This work is a sequel to the author's Godel's Incompleteness Theorems, though it can be read independently by anyone familiar with Godel's incompleteness theorem for Peano arithmetic. The book deals mainly with those aspects of recursiontheory that have applications to the metamathematics of incompleteness, undecidability, and related topics. It is both an introduction to the theory and a presentation of new results in the field.
Volume II of Classical RecursionTheory describes the universe from a local (bottom-up or synthetical) point of view, and covers the whole spectrum, from the recursive to the arithmetical sets. The first half of the book provides a detailed picture of the computable sets from the perspective of Theoretical Computer Science. Besides giving a detailed description of the theories of abstract Complexity Theory and of Inductive Inference, it contributes a uniform picture of the most basic complexity classes, (...) ranging from small time and space bounds to the elementary functions, with a particular attention to polynomial time and space computability. It also deals with primitive recursive functions and larger classes, which are of interest to the proof theorist. The second half of the book starts with the classical theory of recursively enumerable sets and degrees, which constitutes the core of Recursion or Computability Theory. Unlike other texts, usually confined to the Turing degrees, the book covers a variety of other strong reducibilities, studying both their individual structures and their mutual relationships. The last chapters extend the theory to limit sets and arithmetical sets. The volume ends with the first textbook treatment of the enumeration degrees, which admit a number of applications from algebra to the Lambda Calculus. The book is a valuable source of information for anyone interested in Complexity and Computability Theory. The student will appreciate the detailed but informal account of a wide variety of basic topics, while the specialist will find a wealth of material sketched in exercises and asides. A massive bibliography of more than a thousand titles completes the treatment on the historical side. (shrink)
The fundamental ideas concerning computation and recursion naturally find their place at the interface between logic and theoretical computer science. The contributions in this book, by leaders in the field, provide a picture of current ideas and methods in the ongoing investigations into the pure mathematical foundations of computability theory. The topics range over computable functions, enumerable sets, degree structures, complexity, subrecursiveness, domains and inductive inference. A number of the articles contain introductory and background material which it is (...) hoped will make this volume an invaluable resource for specialists and non-specialists alike. (shrink)
What can computers do in principle? What are their inherent theoretical limitations? These are questions to which computer scientists must address themselves. The theoretical framework which enables such questions to be answered has been developed over the last fifty years from the idea of a computable function: intuitively a function whose values can be calculated in an effective or automatic way. This book is an introduction to computability theory (or recursiontheory as it is traditionally known to (...) mathematicians). Dr Cutland begins with a mathematical characterisation of computable functions using a simple idealised computer (a register machine); after some comparison with other characterisations, he develops the mathematical theory, including a full discussion of non-computability and undecidability, and the theory of recursive and recursively enumerable sets. The later chapters provide an introduction to more advanced topics such as Gildel's incompleteness theorem, degrees of unsolvability, the Recursion theorems and the theory of complexity of computation. Computability is thus a branch of mathematics which is of relevance also to computer scientists and philosophers. Mathematics students with no prior knowledge of the subject and computer science students who wish to supplement their practical expertise with some theoretical background will find this book of use and interest. (shrink)
In recent years higher recursiontheory has experienced a deep interaction with other areas of logic, particularly set theory (fine structure, forcing, and combinatorics) and infinitary model theory. In this paper we wish to illustrate this interaction by surveying the progress that has been made in two areas: the global theory of the κ-degrees and the study of closure ordinals.
We define, in the spirit of Fenstad , a higher type computation theory, and show that countable recursion over the continuous functionals forms such a theory. We also discuss Hyland's proposal from  for a scheme with which to supplement S1-S9, and show that this augmented set of schemes fails to generate countable recursion. We make another proposal to which the methods of this section do not apply.
The notion of a function from N to N defined by recursion on ordinal notations is fundamental in proof theory. Here this notion is generalized to functions on the universe of sets, using notations for well-orderings longer than the class of ordinals. The generalization is used to bound the rate of growth of any function on the universe of sets that is Σ1-definable in Kripke-Platek admissible set theory with an axiom of infinity. Formalizing the argument provides an (...) ordinal analysis. (shrink)
A semantics for the lambda-calculus due to Friedman is used to describe a large and natural class of categorical recursion-theoretic notions. It is shown that if e 1 and e 2 are godel numbers for partial recursive functions in two standard ω-URS's 1 which both act like the same closed lambda-term, then there is an isomorphism of the two ω-URS's which carries e 1 to e 2.
