Do numbers, sets, and so forth, exist? What do mathematical statements mean? Are they literally true or false, or do they lack truth values altogether? Addressing questions that have attracted lively debate in recent years, Stewart Shapiro contends that standard realist and antirealist accounts of mathematics are both problematic. As Benacerraf first noted, we are confronted with the following powerful dilemma. The desired continuity between mathematical and, say, scientific language suggests realism, but realism in this context suggests seemingly intractable epistemic (...) problems. As a way out of this dilemma, Shapiro articulates a structuralist approach. On this view, the subject matter of arithmetic, for example, is not a fixed domain of numbers independent of each other, but rather is the natural number structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle. Using this framework, realism in mathematics can be preserved without troublesome epistemic consequences. Shapiro concludes by showing how a structuralist approach can be applied to wider philosophical questions such as the nature of an "object" and the Quinean nature of ontological commitment. Clear, compelling, and tautly argued, Shapiro's work, noteworthy both in its attempt to develop a full-length structuralist approach to mathematics and to trace its emergence in the history of mathematics, will be of deep interest to both philosophers and mathematicians. (shrink)
Embodied cognition often challenges standard cognitive science. In this outstanding introduction, Lawrence Shapiro sets out the central themes and debates surrounding embodied cognition, explaining and assessing the work of many of the key figures in the field, including George Lakoff, Alva Noë, Andy Clark, and Arthur Glenberg. Beginning with an outline of the theoretical and methodological commitments of standard cognitive science, Shapiro then examines philosophical and empirical arguments surrounding the traditional perspective. He introduces topics such as dynamic systems theory, ecological (...) psychology, robotics, and connectionism, before addressing core issues in philosophy of mind such as mental representation and extended cognition. Including helpful chapter summaries and annotated further reading at the end of each chapter, _Embodied Cognition_ is essential reading for all students of philosophy of mind, psychology, and cognitive science. (shrink)
Shapiro tests these hypotheses against two rivals, the mental constraint thesis and the embodied mind thesis. Collecting evidence from a variety of sources (e.g., neuroscience, evolutionary theory, and embodied cognition) he concludes that the multiple realizability thesis, accepted by most philosophers as a virtual truism, is much less obvious than commonly assumed, and that there is even stronger reason to give up the separability thesis. In contrast to views of mind that tempt us to see the mind as simply being (...) resident in a brain or body, Shapiro argues for a far more encompassing integration of mind, brain, and body than philosophers have supposed. (publisher, edited). (shrink)
What is law (and why should we care)? -- Crazy little thing called "law" -- Austin's sanction theory -- Hart and the rule of recognition -- How to do things with plans -- The making of a legal system -- What law is -- Legal reasoning and judicial decision making -- Hard cases -- Theoretical disagreements -- Dworkin and distrust -- The economy of trust -- The interpretation of plans -- The value of legality.
A line of research within embodied cognition seeks to show that an organism’s body is a determinant of its conceptual capacities. Comparison of this claim of body determinism to linguistic determinism bears interesting results. Just as Slobin’s (1996) idea of thinking for speaking challenges the main thesis of linguistic determinism, so too the possibility of thinking for acting raises difficulties for the proponent of body determinism. However, recent studies suggest that the body may, after all, have a determining role in (...) cognitive processes of sentence comprehension. (shrink)
The central contention of this book is that second-order logic has a central role to play in laying the foundations of mathematics. In order to develop the argument fully, the author presents a detailed description of higher-order logic, including a comprehensive discussion of its semantics. He goes on to demonstrate the prevalence of second-order concepts in mathematics and the extent to which mathematical ideas can be formulated in higher-order logic. He also shows how first-order languages are often insufficient to codify (...) many concepts in contemporary mathematics, and thus that both first- and higher-order logics are needed to fully reflect current work. Throughout, the emphasis is on discussing the associated philosophical and historical issues and the implications they have for foundational studies. For the most part, the author assumes little more than a familiarity with logic comparable to that provided in a beginning graduate course which includes the incompleteness of arithmetic and the Lowenheim-Skolem theorems. All those concerned with the foundations of mathematics will find this a thought-provoking discussion of some of the central issues in the field today. (shrink)
