The authors developed this textbook in response to an increasing interest in ethics, and a growing number of courses on this topic that are now being offered in educational leadership programs. It is designed to fill a gap in instructional materials for teaching the ethics component of the knowledge base that has been established for the profession. The text has several purposes: First, it demonstrates the application of different ethical paradigms (the ethics of justice, care, critique, and the profession) through (...) discussion and analysis of real-life moral dilemmas that educational leaders face in their schools and communities. Second, it addresses some of the practical, pedagogical, and curricular issues related to the teaching of ethics for educational leaders. Third, it emphasizes the importance of ethics instruction from a variety of theoretical approaches. Finally, it provides a process that instructors might follow to develop their own ethics unit or course. * Part I provides an overview of why ethics is so important, especially for today's educational leaders, and describes a multiparadigm approach essential to practitioners as they grapple with ethical dilemmas. * Part II deals with the dilemmas themselves. Ethical dilemmas written by the authors' graduate students bring readers face-to-face with the kinds of dilemmas faced by practicing administrators in urban, suburban, and rural settings in an era full of complexities and contradictions. * Part III focuses on pedagogy and provides teaching notes for the instructor. The authors discuss the importance of self-reflection on the part of both instructors and students, and model how they thought through their own personal and professional ethical codes as well as reflected upon the critical incidents in their lives that shaped their teaching and frequently determined what they privileged in class. (shrink)
After a brief account of the problem of higher-order vagueness, and its seeming intractability, I explore what comes of the issue on a linguistic, contextualist account of vagueness. On the view in question, predicates like ‘borderline red’ and ‘determinately red’ are, or at least can be, vague, but they are different in kind from ‘red’. In particular, ‘borderline red’ and ‘determinately red’ are not colours. These predicates have linguistic components, and invoke notions like ‘competent user of the language’. On my (...) view, so-called ‘higher-order vagueness’ is actually ordinary, first-order vagueness in different predicates. I explore the possibility that, nevertheless, a pernicious regress ensues. (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 ( (...) class='Hi'>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)
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)
On Richard’s When Truth Gives Out Content Type Journal Article Pages 1-9 DOI 10.1007/s11098-011-9796-0 Authors Kevin Scharp, Department of Philosophy, The Ohio State University, 350 University Hall, 230 North Oval Mall, Columbus, OH 43210, USA Stewart Shapiro, Department of Philosophy, The Ohio State University, 350 University Hall, 230 North Oval Mall, Columbus, OH 43210, USA Journal Philosophical Studies Online ISSN 1573-0883 Print ISSN 0031-8116.
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)
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)
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 ( (...) class='Hi'>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)
In Your Body Speaks Your Mind, renowned teacher and best-selling author Deb Shapiro shows you how mastering the language of your symptoms can actually increase ...
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)
In Cinematic Political Thought , Michael J. Shapiro investigates aspects of contemporary politics and articulates a critical philosophical perspective with politically disposed treatments of contemporary cinema. Reading such films as Hoop Dreams, Lone Star, Father of the Bride II and To Live and Die in LA through the lens of Deleuze, Derrida, Foucault and Lyotard, Shapiro demonstrates what it can mean to think the political both in terms of cinema studies and in wider aesthetic and social contexts. Cinematic (...) Political Thought is a polemical work, aimed at encouraging critical, ethical and political thinking. Its breadth of theoretical scope and empirical reference, and the innovative style of presentation will make it vital reading for anyone with an interest in the conjunction of culture and politics. (shrink)
In the pursuit of a quality and well-rounded education with philosophy, Shapiro conducts an introductory lesson to students and teachers alike in order to develop deeper, more philosophical questions from their students. Academically, the article expands detail on tutoring in philosophy, analytical practices, and metaphysical activities.
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)
A paper in this journal by Fraser MacBride, ‘Can Ante Rem Structuralism Solve the Access Problem?’, raises important issues concerning the epistemological goals and burdens of contemporary philosophy of mathematics, and perhaps philosophy of science and other disciplines as well. I use a response to MacBride's paper as a framework for developing a broadly holistic framework for these issues, and I attempt to steer a middle course between reductive foundationalism and extreme naturalistic quietism. For this purpose the notion of entitlement (...) is invoked along the way, suitably modified for the present anti-foundationalist setting. (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.
