In this paper, illocutionary acts of commanding will be differentiated from perlocutionary acts that affect preferences of addressees in a new dynamic logic which combines the preference upgrade introduced in DEUL (dynamic epistemic upgrade logic) by van Benthem and Liu with the deontic update introduced in ECL II (eliminative command logic II) by Yamada. The resulting logic will incorporate J. L. Austin’s distinction between illocutionary acts as acts having mere conventional effects and perlocutionary acts as acts having real effects (...) upon attitudes and actions of agents, and help us understand why saying so can make it so in explicit performative utterances. We will also discuss how acts of commanding give rise to so-called “deontic dilemmas” and how we can accommodate most deontic dilemmas without triggering so-called “deontic explosion”. (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.

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)

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)

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)

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 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)

By obtaining several new results on Cook-style two-sorted bounded arithmetic, this paper measures the strengths of the axiom of extensionality and of other weak fundamental set-theoretic axioms in the absence of the axiom of infinity, following the author’s previous work [K. Sato, The strength of extensionality I — weak weak set theories with infinity, Annals of Pure and Applied Logic 157 234–268] which measures them in the presence. These investigations provide a uniform framework in which three different kinds of reverse (...) mathematics–Friedman–Simpson’s “orthodox” reverse mathematics, Cook’s bounded reverse mathematics and large cardinal theory–can be reformulated within one language so that we can compare them more directly. (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 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)

Audrito and Viale introduced the new large cardinal notion of an (α)‐uplifting cardinal (for an ordinal α). We shall show that this notion cannot be defined (or expressed) in the standard first‐order language of set theory for every tranfinite α.

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)

Haptic-based vibrotactile biofeedback (BF) is a promising technique to improve rehabilitation of balance in stroke patients. However, the extent to which BF training changes temporal structure of the center of pressure (CoP) trajectories remains unknown. This study aimed to investigate the effect of vibrotactile BF training on the temporal structure of CoP during quiet stance in chronic stroke patients using detrended fluctuation analysis (DFA). Nine chronic stroke patients (age; 81.56±44 months post-stroke) received a balance training regimen using a vibrotactile BF (...) system twice a week over four weeks. A Wii Balance board was used to record five 30 s trials of quiet stance pre- and post-training at 50 Hz. DFA revealed presence of two linear scaling regions in CoP indicating presence of fast- and slow-scale fluctuations. Averaged across all trials, fast-scale fluctuations showed persistent dynamics ( = 1.05 ±.08 for ML and  = 0.99 ±.17 for AP) and slow-scale fluctuations were anti-persistent ( = 0.35 ±.05 for ML and  = 0.32 ±.05 for AP). The slow-scale dynamics of ML CoP in stroke patients decreased from pre-training to post-BF training ( = 0.40 ±.13 vs. 0.31 ±.09). These results suggest that the vibrotactile BF training affects postural control strategy used by chronic stroke patients in the ML direction. Results of the DFA are further discussed in the context of balance training using vibrotactile BF and interpreted from the perspective of intermittent control of upright stance. (shrink)

The Correspondence of Tiglath-pileser III and Sargon II from Calah/Nimrud. By Mikko Luukko. State Archives of Assyria, vol. 19. Helsinki: Neo-Assyrian Text Corpus Project, 2012. Pp. lxxiv + 287, 3 plts., illus. $89.50.

An emerging perspective on human cognition and performance sees it as a kind of self-organizing phenomenon involving dynamic coordination across the body, brain and environment. Measuring this coordination faces a major challenge. Time series obtained from such cognitive, behavioral, and physiological coordination are often complicated in terms of non-stationarity and non-linearity, and in terms of continuous vs. categorical scales. Researchers have proposed several analytical tools and frameworks. One method designed to overcome these complexities is recurrence quantification analysis, developed in the (...) study of non-linear dynamics. It has been applied in various domains, including linguistic data or motion data. However, most previous studies have applied recurrence methods individually to categorical or continuous data. To understand how complex coordination works, an integration of these types of behavior is needed. We aimed to integrate these methods to investigate the relationship between language and motion directly. To do so, we added temporal information to categorical data, and applied joint recurrence analysis methods to visualize and quantify speech-motion coordination coupling during a rap performance. We illustrate how new dynamic methods may capture this coordination in a small case-study design on this expert rap performance. We describe a case study suggesting this kind of dynamic analysis holds promise, and end by discussing the theoretical implications of studying complex performances of this kind as a dynamic, coordinated phenomenon. (shrink)

