Progressions of iterated reflection principles can be used as a tool for the ordinal analysis of formal systems. We discuss various notions of proof-theoretic ordinals and compare the information obtained by means of the reflection principles with the results obtained by the more usual proof-theoretic techniques. In some cases we obtain sharper results, e.g., we define proof-theoretic ordinals relevant to logical complexity Π1 0 and, similarly, for any class Π n 0 . We provide a more general version of (...) the fine structure relationships for iterated reflection principles (due to U. Schmerl [25]). This allows us, in a uniform manner, to analyze main fragments of arithmetic axiomatized by restricted forms of induction, including IΣ n , IΣ n − , IΠ n − and their combinations. We also obtain new conservation results relating the hierarchies of uniform and local reflection principles. In particular, we show that (for a sufficiently broad class of theories T) the uniform Σ1-reflection principle for T is Σ2-conservative over the corresponding local reflection principle. This bears some corollaries on the hierarchies of restricted induction schemata in arithmetic and provides a key tool for our generalization of Schmerl's theorem. (shrink)

KPM is a subsystem of set theory designed to formalize a recursively Mahlo universe of sets. In this paper we show that a certain ordinal notation system is sufficient to measure the proof-theoretic strength ofKPM. This involves a detour through an infinitary calculus RS(M), for which we prove several cutelimination theorems. Full cut-elimination is available for derivations of $\Sigma (L_{\omega _1^c } )$ sentences, whereω 1 c denotes the least nonrecursive ordinal. This paper is self-contained, at least from a technical (...) point of view. (shrink)

A theistic science would have to represent the integration of all kinds of knowledge intent on explaining the whole of reality. These would include, at least, history, metaphysics, theology, formal logic, mathematics, and experimental sciences. However, what is the whole of reality that one wants to explain? :.

A proof-theoretical analysis of elementary theories of order relations is effected through the formulation of order axioms as mathematical rules added to contraction-free sequent calculus. Among the results obtained are proof-theoretical formulations of conservativity theorems corresponding to Szpilrajn’s theorem on the extension of a partial order into a linear one. Decidability of the theories of partial and linear order for quantifier-free sequents is shown by giving terminating methods of proof-search.

This article investigates the proof theory of the Quantified Argument Calculus as developed and systematically studied by Hanoch Ben-Yami [3, 4]. Ben-Yami makes use of natural deduction, we, however, have chosen a sequent calculus presentation, which allows for the proofs of a multitude of significant meta-theoretic results with minor modifications to the Gentzen’s original framework, i.e., LK. As will be made clear in course of the article LK-Quarc will enjoy cut elimination and its corollaries.

Weak and strong consistency of the Abstract Principal Principle are defined in terms of classical probability measure spaces. It is proved that the Abstract Principal Principle is both weakly and strongly consistent. The Abstract Principal Principle is strengthened by adding a stability requirement to it. Weak and strong consistency of the resulting Stable Abstract Principal Principle are defined. It is shown that the Stable Abstract Principal Principle is weakly consistent. Strong consistency of the Stable Abstract Principal principle remains an open (...) question. (shrink)

We introduce a framework for a graph-theoretic analysis of the semantic paradoxes. Similar frameworks have been recently developed for infinitary propositional languages by Cook and Rabern, Rabern, and Macauley. Our focus, however, will be on the language of first-order arithmetic augmented with a primitive truth predicate. Using Leitgeb’s notion of semantic dependence, we assign reference graphs (rfgs) to the sentences of this language and define a notion of paradoxicality in terms of acceptable decorations of rfgs with truth values. It (...) is shown that this notion of paradoxicality coincides with that of Kripke. In order to track down the structural components of an rfg that are responsible for paradoxicality, we show that any decoration can be obtained in a three-stage process: first, the rfg is unfolded into a tree, second, the tree is decorated with truth values (yielding a dependence tree in the sense of Yablo), and third, the decorated tree is re-collapsed onto the rfg. We show that paradoxicality enters the picture only at stage three. Due to this we can isolate two basic patterns necessary for paradoxicality. Moreover, we conjecture a solution to the characterization problem for dangerous rfgs that amounts to the claim that basically the Liar- and the Yablo graph are the only paradoxical rfgs. Furthermore, we develop signed rfgs that allow us to distinguish between ‘positive’ and ‘negative’ reference and obtain more fine-grained versions of our results for unsigned rfgs. (shrink)

The trope bundle theories of objects are capable of analyzing monadic inherence (objects having tropes), which is one of their main advantage. However, the best current trope theoretical account of relational tropes, namely, the relata specific view leaves relational inherence (a relational trope relating two or more entities) primitive. This article presents the first trope theoretical analysis of relational inherence by generalizing the trope theoretical analysis of inherence to relational tropes. The analysis reduces the (...) holding of relational inherence to the obtaining of certain other facts about entities of the trope theoretical category system. Moreover, I show that the analysis can deal with asymmetric and non-symmetric relations by assuming that all relation-like tropes are quantities. Finally, I provide an account of the spatial location of tropes in the difficult case in which tropes contribute to determining of the location of other entities. (shrink)

