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 [2], 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 [4] 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.
It is shown that the low basis theorem is meaningful and provable in I∑ 1 and that the priority-free solution to Post's problem formalizes in this theory.
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 [1] and [2], 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.
We extend an independence result proved in our earlier paper "Solovay's Theorem Cannot Be Simplified" (Annals of Pure and Applied Logic 112 (2001)). Our method uses the Barwise.
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.
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 ...
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)
“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.
‘‘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)
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)
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)
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)
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)
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)
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 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 [12], 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)
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)
This is about a proposed solution to the exclusion problem, one I've defended elsewhere (for example, in "The Properties of Mental Causation"). Details aside, it's just the identity theory: mental properties face no threat of exclusion from, or preemption by, physical properties, because every mental property is a physical property. Here I elaborate on this solution and defend it from some objections. One of my goals is to place it in the context of a more general ontology of properties, (...) in particular, a trope ontology. (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 thesis I argue that the psychological study of concepts and categorisation, and the philosophical study of reference are deeply intertwined. I propose that semantic intuitions are a variety of categorisation judgements, determined by concepts, and that because of this, concepts determine reference. I defend a dual theory of natural kind concepts, according to which natural kind concepts have distinct semantic cores and non-semantic identification procedures. Drawing on psychological essentialism, I suggest that the cores consist of externalistic placeholder (...) essence beliefs. The identification procedures, in turn, consist of prototypes, sets of exemplars, or possibly also theory-structured beliefs. I argue that the dual theory is motivated both by experimental data and theoretical considerations. The thesis consists of three interrelated articles. Article I examines philosophical causal and description theories of natural kind term reference, and argues that they involve, or need to involve, certain psychological elements. I propose a unified theory of natural kind term reference, built on the psychology of concepts. Article II presents two semantic adaptations of psychological essentialism, one of which is a strict externalistic Kripkean-Putnamian theory, while the other is a hybrid account, according to which natural kind terms are ambiguous between internalistic and externalistic senses. We present two experiments, the results of which support the strict externalistic theory. Article III examines Fodor’s influential atomistic theory of concepts, according to which no psychological capacities associated with concepts constitute them, or are necessary for reference. I argue, contra Fodor, that the psychological mechanisms are necessary for reference. (shrink)
We investigate the validity of the field explanation of the wave function by analyzing the mass and charge density distributions of a quantum system. It is argued that a charged quantum system has effective mass and charge density distributing in space, proportional to the square of the absolute value of its wave function. This is also a consequence of protective measurement. If the wave function is a physical field, then the mass and charge density will be distributed in space simultaneously (...) for a charged quantum system, and thus there will exist a remarkable electrostatic self-interaction of its wave function, though the gravitational self-interaction is too weak to be detected presently. This not only violates the superposition principle of quantum mechanics but also contradicts experimental observations. Thus we conclude that the wave function cannot be a description of a physical field. In the second part of this paper, we further analyze the implications of these results for the main realistic interpretations of quantum mechanics, especially for de Broglie-Bohm theory. It has been argued that de Broglie-Bohm theory gives the same predictions as quantum mechanics by means of quantum equilibrium hypothesis. However, this equivalence is based on the premise that the wave function, regarded as a Ψ-field, has no mass and charge density distributions, which turns out to be wrong according to the above results. For a charged quantum system, both Ψ-field and Bohmian particle have charge density distribution. This then results in the existence of an electrostatic self-interaction of the field and an electromagnetic interaction between the field and Bohmian particle, which contradicts both the predictions of quantum mechanics and experimental observations. Therefore, de Broglie-Bohm theory as a realistic interpretation of quantum mechanics is probably wrong. Lastly, we suggest that the wave function is a description of some sort of ergodic motion (e.g. random discontinuous motion) of particles, and we also briefly analyze the implications of this suggestion for other realistic interpretations of quantum mechanics including many-worlds interpretation and dynamical collapse theories. (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)
This book provides a comprehensive, systematic theory of moral responsibility. The authors explore the conditions under which individuals are morally responsible for actions, omissions, consequences, and emotions. The leading idea in the book is that moral responsibility is based on 'guidance control'. This control has two components: the mechanism that issues in the relevant behavior must be the agent's own mechanism, and it must be appropriately responsive to reasons. The book develops an account of both components. The authors go (...) on to offer a sustained defense of the thesis that moral responsibility is compatible with causal determinism. (shrink)
