Although dual-process or divided-mind models of self-control dominate the literature, they suffer from empirical and conceptual challenges. We propose an alternative approach, suggesting that self-control can be characterized by a fragmented part versus integrated whole dynamic. Whereas responses to events derived from fragmented parts of the mind undermine self-control, responses to events derived from integrated wholes enhance self-control. We review empirical evidence from psychology and related disciplines that support this model. We, moreover, discuss the implications of this work for psychology, (...) neuroscience, economics, and philosophy. In particular, we highlight how this model addresses many of the conceptual and empirical short-comings of divided-mind models. We suggest that understanding self-control as the interplay between fragmented parts versus integrated wholes, moreover, provides novel insights and testable new hypotheses. (shrink)

In this paper, I consider a philosophical model of self-control recently developed by Chandra Sripada and inspired by current dual-process models in both the sciences of the mind and philosophy. Sripada argues that the mind is bifurcated into two motivational systems that correspond to Emotion and Reason and that to exercise self-control is to act in accordance with reason when it comes into conflict with emotion. I argue that Sripada’s model rests on two false assumptions, that emotions are cognitively impenetrable (...) and that self-control is always about taming our emotions. Based on these arguments, I conclude that our capacity for self-control cannot be understood in terms of a divided-mind and consider a structural model of self-control recently developed by Kentaro Fujita. (shrink)

A new research project has, quite recently, been launched to clarify how different, from systems in second order number theory extending ACA0, those in second order set theory extending NBG are. In this article, we establish the equivalence between Δ01-LFP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta^1_0\mbox{\bf-LFP}}$$\end{document} and Δ01-FP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta^1_0\mbox{\bf-FP}}$$\end{document}, which assert the existence of a least and of a fixed point, respectively, for positive elementary operators. Our proof also shows (...) the equivalence between ID1 and ID^1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\widehat{\it ID}_1}$$\end{document}, both of which are defined in the standard way but with the starting theory PA replaced by ZFC. (shrink)

We define and investigate a uniformly locally o-minimal structure of the second kind in this paper. All uniformly locally o-minimal structures of the second kind have local monotonicity, which is a local version of monotonicity theorem of o-minimal structures. We also demonstrate a local definable cell decomposition theorem for definably complete uniformly locally o-minimal structures of the second kind. We define dimension of a definable set and investigate its basic properties when the given structure is a locally o-minimal structure which (...) admits local definable cell decomposition. (shrink)

Consider a definably complete uniformly locally o-minimal expansion of the second kind of a densely linearly ordered abelian group. Let $f:X \rightarrow R^n$ be a definable map, where X is a definable set and R is the universe of the structure. We demonstrate the inequality $\dim ) \leq \dim $ in this paper. As a corollary, we get that the set of the points at which f is discontinuous is of dimension smaller than $\dim $. We also show that the (...) structure is definably Baire in the course of the proof of the inequality. (shrink)

By forcing, we give a direct interpretation of into Avigad's. To the best of the author's knowledge, this is one of the simplest applications of forcing to “real problems”.

Roelcke non-precompactness, simplicity, and non-amenability of the automorphism group of the Fraïssé limit of finite Heyting algebras are proved among others.

The conservativeness argument poses a dilemma to deflationism about truth, according to which a deflationist theory of truth must be conservative but no adequate theory of truth is conservative. The debate on the conservativeness argument has so far been framed in a specific formal setting, where theories of truth are formulated over arithmetical base theories. I will argue that the appropriate formal setting for evaluating the conservativeness argument is provided not by theories of truth over arithmetic but by those over (...) subject matters ‘richer’ than arithmetic, such as set theory. The move to this new formal setting provides deflationists with better defence and brings a broader perspective to the debate. (shrink)