Stewart Shapiro's ambition in Vagueness in Context is to develop a comprehensive account of the meaning, function, and logic of vague terms in an idealized version of a natural language like English. It is a commonplace that the extensions of vague terms vary according to their context: a person can be tall with respect to male accountants and not tall (even short) with respect to professional basketball players. The key feature of Shapiro's account is that the extensions of vague terms (...) also vary in the course of conversations and that, in some cases, a competent speaker can go either way without sinning against the meaning of the words or the non-linguistic facts. As Shapiro sees it, vagueness is a linguistic phenomenon, due to the kinds of languages that humans speak; but vagueness is also due to the world we find ourselves in, as we try to communicate features of it to each other. (shrink)
This paper discusses the neo-logicist approach to the foundations of mathematics by highlighting an issue that arises from looking at the Bad Company objection from an epistemological perspective. For the most part, our issue is independent of the details of any resolution of the Bad Company objection and, as we will show, it concerns other foundational approaches in the philosophy of mathematics. In the first two sections, we give a brief overview of the "Scottish" neo-logicist school, present a generic form (...) of the Bad Company objection and introduce an epistemic issue connected to this general problem that will be the focus of the rest of the paper. In the third section, we present an alternative approach within philosophy of mathematics, a view that emerges from Hilbert's Grundlagen der Geometrie (1899, Leipzig: Teubner; Foundations of geometry (trans.: Townsend, E.). La Salle, Illinois: Open Court, 1959.). We will argue that Bad Company-style worries, and our concomitant epistemic issue, also affects this conception and other foundationalist approaches. In the following sections, we then offer various ways to address our epistemic concern, arguing, in the end, that none resolves the issue. The final section offers our own resolution which, however, runs against the foundationalist spirit of the Scottish neo-logicist program. (shrink)
According to traditional logical expressivism, logical operators allow speakers to explicitly endorse claims that are already implicitly endorsed in their discursive practice — endorsed in virtue of that practice’s having instituted certain logical relations. Here, I propose a different version of logical expressivism, according to which the expressive role of logical operators is explained without invoking logical relations at all, but instead in terms of the expression of discursive-practical attitudes. In defense of this alternative, I present a deflationary account of (...) the expressive role of vocabulary by which we ascribe logical relations. (shrink)
Some authors have claimed that ante rem structuralism has problems with structures that have indiscernible places. In response, I argue that there is no requirement that mathematical objects be individuated in a non-trivial way. Metaphysical principles and intuitions to the contrary do not stand up to ordinary mathematical practice, which presupposes an identity relation that, in a sense, cannot be defined. In complex analysis, the two square roots of –1 are indiscernible: anything true of one of them is true of (...) the other. I suggest that i functions like a parameter in natural deduction systems. I gave an early version of this paper at a workshop on structuralism in mathematics and science, held in the Autumn of 2006, at Bristol University. Thanks to the organizers, particularly Hannes Leitgeb, James Ladyman, and Øystein Linnebo, to my commentator Richard Pettigrew, and to the audience there. The paper also benefited considerably from a preliminary session at the Arché Research Centre at the University of St Andrews. I am indebted to my colleagues Craige Roberts, for help with the linguistics literature, and Ben Caplan and Gabriel Uzquiano, for help with the metaphysics. Thanks also to Hannes Leitgeb and Jeffrey Ketland for reading an earlier version of the manuscript and making helpful suggestions. I also benefited from conversations with Richard Heck, John Mayberry, Kevin Scharp, and Jason Stanley. CiteULike Connotea Del.icio.us What's this? (shrink)