White lies, lies that are beneficial to the addressee and uttered out of concern for them, are pervasive in daily life. This raises a prima facie question: if white lies are so common, are they still lies? I tackle this question from the perspective of speech act theory, using the case of white lies to shed light on the broader question of whether lying itself can be considered a type of speech act. Adopting Sbisà’s (Uptake and Conventionality in Illocution. Lodz (...) Papers in Pragmatics 5 33–52. Reprinted in Marina Sbisà (forthcoming), Essays on Speech Acts and Other Topics in Pragmatics. Oxford: Oxford University Press, 2009) neo-Austinian approach that places the emphasis on the achievement of certain conventional effects, I claim that malicious lying cannot be a type of speech act. However, white lies are a type of speech act, a claim which finds support in three types of evidence: the conventionality of means by which white lies are performed, their online processing, and their acquisition. Moreover, the existence of a continuum between white (harmless) lies (which are a type of speech act) and malicious (harmful) lies (which are not) suggests that whether an utterance performs a certain type of speech act or not can be a matter of degree. In other words, the property itself of being a speech act of a certain kind, an utterance’s speech-act-hood, so to speak, may be graded. This is an interesting result, which applies to speech acts more generally, beyond lying. (shrink)

A sequent calculus methodology for systems of agency based on branching-time frames with agents and choices is proposed, starting with a complete and cut-free system for multi-agent deliberative STIT; the methodology allows a transparent justification of the rules, good structural properties, analyticity, direct completeness and decidability proofs.

I here develop a specific version of the deflationary theory of truth. I adopt a terminology on which deflationism holds that an exhaustive account of truth is given by the equivalence between truth-ascriptions and de-nominalised (or disquoted) sentences. An adequate truth-theory, it is argued, must be finite, non-circular, and give a unified account of all occurrences of “true”. I also argue that it must descriptively capture the ordinary meaning of “true”, which is plausibly taken to be unambiguous. Ch. 2 is (...) a critical historical survey of deflationary theories, where notably disquotationalism is found untenable as a descriptive theory of “true”. In Ch. 3, I aim to show that deflationism cannot be finitely and non-circularly formulated by using “true”, and so must only mention it. Hence, it must be a theory specifically about the word “true” (and its foreign counterparts). To capture the ordinary notion, the theory must thus be an empirical, use-theoretic, semantic account of “true”. The task of explaining facts about truth now becomes that of showing that various sentences containing “true” are (unconditionally) assertible. In Ch. 4, I defend the claim (D) that every sentence of the form “That p is true” and the corresponding “p” are intersubstitutable (in a use-theoretic sense), and show how this claim provides a unified and simple account of a wide variety of occurrences of “true”. Disquotationalism then only has the advantage of avoiding propositions. But in Ch. 5, I note that (D) is not committed to propositions. Use-theoretic semantics is then argued to serve nominalism better than truth-theoretic ditto. In particular, it can avoid propositions while sustaining a natural syntactic treatment of “that”-clauses as singular terms and of “Everything he says is true”, as any other quantification. Finally, Horwich’s problem of deriving universal truth-claims is given a solution by recourse to an assertibilist semantics of the universal quantifier. (shrink)

Teaching has long been considered as one of the most challenging professions worldwide due to the involvement of numerous linguistic, socio-political, social, and psych-emotional factors. Because of these factors, english as a foreign language teachers are psychologically, emotionally, and physically pressed in their job. These damaging pressures often result in negative academic outcomes for teachers, students, and educational systems. Despite dire consequences, few studies have examined the role of psycho-emotional factors in improving teaching performance and reducing negative emotions at the (...) workplace. To fill this gap, this mini-review article aimed to present a theoretical analysis of three constructs of occupational adjustment, psychological hardiness, and burnout. In so doing, the definitions, conceptualizations, dimensions, and empirical studies related to each variable were presented. The study ends with the existing research gaps and offers some implications for EFL teachers and other stakeholders by increasing their knowledge of emotions in occupational environments and the consequences that such emotions can have for an organization. (shrink)