A type-structure of partial effective functionals over the natural numbers, based on a canonical enumeration of the partial recursive functions, is developed. These partial functionals, defined by a direct elementary technique, turn out to be the computable elements of the hereditary continuous partial objects; moreover, there is a commutative system of enumerations of any given type by any type below (relative numberings). By this and by results in  and , the Kleene-Kreisel countable functionals and the hereditary effective operations (HEO) (...) are easily characterized. (shrink)
A set of godel numbers is invariant if it is closed under automorphisms of (ω, ·), where ω is the set of all godel numbers of partial recursive functions and · is application (i.e., n · m ≃ φ n (m)). The invariant arithmetic sets are investigated, and the invariant recursively enumerable sets and partial recursive functions are partially characterized.
This book presents a systematic, unified treatment of fixed points as they occur in Godels incompleteness proofs, recursiontheory, combinatory logic, semantics, and metamathematics. Packed with instructive problems and solutions, the book offers an excellent introduction to the subject and highlights recent research.
Abuse of authority is an unsolved problem in the new institutional theory of the firm. This paper attempts a double attack to this problem by developing a contractarian view of corporate codes of ethics. From the ex-ante standpoint the paper elaborates on the idea of a Social Contract based on Co-operative Bargaining Games and deduces from it the fair/efficient 'Constitution' of the firm endorsed by means of a well-devised corporate code of ethics. From the ex-post standpoint, codes of ethics (...) are proved to be self-enforcing norms, by showing how they put at work the mechanism of a Repeated Game of Reputation within hierarchical transactions (firms) characterised by incomplete contracts and unforeseen events. To accomplish this task a theory of rationality in the face of unforeseen contingencies is sketched by working out the idea that the domain of a principle of ethics defines a fuzzy event, i.e. an event to which also the ex-ante unforeseen, unimaginable states of the world belong to a certain degree. (shrink)
We consider fine hierarchies in recursiontheory, descriptive set theory, logic and complexity theory. The main results state that the sets of values of different Boolean terms coincide with the levels of suitable fine hierarchies. This gives new short descriptions of these hierarchies and shows that collections of sets of values of Boolean terms are almost well ordered by inclusion. For the sake of completeness we mention also some earlier results demonstrating the usefulness (...) of fine hierarchies. (shrink)
This graduate-level_text by a master in the field builds a function theory of the rational field that combines aspects of classical and intuitionist analysis. Topics include recursive convergence, recursive and relative continuity, recursive and relative differentiability, the relative integral, elementary functions, and transfinite ordinals. 1961 edition.
There are many algorithm texts that provide lots of well-polished code and proofs of correctness. Instead, this book presents insights, notations, and analogies to help the novice describe and think about algorithms like an expert. By looking at both the big picture and easy step-by-step methods for developing algorithms, the author helps students avoid the common pitfalls. He stresses paradigms such as loop invariants and recursion to unify a huge range of algorithms into a few meta-algorithms. Part of the (...) goal is to teach the students to think abstractly. Without getting bogged with formal proofs, the book fosters a deeper understanding of how and why each algorithm works. These insights are presented in a slow and clear manner accessible to second- or third-year students of computer science, preparing them to find their own innovative ways to solve problems. (shrink)
The first example of a simultaneous inductive-recursive definition in intuitionistic type theory is Martin-Löf's universe á la Tarski. A set U 0 of codes for small sets is generated inductively at the same time as a function T 0 , which maps a code to the corresponding small set, is defined by recursion on the way the elements of U 0 are generated. In this paper we argue that there is an underlying general notion of simultaneous inductive-recursive definition (...) which is implicit in Martin-Löf's intuitionistic type theory. We extend previously given schematic formulations of inductive definitions in type theory to encompass a general notion of simultaneous induction-recursion. This enables us to give a unified treatment of several interesting constructions including various universe constructions by Palmgren, Griffor, Rathjen, and Setzer and a constructive version of Aczel's Frege structures. Consistency of a restricted version of the extension is shown by constructing a realisability model in the style of Allen. (shrink)
MOTIVATION The constructivization of ; => D(_£^') poses several problems. For some of these the tools of MD can be modified; for others new methods will need to be established. What must we do to make a full approximation to ; * D? We ...
The aim of this paper is to enrich the algebraic-axiomatic approach to recursiontheory developed in  by an analogue to the classical arithmetical hierarchy and an abstract notion of degree. The results presented here are rather initial and elementary; indeed, the main problem was the very choice of right abstract concepts.
