Since Hilary Putnam offered multiple realization as an empirical hypothesis in the 1960s, philosophical consensus has turned against the idea that mental processes are identifiable with brain processes, and multiple realization has become the keystone of the 'antireductive consensus' across philosophy of science. Thomas W. Polger and Lawrence A. Shapiro offer the first book-length investigation of multiple realization, which serves as a starting point to a series of philosophically sophisticated and empirically informed arguments that cast doubt on the generality of (...) multiple realization in the cognitive sciences. They argue that mind-brain identities have played an important role in the growth and achievements of the cognitive sciences, and suggest that there is little prospect for multiple realization in an empirically-based theory of mind. This leads Polger and Shapiro to offer an alternative framework for understanding explanations in the cognitive sciences, as well as in chemistry, biology, and other non-basic sciences. (shrink)

Logical pluralism is the view that different logics are equally appropriate, or equally correct. Logical relativism is a pluralism according to which validity and logical consequence are relative to something. Stewart Shapiro explores various such views. He argues that the question of meaning shift is itself context-sensitive and interest-relative.

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)

Moving beyond both realist and anti-realist accounts of mathematics, Shapiro articulates a "structuralist" approach, arguing that the subject matter of a mathematical theory is not a fixed domain of numbers that exist independent of each other, but rather is the natural structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle.

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)

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.

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)

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 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)

Presents John Locke's seventeenth-century classic work on political and social theory; and includes a history of the text, as well as notes and a bibliography.

The notion of potential infinity dominated in mathematical thinking about infinity from Aristotle until Cantor. The coherence and philosophical importance of the notion are defended. Particular attention is paid to the question of whether potential infinity is compatible with classical logic or requires a weaker logic, perhaps intuitionistic.

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)

Democracy and justice are often mutually antagonistic ideas, but in this innovative book Ian Shapiro shows how and why they should be pursued together. Justice must be sought democratically if it is to garner legitimacy in the modern world, he claims, and democracy must be justice-promoting if it is to sustain allegiance over time. _Democratic Justice_ meets these criteria, offering an attractive vision of a practical path to a better future. Wherever power is exercised in human affairs, Shapiro argues, the (...) lack of democracy will be experienced as injustice. The challenge is to democratize social relations so as to diminish injustice, but to do this in ways that are compatible with people’s values and goals. Shapiro shows how this can be done in different phases of the human life cycle, from childhood through the adult worlds of work and domestic life, retirement, old age, and approaching death. He spells out the implications for pressing debates about authority over children, the law of marriage and divorce, population control, governing the firm, basic income guarantees, health insurance, retirement policies, and decisions made by and for the infirm elderly. This refreshing encounter between political philosophy and practical politics will interest all those who aspire to bequeath a more just world to our children than the one we have inherited. (shrink)

When philosophers defend epiphenomenalist doctrines, they often do so by way of a priori arguments. Here we suggest an empirical approach that is modeled on August Weismann’s experimental arguments against the inheritance of acquired characters. This conception of how epiphenomenalism ought to be developed helps clarify some mistakes in two recent epiphenomenalist positions – Jaegwon Kim’s (1993) arguments against mental causation, and the arguments developed by Walsh (2000), Walsh, Lewens, and Ariew (2002), and Matthen and Ariew (2002) that natural selection (...) and drift are not causes of evolution. A manipulationist account of causation (Woodward 2003) leads naturally to an account of how macro- and micro-causation are related and to an understanding of how epiphenomenalism at different levels of organization should be understood. (shrink)

According to Ole Hjortland, Timothy Williamson, Graham Priest, and others, anti-exceptionalism about logic is the view that logic “isn’t special”, but is continuous with the sciences. Logic is revisable, and its truths are neither analytic nor a priori. And logical theories are revised on the same grounds as scientific theories are. What isn’t special, we argue, is anti-exceptionalism about logic. Anti-exceptionalists disagree with one another regarding what logic and, indeed, anti-exceptionalism are, and they are at odds with naturalist philosophers of (...) logic, who may have seemed like natural allies. Moreover, those internal battles concern well-trodden philosophical issues, and there is no hint as to how they are to be resolved on broadly scientific grounds. We close by looking at three of the founders of logic who may have seemed like obvious enemies of anti-exceptionalism—Aristotle, Frege, and Carnap—and conclude that none of their positions is clearly at odds with at least some of the main themes of anti-exceptionalism. We submit that, at least at present, anti-exceptionalism is too vague or underspecified to characterize a coherent conception of logic, one that stands opposed to more traditional approaches. (shrink)

The present work is a systematic study of five frameworks or perspectives articulating mathematical structuralism, whose core idea is that mathematics is concerned primarily with interrelations in abstraction from the nature of objects. The first two, set-theoretic and category-theoretic, arose within mathematics itself. After exposing a number of problems, the book considers three further perspectives formulated by logicians and philosophers of mathematics: sui generis, treating structures as abstract universals, modal, eliminating structures as objects in favor of freely entertained logical possibilities, (...) and finally, modal-set-theoretic, a sort of synthesis of the set-theoretic and modal perspectives. (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)

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)

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)

Moving beyond both realist and anti-realist accounts of mathematics, Shapiro articulates a "structuralist" approach, arguing that the subject matter of a mathematical theory is not a fixed domain of numbers that exist independent of each other, but rather is the natural structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle.