When I deliver an introductory lecture on Japanese Philosophy, I always raise the following question: Is it appropriate to modify the word philosophy with an adjective such as Japanese? Philosophy is, after all, a discipline that addresses universal problems, and so transcends the restrictions implied in geographical descriptors. However, as Kuki Shūzō argues in his essay “Tokyo and Kyoto,” I think that this is only part, and not the whole truth of the matter.One’s thinking takes place within the framework of (...) one’s cultural heritage, and the different nuances of each of the words one uses can influence how one thinks. It is for this reason that every philoso­phy has its own unique character. As Otto Pöggeler suggests, there is something about the thought of Japanese philosophers such as Nishida Kitarō and Nishitani Keiji that does not fit easily into the framework of “philosophy” in the Western tradition. This is a conse­quence of the fact that they did not simply passively adopt, but rather attempted to critically challenge Western philosophy. I suppose that their grounding in Japanese and other Eastern traditions contributed to their critical challenge of Western philosophy. And I submit that there is a strong tendency in traditional East Asian thought to not simply grasp things within a presupposed framework of “knowledge,” but rather, since “knowledge” itself is understood to be a certain kind of restriction, to return to its roots.Needless to say, neither Nishida’s nor Nishitani’s thought is merely a philosophical reiteration of such traditional East Asian teachings. Nevertheless, we can say that the East Asian idea that knowledge is at root something restrictive lives on in their thinking. The radical­ity of Nishida’s and Nishitani’s thought can be understood to lie in the manner in which they cast light on the limits of the “knowledge” pursued by Western philosophy, problematizing the basis on which this knowledge is established as well as the framework it sets up.I think that the “character” of this or that philosophy arises from such different ways of seeing things and different attitudes toward “knowledge.” It is crucial to point out, however, that the gaps resulting from these differences need not become hindrances for philosophical thinking. Indeed, I think that the existence of such gaps, rather than hindering “dialogues” between different philosophies, is precisely what enables them to be meaningful. This is also what I have in mind when I stress the importance of dialogue in my lectures on Japanese philoso­phy. It is, after all, the creative dialogue engendered in this manner that enables philosophy to progress along its path of radical inquiry. (shrink)

We consider locally o-minimal structures possessing tame topological properties shared by models of DCTC and uniformly locally o-minimal expansions of the second kind of densely linearly ordered abelian groups. We derive basic properties of dimension of a set definable in the structures including the addition property, which is the dimension equality for definable maps whose fibers are equi-dimensional. A decomposition theorem into quasi-special submanifolds is also demonstrated.

We first show that the projection image of a discrete definable set is again discrete for an arbitrary definably complete locally o‐minimal structure. This fact together with the results in a previous paper implies a tame dimension theory and a decomposition theorem into good‐shaped definable subsets called quasi‐special submanifolds. Using this fact, we investigate definably complete locally o‐minimal expansions of ordered groups when the restriction of multiplication to an arbitrary bounded open box is definable. Similarly to o‐minimal expansions of ordered (...) fields, Łojasiewicz's inequality, Tietze's extension theorem and affiness of pseudo‐definable spaces hold true for such structures under the extra assumption that the domains of definition and the pseudo‐definable spaces are definably compact. Here, a pseudo‐definable space is a topological space having finite definable atlases. We also demonstrate Michael's selection theorem for definable set‐valued functions with definably compact domains of definition. (shrink)

This article studies three most basic systems of truth as well as their subsystems over set theory ZF possibly with AC or the axiom of global choice GC, and then correlates them with subsystems of Morse–Kelley class theory MK. The article aims at making an initial step towards the axiomatic study of truth in set theory in connection with class theory. Some new results on the side of class theory, such as conservativity, forcing and some forms of the reflection principle, (...) are also presented. The equivalence results among systems of truth and classes obtained in this article are summarized in Theorem 104 , Theorem 107 and Theorem 108. (shrink)

We investigate the role of coalgebraic predicate logic, a logic for neighborhood frames first proposed by Chang, in the study of monotonic modal logics. We prove analogues of the Goldblatt–Thomason theorem and Fine’s canonicity theorem for classes of monotonic neighborhood frames closed under elementary equivalence in coalgebraic predicate logic. The elementary equivalence here can be relativized to the classes of monotonic, quasi-filter, augmented quasi-filter, filter, or augmented filter neighborhood frames, respectively. The original, Kripke-semantic versions of the theorems follow as a (...) special case concerning the classes of augmented filter neighborhood frames. (shrink)

Truth is often considered to be a logico-linguistic tool for expressing indirect endorsements and infinite conjunctions. In this article, I will point out another logico-linguistic function of truth: to enable and validate what I call a blind argument, namely, an argument that involves indirectly endorsed statements. Admitting this function among the logico-linguistic functions of truth has some interesting consequences. In particular, it yields a new type of so-called conservativeness argument, which poses a new type of threat to deflationism about truth.