This unique book by Stewart Shapiro looks at a range of philosophical issues and positions concerning mathematics in four comprehensive sections. Part I describes questions and issues about mathematics that have motivated philosophers since the beginning of intellectual history. Part II is an historical survey, discussing the role of mathematics in the thought of such philosophers as Plato, Aristotle, Kant, and Mill. Part III covers the three major positions held throughout the twentieth century: the idea that mathematics is logic (logicism), (...) the view that the essence of mathematics is the rule-governed manipulation of characters (formalism), and a revisionist philosophy that focuses on the mental activity of mathematics (intuitionism). Finally, Part IV brings the reader up-to-date with a look at contemporary developments within the discipline. This sweeping introductory guide to the philosophy of mathematics makes these fascinating concepts accessible to those with little background in either mathematics or philosophy. (shrink)
Deflationists about truth seek to undermine debates about the nature of truth by arguing that the truth predicate is merely a device that allows us to express a certain kind of generality. I argue that a parallel approach is available in the case of logical consequence. Just as deflationism about truth offers an alternative to accounts of truth's nature in terms of correspondence or justification, deflationism about consequence promises an alternative to model-theoretic or proof-theoretic accounts of consequence's nature. I then (...) argue, against considerations put forward by Field and Beall, that Curry's paradox no more rules out deflationism about consequence than the liar paradox rules out deflationism about truth. (shrink)
In this article, we propose a novel account of general jurisprudence by situating it within the broader project of metanormative inquiry. We begin by showing how general jurisprudence is parallel to another well-known part of that project, namely, metaethics. We then argue that these projects all center on the same task: explaining how a certain part of thought, talk, and reality fits into reality overall. Metalegal inquiry aims to explain how legal thought, talk, and reality fit into reality. General jurisprudence (...) is the part of metalegal inquiry that focuses on universal legal thought, talk, and reality. (shrink)
This project continues our interdisciplinary research into computational and cognitive aspects of narrative comprehension. Our ultimate goal is the development of a computational theory of how humans understand narrative texts. The theory will be informed by joint research from the viewpoints of linguistics, cognitive psychology, the study of language acquisition, literary theory, geography, philosophy, and artiﬁcial intelligence. The linguists, literary theorists, and geographers in our group are developing theories of narrative language and spatial understanding that are being tested by the (...) cognitive psychologists and language researchers in our group, and a computational model of a reader of narrative text is being developed by the AI researchers, based in part on these theories and results and in part on research on knowledge representation and reasoning. This proposal describes the knowledge-representation and natural-language-processing issues involved in the computational implementation of the theory; discusses a contrast between communicative and narrative uses of language and of the relation of the narrative text to the story world it describes; investigates linguistic, literary, and hermeneutic dimensions of our research; presents a computational investigation of subjective sentences and reference in narrative; studies children’s acquisition of the ability to take third-person perspective in their own storytelling; describes the psychological validation of various linguistic devices; and examines how readers develop an understanding of the geographical space of a story. This report is a longer version of a project description submitted to NSF. This document, produced in May 2007, is a L ATEX version of Technical Report 89-07 (Buffalo: SUNY Buffalo Department of Computer Science, August 1989), with slightly.. (shrink)
When conceived as an empirical claim, it is natural to wonder how one might test the hypothesis of multiple realization. I consider general issues of testability, show how they apply specifically to the hypothesis of multiple realization, and propose an auxiliary assumption that, I argue, must be conjoined to the hypothesis of multiple realization to ensure its testability. I argue further that Bechtel and Mundale go astray because they fail to appreciate the need for this auxiliary assumption. †To contact the (...) author, please write to: Department of Philosophy, University of Wisconsin–Madison, 5185 Helen C. White Hall, 600 North Park Street, Madison, WI 53706; e‐mail: email@example.com. (shrink)
Jaegwon Kim’s causal exclusion argument has rarely been evaluated from an empirical perspective. This is puzzling because its conclusion seems to be making a testable claim about the world: supervenient properties are causally inefficacious. An empirical perspective, however, reveals Kim’s argument to rest on a mistaken conception about how to test whether a property is causally efficacious. Moreover, the empirical perspective makes visible a metaphysical bias that Kim brings to his argument that involves a principle of non-inclusion.