This two-volume work bridges the gap between introductory expositions of logic or set theory on one hand, and the research literature on the other. It can be used as a text in an advanced undergraduate or beginning graduate course in mathematics, computer science, or philosophy. The volumes are written in a user-friendly conversational lecture style that makes them equally effective for self-study or class use. Volume II, on formal (ZFC) set theory, incorporates a self-contained 'chapter 0' on proof (...) techniques so that it is based on formal logic, in the style of Bourbaki. The emphasis on basic techniques will provide the reader with a solid foundation in set theory and provides a context for the presentation of advanced topics such as absoluteness, relative consistency results, two expositions of Godel's constructible universe, numerous ways of viewing recursion, and a chapter on Cohen forcing. (shrink)
In light of the close connection between the ontological hierarchy of set theory and the ideological hierarchy of type theory, Øystein Linnebo and Agustín Rayo have recently offered an argument in favour of the view that the set-theoretic universe is open-ended. In this paper, we argue that, since the connection between the two hierarchies is indeed tight, any philosophical conclusions cut both ways. One should either hold that both the ontological hierarchy and the ideological hierarchy are open-ended, (...) or that neither is. If there is reason to accept the view that the set-theoretic universe is open-ended, that will be because such a view is the most compelling one to adopt on the purely ontological front. (shrink)
This book gives a comprehensive overview of central themes of finite model theory â expressive power, descriptive complexity, and zero-one laws â together with selected applications relating to database theory and artificial intelligence, especially constraint databases and constraint satisfaction problems. The final chapter provides a concise modern introduction to modal logic, emphasizing the continuity in spirit and technique with finite model theory. This underlying spirit involves the use of various fragments of and hierarchies within first-order, second-order, (...) fixed-point, and infinitary logics to gain insight into phenomena in complexity theory and combinatorics. The book emphasizes the use of combinatorial games, such as extensions and refinements of the Ehrenfeucht-Fraissé pebble game, as a powerful way to analyze the expressive power of such logics, and illustrates how deep notions from model theory and combinatorics, such as o-minimality and treewidth, arise naturally in the application of finite model theory to database theory and AI. Students of logic and computer science will find here the tools necessary to embark on research into finite model theory, and all readers will experience the excitement of a vibrant area of the application of logic to computer science. (shrink)
Machine generated contents note: 1. Introduction Juliette Kennedy and Roman Kossak; 2. Historical remarks on Suslin's problem Akihiro Kanamori; 3. The continuum hypothesis, the generic-multiverse of sets, and the [OMEGA] conjecture W. Hugh Woodin; 4. [omega]-Models of finite set theory Ali Enayat, James H. Schmerl and Albert Visser; 5. Tennenbaum's theorem for models of arithmetic Richard Kaye; 6. Hierarchies of subsystems of weak arithmetic Shahram Mohsenipour; 7. Diophantine correct open induction Sidney Raffer; 8. Tennenbaum's theorem and recursive reducts (...) James H. Schmerl; 9. History of constructivism in the 20th century A. S. Troelstra; 10. A very short history of ultrafinitism Rose M. Cherubin and Mirco A. Mannucci; 11. Sue Toledo's notes of her conversations with Gödel in 1972-1975 Sue Toledo; 12. Stanley Tennenbaum's Socrates Curtis Franks; 13. Tennenbaum's proof of the irrationality of [the square root of] 2́. (shrink)
Pierre Bourdieu's theory of cultural change is more powerful and comprehensive than other recent theories, which neglect one or another of the important dimensions of cultural markets. Bourdieu's theory conceptualizes both the supply and demand sides of the market, as well as specifying their interaction with external social factors. Two cases from American culture are developed to demonstrate the explanatory power of Bourdieu's theory of cultural change: the demise of tail fins in automobile design and the fall (...) of modernism in architecture. These cases reveal, however, that Bourdieu's theory fails to account for the leveling of cultural hierarchies and the emergence of pluralized cultural fields. The general conditions for such leveling and pluralization are developed from a comparison of the two cases. (shrink)
“Small” large cardinal notions in the language of ZFC are those large cardinal notions that are consistent with V = L. Besides their original formulation in classical set theory, we have a variety of analogue notions in systems of admissible set theory, admissible recursiontheory, constructive set theory, constructive type theory, explicit mathematics and recursive ordinal notations (as used in proof theory). On the face of it, it is surprising that such distinctively set-theoretical (...) notions have analogues in such disaparate and relatively constructive contexts. There must be an underlying reason why that is possible (and, incidentally, why “large” large cardinal notions have not led to comparable analogues). My long term aim is to develop a common language in which such notions can be expressed and can be interpreted both in their original classical form and in their analogue form in each of these special constructive and semi-constructive cases. This is a program in progress. What is done here, to begin with, is to show how that can be done to a considerable extent in the settings of classical and admissible set theory (and thence, admissible recursiontheory). The approach taken here is to expand the language of set theory to allow us to talk about (possibly partial) operations applicable both to sets and to operations and to formulate the large cardinal notions in question in terms of operational closure conditions; at the same time only minimal existence axioms are posited for sets. The resulting system, called Operational Set Theory, is a partial adaptation to the set-theoretical framework of the explicit mathematics framework Feferman (1975). The.. (shrink)
How do ordinals measure the strength and computational power of formal theories? This paper is concerned with the connection between ordinal representation systems and theories established in ordinal analyses. It focusses on results which explain the nature of this connection in terms of semantical and computational notions from model theory, set theory, and generalized recursiontheory.