This article reports that some robustness of the notions of predicativity and of autonomous progression is broken down if as the given infinite total entity we choose some mathematical entities other than the traditionalω. Namely, the equivalence between normal transfinite recursion scheme and newdependent transfinite recursionscheme, which does hold in the context of subsystems of second order number theory, does not hold in the context of subsystems of second order set theory where the universeVof sets is treated as the given (...) totality. (shrink)

The present paper suggests relative truth definability as a tool for comparing conceptual aspects of axiomatic theories of truth and gives an overview of recent developments of axiomatic theories of truth in the light of it. We also show several new proof-theoretic results via relative truth definability including a complete answer to the conjecture raised by Feferman in [13].

In this article we study the systems KF and VF of truth over set theory as well as related systems and compare them with the corresponding systems over arithmetic.

We introduce a new axiom called inductive dichotomy, a weak variant of the axiom of inductive definition, and analyze the relationships with other variants of inductive definition and with related axioms, in the general second order framework, including second order arithmetic, second order set theory and higher order arithmetic. By applying these results to the investigations on the determinacy axioms, we show the following. (i) Clopen determinacy is consistency-wise strictly weaker than open determinacy in these frameworks, except second order arithmetic; (...) this is an enhancement of Schweber–Hachtman separation of open and clopen determinacy into the consistency-wise separation. (ii) Hausdorff–Kuratowski hierarchy of differences of opens is faithfully reflected by the hierarchy of consistency strengths of corresponding parameter-free determinacies in the aforementioned frameworks; this result is valid also in second order arithmetic only except clopen determinacy. (shrink)

In his previous work, the author has introduced the axiom schema of inductive dichotomy, a weak variant of the axiom schema of inductive definition, and used this schema for elementary ) positive operators to separate open and clopen determinacies for those games in which two players make choices from infinitely many alternatives in various circumstances. Among the studies on variants of inductive definitions for bounded ) positive operators, the present article investigates inductive dichotomy for these operators, and applies it to (...) constructive investigations of variants of determinacy statements for those games in which the players make choices from only finitely many alternatives. As a result, three formulations of open determinacy, that are all classically equivalent with each other, are equivalent to three different semi-classical principles, namely Markov’s Principle, Lesser Limited Principle of Omniscience and Limited Principle of Omniscience, over a suitable constructive base theory that proves clopen determinacy. Open and clopen determinacies for these games are thus separated. Some basic results on variants of inductive definitions for \ positive operators will also be given. (shrink)

We consider two variants of transfinite induction, one with monotonicity assumption on the predicate and one with the induction hypothesis only for cofinally many below. The latter can be seen as a transfinite analogue of the successor induction, while the usual transfinite induction is that of cumulative induction. We calculate the supremum of ordinals along which these schemata for \ formulae are provable in \. It is shown to be larger than the proof-theoretic ordinal \ by power of base 2. (...) We also show a similar result for the structural transfinite induction, defined with fundamental sequences. (shrink)

Legislative scholars have debated what factors (e.g. divided government) account for the number of important laws a legislative body passes per year. This paper presents a monopoly model for explaining legislative production. It assumes that a legislature adjusts its law production so as to maximize its utility. The model predicts that socio-economic and political changes increase the marginal benefit of law production, whereas low negotiation costs and ample legislative resources decrease the marginal cost of law production. The model is tested (...) in two ways. The first approach compares the legislatures of 42 developed and developing countries. The second analyzes Japanese lawmaking from 1949 to 1990, using an appropriate method for event count time series data. Both empirical investigations support the model's predictions for legislative production. (shrink)