Carl Gillett has defended what he calls the “dimensioned” view of the realization relation, which he contrasts with the traditional “flat” view of realization (2003, 2007; see also Gillett 2002). Intuitively, the dimensioned approach characterizes realization in terms of composition whereas the flat approach views realization in terms of occupiers of functional roles. Elsewhere we have argued that the general view of realization and multiple realization that Gillett advances is not able to discharge the theoretical duties of those relations (Shapiro (...) 2004, unpublished manuscript; Polger 2004, 2007, forthcoming). Here we focus on an internal objection to Gillett’s account and then raise some broader reasons to reject it. (shrink)
A statement of the form ‘C caused E’ obeys the requirement of proportionality precisely when C says no more than what is necessary to bring about E. The thesis that causal statements must obey this requirement might be given a semantic or a pragmatic justification. We use the idea that causal claims are contrastive to criticize both.
Christian List and Peter Menzies 2009 have looked to interventionist theories of causation for an answer to Jaegwon Kim's causal exclusion problem. Important to their response is the idea of realization-insensitivity. However, this idea becomes mired in issues concerning multiple realization, leaving it unable to fulfil its promise to block exclusion. After explaining why realization-insensitivity fails as a solution to Kim's problem, I look to interventionism to describe a different kind of solution.
Jaegwon Kim's causal exclusion argument has rarely been evaluated from an empirical perspective. This is puzzling because its conclusion seems to be making a testable claim about the world: supervenient properties are causally inefficacious. An empirical perspective, however, reveals Kim's argument to rest on a mistaken conception about how to test whether a property is causally efficacious. Moreover, the empirical perspective makes visible a metaphysical bias that Kim brings to his argument that involves a principle of non-inclusion.
One of the first volumes in the new series of prestigious Oxford Handbooks, The Oxford Handbook of Jurisprudence and Philosophy of Law brings together specially commissioned essays by twenty-seven of the foremost legal theorists currently writing, to provide a state of the art overview of jurisprudential scholarship. Each author presents an account of the contending views and scholarly debates animating their field of enquiry as well as setting the agenda for further study. This landmark publication will be essential reading for (...) anyone working in legal theory and of interest to legal scholars generally, philosophers and legal theorists looking for a way in to understand current jurisprudential thinking. (shrink)
Many who advocate dynamical systems approaches to cognitive science believe themselves committed to the thesis of extended cognition and to the rejection of representation. I argue that this belief is false. In part, this misapprehension rests on a warrantless re-conception of cognition as intelligent behavior. In part also, it rests on thinking that conceptual issues can be resolved empirically. Once these issues are sorted out, the way is cleared for a dynamical systems approach to cognition that is free to retain (...) the standard conception of cognition as taking place in the head, and over representations. (shrink)
The revisionary approach to semantic paradox is commonly thought to have a somewhat uncomfortable corollary, viz. that, on pain of triviality, we cannot affirm that all valid arguments preserve truth (Beall2007, Beall2009, Field2008, Field2009). We show that the standard arguments for this conclusion all break down once (i) the structural rule of contraction is restricted and (ii) how the premises can be aggregated---so that they can be said to jointly entail a given conclusion---is appropriately understood. In addition, we briefly rehearse (...) some reasons for restricting structural contraction. (shrink)
_Arguing About the Mind_ is an accessible, engaging introduction to the core questions in the philosophy of mind. This collection offers a selection of thought-provoking articles that examine a broad range of issues from the mind and body relation to animal and artificial intelligence. Topics addressed include: the problem of consciousness; the nature of the mind; the relationship between the mind, body and world; the notion of selfhood; pathologies and behavioural problems; animal, machine and extra-terrestrial intelligence. The editors provide lucid (...) introductions to each section, give an overview of the debate and outline the arguments of the papers. An original and stimulating reader, _Arguing About the Mind_ is ideal for students new to the philosophy of mind. (shrink)
