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.

Zermelo’s Theorem that the axiom of choice is equivalent to the principle that every set can be well-ordered goes through in third-order logic, but in second-order logic we run into expressivity issues. In this note, we show that in a natural extension of second-order logic weaker than third-order logic, choice still implies the well-ordering principle. Moreover, this extended second-order logic with choice is conservative over ordinary second-order logic with the well-ordering principle. We also discuss a variant choice principle, due to (...) Hilbert and Ackermann, which neither implies nor is implied by the well-ordering principle. (shrink)

It has long been known that (classical) Peano arithmetic is, in some strong sense, “equivalent” to the variant of (classical) Zermelo–Fraenkel set theory (including choice) in which the axiom of infinity is replaced by its negation. The intended model of the latter is the set of hereditarily finite sets. The connection between the theories is so tight that they may be taken as notational variants of each other. Our purpose here is to develop and establish a constructive version of this. (...) We present an intuitionistic theory of the hereditarily finite sets, and show that it is definitionally equivalent to Heyting Arithmetic, in a sense to be made precise. Our main target theory, the intuitionistic small set theory is remarkably simple, and intuitive. It has just one non-logical primitive, for membership, and three straightforward axioms plus one axiom scheme. We locate our theory within intuitionistic mathematics generally. (shrink)

Newton se rehusó a usar el término “filosofía experimental”, ampliamente usado en la Inglaterra de la Restauración al comienzo de su carrera, hasta 1712 cuando añadió un pasaje al Escolio General de los Principia que exponía brevemente su metodología anti-hipotética. No obstante, los borradores para la Cuestión 23 de la segunda edición de la Óptica (1706) (que se convertiría en la Cuestión 31 en la tercera edición) muestran que con anterioridad había intentado introducir el término para explicar su metodología. Newton (...) introdujo el término por propósitos polémicos para defender su teoría de la gravedad contra las críticas de los cartesianos y los leibnizianos pero, especialmente en los Principia, contra Leibniz mismo. La "filosofía experimental" tiene poco que ver directamente con el experimento, sino que más bien designa de manera más amplia la ciencia empírica. Los manuscritos de Newton proporcionan la oportunidad de comprender el uso que hace de la “filosofía experimental” y la formulación de su metodología, especialmente de términos claves como “deducir”, “inducción” y “fenómenos”, a comienzos del siglo XVIII. (shrink)

Many philosophers and psychologists who approach the issue of representation from a computational or measurement theoretical perspective end up having to deny the possibility of junk representations—representations present in an organism's head but that enter into no psychological processes or produce no behaviour. However, I argue, a more functional perspective makes the possibility of junk representations intuitively quite plausible—so much so that we may wish to question those views of representation that preclude the possibility of junk representations. I explore some (...) of the reasons we should care about the possibility of junk representations and conclude with some speculation about whether junk representations are in fact present in our heads. (shrink)

A growing sense of the exhaustion of both liberalism and Marxism has fueled a revival of interest in civic republicanism among historians, political theorists, and social commentators. This turn is evaluated via an examination of the normative implications off. G. A. Pocock's account of civic republicanism. Arguing that what is at issue between liberals and republicans has been misunderstood by both sides in the debate, the author shows that the turn to republicanism fails to address the most vexing problems liberalism (...) confronts in the modern world, and that it is and has been compatible with much of what critics of liberalism dislike. He argues, further, that the civic republican view involves an instrumental attitude to outsiders that cannot be justified in today's world and has other unattractive dimensions of which too little account has been taken by defenders and detractors alike. (shrink)

I would like to nominate one more principle for initial inclusion in the science of teleonomy. This principle is that the nature of the stimuli that initiate and regulate a response may be no indication of the function of the response.George Williams could not have anticipated the special relevance his principle has for contemporary analyses of representational content. In particular, his principle provides both a concise statement of where a currently popular strategy for naturalizing representational content has gone wrong and (...) a positive suggestion for how we should right this wrong. I characterize the kind of naturalistic analysis of representation I have in mind as bottom-up because it seeks to build representation up from a non-intentional, and hence naturalistically unimpeachable, correlation relation. Many authors have suggested such an approach to naturalizing intentionality, but for clarity and completeness perhaps Fred Dretske's Explaining Behavior: Reasons in a World of Causes ought to be construed as the exemplary source. (shrink)

Some central philosophical issues concern the use of mathematics in putatively non-mathematical endeavors. One such endeavor, of course, is philosophy, and the philosophy of mathematics is a key instance of that. The present article provides an idiosyncratic survey of the use of mathematical results to provide support or counter-support to various philosophical programs concerning the foundations of mathematics.