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

In his “A new argument for evidentialism” (Shah, Philos Q 56(225): 481–498, 2006 ), Nishi Shah argues that the best explanation of a feature of deliberation whether to believe that p which he calls transparency entails that only evidence can be reason to believe that p. I show that his argument fails because a crucial lemma that his argument appeals to cannot be supported without assuming evidentialism to be true in the first place.

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].

The Geach‐Kaplan sentence is alleged to be an example of a non‐first‐orderizable sentence, and the proof of the alleged non‐first‐orderizability is credited to David Kaplan. However, there is also a widely shared intuition that the Geach‐Kaplan sentence is still first‐orderizable by invoking sets or other extra non‐logical resources. The plausibility of this intuition is particularly crucial for first‐orderism, namely, the thesis that all our scientific discourse and reasoning can be adequately formalized by first‐order logic. I first argue that the Geach‐Kaplan (...) sentence is, in fact, not first‐orderizable even by invoking extra non‐logical resources, in any sense that is acceptable for first‐orderism and adequately corresponds to the sense in which the Geach‐Kaplan sentence is deemed to be non‐first‐orderizable simpliciter via Kaplan's proof. To address this problem on behalf of first‐orderism, I then propose an alternative conception of first‐orderizability in the sense of which the Geach‐Kaplan sentence and any other second‐order sentences become first‐orderizable by invoking extra non‐logical resources; furthermore, in certain circumstances, they are first‐orderizable without incurring any extra ontological commitment. My analysis also turns out to yield (as a biproduct) a significant enhancement of the so‐called paradox of plurality. (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)

One prominent feature of belief is that a belief cannot be formed at will. This paper argues that the best explanation of this fact is that belief formation is a process that takes aim at the truth. Taking aim at the truth is to be understood as causal responsiveness of the processes constituting belief formation to what facilitates achieving true beliefs. The requirement for this responsiveness precludes the possibility of belief formation responding to intentions in a way that would count (...) as forming a belief at will. (shrink)

We introduce and analyze a new axiomatic theory$\mathsf {CD}$of truth. The primitive truth predicate can be applied to sentences containing the truth predicate. The theory is thoroughly classical in the sense that$\mathsf {CD}$is not only formulated in classical logic, but that the axiomatized notion of truth itself is classical: The truth predicate commutes with all quantifiers and connectives, and thus the theory proves that there are no truth value gaps or gluts. To avoid inconsistency, the instances of the T-schema are (...) restricted todeterminatesentences. Determinateness is introduced as a further primitive predicate and axiomatized. The semantics and proof theory of$\mathsf {CD}$are analyzed. (shrink)

Prediction is essential for the efficiency of many cognitive processes; however, this process is not always perfect. Predictive coding theory suggests that the brain generates and updates a prediction to respond to an upcoming event. Although an electrophysiological index of prediction, the stimulus preceding negativity, has been reported, it remains unknown whether the SPN reflects the prediction accuracy, or whether it is associated with the prediction error, which corresponds to a mismatch between a prediction and an actual input. Thus, the (...) present study aimed to investigate this question using electroencephalography. Participants were asked to predict the original pictures from pictures that had undergone different levels of pixelation. The SPN amplitude was affected by the level of pixelation and correlated with the subjective evaluation of the prediction accuracy. Furthermore, late positive components were negatively correlated with SPN. These results suggest that the amplitude of SPN reflects the prediction accuracy; more accurate prediction increases the SPN and reduces the prediction error, resulting in reduced LPC amplitudes. (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)