In the literature, predicativism is connected not only with the Vicious Circle Principle but also with the idea that certain totalities are inherently potential. To explain the connection between these two aspects of predicativism, we explore some approaches to predicativity within the modal framework for potentiality developed in Linnebo (2013) and Linnebo and Shapiro (2019). This puts predicativism into a more general framework and helps to sharpen some of its key theses.

ABSTRACT:I reflect critically on the early modern philosophical canon in light of the entrenchment and homogeneity of the lineup of seven core figures: Descartes, Spinoza, Leibniz, Locke, Berkeley, Hume, and Kant. After distinguishing three elements of a philosophical canon—a causal story, a set of core philosophical questions, and a set of distinctively philosophical works—I argue that recent efforts contextualizing the history of philosophy within the history of science subtly shift the central philosophical questions and allow for a greater range of (...) figures to be philosophically central. However, the history of science is but one context in which to situate philosophical works. Looking at the historical context of seventeenth-century philosophy of mind, one that weaves together questions of consciousness, rationality, and education, does more than shift the central questions—it brings new ones to light. It also shows that a range of genres can be properly philosophical and seamlessly diversifies the central philosophers of the period. (shrink)

According to commitment accounts of assertion, asserting is committing oneself to something’s being the case, where such commitment is understood in terms of norms governing a social practice. I elaborate and compare two version of such accounts, liability accounts (associated with C.S. Peirce) and dialectical norm accounts (associated with Robert Brandom), concluding that the latter are more defensible. I argue that both versions of commitment account possess a potential advantage over rival normative accounts of assertion in that they needn’t presuppose (...) any notion of an assertion’s correctness. Additionally, I show how dialectical norm accounts can explain relations between assertion and truth. After setting forth objections that have been raised against commitment accounts, I argue that responses are available on behalf of dialectical norm accounts. Finally, I propose that a liberalized dialectical norm account can illuminate phenomena sometimes seen as supporting truth relativism. (shrink)

Embodied cognition is one of the foremost areas of study and research in philosophy of mind, philosophy of psychology and cognitive science. The Routledge Handbook of Embodied Cognition is an outstanding guide and reference source to the key philosophers, topics and debates in this exciting subject and essential reading for any student and scholar of philosophy of mind and cognitive science. Comprising over thirty chapters by a team of international contributors, the Handbook is divided into six parts: Historical Underpinnings Perspectives (...) on Embodied Cognition Applied Embodied Cognition: Perception, Language and Reasoning Applied Embodied Cognition: Social and Moral Cognition and Emotion Applied Embodied Cognition: Memory, Attention and Group Cognition Meta-Topics. The early chapters of the Handbook cover empirical and philosophical foundations of embodied cognition, focusing on Gibsonian, phenomenological and cybernetic approaches. Subsequent chapters cover additional, important themes common to work in embodied cognition, incuding embedded , extended and enactive cognition as well as chapters on embodied cognition and empirical research in perception, language, reasoning, social and moral cognition, emotion, consciousness, memory and learning and development. (shrink)

We have Nietzsche to thank for some of the most important accomplishments in intellectual history, but as Gary Shapiro shows in this unique look at Nietzsche’s thought, the nineteenth-century philosopher actually anticipated some of the most pressing questions of our own era. Putting Nietzsche into conversation with contemporary philosophers such as Deleuze, Agamben, Foucault, Derrida, and others, Shapiro links Nietzsche’s powerful ideas to topics that are very much on the contemporary agenda: globalization, the nature of the livable earth, and the (...) geopolitical categories that characterize people and places. Shapiro explores Nietzsche’s rejection of historical inevitability and its idea of the end of history. He highlights Nietzsche’s prescient vision of today’s massive human mobility and his criticism of the nation state’s desperate efforts to sustain its exclusive rule by declaring emergencies and states of exception. Shapiro then explores Nietzsche’s vision of a transformed garden earth and the ways it sketches an aesthetic of the Anthropocene. He concludes with an explanation of the deep political structure of Nietzsche’s “philosophy of the Antichrist,” by relating it to traditional political theology. By triangulating Nietzsche between his time and ours, between Bismarck’s Germany and post-9/11 America, Nietzsche’s Earth invites readers to rethink not just the philosopher himself but the very direction of human history. (shrink)

An outstanding reference source for the wide range of philosophical contributions made by women writing in Europe from about 1560 to 1780. It shows the range of genres and methods used by women writing in these centuries in Europe, thus encouraging an expanded understanding of our historical canon.