In this paper, I present a new argument against inclusive legal positivism. As I show, any theory which permits morality to be a condition on legality cannot account for a core feature of legal activity, namely, that it is an activity of social planning. If the aim of a legal institution is to guide the conduct of the community through plans, it would be self-defeating if the existence of these plans could only be determined through deliberation on the merits. I (...) also argue that, insofar as inclusive legal positivism was developed as a response to Ronald Dworkin's critique of H. L. A. Hart's theory of law, it was founded on a mistake. For once we appreciate the role that planning plays in legal regulation, we will see that Dworkin's objection is based on a flawed conception of legal obligations and rights and hence does not present an objection that inclusive legal positivists were required to answer. (shrink)
At the beginning of Die Grundlagen der Arithmetik (§2) [1884], Frege observes that “it is in the nature of mathematics to prefer proof, where proof is possible”. This, of course, is true, but thinkers differ on why it is that mathematicians prefer proof. And what of propositions for which no proof is possible? What of axioms? This talk explores various notions of self-evidence, and the role they play in various foundational systems, notably those of Frege and Zermelo. I argue that (...) both programs are undermined at a crucial point, namely when self-evidence is supported by holistic and even pragmatic considerations. (shrink)
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.
One of the principal lessons of The Concept of Law is that legal systems are not only comprised of rules, but founded on them as well. As Hart painstakingly showed, we cannot account for the way in which we talk and think about the law - that is, as an institution which persists over time despite turnover of officials, imposes duties and confers powers, enjoys supremacy over other kinds of practices, resolves doubts and disagreements about what is to be done (...) in a community and so on - without supposing that it is at bottom regulated by what he called the secondary rules of recognition, change and adjudication. Given this incontrovertible demonstration that every legal system must contain rules constituting its foundation, it might seem puzzling that many philosophers have contested Hart's view. In particular, they have objected to his claim that every legal system contains a rule of recognition. More surprisingly, these critiques span different jurisprudential schools. Positivists such as Joseph Raz, as well as natural lawyers such as Ronald Dworkin and John Finnis, have been among Hart's most vocal critics. In this essay, I would like to examine the opposition to the rule of recognition. What is objectionable about Hart's doctrine? Why deny that every legal system necessarily contains a rule setting out the criteria of legal validity? And are these objections convincing? Does the rule of recognition actually exist? This essay has five parts. In Part One, I try to state Hart's doctrine of the rule of recognition with some precision. As we will see, this task is not simple, insofar as Hart's position on this crucial topic is often frustratingly unclear. I also explore in this part whether the United States Constitution, or any of its provisions, can be considered the Hartian rule of recognition for the United States legal system. In Part Two, I attempt to detail the many roles that the rule of recognition plays within Hart's theory of law. In addition to the function that Hart explicitly assigned to it, namely, the resolution of normative uncertainty within a community, I argue that the rule of recognition, and the secondary rules more generally, also account for the law's dexterity, efficiency, normativity, continuity, persistence, supremacy, independence, identity, validity, content and existence. In Part Three, I examine three important challenges to Hart's doctrine of the rule of recognition. They are: 1) Hart's rule of recognition is under- and over-inclusive; 2) Hart cannot explain how social practices are capable of generating rules that confer powers and impose duties and hence cannot account for the normativity of law; 3) Hart cannot explain how disagreements about the criteria of legal validity that occur within actual legal systems, such as in American law, are possible. In Parts Four and Five, I address these various objections. I argue that although Hart's particular account of the rule of recognition is flawed and should be rejected, a related notion can be fashioned and should be substituted in its place. The idea, roughly, is to treat the rule of recognition as a shared plan which sets out the constitutional order of a legal system. As I try to show, understanding the rule of recognition in this new way allows the legal positivist to overcome the challenges lodged against Hart's version while still retaining the power of the original idea. (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)
The purpose of this paper is to apply Crispin Wright’s criteria and various axes of objectivity to mathematics. I test the criteria and the objectivity of mathematics against each other. Along the way, various issues concerning general logic and epistemology are encountered.
The article is part of a symposium on Hartry Field’s “Saving truth from paradox”. The book is one of the most significant intellectual achievements of the past decades, but it is not clear what, exactly, it accomplishes. I explore some alternatives, relating the developed view to the intuitive, pre-theoretic notion of truth.