Frances Egan argues that the states of computational theories of vision are individuated individualistically and, as far as the theory is concerned, are not intentional. Her argument depends on equating the goals and explanatory strategies of computational psychology with those of its algorithmic level. However, closer inspection of computational psychology reveals that the computational level plays an essential role in explaining visual processes and that explanations at this level are nonindividualistic and intentional. In conclusion, I sketch an account of content (...) in which content does the sort of explanatory work that Egan denies is possible. (shrink)

Between the years 1643 and 1649, Princess Elisabeth of Bohemia and René Descartes exchanged fifty-eight letters—thirty-two from Descartes and twenty-six from Elisabeth. Their correspondence contains the only known extant philosophical writings by Elisabeth, revealing her mastery of metaphysics, analytic geometry, and moral philosophy, as well as her keen interest in natural philosophy. The letters are essential reading for anyone interested in Descartes’s philosophy, in particular his account of the human being as a union of mind and body, as well as (...) his ethics. They also provide a unique insight into the character of their authors and the way ideas develop through intellectual collaboration. Philosophers have long been familiar with Descartes’s side of the correspondence. Now Elisabeth’s letters—never before available in translation in their entirety—emerge this volume, adding much-needed context and depth both to Descartes’s ideas and the legacy of the princess. Lisa Shapiro’s annotated edition—which also includes Elisabeth’s correspondence with the Quakers William Penn and Robert Barclay—will be heralded by students of philosophy, feminist theorists, and historians of the early modern period. (shrink)

Among the aims of this book are: - The discussion of some important philosophical issues using the precision of mathematics. - The development of formal systems that contain both classical and constructive components. This allows the study of constructivity in otherwise classical contexts and represents the formalization of important intensional aspects of mathematical practice. - The direct formalization of intensional concepts (such as computability) in a mixed constructive/classical context.

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)

Next SectionIntensification of poverty and degradation of health infrastructure over recent decades in countries most affected by HIV/AIDS present formidable challenges to clinical research. This paper addresses the overall standard of health care (SOC) that should be provided to research participants in developing countries, rather than the narrow definition of SOC that has characterised the international debate on standards of health care. It argues that contributing to sustainable improvements in health by progressively ratcheting the standard of care upwards for research (...) participants and their communities is an ethical obligation of those in resource-rich countries who sponsor and implement research in poorer ones. (shrink)

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)

Intersubjectivity is the proposition that human experience occurs in a world of shared and embodied understandings, mediated by culture and language. Nursing is fundamentally relational, and nursing research stems from an exchange between participants and researchers and indeed around the transaction of the patient and the nurse in the intersubjective space of clinical settings. Through the philosophical standpoints of Husserl, Merleau‐Ponty, Heidegger, and Gadamer we examine these differing philosophical constructs of intersubjectivity and the contribution of these positions to phenomenological nursing (...) inquiry. Particular framings of intersubjectivity should influence the way researchers interact with their participants and data so that the chosen philosophy sits coherently within a research plan and methodology. This exploration of philosophical standpoints is extended through examples of, and reflections upon, the authors' experiences of intersubjectivity in our published phenomenological nursing studies and through dynamic interactions that characterise interpretive activities within a research team. (shrink)

Stewart Shapiro's aim in Vagueness in Context is to develop both a philosophical and a formal, model-theoretic 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 with such contextual factors as the comparison class and paradigm cases. A person can be tall with respect to male accountants and not tall with respect to professional basketball players. The main (...) feature of Shapiro's account is that the extensions of vague terms also vary in the course of a conversation, even after the external contextual features, such as the comparison class, are fixed. A central thesis is that in some cases, a competent speaker of the language can go either way in the borderline area of a vague predicate without sinning against the meaning of the words and the non-linguistic facts. Shapiro calls this open texture, borrowing the term from Friedrich Waismann.The formal model theory has a similar structure to the supervaluationist approach, employing the notion of a sharpening of a base interpretation. In line with the philosophical account, however, the notion of super-truth does not play a central role in the development of validity. The ultimate goal of the technical aspects of the work is to delimit a plausible notion of logical consequence, and to explore what happens with the sorites paradox.Later chapters deal with what passes for higher-order vagueness - vagueness in the notions of 'determinacy' and 'borderline' - and with vague singular terms, or objects. In each case, the philosophical picture is developed by extending and modifying the original account. This is followed with modifications to the model theory and the central meta-theorems.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. Vagueness is also due to the kinds of beings we are. There is no need to blame the phenomenon on any one of those aspects. (shrink)

Embodied cognition often challenges standard cognitive science. In this outstanding introduction, Lawrence Shapiro sets out the central themes and debates surrounding embodied cognition, explaining and assessing the work of many of the key figures in the field, including George Lakoff, Alva Noë, Andy Clark, and Arthur Glenberg. Beginning with an outline of the theoretical and methodological commitments of standard cognitive science, Shapiro then examines philosophical and empirical arguments surrounding the traditional perspective. He introduces topics such as dynamic systems (...) theory, ecological psychology, robotics, and connectionism, before addressing core issues in philosophy of mind such as mental representation and extended cognition. Including helpful chapter summaries and annotated further reading at the end of each chapter, _Embodied Cognition_ is essential reading for all students of philosophy of mind, psychology, and cognitive science. (shrink)