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)

Global Cumulative Treatment Analysis is a novel clinical research model combining expert knowledge, and treatment coordination based upon global information-gain, to treat every patient optimally while efficiently searching the vast space that is the realm of cancer research.

While sets are combinatorial collections, defined by their elements, classes are logical collections, defined by their membership conditions. We develop, in a potentialist setting, a predicative approach to (logical) classes of (combinatorial) sets. Some reasons emerge to adopt a stricter form of potentialism, which insists, not only that each object is generated at some stage of an incompletable process, but also that each truth is “made true” at some such stage. The natural logic of this strict form of potentialism is (...) semi-intuitionistic: where each set-sized domain is classical, the domain of all sets or all classes is intuitionistic. (shrink)

Perhaps the most pressing challenge for singularism—the predominant view that definite plurals like ‘the students’ singularly refer to a collective entity, such as a mereological sum or set—is that it threatens paradox. Indeed, this serves as a primary motivation for pluralism—the opposing view that definite plurals refer to multiple individuals simultaneously through the primitive relation of plural reference. Groups represent one domain in which this threat is immediate. After all, groups resemble sets in having a kind of membership-relation and iterating: (...) we can have groups of groups, groups of groups of groups, etc. Yet there cannot be a group of all non-self-membered groups. In response, we develop a potentialist theory of groups according to which we always can, but do not have to, form a group from any sum. Modalizing group-formation makes it a species of potential, as opposed to actual or completed, infinity. This allows for a consistent, plausible, and empirically adequate treatment of natural language plurals, one which is motivated by the iterative nature of syntactic and semantic processes more generally. (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.

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.

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)

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)

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.

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)

Abstract Building on Philip Converse's understanding of public opinion, John Zaller sees the evidence for the public's ?nonattitudes? as reflecting individuals? ambivalence concerning political issues. Because neither individuals nor the public collectively have what Zaller would call real attitudes, he concludes that the effectiveness of democracy rests on competition among intellectual and political elites. In truth, however, the public has many real attitudes that depend heavily on elite leadership, in ways that Converse did not initially emphasize but that are consistent (...) with both his observations and Zaller's model of mass opinion. The quality of the public's attitudes are, however, a point of serious contention. (shrink)

This paper contrasts two versions of a pragmatist critique of deflationism about truth. According to the critique, understanding the practice of factual discourse requires understanding a role played in that practice by speakers’ use of the concept of truth. Huw Price takes this role to lie in the expression of attitudes of approval and disapproval toward other speakers’ assertions. Proceeding from Robert Brandom’s analysis of assertion, I defend an alternative account of truth’s role in terms of the acknowledgement and disacknowledgement (...) of communicative authority. I explain why this account fails to yield Price’s key anti-deflationary conclusion, namely that engaging in factual discourse requires holding that false assertions are ipso facto normatively incorrect. (shrink)

Deforming American Political Thoughtoffers an alternative to the dominant American historical imagination, treating issues that range from the nature of Thomas Jefferson's vision of an egalitarian nation to the persistence of racial inequality. Presenting multifaceted arguments that transcend the myopic scope of traditional political discourses, Michael J. Shapiro summons disparate disciplines and genres - architecture, crime stories, novels, films, and jazz/blues music to provide approaches to the comprehension of diverse facets of American political thought from the founding to the (...) present. The book's various investigations disclose that there have always been dissenting voices, articulated in diverse genres of expression that cast doubt on the moral purpose and exceptionalism of the American mind. This highly anticipated updated second edition features a preface focusing on aesthetic theory and the contributions of artistic genres for political analysis, and a completely new chapter on critical thinking about the US western and urban encounters afforded by the two HBO series, Deadwood and The Wire respectively. (shrink)

I respond to Fishkin?s critique of my book The State of Democratic Theory. I reiterate my defense of a competitive model of democracy geared to reducing domination, rather than Fishkin?s deliberative model that deploys structured discussion to enlighten mass preferences. In light of the literatures on framing effects and the value of mutually independent judgments, I question whether the procedures Fishkin recommends would produce outcomes that are better informed rather than differently informed. Recognizing that deliberation might sometimes be helpful in (...) reducing domination, I note that sometimes it will not, and I fault Fishkin for his indiscriminate embrace of exceedingly costly deliberative mechanisms that promise dubious benefits? notably his and Bruce Ackerman?s?Deliberation Day? (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.