It is sometimes said that there are two, competing versions of W. V. O. Quine’s unrelenting empiricism, perhaps divided according to temporal periods of his career. According to one, logic is exempt from, or lies outside the scope of, the attack on the analytic-synthetic distinction. This logic-friendly Quine holds that logical truths and, presumably, logical inferences are analytic in the traditional sense. Logical truths are knowable a priori, and, importantly, they are incorrigible, and so immune from revision. The other, radical (...) reading of Quine does not exempt logic from the attack on analyticity and a priority. Logical truths and inferences are themselves part of the web of belief, and the same global methodology applies to logic as to any other part of the web, such as theoretical chemistry or ordinary beliefs about ordinary objects. Everything, including logic, is up for grabs in our struggle for holistic confirmation. The purpose of this paper is to examine the law of non-contradiction, and the concomitant principle of ex falso quodlibet, from the perspective of the principles advocated by the radical Quine. I show that he has no compelling reason to accept either of these. To put it bluntly, neither the law of non-contradiction nor the rule of ex falso quodlibet is empirically confirmed, and these principles fare poorly on the various criteria for theory acceptance on the methodology of the radical Quine. So the radical Quine is led rather quickly and rather directly into something in the neighborhood of Graham Priest’s dialetheism. (shrink)
Brandom's "inferentialism"—his theory that contentfulness consists in being governed by inferential norms—proves dubiously compatible with his own deflationary approach to intentional objectivity. This is because a deflationist argument, adapted from the case of truth to that of correct inference, undermines the criterion of adequacy Brandom employs in motivating inferentialism. Once that constraint is abandoned, moreover, the very constitutive-explanatory availability of Brandom's inferential norms becomes suspect. Yet Brandom intertwines inferentialism with a separate explanatory project, one that in explaining the pragmatic significance (...) of meaning-attributions does yield a convincing construal of the claim that the concept of meaning is normative. (shrink)
The purpose of this article is to delimit what can and cannot be claimed on behalf of second-order logic. The starting point is some of the discussions surrounding my Foundations without Foundationalism: A Case for Secondorder Logic.
The purpose of this paper is to present a thought experiment and argument that spells trouble for “radical” deflationism concerning meaning and truth such as that advocated by the staunch nominalist Hartry Field. The thought experiment does not sit well with any view that limits a truth predicate to sentences understood by a given speaker or to sentences in (or translatable into) a given language, unless that language is universal. The scenario in question concerns sentences that are not understood but (...) are known to be logical consequences of known and understood sentences. Ultimately, the issue turns on the notion of logical consequence that is available to various versions of deflationism. (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)
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.
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)
The discovery of mirror neurons has been hailed as one of the most exciting developments in neuroscience in the past few decades. These neurons discharge in response to the observation of others’ actions. But how are we to understand the function of these neurons? In this paper I defend the idea that mirror neurons are best conceived as components of a sensory system that has the function to perceive action. In short, mirror neurons are part of a hitherto unrecognized “sixth (...) sense”. In this spirit, research should move toward developing a psychophysics of mirror neurons. (shrink)
Andy Clark's Supersizing the Mind begins as a manifesto in which the components of an embodied theory of mind are carefully moved into place, proceeds to a defense of these components from recent critical attacks, and ends with words of caution to those who would seek to extract too much from the embodied perspective. Readers unfamiliar with Clark's earlier works are likely to find the result dazzling -- an exciting, novel, and coherent conception of the mind that dares one to (...) abandon nearly every vestige of a comfortably Cartesian view of mind. Of course, philosophers of mind have, for the most part, already jettisoned the idea that minds are an ethereal sort of non-physical substance. We can now assert with no great temerity that Descartes was wrong about that. Even so, one might still agree with Descartes that minds are in some sense distinct from bodies. They are, as it were, in the head. Yet, if Clark's case for embodiment is on track, minds are not in the head. The supervenience base for a mind (and not simply mental content) can include pieces of the extracranial body and, indeed, objects in the world beyond. (shrink)
There is a standard objection against purported explanations of how a language L can express the notion of being a true sentence of L. According to this objection, such explanations avoid one paradox (the Liar) only to succumb to another of the same kind. Even if L can contain its own truth predicate, we can identify another notion it cannot express, on pain of contradiction via Liar-like reasoning. This paper seeks to undermine such ‘revenge’ by arguing that it presupposes a (...) dubious assumption about the linguistic expression of concepts. Successful revenge would require that there be a notion other than truth that plays the same role with respect to concept-expression that truth is naturally thought to play before we are confronted with the Liar paradox. (shrink)
The purpose of this note is to examine the relationship between the practice of mathematics and the philosophy of mathematics, ontology in particular. One conclusion is that the enterprises are (or should be) closely related, with neither one dominating the other. One cannot 'read off' the correct way to do mathematics from the true ontology, for example, nor can one ‘read off’ the true ontology from mathematics as practiced.
