmas is a reflection of the more general problem that their commitment to the mentalist assumption prevents them from flexibly adopting or dropping axioms in their semantic theories to get the right technical results. (shrink)

進化論・国家有機体説から生命主義・歴史への回帰まで、デモクラシーと煩悶の時代における「国体」の地平.

We develop intuitionistic public announcement logic over intuitionistic \({\textbf{K}}\), \({{\textbf{K}}}{{\textbf{T}}}\), \({{\textbf{K}}}{{\textbf{4}}}\), and \({{\textbf{S}}}{{\textbf{4}}}\) with distributed knowledge. We reveal that a recursion axiom for the distributed knowledge is _not_ valid for a frame class discussed in [ 12 ] but valid for the restricted frame class introduced in [ 20, 26 ]. The semantic completeness of the static logics for this restricted frame class is established via the concept of pseudo-model.

U ovom radu, koristeći Mark Schroederov (2008a) semantički okvir za ekspresivistički normativni jezik kao studiju slučaja, identificirat ću poteškoće s kojima će se čak i ekspresivistička semantička teorija sposobna za rješavanje Frege-Geach problema susresti pri objašnjenju logičke mogućnosti moralnih dilema. U tu svrhu, oslonit ću se na klasičnu zagonetku koju je formulirao McConnell (1978)a pokazuje da se logička mogućnost moralnih dilema sukobljava s nekim od naizgled opravdanih aksioma standardne deontičke logike, među kojima je i aksiom da obaveza implicira dopuštenost. Na (...) temelju tentativne pretpostavke da zastupnici etičkog ekspresivizma trebaju općenito biti posvećeni osiguravanju logičke mogućnosti moralnih dilema u svojim semantičkim teorijama, istražit ću da li i kako ekspresivisti mogu uspješno opovrgnuti aksiom da obaveza implicira dopuštenje unutar okvira koji je razvio Schroeder. Studija slučaja konačno otkriva da to može biti zaista težak zadatak za ekspresiviste. Generalizirajući iz studije slučaja, sugerirat ću da izvor poteškoće leži u mentalističkoj pretpostavci ekspresivističkog semantičkog projekta da bi logičko-semantički odnosi prikazani normativnim rečenicama trebali biti modelirani pomoću psiholoških stavova koje govornici izražavaju izgovarajući ih. Moj konačni cilj će biti pokazati da je poteškoća s kojom se ekspresivisti susreću u suočavanju s logičkom mogućnosti moralnih dilema odraz općeg problema da njihova predanost mentalističkoj pretpostavci sprječava fleksibilno usvajanje ili odbacivanje aksioma u njihovim semantičkim teorijama kako bi dobili ispravne tehničke rezultate. (shrink)

The most famous chapter of Montesquieu’s _ The Spirit of the Laws _ (1748), Book XI, Chapter 6, 'On the constitution of England,' was an important i nspiration to the creators of modern constitutions, to which they often referred. However, as a result of scholarly focus on the political institutions discussed in this book, Montesquieu’s economic analysis has been woefully neglected. In order to correct this scholarly imbalance, this paper will elucidate the essential significance of Montesquieu’s comparison between the constitution (...) of modern England and that of ancient Rome in Book XI of _ The Spirit of the Laws _ ; inextricable relationship between military and political institutions on the one hand, and the transfer and distribution of wealth on the other. To argue this point, this paper will focus on Montesquieu’s other writings in the same year and shortly after the publication of _ The Spirit of the Laws _ : the revised edition in 1748 of _ The Considerations on the Causes of the Greatness of t... _. (shrink)

人道的介入がもたらす非人道性、対テロ戦争における標的殺害の是非、平和構築や民主化の直面する矛盾―現代の国際社会が直面する、戦争と平和をめぐる「道義的難問」に挑む。.