The aim of this paper is to introduce a formal system STW of self-referential truth, which extends the classical first-order theory of pure combinators with a truth predicate and certain approximation axioms. STW naturally embodies the mechanisms of general predicate application/abstraction on a par with function application/abstraction; in addition, it allows non-trivial constructions, inspired by generalized recursiontheory. As a consequence, STW provides a smooth inner model for Myhill's systems with levels of implication.
The recursion theorem in abstract partially ordered algebras, such as operative spaces and others, is the most fundamental result of algebraic recursiontheory. The primary aim of the present paper is to prove this theorem for iterative operative spaces in full generality. As an intermediate result, a new and rather large class of models of the combinatory logic is obtained.
This book describes computability theory and provides an extensive treatment of data structures and program correctness. It makes accessible some of the author's work on generalized recursiontheory, particularly the material on the logic programming language PROLOG, which is currently of great interest. Fitting considers the relation of PROLOG logic programming to the LISP type of language.
We design functional algebras that characterize various complexity classes of global functions. For this purpose, classical schemata from recursiontheory are tailored for capturing complexity. In particular we present a functional analog of first-order logic and describe algebras of the functions computable in nondeterministic logarithmic space, deterministic and nondeterministic polynomial time, and for the functions computable by AC 1 -circuits.
This book describes a program of research in computable structure theory. The goal is to find definability conditions corresponding to bounds on complexity which persist under isomorphism. The results apply to familiar kinds of structures (groups, fields, vector spaces, linear orderings Boolean algebras, Abelian p-groups, models of arithmetic). There are many interesting results already, but there are also many natural questions still to be answered. The book is self-contained in that it includes necessary background material from recursion (...) class='Hi'>theory (ordinal notations, the hyperarithmetical hierarchy) and model theory (infinitary formulas, consistency properties). (shrink)
‘‘Theoretical biology’’ is a surprisingly heter- ogeneous field, partly because it encompasses ‘‘doing the- ory’’ across disciplines as diverse as molecular biology, systematics, ecology, and evolutionary biology. Moreover, it is done in a stunning variety of different ways, using anything from formal analytical models to computer sim- ulations, from graphic representations to verbal arguments. In this essay I survey a number of aspects of what it means to do theoretical biology, and how they compare with the allegedly much more restricted (...) sense of theory in the physical sciences. I also tackle a recent trend toward the presentation of all-encompassing theories in the biological sciences, from general theories of ecology to a recent attempt to provide a conceptual framework for the entire set of biological disciplines. Finally, I discuss the roles played by philosophers of science in criticizing and shap- ing biological theorizing. (shrink)
What should our theorizing about social justice aim at? Many political philosophers think that a crucial goal is to identify a perfectly just society. Amartya Sen disagrees. In The Idea of Justice, he argues that the proper goal of an inquiry about justice is to undertake comparative assessments of feasible social scenarios in order to identify reforms that involve justice-enhancement, or injustice-reduction, even if the results fall short of perfect justice. Sen calls this the “comparative approach” to the theory (...) of justice. He urges its adoption on the basis of a sustained critique of the former approach, which he calls “transcendental.” In this paper I pursue two tasks, one critical and the other constructive. First, I argue that Sen’s account of the contrast between the transcendental and the comparative approaches is not convincing, and second, I suggest what I take to be a broader and more plausible account of comparative assessments of justice. The core claim is that political philosophers should not shy away from the pursuit of ambitious theories of justice (including, for example, ideal theories of perfect justice), although they should engage in careful consideration of issues of political feasibility bearing on their practical implementation. (shrink)
Are government restrictions on hate speech consistent with the priority of liberty? This relatively narrow policy question will serve as the starting point for a wider discussion of the use and abuse of nonideal theory in contemporary political philosophy, especially as practiced on the academic left. I begin by showing that hate speech (understood as group libel) can undermine fair equality of opportunity for historically-oppressed groups but that the priority of liberty seems to forbid its restriction. This tension between (...) free speech and equal opportunity creates a dilemma for liberal egalitarians. Nonideal theory apparently offers an escape from this dilemma, but after examining three versions of such an escape strategy, I conclude that none is possible: liberal egalitarians are indeed forced to choose between liberty and equality in this case and others. I finish the paper by examining its implications for other policy arenas, including markets in transplantable human organs and women’s reproductive services. (shrink)
: Liberal rights theory can be used either to challenge or to support social hierarchies of power. Focusing on Ronald Dworkin's theory of rights and Catharine MacKinnon's feminist critique of liberalism, I identify a number of problems with the way that liberal theorists conceptualize rights. I argue that rights can be used to chal-lenge oppressive practices and structures only if they are defined and employed with an awareness and critique of social relations of power.