Though the “internal point of view” is perhaps H.L.A. Hart’s greatestcontribution to legal theory, this concept is also often and easily misunderstood. This is unfortunate, not only because these misreadings distort Hart’s theory, but, more importantly, because they prevent us from appreciating the infirmities of sanction-centered theories of law and the compelling reasons why they ought to be rejected. In this paper, I try to address some of these confusions. What, exactly, is the internal point of view? What role (or (...) roles) does it play in Hart’s theory? And how does an adequate appreciation for the centrality of the internal point of view lead to the rejection of sanction-centered theories? (shrink)
Some philosophers have argued that moral agency is characteristic of humans alone and that its absence from other animals justifies granting higher moral status to humans. However, human beings do not have a monopoly on moral agency, which admits of varying degrees and does not require mastery of moral principles. The view that all and only humans possess moral agency indicates our underestimation of the mental lives of other animals. Since many other animals are moral agents (to varying degrees), they (...) are also subject to (limited) moral obligations, examples of which are provided in this paper. But, while moral agency is sufficient for significant moral status, it is by no means necessary. (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.
It is generally assumed that Descartes invokes “objective being in the intellect” in order to explain or describe an idea’s status as being “of something.” I argue that this assumption is mistaken. As emerges in his discussion of “materially false ideas” in the Fourth Replies, Descartes recognizes two senses of ‘idea of’. One, a theoretical sense, is itself introduced in terms of objective being. Hence Descartes can’t be introducing objective being to explain or describe “ofness” understood in this sense. Descartes (...) also appeals to a pretheoretical sense of ‘idea of’. I will argue that the notion of objective being can’t serve to explain or describe this “ofness” either. I conclude by proposing an alternative explanation of the role of objective being, according to which Descartes introduces this notion to explain the mind’s ability to attain clear and distinct ideas. (shrink)
Within a decade or so following publication of Barkow, Cosmides and Tooby’s landmark book The Adapted Mind: Evolutionary Psychology and the Generation of Culture (1992), evolutionary psychology had bulldozed its way into the public eye. Its topics were sexy, and not just figuratively. Among them were questions about why men prefer nubile women with large breasts, why women prefer broad-chested men who drive fancy automobiles, why men view sexual infidelity as more serious than emotional infidelity while women show the opposite (...) pattern, why people view incest with revulsion. Evolutionary psychologists also sought to explain why stepfathers abuse their stepchildren more often than their biological children, and why rules of reasoning, such as material implication, are easier to apply when trying to spot a cheater than when deciding whether an odd number would be on one side of a card if a vowel was on the other. And while there were critics (e.g. Stephen Gould, ‘‘Evolution: The Pleasures of Pluralism’’, 1997), evolutionary psychology had built a head of steam and its shibboleths soon became the darlings of the popular media. Of course men prefer nubile women: natural selection would have eliminated men who chose to mate with females too young or old to bear children. Obviously women prefer high status males – women who preferred mates who could not provide for their children would not have spread their genes beyond the next generation. And what else but natural selection could explain why people react with disgust to incest? The most significant bump in the road for evolutionary psychology arose with the publication of David Buller’s exhaustive critique.. (shrink)
Unifying traditional cognitive science is the idea that thinking is a process of symbol manipulation, where symbols lead both a syntactic and a semantic life. The syntax of a symbol comprises those properties in virtue of which the symbol undergoes rule-dictated transformations. The semantics of a symbol constitute the symbolsÕ meaning or representational content. Thought consists in the syntactically determined manipulation of symbols, but in a way that respects their semantics. Thus, for instance, a calculating computer sensitive only to the (...) shape of symbols might produce the symbol Ô5Õ in response to the inputs Ô2Õ, Ô+Õ, and Ô3Õ. As far as the computer is concerned, these symbols have no meaning, but because of its program it will produce outputs that, to the user, Òmake senseÓ given the meanings the user attributes to the symbols. (shrink)