In this article, I attempt to resuscitate the perennially unfashionable distinctive feeling theory of pleasure (and pain), according to which for an experience to be pleasant (or unpleasant) is just for it to involve or contain a distinctive kind of feeling. I do this in two ways. First, by offering powerful new arguments against its two chief rivals: attitude theories, on the one hand, and the phenomenological theories of Roger Crisp, Shelly Kagan, and Aaron Smuts, on the other. Second, (...) by showing how it can answer two important objections that have been made to it. First, the famous worry that there is no felt similarity to all pleasant (or unpleasant) experiences (sometimes called ‘the heterogeneity objection’). Second, what I call ‘Findlay’s objection’, the claim that it cannot explain the nature of our attraction to pleasure and aversion to pain. (shrink)
The causal theory of action has been the standard view in the philosophy of action and mind. In this chapter, I will present responses to two challenges to the theory. The first says, basically, that there is no positive argument in favour of the causal theory, as the only reason that supports it consists in the apparent lack of tenable alternatives. The second challenge says that the theory fails to capture the phenomenon of agency, as it (...) reduces activity to mere happenings (events and event-causal processes). This is often referred to as the problem of "disappearing agency". My main aim is to show that there is no problem of disappearing agency, and we will see that my response to the first challenge will be conducive to this end. I will present a positive argument for the causal theory on the basis of considerations concerning the metaphysics of agency, and I will suggest that we "own" the agency that springs from our mental states and events "by default". (shrink)
Advocates of the computational theory of mind claim that the mind is a computer whose operations can be implemented by various computational systems. According to these philosophers, the mind is multiply realisable because—as they claim—thinking involves the manipulation of syntactically structured mental representations. Since syntactically structured representations can be made of different kinds of material while performing the same calculation, mental processes can also be implemented by different kinds of material. From this perspective, consciousness plays a minor role in (...) mental activity. However, contemporary neuroscience provides experimental evidence suggesting that mental representations necessarily involve consciousness. Consciousness does not only enable individuals to become aware of their own thoughts, it also constantly changes the causal properties of these thoughts. In light of these empirical studies, mental representations appear to be intrinsically dependent on consciousness. This discovery represents an obstacle to any attempt to construct an artificial mind. (shrink)
This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability. The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive notation facilitates (...) proofs of the classical incompleteness and undecidability theorems which are very elegant and easy to understand. The discussion of semantics makes clear the important distinction between standard and nonstandard models which is so important in understanding puzzling phenomena such as the incompleteness theorems and Skolem's Paradox about countable models of set theory. Some of the numerous exercises require giving formal proofs. A computer program called ETPS which is available from the web facilitates doing and checking such exercises. Audience: This volume will be of interest to mathematicians, computer scientists, and philosophers in universities, as well as to computer scientists in industry who wish to use higher-order logic for hardware and software specification and verification. (shrink)
Game theory is the mathematical study of strategy and conflict. It has wide applications in economics, political science, sociology, and, to some extent, in philosophy. Where rational choice theory or decision theory is concerned with individual agents facing games against nature, game theory deals with games in which all players have preference orderings over the possible outcomes of the game. This paper gives an informal introduction to the theory and a survey of applications in diverse (...) branches of philosophy. No criticism is reviewed. Game theory is shown at work in discussions about epistemological dependence (prisoner’s dilemma), liberalism and efficiency (Nash equilibrium), Hume’s concept of convention (correlated equilibrium), morality and rationality (bargaining games), and distributive justice and egalitarianism (evolutionary game theory). A guide to the literature provides hints at applications in collective intentionality, epistemology, ethics, history of philosophy, logic, philosophy of language, and political philosophy. (shrink)
Richard Harland provides a lucid account of all the major movements in literary theory up to the late 1960s. In a lucid and accessible style, he unfolds a comprehensive "story" of literary theory in all its manifestations. Because contemporary literary theory depends heavily upon European thinkers, the book has an international focus, and its coverage extends from philosophers to social theorists to linguists. Harland explains the essential principles of each theoretical position, looking behind particular critical judgments and (...) interpretations in order to convey a core grasp of underlying positions. (shrink)
I offer an account of how the quantum theory we have helps us explain so much. The account depends on a pragmatist interpretation of the theory: This takes a quantum state to serve solely as a source of sound advice to physically situated agents on the content and appropriate degree of belief about matters concerning which they are currently inevitably ignorant. The general account of how to use quantum states and probabilities to explain otherwise puzzling regularities is then (...) illustrated by showing how we can explain single particle interference phenomena, the stability of matter, and interference of Bose-Einstein condensates. Finally I note some open problems and relate this account to alternative approaches to explanation that emphasize the importance of causation, of unification, and of structure. (shrink)