A succinct introduction to mathematical logic and set theory, which together form the foundations for the rigorous development of mathematics. Suitable for all introductory mathematics undergraduates, Notes on Logic and Set Theory covers the basic concepts of logic: first-order logic, consistency, and the completeness theorem, before introducing the reader to the fundamentals of axiomatic set theory. Successive chapters examine the recursive functions, the axiom of choice, ordinal and cardinal arithmetic, and the incompleteness theorems. Dr. Johnstone has included (...) numerous exercises designed to illustrate the key elements of the theory and to provide applications of basic logical concepts to other areas of mathematics. (shrink)
Judgment aggregation theory, or rather, as we conceive of it here, logical aggregation theory generalizes social choice theory by having the aggregation rule bear on judgments of all kinds instead of merely preference judgments. It derives from Kornhauser and Sager’s doctrinal paradox and List and Pettit’s discursive dilemma, two problems that we distinguish emphatically here. The current theory has developed from the discursive dilemma, rather than the doctrinal paradox, and the final objective of the paper is (...) to give the latter its own theoretical development along the line of recent work by Dietrich and Mongin. However, the paper also aims at reviewing logical aggregation theory as such, and it covers impossibility theorems by Dietrich, Dietrich and List, Dokow and Holzman, List and Pettit, Mongin, Nehring and Puppe, Pauly and van Hees, providing a uniform logical framework in which they can be compared with each other. The review goes through three historical stages: the initial paradox and dilemma, the scattered early results on the independence axiom, and the so-called canonical theorem, a collective achievement that provided the theory with its specific method of analysis. The paper goes some way towards philosophical logic, first by briefly connecting the aggregative framework of judgment with the modern philosophy of judgment, and second by thoroughly discussing and axiomatizing the "general logic" built in this framework. (shrink)
Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes (...) that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science. (shrink)
Recent work in the ethics of war has done much to challenge the collectivism of the convention-based, Walzerian just war theory. In doing so, it raises the question of when it is permissible for soldiers to resort to force. This article considers this issue and, in doing so, argues that the rejection of collectivism in just war should go further still. More specifically, it defends the ‘Individual-Centric Approach’ to the deep morality of war, which asserts that the justifiability of (...) an individual’s contribution to the war, rather than the justifiability of the war more generally, determines the moral acceptability of their participation. It then goes on to present five implications of the Individual-Centric Approach, including for individual liability to attack in war. (shrink)
We consider the informal concept of "computability" or "effective calculability" and two of the formalisms commonly used to define it, "(Turing) computability" and "(general) recursiveness". We consider their origin, exact technical definition, concepts, history, general English meanings, how they became fixed in their present roles, how they were first and are now used, their impact on nonspecialists, how their use will affect the future content of the subject of computability theory, and its connection to other related areas. After a (...) careful historical and conceptual analysis of computability and recursion we make several recommendations in section §7 about preserving the intensional differences between the concepts of "computability" and "recursion." Specifically we recommend that: the term "recursive" should no longer carry the additional meaning of "computable" or "decidable;" functions defined using Turing machines, register machines, or their variants should be called "computable" rather than "recursive;" we should distinguish the intensional difference between Church's Thesis and Turing's Thesis, and use the latter particularly in dealing with mechanistic questions; the name of the subject should be "Computability Theory" or simply Computability rather than "Recursive Function Theory.". (shrink)
New natural lawyers--notably Grisez, Finnis, and George--have written much on civil marriage's moral boundaries and grounds, but with slight influence. The peripheral place of the new natural law theory (NNLT) results from the marital grounds they suggest and the exclusionary moral conclusions they draw from them. However, I argue a more authentic and attractive NNLT account of marriage is recoverable through overlooked resources within the theory itself: friendship and moral self-constitution. This reconstructed account allows us to identify the (...) relation between marriage and human flourishing and the morality of same-sex marriage without making marriage infinitely plastic. (shrink)
One way of providing a focus for critical theory today is to articulate those substantive and robust norms of egalitarian justice that would appear to be presupposed by the idea of a republican and democratic constitutional order. It is suggested here that democratic justice requires the equalisation of effective communicative freedom among all structurally constituted social groups (SCSGs) and that this will have far-reaching implications that entail the deconstruction of all social hierarchies in both domestic and global orders. (...) This argument is presented in three sections. The first defends the focus on groups rather than individuals in theorising democratic justice. The second intervenes critically in contemporary debates surrounding the theoretical relation between various aspects of justice including the demands of redistribution, recognition and political empowerment. The third turns to the challenges for critical theory presented by a complex and multifaceted process of globalisation and it defends a qualified form of cosmopolitanism and highlights the need for a radical democratisation of the international order. (shrink)