Ideas play at least two roles in Locke's theory of the understanding. They are constituents of ‘propositions,’ and some of them ‘represent’ the qualities and sorts of surrounding bodies. I argue that each role involves a distinct kind of intentional directedness. The same idea will in general be an ‘idea of’ two different objects, in different senses of the expression. Identifying Locke's scheme of twofold ‘ofness’ reveals a common structure to his accounts of simple ideas and complex ideas of substances. (...) A consequence is a distinction among substance sorts parallel to one of his distinctions between primary and secondary qualities. (shrink)
A number of authors have recently weighed in on the issue of whether it is coherent to have bound variables that range over absolutely everything. Prima facie, it is difficult, and perhaps impossible, to coherently state the “relativist” position without violating it. For example, the relativist might say, or try to say, that for any quantifier used in a proposition of English, there is something outside of its range. What is the range of this quantifier? Or suppose we ask the (...) relativist if there are some things that cannot appear in the range of any bound variable. The likely response would be along these lines: “No. For each object o, it possible to include o in the range of quantifiers, but one cannot quantify over everything at once.” This sentence contains unrestricted quantifiers, or so it seems, pending some clever move from a relativist. On the other hand, in the context of set theory, the reasoning behind the Burali-Forti paradox strongly suggests that there are well-orderings strictly longer than the collection of all ordinals. And set theorists regularly do transfinite recursions and transfinite reductions along such well-orderings. The relativist simply points out that one can always define new ordinals, and thus expand the range of one’s bound variables. The purpose of this paper is to explore the iterative framework, proposed in Zermelo’s 1930 paper, “Über Grenzzahlen und Mengenbereiche” (“On boundary numbers and domains of sets”), in order to shed light on these issues, and see what is involved in resolving them. (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 (1999) 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: lshapiro@wisc.edu. (shrink)
He argues that the intuitively provable arithmetic sentences constitute a recursively enumerable set, which has a Gödel sentence which is itself intuitively provable. The incompleteness theorem does not apply, since the set of provable arithmetic sentences is not consistent. The purpose of this article is to sharpen Priest's argument, avoiding reference to informal notions, consensus, or Church's thesis. We add Priest's dialetheic semantics to ordinary Peano arithmetic PA, to produce a recursively axiomatized formal system PA that contains its own truth (...) predicate. Whether one is a dialetheist or not, PA is a legitimate, rigorously defined formal system, and one can explore its proof-theoretic properties. The system is inconsistent (but presumably non-trivial), and it proves its own Gödel sentence as well as its own soundness. Although this much is perhaps welcome to the dialetheist, it has some untoward consequences. There are purely arithmetic (indeed, 0) sentences that are both provable and refutable in PA. So if the dialetheist maintains that PA is sound, then he must hold that there are true contradictions in the most elementary language of arithmetic. Moreover, the thorough dialetheist must hold that there is a number g which both is and is not the code of a derivation of the indicated Gödel sentence of PA. For the thorough dialetheist, it follows ordinary PA and even Robinson arithmetic are themselves inconsistent theories. I argue that this is a bitter pill for the dialetheist to swallow. (shrink)
Sections 3.16 and 3.23 of Roger Penrose's Shadows of the mind (Oxford, Oxford University Press, 1994) contain a subtle and intriguing new argument against mechanism, the thesis that the human mind can be accurately modeled by a Turing machine. The argument, based on the incompleteness theorem, is designed to meet standard objections to the original Lucas–Penrose formulations. The new argument, however, seems to invoke an unrestricted truth predicate (and an unrestricted knowability predicate). If so, its premises are inconsistent. The usual (...) ways of restricting the predicates either invalidate Penrose's reasoning or require presuppositions that the mechanist can reject. (shrink)