Distracted attention is considered responsible for most car accidents, and many functional magnetic resonance imaging researchers have addressed its neural correlates using a car-driving simulator. Previous studies, however, have not directly addressed safe driving performance and did not place pedestrians in the simulator environment. In this fMRI study, we simulated a pedestrian-rich environment to explore the neural correlates of three types of safe driving performance: accurate lane-keeping during driving, the braking response to a preceding car, and the braking response to (...) a crossing pedestrian. Activation of the bilateral frontoparietal control network predicted high driving accuracy. On the other hand, activation of the left posterior and right anterior superior temporal sulci preceding a sudden pedestrian crossing predicted a slow braking response. The results suggest the involvement of different cognitive processes in different components of driving safety: the facilitatory effect of maintained attention on driving accuracy and the distracting effect of social–cognitive processes on the braking response to pedestrians. (shrink)

Classes are the objects of the second sort of second-order set theory. They have sets as their members and behave like sets, but paradoxes tell us that many classes cannot be sets. Then, what are classes? Predicativism about classes suggests that classes are predicates of sets, and this article investigates the question from the predicativist point of view in light of recent developments in the use of classes in set theory. Predicativism has been considered too restrictive and unable to accommodate (...) the use of classes in set theory. This diagnosis, however, is only true of a certain specific type of predicativism. In this article, we propose a new type of predicativism, which we call liberal predicativism, and argue that predicativism is still a highly viable option, and our liberal version provides a sufficiently versatile and workable nominalist concept of classes for set theory. (shrink)

We consider iterations of general elementary embeddings and, using this notion, point out helices of consistency-wise implications between large large cardinals.Up to now, large cardinal properties have been considered as properties which cannot be accessed by any weaker properties and it has been known that, with respect to this relation, they form a proper hierarchy. The helices we point out significantly change this situation: the same sequence of large cardinal properties occurs repeatedly, changing only the parameters.As results of our investigation (...) of this helical structure, we have new characterizations of extendible cardinals and of Vopěnkan cardinals in terms of elementary embeddings from the universe V, a new large large cardinal property which looks like Shelahness properly between Vopěnkaness and almost hugeness, and a more direct relation between Vopěnkaness and Woodinness than already known.We also consider limits of the helices and relations with the axioms I1–I3. (shrink)

Deflationism about truth describes truth as a logical notion. In the present paper, I explore the implication of the alleged logicality of truth from the perspective of axiomatic theories of truth, and argue that the deflationist doctrine of the logicality of truth gives rise to two types of self-undermining arguments against deflationism, which I call the conservativeness argument from logicality and the topic-neutrality argument.

We measure, in the presence of the axiom of infinity, the proof-theoretic strength of the axioms of set theory which make the theory look really like a “theory of sets”, namely, the axiom of extensionality Ext, separation axioms and the axiom of regularity Reg . We first introduce a weak weak set theory as a base over which to clarify the strength of these axioms. We then prove the following results about proof-theoretic ordinals:1. and ,2. and . We also show (...) that neither Reg nor affects the proof-theoretic strength, i.e., where T is Basic plus any combination of Ext and. (shrink)

The third author gave a natural deduction style proof system called the \-calculus for implicational fragment of classical logic in. In -calculus, 2015, Post-proceedings of the RIMS Workshop “Proof Theory, Computability Theory and Related Issues”, to appear), the fourth author gave a natural subsystem “intuitionistic \-calculus” of the \-calculus, and showed the system corresponds to intuitionistic logic. The proof is given with tree sequent calculus, but is complicated. In this paper, we introduce some reduction rules for the \-calculus, and give (...) a simple and purely syntactical proof to the theorem by use of the reduction. In addition, we show that we can give a computation model with rich expressive power with our system. (shrink)

We introduce a new simple way of defining the forcing method that works well in the usual setting under FA, the Foundation Axiom, and moreover works even under Aczel's AFA, the Anti-Foundation Axiom. This new way allows us to have an intuition about what happens in defining the forcing relation. The main tool is H. Friedman's method of defining the extensional membership relation ∈ by means of the intensional membership relation ε .Analogously to the usual forcing and the usual generic (...) extension for FA-models, we can justify the existence of generic filters and can obtain the Forcing Theorem and the Minimal Model Theorem with some modifications. These results are on the line of works to investigate whether model theory for AFA-set theory can be developed in a similar way to that for FA-set theory.Aczel pointed out that the quotient of transition systems by the largest bisimulation and transition relations have the essentially same theory as the set theory with AFA. Therefore, we could hope that, by using our new method, some open problems about transition systems turn out to be consistent or independent. (shrink)