This article uses social dominance theory (SDT) to explore the dynamic and systemic nature of the initiation and maintenance of organizational corruption. Rooted in the definition of organizational corruption as misuse of power or position for personal or organizational gain, this work suggests that organizational corruption is driven by the individual and institutional tendency to structure societies as group-based social hierarchies. SDT describes a series of factors and processes across multiple levels of analysis that systemically contribute to the (...) initiation and maintenance of social hierarchies and associated power inequalities, favoritism, and discrimination. I posit that the same factors and processes also contribute to individuals’ lower awareness of the misuse of power and position within the social hierarchies, leading to the initiation and maintenance of organizational corruption. Specifically, individuals high in social dominance orientation, believing that they belong to superior groups, are likely to be less aware of corruption because of their feeling of entitlement to greater power and their desire to maintain dominance even if that requires exploiting others. Members of subordinate groups are also likely to have lower awareness of corruption if they show more favoritism toward dominant group members to enhance their sense of worth and preserve social order. Institutions contribute to lower awareness of corruption by developing and enforcing structures, norms, and practices that promote informational ambiguity and maximize focus on dominance and promotion. Dynamic coordination among individuals and institutions is ensured through the processes of person-environment fit and legitimizing beliefs, ideologies, or rationalizations. (shrink)
According to moral error theory, moral discourse is error-ridden. Establishing error theory requires establishing two claims. These are that moral discourse carries a non-negotiable commitment to there being a moral reality and that there is no such reality. This paper concerns the first and so-called non-negotiable commitment claim. It starts by identifying the two existing argumentative strategies for settling that claim. The standard strategy is to argue for a relation of conceptual entailment between the moral statements that comprise (...) moral discourse and the statement that there is a moral reality. The non-standard strategy is to argue for a presupposition relation instead. Error theorists have so far failed to consider a third strategy, which uses a general entailment relation that doesn’t require intricate relations between concepts. The paper argues that both entailment claims struggle to meet a new explanatory challenge and that since the presupposition option doesn’t we have prima facie reason to prefer it over the entailment options. The paper then argues that suitably amending the entailment claims enables them to meet this challenge. With all three options back on the table the paper closes by arguing that error theorists should consider developing the currently unrecognised, non-conceptual entailment claim. (shrink)
Theory-of-mind (ToM) involves modeling an individual’s mental states to plan one’s action and to anticipate others’ actions through recursive reasoning that may be myopic (with limited recursion) or predictive (with full recursion). ToM recursion was examined using a series of two-player, sequential-move matrix games with a maximum of three steps. Participants were assigned the role of Player I, controlling the initial and the last step, or of Player II, controlling the second step. Appropriate for the assigned (...) role, participants either anticipated or planned Player II’s strategy at the second step, and then determined Player I’s optimal strategy at the first step. Participants more readily used predictive reasoning as Player II (i.e., planning one’s own move) than as Player I (i.e., anticipating an opponent’s move), although they did not differ when translating reasoning outcome about the second step to optimal action in the first step. Perspective-taking influenced likelihood of predictive reasoning, but it did not affect the rate at which participants acquired it during the experimental block. We conclude that the depth of ToM recursion (related to perspective-taking mechanisms) and rational application of belief–desire to action (instrumental rationality) constitute separate cognitive processes in ToM reasoning. (shrink)
The Austrian philosopher Christian von Ehrenfels published his essay "On 'Gestalt Qualities'" in 1890. The essay initiated a current of thought which enjoyed a powerful position in the philosophy and psychology of the first half of this century and has more recently enjoyed a minor resurgence of interest in the area of cognitive science, above all in criticisms of the so-called 'strong programme' in artificial intelligence. The theory of Gestalt is of course associated most specifically with psychologists of the (...) Berlin school such as Max Wertheimer, Wolfgang Kohler and Kurt Koffka. We shall see in what follows, however, that an adequate philosophical understanding of the Gestalt idea and of Ehrenfels' achievement will require a close examination not merely of the work of the Berlin school but also of a much wider tradition in Austrian and German philosophy in general. (shrink)
The separation, uniformization, and other properties of the Borel and projective hierarchies over hyperfinite sets are investigated and compared to the corresponding properties in classical descriptive set theory. The techniques used in this investigation also provide some results about countably determined sets and functions, as well as an improvement of an earlier theorem of Kunen and Miller.