In this paper today, I would like to offer a new analysis of causation and of causal claims. It is an unorthodox one, as you will see, but I suspect that in the not too distant future it will be seen as intuitively, perhaps even trivially, true. I hardly need defend the urgency of my project. Ever since Hume, philosophers have wondered whether there are causes. This is a desperate situation. With no causes, it's hard to see how brushing my (...) teeth is likely to prevent tooth decay. Indeed, it would not be unreasonable to read Hume as an advocate of rotten teeth, which might explain the sad state that many British mouths find themselves in today. The attentive listener will have noted that I said Hume's advocacy of rotten teeth might explain the abysmal state of British oral hygiene. Of course, if Hume is right about causation then nothing explains anything, and that explains why I have been tentative in my claim. The account I would like to propose is this. The claim ‘x causes y’ is to be understood in the following way: ‘x makes y happen’. That is, to say that x is the cause of y is just to say that x makes y happen. Or, to put it more succinctly, if x is the cause of y, then x makes y happen. This is no doubt a startling claim, and one in need of further clarification and defense. To begin, I should like to contrast my analysis with another that might, on its surface, appear similar. Suppose one were to claim that 'x is the cause of y' means that x brings y about. But ‘bringing about’ is hardly an informative verbal clause, and does little ampliative work. This way of putting it lacks the opaque transparency that we’ve come to expect of philosophical analyses of causation. Now this new account is not necessarily inconsistent with other, more traditional analyses, such as Lewis and Hausman's analyses of causation in terms of counterfactuals or Eells' probabilistic theory of causation. Consider first counterfactual analyses of causation. These are efforts to account for the meaning of causal dependencies.. (shrink)
It is a commonplace that the extensions of most, perhaps all, vague predicates vary with such features as comparison class and paradigm and contrasting cases. My view proposes another, more pervasive contextual parameter. Vague predicates exhibit what I call open texture: in some circumstances, competent speakers can go either way in the borderline region. The shifting extension and anti-extensions of vague predicates are tracked by what David Lewis calls the “conversational score”, and are regulated by what Kit Fine calls penumbral (...) connections, including a principle of tolerance. As I see it, vague predicates are response-dependent, or, better, judgement-dependent, at least in their borderline regions. This raises questions concerning how one reasons with such predicates. In this paper, I present a model theory for vague predicates, so construed. It is based on an overall supervaluationist-style framework, and it invokes analogues of Kripke structures for intuitionistic logic. I argue that the system captures, or at least nicely models, how one ought to reason with the shifting extensions (and anti-extensions) of vague predicates, as borderline cases are called and retracted in the course of a conversation. The model theory is illustrated with a forced march sorites series, and also with a thought experiment in which vague predicates interact with so-called future contingents. I show how to define various connectives and quantifiers in the language of the system, and how to express various penumbral connections and the principle of tolerance. The project fits into one of the topics of this special issue. In the course of reasoning, even with the external context held fixed, it is uncertain what the future extension of the vague predicates will be. Yet we still manage to reason with them. The system is based on that developed, more fully, in my Vagueness in Context , Oxford, Oxford University Press, 2006, but some criticisms and replies to critics are incorporated. (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)
Critics of attempts to explain meaning in terms of truth-conditions have tended to charge their opponents with misconceptions regarding truth. I shall argue that the 'naïve' version of the truth-conditional theory which best accounts for its resilience fails for a different and more basic reason, namely, circularity arising from the contingency of meaning. One reason why this problem has been overlooked is a tendency (noted by Dummett in a different connection) to assimilate the naïve truth-conditional theory to an idealized verificationism.