The paper has a twofold aim. On the one hand, it provides what appears to be the first game-theoretic modeling of Napoleon’s last campaign, which ended dramatically on 18 June 1815 at Waterloo. It is specifically concerned with the decision Napoleon made on 17 June 1815 to detach part of his army against the Prussians he had defeated, though not destroyed, on 16 June at Ligny. Military historians agree that this decision was crucial but disagree about whether it was rational. (...) Hypothesizing a zero-sum game between Napoleon and Blücher, and computing its solution, we show that it could have been a cautious strategy on the former's part to divide his army, a conclusion which runs counter to the charges of misjudgement commonly heard since Clausewitz. On the other hand, the paper addresses methodological issues. We defend its case study against the objections of irrelevance that have been raised elsewhere against “analytic narratives”, and conclude that military campaigns provide an opportunity for successful application of the formal theories of rational choice. Generalizing the argument, we finally investigate the conflict between narrative accounts – the historians' standard mode of expression – and mathematical modeling. (shrink)

By a result of Paris and Friedman, the collection axiom schema for $\Sigma_{n+1}$ formulas, $B\Sigma_{n+1}$ , is $\Pi_{n+2}$ conservative over $I\Sigma_n$ . We give a new proof-theoretic proof of this theorem, which is based on a reduction of $B\Sigma_n$ to a version of collection rule and a subsequent analysis of this rule via Herbrand's theorem. A generalization of this method allows us to improve known results on reflection principles for $B\Sigma_n$ and to answer some technical questions left open by (...) Sieg [23] and Hájek [9]. We also give a new proof of independence of $B\Sigma_{n+1}$ over $I\Sigma_n$ by a direct recursion-theoretic argument and answer an open problem formulated by Gaifman and Dimitracopoulos [8]. (shrink)

This book is a theoretical and completely rigorous analysis of voting in committees that provides mathematical proof of the existence of democratic voting systems, which are immune to the manipulation of preferences of coalitions of voters. The author begins by determining the power distribution among voters that is induced by a voting rule, giving particular consideration to choice by plurality voting and Borda's rule. He then constructs, for all possible committees, well-behaved representative voting procedures which are not distorted (...) by strategic voting, giving complete solutions for certain important classes of committees. The solution to the problem of mass elections is fully characterised. (shrink)

In this paper we adopt a category-theoretic viewpoint in order to analyze the semantics of complementarity for quantum systems. Based on the existence of a pair of adjoint functors between the topos of presheaves of the Boolean kind of structure and the category of the quantum kind of structure, we establish a twofold complementarity scheme which constitutes an instance of the concept of adjunction. It is further argued that the established scheme is inextricably connected with a realistic philosophical attitude, although (...) substantially different from the classical one. (shrink)

This article provides the proof-theoretic analysis of the transfinitely iterated fixed point theories $\widehat{ID}_\alpha and \widehat{ID}_{ the exact proof-theoretic ordinals of these systems are presented.

In this paper we apply the idea of Revision Rules, originally developed within the framework of the theory of truth and later extended to a general mode of definition, to the analysis of the arithmetical hierarchy. This is also intended as an example of how ideas and tools from philosophical logic can provide a different perspective on mathematically more “respectable” entities. Revision Rules were first introduced by A. Gupta and N. Belnap as tools in the theory of truth, and (...) they have been further developed to provide the foundations for a general theory of (possibly circular) definitions. Revision Rules are non-monotonic inductive operators that are iterated into the transfinite beginning with some given “bootstrapper” or “initial guess.” Since their iteration need not give rise to an increasing sequence, Revision Rules require a particular kind of operation of “passage to the limit,” which is a variation on the idea of the inferior limit of a sequence. We then define a sequence of sets of strictly increasing arithmetical complexity, and provide a representation of these sets by means of an operator G(x, φ) whose “revision” is carried out over ω2 beginning with any total function satisfying certain relatively simple conditions. Even this relatively simple constraint is later lifted, in a theorem whose proof is due to Anil Gupta. (shrink)

Psychological essentialism is a cognitive bias through which human beings conceive the entities around them as having inner essences and basic natures. Social scientists routinely generate flawed inferences because their methods require the truth of psychological essentialism. This article develops set-theoretic analysis as a scientific-constructivist approach that overcomes the bias of psychological essentialism. With this approach, the “sets” of set-theoretic analysis are mental phenomena that establish boundaries and identify similarities and differences among entities whose natural kind composition is (...) not known. The approach is illustrated through a consideration of research on intelligence, race, and poverty in the United States. (shrink)

The starting point of this article is an old question asked by Feferman in his paper on Hancock's conjecture [6] about the strength of ${\rm ID}_{1}^{\ast}$. This theory is obtained from the well-known theory ID₁ by restricting fixed point induction to formulas that contain fixed point constants only positively. The techniques used to perform the proof-theoretic analysis of ${\rm ID}_{1}^{\ast}$ also permit to analyze its transfinitely iterated variants ${\rm ID}_{\alpha}^{\ast}$. Thus, we eventually know that $|\widehat{{\rm ID}}_{\alpha}|=|{\rm ID}_{\alpha}^{\ast}|$.