Kirsten Walsh has criticized my interpretation of Newton’s view on the certainty of his new science of color, namely, that it shifted through his long career from one of certainty to probabilism. I...

Preview: /Scott Shapiro interviewed by Eli Kramer / EK: Thanks for talking with me today. Your book, The Internationalists: How a Radical Plan to Outlaw War Remade the World is not only kind of groundbreaking in the way it changes how we think about the role of international law in the history and philosophy of culture, and some of our progressive success of not having disastrous violence shape us each generation, but it has only become more relevant since the (...) war in Ukraine was launched. As a starting point for our conversation, can you summarize the main premise of the work? SS: It’s a story about the modern international order. Despite its imperfections, it needs to be defended now more than ever. The central argument of the book is that the origins of the modern international order can be traced to a specific date in history. Namely August 27th, 1928, when the great leaders of the world gathered in Paris to outlaw war. The treaty that was signed on that day is sometimes called the Kellogg-Briand Pact, the Peace Pact, or the Paris Peace Pact. Its actual formal designation was “The General Treaty for the Renunciation of War,” basically saying it all was an attempt to outlaw war. Now, of course most people have never heard of it. It’s amazing that basically all the countries in the world decide to outlaw war, which in itself is initially a strange thing to do, but then nobody knows about it. (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.

Introduction. This study examines differences in students’ perceived value of three artmaking modalities and whether the resulting creative projects offer similar or different insights into medical students’ professional identity formation. Methods. Mixed-methods design using a student survey, student narrative comments and qualitative analysis of students’ original work. Results. Poetry and comics stimulated insight, but masks were more enjoyable and stress-reducing. All three art modalities expressed tension between personal and professional identities. Discussion. Regardless of type of artmaking, students express concern about (...) encroachments of training on personal identity but hoped that personal and professional selves could be integrated. (shrink)

The purpose of this article is to examine aspects of the development of the concept and theory of computability through the theory of recursive functions. Following a brief introduction, Section 2 is devoted to the presuppositions of computability. It focuses on certain concepts, beliefs and theorems necessary for a general property of computability to be formulated and developed into a mathematical theory. The following two sections concern situations in which the presuppositions were realized and the theory of computability was developed. (...) It is suggested in Section 3 that a central item was the problem of generalizing Gödel's incompleteness theorem. It is shown that this involved both the characterization of recursiveness and the attempt to clarify and formulate the notion of an effective process as it relates to the syntax of deductive systems. Section 4 concerns the decision problems which grew from the Hilbert program. Section 5 is devoted to the development of an informal' technique in the theory of computability often called ?argument by Church's thesis? (shrink)

Around the turn of the century, Poincare and Hilbert each published an account of geometry that took the discipline to be an implicit definition of its concepts. The terms ‘point’, ‘line’, and ‘plane’ can be applied to any system of objects that satisfies the axioms. Each mathematician found spirited opposition from a different logicist—Russell against Poincare' and Frege against Hilbert— who maintained the dying view that geometry essentially concerns space or spatial intuition. The debates illustrate the emerging idea of mathematics (...) as the science of structure. The article closes with some remarks on structuralist and nonstructuralist themes in Frege's own development of arithmetic. (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)

The is an old question over whether there is a substantial disagreement between advocates of different logics, as they simply attach different meanings to the crucial logical terminology. The purpose of this article is to revisit this old question in light a pluralism/relativism that regards the various logics as equally legitimate, in their own contexts. We thereby address the vexed notion of translation, as it occurs between mathematical theories. We articulate and defend a thesis that the notion of “same meaning” (...) is itself context-sensitive, depending on the purposes of a given conversation. (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)

Huw Price holds that a recognizable version of expressivism about normative and modal language can be “globalized” so as to apply to all areas of discourse. He focuses on globalizing the anti-representationalism of expressivist theories. By contrast, this paper’s topic is the seldom-discussed way Price seeks to globalize the expressivist view that “non-descriptive” discourse exhibits subjectivity. I argue that Price’s own argument against the possibility of a purely objective domain conflicts with his anti-representationalism and is self-undermining. I then defend a (...) different strategy for arguing that a kind of subjectivity can emerge even in domains traditional expressivists have regarded as purely objective. I do so by using an account of assertoric practice to offer a new solution to a puzzle concerning how to describe contingent histories in the use of natural kind terms. (shrink)