To the extent, then, that we set our face against admitting the truth of Humeanism in the theory of motivation, to that extent we are probably going to feel that there is no such thing as the theory of motivation, so conceived, at all. And that will be the position that this paper is trying to defend, though not only for this reason. It might seem miraculous that so much can be extracted from the little distinction with which (...) we started, between the reasons why an action was right and the agent's reasons for doing it. It is not so much the distinction itself which is the culprit, however, as the account of it that sees motivating reasons as complexes of beliefs and desires, i.e. as complexes of psychological states of whatever sort, and sees justifying reasons as truths. It is this account, which puts into form the attempt to combine value realism with Humean philosophical psychology, that leads to the results I have outlined above. (shrink)
Abstract: I examine virtue theory, especially as expressed by Rosalind Hursthouse. In its canonical form, the theory claims that living a life of virtue constitutes flourishing, although it also has a possible fall-back claim that a life of virtue is a means to the end of flourishing. I argue that in both interpretations, virtue theory is mistaken. It cannot give any convincing account of how the concepts of wanting, flourishing, and the virtues are connected, nor can it (...) deal adequately with the counter-examples of flourishing by the wicked, and torment for the virtuous. However, I allow that stripped of all its pretensions to universality, there are grounds for some people in some restricted sets circumstances, to follow the path of virtue solely because they will thereby flourish. (shrink)
So what is feminism anyway? Why are all the experts so reluctant to give us a clear definition? Is it possible to make sense of the complex and often contradictory debates? In this concise and accessible introduction to feminist theory, Chris Beasley provides clear explanations of the many types of feminism. She outlines the development of liberal, radical and Marxist//socialist feminism, and reviews the more contemporary influences of psychoanalysis, postmodernism, theories of the body, queer theory, and attends to (...) the ongoing significance of race and ethnicity. Given the diversity of feminist ideas, Chris Beasley a number of ways of looking at feminist theory and offer an open-ended approach which allows for variety and change. What is Feminism? is a clear and up-to-date guide to Western feminist theory for students, their teachers, researchers and anyone else who wants to understand and engage in current feminist debates. `Over the last three decades feminist theories and methodologies have become an increasingly complex as well as somewhat fraught terrain where ideas and egos alternately clash productively and destructively. This is an up-to-date and intelligent introduction to a field which remains a vital component of contemporary sociopolitical issues and debates' - Sneja Gunew, Professor of English and Women’s Studies, University of British Columbia. (shrink)
The theory of mind (ToM) deficit associated with autism has been a central topic in the debate about the modularity of the mind. Most involved in the debate about the explanation of the ToM deficit have failed to notice that autism’s status as a spectrum disorder has implications about which explanation is more plausible. In this paper, I argue that the shift from viewing autism as a unified syndrome to a spectrum disorder increases the plausibility of the explanation of (...) the ToM deficit that appeals to a domain-specific, higher-level ToM module. First, I discuss what it means to consider autism as a spectrum rather than as a unified disorder. Second, I argue for the plausibility of the modular explanation on the basis that autism is better considered as a spectrum disorder. Third, I respond to a potential challenge to my account from Philip Gerrans and Valerie Stone’s recent work (Gerrans, Biol Philos 17:305–321, 2002; Stone and Gerrans, Trends Cogn Sci 10:3–4, 2006a; Soc Neurosci 1:309–319, 2006b; Gerrans and Stone, Br J Philos Sci 59:121–141, 2008). (shrink)
Alison Gopnik and Andrew Meltzoff have argued for a view they call the ‘theorytheory’: theory change in science and children are similar. While their version of the theorytheory has been criticized for depending on a number of disputed claims, we argue that there is a fundamental problem which is much more basic: the theorytheory is multiply ambiguous. We show that it might be claiming that a similarity holds between theory (...) change in children and (i) individual scientists, (ii) a rational reconstruction of a Superscientist, or (iii) the scientific community. We argue that (i) is false, (ii) is non-empirical (which is problematic since the theorytheory is supposed to be a bold empirical hypothesis), and (iii) is either false or doesn’t make enough sense to have a truth-value. We conclude that the theorytheory is an interesting failure. Its failure points the way to a full, empirical picture of scientific development, one that marries a concern with the social dynamics of science to a psychological theory of scientific cognition. 2002 Elsevier Science Ltd. All rights reserved. (shrink)
The measurement problem of quantum theory is discussed, and the difficulty of trying to solve it within the confines of a local, Lorentz-invariant physics is emphasised. This leads to the obvious suggestion to seek a solution beyond physics, in particular, by introducing the concept of consciousness. The resulting dualistic model, in the natural form suggested by quantum theory, is shown to differ in several respects from the classical model of Descartes, and to suggest solutions to some of the (...) long-standing problems concerning the relation of consciousness to the physical world. (shrink)
The theory of mind (ToM) deficit associated with autism spectrum disorder has been a central topic in the debate about the modularity of the mind. In a series of papers, Philip Gerrans and Valerie Stone argue that positing a ToM module does not best explain the deficits exhibited by individuals with autism (Gerrans 2002; Stone & Gerrans 2006a, 2006b; Gerrans & Stone 2008). In this paper, I first criticize Gerrans and Stone’s (2008) account. Second, I discuss various studies of (...) individuals with autism and argue that they are best explained by positing a higher-level, domain-specific ToM module. (shrink)