In his Just and Unjust Wars, Michael Walzer claims that his theory of just war is based on the rights of individuals to life and liberty. This is not the case. Walzer in fact bases his theory of jus ad bellum on the supreme rights of supra-individual political communities. According to his theory of jus ad bellum, the rights of political communities are of utmost importance, and individuals can be sacrificed for the sake of these communal rights. (...) At the same time, Walzer bases his theory of jus in bello on the supreme rights of individuals to life and liberty. According to his theory of jus in bello, the rights of individuals are of utmost importance, and political communities can never permissibly violate them in war. Thus, Walzer’s theory of just war is based on two incompatible theories of justice. This explains why Walzer’s theory produces incoherent practical prescriptions in cases of supreme emergencies. Furthermore, it is impossible for Walzer to base his theory of jus ad bellum on the rights of individuals as he conceives them. The theory of jus ad bellum holds that soldiers are obligated to obey the commands of their political superiors. However, this obligation violates the rights of individuals in a number of respects. This is why Walzer does not base the theory of jus ad bellum on individual rights, and produces an incoherent theory. (shrink)
Theory appears to have played the ideological-institutional role of enfranchiser, even if the role was ulti-mately an epiphenomenal one. Furthermore, the expectation of gold in "them thar hills" also encouraged too many university presses to invest in film publications, especially when the arcane peregrinations of Theory facilitated their rationalization of their relaxation of their traditional role as academic gatekeepers. Hence film studies has been flooded with repetitive decoctions of the Theory in search of the same market in (...) much the same way that con-sumers are confronted with so many marginally differentiated shampoos. (shrink)
Sociological explanations of racism tend to concentrate on the structures and dynamics of modern life that facilitate discrimination and hierarchies of inequality. In doing so, they often fail to address why racial hatred arises (as opposed to how it arises) as well as to explain why it can be so visceral and explosive in character. Bringing together sociological perspectives with psychoanalytic concepts and tools, this text offers a clear, accessible and thought-provoking synthesis of varieties of theory, with the (...) aim of clarifying the complex character of racism, discrimination and social exclusion in the contemporary world. (shrink)
In this note I discuss some topics recently analysed by C.U. Moulines in Pluralidad y recursión showing the interest of Frege’s ontosemantic theory for the study of scientific theories. I point out some misunderstandings in making use of fregean view by clarifying the basic notions of objectivity, sense, reference, concept, and object. It is not my aim here to solve the difficulties arising the possibility of identifying two theories as one. Nevertheless, I ofter some clues to achieve such an (...) identity theory that stricto sensu would be an equivalence theory. (shrink)
I argue that algebraic quantum field theory (AQFT) permits an undisturbed view of the right ontology for fundamental physics, whereas standard (or Lagrangian) QFT offers different mutually incompatible ontologies.My claim does not depend on the mathematical inconsistency of standard QFT but on the fact that AQFT has the same concerns as ontology, namely categorical parsimony and a clearly structured hierarchy of entities.
I this paper, I draw on recent research on the radically embodied and perceptual bases of conceptualization in linguistics and cognitive science to develop a new way of reading and evaluating abstract concepts in social theory. I call this approach Sociological Idea Analysis. I argue that, in contrast to the traditional view of abstract concepts, which conceives them as amodal “presuppositions” removed from experience, abstract concepts are irreducibly grounded in experience and partake of non-negotiable perceptual-symbolic features from which a (...) non-propositional “logic” naturally follows. This implies that uncovering the imagistic bases of allegedly abstract notions should be a key part of theoretical evaluation of concepts in social theory. I provide a case study of the general category of “structure” in the social and human sciences to demonstrate the analytic utility of the approach. (shrink)
Among others we will prove that the equational theory of ω dimensional representable polyadic equality algebras (RPEA ω 's) is not schema axiomatizable. This result is in interesting contrast with the Daigneault-Monk representation theorem, which states that the class of representable polyadic algebras is finite schema-axiomatizable (and hence the equational theory of this class is finite schema-axiomatizable, as well). We will also show that the complexity of the equational theory of RPEA ω is also extremely high in (...) the recursion theoretic sense. Finally, comparing the present negative results with the positive results of Ildiko Sain and Viktor Gyuris , the following methodological conclusions will be drawn: The negative properties of polyadic (equality) algebras can be removed by switching from what we call the "polyadic algebraic paradigm" to the "cylindric algebraic paradigm". (shrink)
Following a short introduction, this chapter begins by contrasting two different forms of higher-order perception (HOP) theory of phenomenal consciousness - inner sense theory versus a dispositionalist kind of higher-order thought (HOT) theory - and by giving a brief statement of the superiority of the latter. Thereafter the chapter considers arguments in support of HOP theories in general. It develops two parallel objections against both first-order representationalist (FOR) theories and actualist forms of HOT theory. First, neither (...) can give an adequate account of the distinctive features of our recognitional concepts of experience. And second, neither can explain why there are some states of the relevant kinds that are phenomenal and some that aren. (shrink)