This article provides the proof-theoretic analysis of the transfinitely iterated fixed point theories $\widehat{ID}_\alpha and \widehat{ID}_{<\alpha};$ the exact proof-theoretic ordinals of these systems are presented.

The defence of the market and economic freedom have been the main objectives of the investigations by liberal thinkers such as Milton Friedman, Gary Becker, F Hayek and L Von Mises. Bearing in mind that the first two economists are the maximum exponents of the Chicago School and the last two of the Austrian School, it is often concluded that the theories of both schools are similar. This book demonstrates that in reality, there is no convergence or complementariness to be (...) found between both schools of thought. The anthropological categories, contributed by Mises, allow us to understand all human phenomena from the view of the man who acts. In this view, economics is part of a philosophical system whose core is the creative capacity of people. Becker’s work, on the other hand, is concentrated on the generalization of the _homo economicus_ as the basis for explaining all human behaviour. He generalizes the maximizing principle to explain all human reality, and extends the scope of the application of a so-called scientific and technical view of the world. In this key volume, an important read for those in the fields of economic theory and political economy, Javier Aranzadi argues, in essence, that the tradition of Hayek and Mises encourages a humanistic liberalism, whereas the Chicago School proposes only a technical humanism. (shrink)

This paper intends to open a discussion on how certain dangerous kinds of deceptive reasoning can be defined, in which way it is achieved in a discussion, and which would be the strategies for defense against such deceptive attacks on the light of some principles accepted as fundamental for rationality and logic.

This paper considers the goals and methods of theoretical sociology. The chief goal of theoretical work is a theory in two parts-postulates and predictions-the key challenge being to minimize the number of postulates and maximize the number and variety of predictions. The paper discusses the distinctive character of the sentences in each part of the theory and, in light of that bipartite structure, the two main activities of theoretical analysis: (i) speculative thinking, whereby the theorist identifies (...) the starting ideas for the postulates; and (ii) formal reasoning, whereby the theorist constructs the postulates and derives predictions from them. To illustrate the features of a theory and the tasks of theoretical analysis, the paper briefly sketches the theory of the distributive-justice force. (shrink)

First Published in 2002. Routledge is an imprint of Taylor & Francis, an informa company.

Thomas Elsaesser and Warren Buckland _Studying Contemporary American Film: A Guide to Movie Analysis_ Arnold: London 2002 ISBN 0 340 76206 3 (PB) x + 309 pp.

This article provides an ordinal analysis of Σ11 transfinite dependent choice.

Professions are granted autonomy by society, to regulate their own affairs. In return for the economic benefits autonomy grants to professions, society expects professions to act in a socially responsible manner. This paper presents a game-theoretic analysis of the relationship between society and professions, which shows that the relationship is unstable in the face of opportunities for professions to renege on the social contract. It also shows how periodic controversies regarding the degree to which professionals act in the public (...) interest are expected to occur periodically, and how they are resolved. (shrink)

In this paper, the class of Fidel-structures for the paraconsistent logic mbC is studied from the point of view of Model Theory and Category Theory. The basic point is that Fidel-structures for mbC can be seen as first-order structures over the signature of Boolean algebras expanded by two binary predicate symbols N and O satisfying certain Horn sentences. This perspective allows us to consider notions and results from Model Theory in order to analyze the class of mbC-structures. Thus, substructures, union (...) of chains, direct products, direct limits, congruences and quotient structures can be analyzed under this perspective. In particular, a Birkhoff-like representation theorem for mbC-structures as subdirect products in terms of subdirectly irreducible mbC-structures is obtained by adapting a general result for first-order structures due to Caicedo. Moreover, a characterization of all the subdirectly irreducible mbC-structures is also given. An alternative decomposition theorem is obtained by using the notions of weak substructure and weak isomorphism considered by Fidel for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_n$$\end{document}-structures. (shrink)

In this paper we study interpretations and equivalences of propositional deductive systems by using a quantale-theoretic approach introduced by Galatos and Tsinakis. Our aim is to provide a general order-theoretic framework which is able to describe and characterize both strong and weak forms of interpretations among propositional deductive systems also in the cases where the systems have different underlying languages.

Anarchism has not been well served by the academy, but if the books under review are any indication, perhaps things are changing. Alan Ritter's Anarchism: A Theoretical Analysis and Michael Taylor's Community, Anarchy and Liberty both make original contributions to anarchist theory, while David Miller's Anarchism constitutes a thorough and competent introduction to the subject. Ostensibly providing an analysis of classical anarchist theory as developed by Godwin, Proudhon, Bakunin and Kropotkin, Ritter has in fact achieved a modest (...) conceptual breakthrough. Anarchism has been traditionally conceived as the most uncompromising libertarian ideology, completely opposed to all limitations and constraints on human freedom. (shrink)