For the past four decades, Anglo-American legal philosophy has been preoccupied – some might say obsessed – with something called the “Hart-Dworkin” debate. Since the appearance in 1967 of “The Model of Rules I,” Ronald Dworkin’s seminal critique of H.L.A. Hart’s theory of legal positivism, countless books and articles have been written either defending Hart against Dworkin’s objections or defending Dworkin against Hart’s defenders. My purpose in this essay is not to declare an ultimate victor; rather it is to identify (...) precisely the core issue around which the debate is organized. Is the Hart-Dworkin debate, for example, about whether the law contains principles, as well as rules? Or does it concern whether judges have discretion in hard cases? Is it about the proper way to interpret legal texts in the American legal system? Or is it about the very possibility of conceptual jurisprudence? Although trying to capture the essence of a philosophical debate can be tricky, I think that there is an important unity to the Hart-Dworkin debate that can be described in a relatively straightforward manner. I suggest that the debate is organized around one of the most profound issues in the philosophy of law, namely, the relation between legality and morality. Dworkin’s basic strategy throughout the course of the debate has been to argue that, in one form or another, legality is ultimately determined not by social facts alone, but by moral facts as well. This contention directly challenges, and threatens to undermine, the positivist picture about the nature of law, in which legality is never determined by morality, but solely by social practice. As one might expect, the response by Hart and his followers has been to argue that this dependence of legality on morality is either merely apparent or does not, in fact, undermine the social foundations of law. The Hart-Dworkin debate, I also try to show, is not a monolithic entity. In the second half of the paper, I describe how Dworkin modified his critique to circumvent the responses of Hart’s followers, thereby inaugurating a new phase in the debate. Virtually no attention, however, has been paid to this latter challenge, which is especially surprising given that none of the previous positivistic defenses are helpful against it. I then sketch out a possible response positivists might offer to this extremely powerful objection. (shrink)
Next SectionIntensification of poverty and degradation of health infrastructure over recent decades in countries most affected by HIV/AIDS present formidable challenges to clinical research. This paper addresses the overall standard of health care (SOC) that should be provided to research participants in developing countries, rather than the narrow definition of SOC that has characterised the international debate on standards of health care. It argues that contributing to sustainable improvements in health by progressively ratcheting the standard of care upwards for research (...) participants and their communities is an ethical obligation of those in resource-rich countries who sponsor and implement research in poorer ones. (shrink)
There is a parallel between the debate between Gottlob Frege and David Hilbert at the turn of the twentieth century and at least some aspects of the current controversy over whether category theory provides the proper framework for structuralism in the philosophy of mathematics. The main issue, I think, concerns the place and interpretation of meta-mathematics in an algebraic or structuralist approach to mathematics. Can meta-mathematics itself be understood in algebraic or structural terms? Or is it an exception to the (...) slogan that mathematics is the science of structure? (shrink)
ABSTRACT Proponents of mechanistic explanation have recently suggested that all explanation in the cognitive sciences is mechanistic, even functional explanation. This last claim is surprising, for functional explanation has traditionally been conceived as autonomous from the structural details that mechanistic explanations emphasize. I argue that functional explanation remains autonomous from mechanistic explanation, but not for reasons commonly associated with the phenomenon of multiple realizability. 1Introduction 2Mechanistic Explanation: A Quick Primer 3Functional Explanation: An Example 4Autonomy as Lack of Constraint 5The Price (...) of Autonomy 6Another Argument against Autonomy 7Conclusion: Autonomy and Multiple Realization. (shrink)
Mathematics and logic have been central topics of concern since the dawn of philosophy. Since logic is the study of correct reasoning, it is a fundamental branch of epistemology and a priority in any philosophical system. Philosophers have focused on mathematics as a case study for general philosophical issues and for its role in overall knowledge- gathering. Today, philosophy of mathematics and logic remain central disciplines in contemporary philosophy, as evidenced by the regular appearance of articles on these topics in (...) the best mainstream philosophical journals; in fact, the last decade has seen an explosion of scholarly work in these areas. This volume covers these disciplines in a comprehensive and accessible manner, giving the reader an overview of the major problems, positions, and battle lines. The 26 contributed chapters are by established experts in the field, and their articles contain both exposition and criticism as well as substantial development of their own positions. The essays, which are substantially self-contained, serve both to introduce the reader to the subject and to engage in it at its frontiers. Certain major positions are represented by two chapters--one supportive and one critical. The Oxford Handbook of Philosophy of Math and Logic is a ground-breaking reference like no other in its field. It is a central resource to those wishing to learn about the philosophy of mathematics and the philosophy of logic, or some aspect thereof, and to those who actively engage in the discipline, from advanced undergraduates to professional philosophers, mathematicians, and historians. (shrink)