Limiting identification of r.e. indexes for r.e. languages (from a presentation of elements of the language) and limiting identification of programs for computable functions (from a graph of the function) have served as models for investigating the boundaries of learnability. Recently, a new approach to the study of "intrinsic" complexity of identification in the limit has been proposed. This approach, instead of dealing with the resource requirements of the learning algorithm, uses the notion of reducibility from recursiontheory (...) to compare and to capture the intuitive difficulty of learning various classes of concepts. Freivalds, Kinber, and Smith have studied this approach for function identification and Jain and Sharma have studied it for language identification. The present paper explores the structure of these reducibilities in the context of language identification. It is shown that there is an infinite hierarchy of language classes that represent learning problems of increasing difficulty. It is also shown that the language classes in this hierarchy are incomparable, under the reductions introduced, to the collection of pattern languages. Richness of the structure of intrinsic complexity is demonstrated by proving that any finite, acyclic, directed graph can be embedded in the reducibility structure. However, it is also established that this structure is not dense. The question of embedding any infinite, acyclic, directed graph is open. (shrink)
The problem of personal identity is often said to be one of accounting for what it is that gives persons their identity over time. However, once the problem has been construed in these terms, it is plain that too much has already been assumed. For what has been assumed is just that persons do have an identity. A new interpretation of Hume's no-self theory is put forward by arguing for an eliminative rather than a reductive view of personal identity, (...) and by approaching the problem in terms of phenomenology, Buddhist psychology, and the idea of a constructed self-image. (shrink)
Causal Decision Theory (CDT) cares only about the effects of a contemplated act, not its causes. The paper constructs a case in which CDT consequently recommends a bet that the agent is certain to lose, rather than a bet that she is certain to win. CDT is plainly giving wrong advice in this case. It therefore stands refuted.
David Lewis advised essentialists to judge his counterpart theory a false friend. He also argued that counterpart theory needs natural properties. This essay argues that natural properties are all essentialists need to find a true friend in counterpart theory. Section one explains why Lewis takes counterpart theory to be anti-essentialist and why he thinks it needs natural properties. Section two establishes the connection between the natural properties counterpart theory needs and the essentialist consequences Lewis disavows. (...) Section three answers two objections: the first attempts to block the consequences of adding natural properties to counterpart theory; the second grants the consequences, but denies that they amount to essentialism. –Correspondence to: Todd_Buras@baylor.edu. (shrink)
We use evidence from cognitive psychology and the history of science to examine the issue of the theory-ladenness of perceptual observation. This evidence shows that perception is theory-laden, but that it is only strongly theory-laden when the perceptual evidence is ambiguous or degraded, or when it requires a difficult perceptual judgment. We argue that debates about the theory-ladenness issue have focused too narrowly on the issue of perceptual experience, and that a full account of the scientific (...) process requires an examination of theory-ladenness in attention, perception, data interpretation, data production, memory, and scientific communication. We conclude that the evidence for theory-ladenness does not lead to a relativist account of scientific knowledge. (shrink)
Over the last decade, Axel Honneth has established himself as one of the leading social and political philosophers in the world today. Rooted in the tradition of critical theory, his writings have been central to the revitalization of critical theory and have become increasingly influential. His theory of recognition has gained worldwide attention and is seen by some as the principal counterpart to Habermass theory of discourse ethics. In this important new volume, Honneth pursues his path-breaking (...) work on recognition by exploring the moral experiences of disrespect that underpin the conduct of social and political critique. What we might conceive of as a striving for social recognition initially appears in a negative form as the experience of humiliation or disrespect. Honneth argues that disrespect constitutes the systematic key to a comprehensive theory of recognition that seeks to clarify the sense in which institutionalized patterns of social recognition generate justified demands on the way subjects treat each other. This new book by one of the leading social and political philosophers of our time will be of particular interest to students and scholars in social and political theory and philosophy. (shrink)
In this commentary I criticize David Rosenthal’s higher order thought theory of consciousness (HOT). This is one of the best articulated philosophical accounts of consciousness available. The theory is, roughly, that a mental state is conscious in virtue of there being another mental state, namely, a thought to the effect that one is in the first state. I argue that this account is open to the objection that it makes “HOT-zombies” possible, i.e., creatures that token higher order mental (...) states, but not the states that the higher order states are about. I discuss why none of the ways to accommodate this problem within HOT leads to viable positions. (shrink)