: McDowell opposes the view that the intentionality of language and thought remains mysterious unless it can be understood ‘from outside the conceptual order’. While he thinks the demand for such a ‘sideways-on’ understanding can be the result of ‘scientistic prejudice’, he points to Sellars's thought as exhibiting a different source: a distortion of our perspective ‘from within the conceptual order’. The distortion involves a failure on Sellars's part to see how descriptions from within the conceptual order can present expressions (...) and mental acts as related to extra-conceptual objects (a failure in turn explained by his failure to see how such relations could have normative import). In this paper, I argue that Sellars's thought suffers from no such distortion. If that is right, McDowell's examination of Sellars has not uncovered a disorder whose treatment might help relieve the desire for a sideways-on view. (shrink)
The neo-logicist argues tliat standard mathematics can be derived by purely logical means from abstraction principles—such as Hume's Principle— which are held to lie 'epistcmically innocent'. We show that the second-order axiom of comprehension applied to non-instantiated properties and the standard first-order existential instantiation and universal elimination principles are essential for the derivation of key results, specifically a theorem of infinity, but have not been shown to be epistemically innocent. We conclude that the epistemic innocence of mathematics has not been (...) established by the neo-logicist. (shrink)
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)
institutional framework ~ or rather a family of frameworks — for realizing the democratic ideal of giving kmms t0 the demos, power to the people. The distinction between a participatory and a representative system is not one between democracy proper and some faint approximation but a distinction between rival proposals for the implementation of democracy. My focus in this chapter is on representation in this democratic, popularly enabling scnsc. Thus the target of the chapter is narrower than it might have (...) been. As Hcbbcs in particular argues, the idea 0f representation may bc used, not just of representatives who are subject t0 the continuing 0r periodic control 0f the people, but also 0f a hereditary, absolute: monarch. The defenders of parliament in the 1640s tried to give its members a monop01y right on the use 0f thc word (Skinner 2005), but Hobbes argued against them that it was absurd that a monarch who "had the sovcreignty" 0vcr his subjects "from a descent 0f 600 ycars’ should not be "considcrcd as their rcprcsc-:mtativc" (Hobbes 1994: 19.3). His Qwn view, to thc contrary, was that "thc King himself did. . . ever represent the person of the people of Eng12md" (Hobbes 1990: 120). But though my focus is narrower than I-I0bbcs’s, it is broader than the targét t0 which many contcmporary thcorists give their attention. As will appear, I use the notion 0f representation in such a way that any public authorities, and any citizens wh0 assume a legitimate r01e in public.. (shrink)
Cognitive agents, whether human or computer, that engage in natural-language discourse and that have beliefs about the beliefs of other cognitive agents must be able to represent objects the way they believe them to be and the way they believe others believe them to be. They must be able to represent other cognitive agents both as objects of beliefs and as agents of beliefs. They must be able to represent their own beliefs, and they must be able to represent beliefs (...) as objects of beliefs. These requirements raise questions about the number of tokens of the belief representation language needed to represent believers and propositions in their normal roles and in their roles as objects of beliefs. In this paper, we explicate the relations among nodes, mental tokens, concepts, actual objects, concepts in the belief spaces of an agent and the agent's model of other agents, concepts of other cognitive agents, and propositions. We extend, deepen, and clarify our theory of intensional knowledge representation for natural-language processing, as presented in previous papers and in light of objections raised by others. The essential claim is that tokens in a knowledge-representation system represent only intensions and not extensions. We are pursuing this investigation by building CASSIE, a computer model of a cognitive agent and, to the extent she works, a cognitive agent herself. CASSIE's mind is implemented in the SNePS knowledge-representation and reasoning system. (shrink)
Quite unexpectedly, cognitive psychologists find their field intimately connected to a whole new intellectual landscape that had previously seemed remote, unfamiliar, and all but irrelevant. Yet the proliferating connections tying together the cognitive and evolutionary communities promise to transform both fields, with each supplying necessary principles, methods, and a species of rigor that the other lacks. (Cosmides and Tooby, 1994, p. 85).
Since virtually every mathematical theory can be interpreted in set theory, the latter is a foundation for mathematics. Whether set theory, as opposed to any of its rivals, is the right foundation for mathematics depends on what a foundation is for. One purpose is philosophical, to provide the metaphysical basis for mathematics. Another is epistemic, to provide the basis of all mathematical knowledge. Another is to serve mathematics, by lending insight into the various fields. Another is to provide an arena (...) for exploring relations and interactions between mathematical fields, their relative strengths, etc. Given the different goals, there is little point to determining a single foundation for all of mathematics. (shrink)
Famously, Michael Dummett argues that considerations concerning the role of language in communication lead to the rejection of classical logic in favor of intuitionistic logic. Potentially, this results in massive revisions of established mathematics. Recently, Neil Tennant (“The law of excluded middle is synthetic a priori, if valid”, Philosophical Topics 24 (1996), 205-229) suggested that a Dummettian anti-realist can accept the law of excluded middle as a synthetic, a priori principle grounded on a metaphysical principle of determinacy. This article shows (...) that the for the anti-realist, the law of excluded middle entails that humans have wildly implausible abilities. The proposed synthesis between anti-realism and classical mathematics thus fails. (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)