Michael Lynch’s Truth as One and Many is a contribution to the large body of philosophical literature on the nature of truth. Within that genre, advocates of truth-as-correspondence, advocates of truth-as-coherence, and the like, all hold that truth has a single underlying metaphysical nature, but they sharply disagree as to what this nature is. Lynch argues that many of these views make good sense of truth attributions for a limited stretch of discourse, but he adds that each of the contenders (...) also faces a ‘scope problem’, in that none of them makes sense of all legitimate truth attributions. Some deflationists make similar observations – usually less concessive – and conclude that truth simply has no substantial, underlying nature. There is nothing for the philosopher to articulate and defend. Lynch agrees with deflationists that the realm of discourse is too diverse for any single ‘first-level’ property, such as correspondence or coherence, to fully characterize it, but against deflationism, he holds that truth does have a nature. He presents a functionalist theory. The definition is this: x is true if, and only if, x has a property that plays the truth-role. According to Lynch, the truth-role is given in terms of what he calls the ‘core truisms’ of the folk concept of truth. These are platitudes that hold of the everyday notion, and are such that anyone who denies all of them can be accused of changing the subject – of not talking about truth. A given property T plays the truth-role for a batch of propositions, just in case, for any proposition P in the batch: P is T if, and only if, where P is believed, things are as they are believed to be; other things being equal, it is a worthy goal …. (shrink)
The purpose of this paper is to assess the prospects for a neo-logicist development of set theory based on a restriction of Frege's Basic Law V, which we call (RV): PQ[Ext(P) = Ext(Q) [(BAD(P) & BAD(Q)) x(Px Qx)]] BAD is taken as a primitive property of properties. We explore the features it must have for (RV) to sanction the various strong axioms of Zermelo–Fraenkel set theory. The primary interpretation is where ‘BAD’ is Dummett's ‘indefinitely extensible’. 1 Background: what and why? (...) 2 Framework 3 GOOD candidates, indefinite extensibility 4 The framework of (RV) alone, or almost alone 5 The axioms 6 Brief closing. (shrink)
Several authors have argued that a version of Curry's paradox involving validity motivates rejecting the structural rule of contraction. This paper criticizes two recently suggested alternative responses to “validity Curry.” There are three salient stages in a validity Curry derivation. Rejecting contraction blocks the first, while the alternative responses focus on the second and third. I show that a distinguishing feature of validity Curry, as contrasted with more familiar forms of Curry's paradox, is that paradox arises already at the first (...) stage. Accordingly, blocking the second or third stages won't suffice for resolving the paradox. (shrink)
Several scholarly trends, such as narrative medicine, patient-centered and relationship-centered care, have long advocated for the value of the patient's voice in the practice of medicine. As theories of textual analysis are applied to the understanding of stories of illness, doctors and scholars have the opportunity to develop more nuanced and multifaceted appreciation for these accounts. We realize, for example, that a patient's story is rarely “just a story,” but is rather the conscious and unconscious representation and performance of intricate (...) personal motives and dominant meta-narrative influences. Overall, this complexifying of narrative is beneficial as it reduces readers' and listeners' naïve assumptions about reliability and authenticity. However, the growing body of scholarship contesting various aspects of personal narratives may have the unintended effect of de-legitimizing the patient's voice because of concerns regarding its trustworthiness. Further, the academy's recent focus on transgressive, boundary-violating counternarratives, while meant to right the balance of what constitutes acceptable, even valuable stories in medicine, may inadvertently trivialize more conventional, conformist stories as inauthentic. While acknowledging the not inconsiderable pitfalls awaiting the interpreter of illness narratives, I argue that ultimately, physicians and scholars should approach patient stories with an attitude of narrative humility, despite inevitable limits on reliability and authenticity. While critical inquiry is an essential part of both good clinical practice and scholarship, first and foremost both types of professionals should respect that patients tell the stories they need to tell. (shrink)