This chapter provides broad coverage of the notion of logical consequence, exploring its modal, semantic, and epistemic aspects. It develops the contrast between proof-theoretic notion of consequence, in terms of deduction, and a model-theoretic approach, in terms of truth-conditions. The main purpose is to relate the formal, technical work in logic to the philosophical concepts that underlie reasoning.

According to the multiple realization argument, mental states or processes can be realized in diverse and heterogeneous physical systems; and that fact implies that mental state or process kinds cannot be identified with particular kinds of physical states or processes. More specifically, mental processes cannot be identified with brain processes. Moreover, the argument provides a general model for the autonomy of the special sciences. The multiple realization argument is widely influential, but over the last thirty years it has also faced (...) serious objections. Despite those objections, most philosophers regard the fact of multiple realization and the cogency of the multiple realization argument as plainly correct. Why is that? What is it about the multiple realization argument that makes it so resilient? One reason is that the multiple realization argument is deeply intertwined with a view that minds are, in some sense, computational. But we argue that the sense in which minds are computational does not support the conclusion that they are ipso facto multiply realized. We argue that the sense in which brains compute does not imply that brains implement multiply realizable computational processes, and it does not provide a general model for the autonomy of the special sciences. (shrink)

This Oxford Handbook covers the current state of the art in the philosophy of maths and logic in a comprehensive and accessible manner, giving the reader an overview of the major problems, positions, and battle lines. The 26 newly-commissioned chapters are by established experts in the field and contain both exposition and criticism as well as substantial development of their own positions. Select major positions are represented by two chapters - one supportive and one critical. The book includes a comprehensive (...) bibliography. (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)

This paper uses neo-Fregean-style abstraction principles to develop the integers from the natural numbers (assuming Hume’s principle), the rational numbers from the integers, and the real numbers from the rationals. The first two are first-order abstractions that treat pairs of numbers: (DIF) INT(a,b)=INT(c,d) ≡ (a+d)=(b+c). (QUOT) Q(m,n)=Q(p,q) ≡ (n=0 & q=0) ∨ (n≠0 & q≠0 & m⋅q=n⋅p). The development of the real numbers is an adaption of the Dedekind program involving “cuts” of rational numbers. Let P be a property (of (...) rational numbers) and r a rational number. Say that r is an upper bound of P, written P≤r, if for any rational number s, if Ps then either s<r or s=r. In other words, P≤r if r is greater than or equal to any rational number that P applies to. Consider the Cut Abstraction Principle: (CP) ∀P∀Q(C(P)=C(Q) ≡ ∀r(P≤r ≡ Q≤r)). In other words, the cut of P is identical to the cut of Q if and only if P and Q share all of their upper bounds. The axioms of second-order real analysis can be derived from (CP), just as the axioms of second-order Peano arithmetic can be derived from Hume’s principle. The paper raises some of the philosophical issues connected with the neo-Fregean program, using the above abstraction principles as case studies. (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.

The subject of this paper is the philosophical problem of accounting for the relationship between mathematics and non-mathematical reality. The first section, devoted to the importance of the problem, suggests that many of the reasons for engaging in philosophy at all make an account of the relationship between mathematics and reality a priority, not only in philosophy of mathematics and philosophy of science, but also in general epistemology/metaphysics. This is followed by a (rather brief) survey of the major, traditional philosophies (...) of mathematics indicating how each is prepared to deal with the present problem. It is shown that (the standard formulations of) some views seem to deny outright that there is a relationship between mathematics and any non-mathematical reality; such philosophies are clearly unacceptable. Other views leave the relationship rather mysterious and, thus, are incomplete at best. The final, more speculative section provides the direction of a positive account. A structuralist philosophy of mathematics is outlined and it is proposed that mathematics applies to reality though the discovery of mathematical structures underlying the non-mathematical universe. (shrink)

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)

Modal logic has been used to analyze potential infinity and potentialism more generally. However, the standard analysis breaks down in cases of divergent possibilities, where there are two or more possibilities that can be individually realized but which are jointly incompatible. This paper has three aims. First, using the intuitionistic theory of choice sequences, we motivate the need for a modal analysis of divergent potentialism and explain the challenges this involves. Then, using Beth–Kripke semantics for intuitionistic logic, we overcome those (...) challenges. Finally, we apply our modal analysis of divergent potentialism to make choice sequences comprehensible in classical terms. (shrink)

Hellman and Shapiro explore the development of the idea of the continuous, from the Aristotelian view that a true continuum cannot be composed of points to the now standard, entirely punctiform frameworks for analysis and geometry. They then investigate the underlying metaphysical issues concerning the nature of space or space-time.

Embodied Cognition is an approach to cognition that departs from traditional cognitive science in its reluctance to conceive of cognition as computational and in its emphasis on the significance of an organism's body in how and what the organism thinks. Three lines of embodied cognition research are described and some thoughts on the future of embodied cognition offered.