Over the last few decades Michael Dummett developed a rich program for assessing logic and the meaning of the terms of a language. He is also a major exponent of Frege's version of logicism in the philosophy of mathematics. Over the last decade, Neil Tennant developed an extensive version of logicism in Dummettian terms, and Dummett influences other contemporary logicists such as Crispin Wright and Bob Hale. The purpose of this paper is to explore the prospects for Fregean logicism within (...) a broadly Dummettian framework. The conclusions are mostly negative: Dummett's views on analyticity and the logical/non-logical boundary leave little room for logicism. Dummett's considerations concerning manifestation and separability lead to a conservative extension requirement: if a sentence S is logically true, then there is a proof of S which uses only the introduction and elimination rules of the logical terms that occur in S. If basic arithmetic propositions are logically true - as the logicist contends - then there is tension between this conservation requirement and the ontological commitments of arithmetic. It follows from Dummett's manifestation requirements that if a sentence S is composed entirely of logical terminology, then there is a formal deductive system D such that S is analytic, or logically true, if and only if S is a theorem of D. There is a deep conflict between this result and the essential incompleteness, or as Dummett puts it, the indefinite extensibility, of arithmetic truth. (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)
Institutional investors are increasingly focusing on firms that prioritise Corporate Social Responsibility (CSR). In the absence of any objective measure of a firm's CSR Performance (CSP), their investment choices are largely guided by independent rating indices that rank firms according to their social performance metrics. As a result, firms looking to increase their attractiveness as targets of social investment focus their CSR efforts on increasing the visibility of activities that are recognised by such indices. However, the validity of these indices (...) as accurate measures of firms' actual social performance has repeatedly been called into question. This means that the ability of these indices to measure and report on firms' actual social impact cannot be ascertained with any degree of accuracy. The result is that firms are incentivised to engage in activities (whether genuine or 'greenwashing') that cannot be said to improve social responsibility, and may even ultimately harm society. Thus, another method of measuring CSP must be found that enables firms to measure their true impact on society. We propose a new approach to measuring CSP that is integrated with stakeholder theory. Such an approach provides managers of firms with an interest in engaging in real social development for the purposes of ensuring firm survival with the ability to understand their social obligations, and the ability to measure the resulting benefit to society. (shrink)
This article is an extended critical study of Kit Fine’s The limits of abstraction, which is a sustained attempt to take the measure of the neo-logicist program in the philosophy and foundations of mathematics, founded on abstraction principles like Hume’s principle. The present article covers the philosophical and technical aspects of Fine’s deep and penetrating study.
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)
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.
It is an old charge against Locke that his commitment to a common substratum for the observable qualities of particular objects and his empiricist theory about the origin of ideas are inconsistent with one another. How could we have an idea of something in which observable qualities inhere if all our ideas are constructed from ideas of observable qualities? In this paper, I propose an interpretation of the crucial passages in Locke, according to which the idea of substratum is formed (...) through an elaborate mental process which he calls “supposition.” It is the same process we use when we form the idea of infinity − another problematic idea for an empiricist. In the end, Locke was more liberal than most empiricists in subscribing to the existence of ideas far removed from experience, because he accepted supposition as a legitimate way of constructing new ideas. (shrink)
Computationalism, the notion that cognition is computation, is a working hypothesis of many AI researchers and Cognitive Scientists. Although it has not been proved, neither has it been disproved. In this paper, I give some refutations to some well-known alleged refutations of computationalism. My arguments have two themes: people are more limited than is often recognized in these debates; computer systems are more complicated than is often recognized in these debates. To underline the latter point, I sketch the design and (...) abilities of a possible embodied computer system. (shrink)
Typically, a logic consists of a formal or informal language together with a deductive system and/or a model-theoretic semantics. The language is, or corresponds to, a part of a natural language like English or Greek. The deductive system is to capture, codify, or simply record which inferences are correct for the given language, and the semantics is to capture, codify, or record the meanings, or truth-conditions, or possible truth conditions, for at least part of the language.
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)
Ketelaar and Ellis have provided a remarkably clear and succinct statement of Lakatosian philosophy of science and have also argued compellingly that the neo-Darwinian theory of evolution fills the Lakatosian criteria of progressivity. We find ourselves in agreement with much of what Ketelaar and Ellis say about Lakatosian philosophy of science, but have some questions about (1) the place of evolutionary psychology in a Lakatosian framework, and (2) the extent to which evolutionary psychology truly predicts new findings.
