The purpose of this article is to assess the prospects for a Scottish neo-logicist foundation for a set theory. We show how to reformulate a key aspect of our set theory as a neo-logicist abstraction principle. That puts the enterprise on the neo-logicist map, and allows us to assess its prospects, both as a mathematical theory in its own right and in terms of the foundational role that has been advertised for set theory. On the positive side, we show that (...) our abstraction based theory can be modified to yield much of ordinary mathematics, indeed everything needed to recapture all branches of mathematics short of set theory itself. However, our conclusions are mostly negative. The theory will fall far short of the power of ordinary Zermelo-Fraenkel set theory. It is consistent that our set theory has models that are relatively small, smaller than the first cardinal with an uncountable index. More important, there is a strong tension between the idea that the iterative hierarchy is somehow ineffable, or indefinitely extensible, and the neo-logicist theme of capturing mathematical theories with abstraction principles. (shrink)

According to the Categories, predicates can be ‘said of’ their subjects or they can be ‘present in’ their subjects. The said-of relation has received relatively little scholarly attention, and scholars disagree on the answers to four foundational questions about the relation. (i) What is it? (ii) Is it an essential relation? (iii) How is it related to predication? (iv) Is it primitive? I argue that A is said-of B just in case A is a formal part of B. On this (...) account, said-of is an essential relation and it is definable, but it is not defined in terms of predication. (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)

There is a line of argument which aims to show that certain ontological claims are harmless by making use of conservativity results. The argument goes back to Hilbert who set its general frame. Hilbert’s concern was with certain abstract (ideal) entities in mathematics but the argument has been applied without discrimination to avoid ontological commitment to abstract entities in physics (Field) or to avoid ontological commitment to semantical properties like truth (Shapiro).

This new anthology of early modern philosophy enriches the possibilities for teaching this period by highlighting not only metaphysics and epistemology, but also new themes such as virtue, equality and difference, education, the passions, and love. It contains the works of forty-three philosophers, including traditionally taught figures such as Descartes, Spinoza, Leibniz, Locke, Berkeley, Hume, and Kant, as well as less familiar writers such as Lord Shaftesbury, Anton Amo, Julien Offray de La Mettrie, and Denis Diderot. It also highlights the (...) contributions of women philosophers, including Margaret Cavendish, Anne Conway, Gabrielle Suchon, Sor Juana Inéz de la Cruz, and Emilie Du Châtelet. (shrink)

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

The revisionary approach to semantic paradox is commonly thought to have a somewhat uncomfortable corollary, viz. that, on pain of triviality, we cannot affirm that all valid arguments preserve truth (Beall2007, Beall2009, Field2008, Field2009). We show that the standard arguments for this conclusion all break down once (i) the structural rule of contraction is restricted and (ii) how the premises can be aggregated---so that they can be said to jointly entail a given conclusion---is appropriately understood. In addition, we briefly rehearse (...) some reasons for restricting structural contraction. (shrink)

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

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.

In The Phenomenology of Religious Belief, the renowned philosopher Michael J. Shapiro investigates how art - and in particular literature and film - can impact upon both traditional interpretations and critical studies of religious beliefs and experiences. In doing so, he examines the work of prolific and award-winning writers such as Toni Morrison, Philip K. Dick and Robert Coover. By placing their work in conjunction with critical analyses of media by the likes of Ingmar Bergman and Pier Paolo Pasolini (...) and combining it with the work of groundbreaking thinkers such as George Canguilhem, Giorgio Agamben and Slavoj Žižek, Shapiro takes a truly interdisciplinary approach to the question of how life should be lived. His assessment of phenomenological subjectivity also leads him to question the nature of political theology and extend the criticism of Pauline theology. (shrink)

Holding life and death in their hands -- Is this for me? -- The intensive care unit. Personnel ; Rhythms ; Economics -- Actors. Patients ; Friends, family, and significant others ; Health care professionals -- Decisions. Informed consent ; Venues ; Affect ; Conflict -- Prognosis. Evidence ; Timing ; Mixed messages ; Negotiation ; Accuracy ; Prognostic framing -- Decision-making scripts. The legal script ; Cognitive scripts ; Conflicts of interest ; Law at the bedside -- Improvisation: decisions (...) in the real world. The patient should decide ; Reprising patient instructions ; Standing in the patient's shoes ; Beneficence ; It's God's decision ; What we want ; Denial, opting out -- Making a difference? The role of physicians ; Opting for a trajectory ; Outcomes ; I thought the law would take care of this ; Does any of this matter? -- The end. Implications ; Before it's too late ; When it's too late ; When "this" happens to me. (shrink)

ABSTRACT Michael Rescorla has argued that it makes sense to compute directly with numbers, and he faulted Turing for not giving an analysis of number-theoretic computability. However, in line with a later paper of his, it only makes sense to compute directly with syntactic entities, such as strings on a given alphabet. Computing with numbers goes via notation. This raises broader issues involving de re propositional attitudes towards numbers and other non-syntactic abstract entities.

_A spirited defense of the Enlightenment against assaults from both the left and the right that explains its urgent implications for our contemporary politics_ Ours is an age when optimism about politics is hard to come by. Ian Shapiro explains why this is so and, without minimizing the daunting challenges, spells out an appropriate response. Written in the indomitable spirit exemplified by Tom Paine, _Uncommon Sense_ is a rich source of insight and inspiration in dark political times. The Enlightenment (...) commitments to reason and science are under assault from the Postmodern Left and the Authoritarian Right. Shapiro explains why the attacks are misguided and politically destructive. He agrees with the critics that there are no universal principles of justice that transcend political battles and no fair, impartial rules to govern the distribution of income, wealth, rights, or opportunities. But abandoning the search for them as futile does not mean junking the Enlightenment’s core political goal: to deploy the tools of reason and science to fight domination. Democracy is essential to vindicating that goal, yet citizens in many democracies are profoundly alienated and many democracies are in danger of failing. Shapiro explains what has gone wrong, debunks ill-considered remedies, and spells out better ones—deepening and extending his previous writing on political theory and democratic politics. (shrink)

This chapter wades into the growing discussion surrounding embodied cognition and predictive processing. After surveying a recent debate between Jakob Hohwy and Andy Clark, it articulates two outstanding issues facing discussions of compatibility. It argues that headway on these issues can be made by drawing on the resources of philosophy of science.

A consideration of how segments of Orthodox society rewrite the past by eliminating that which does not fit in with their contemporary world-view. This wide-ranging and original review of how this policy is applied in practice adds a new perspective to Jewish intellectual history and to the understanding of the contemporary Jewish world.

This philosophical game changer looks critically at the Golden Rule in the context of game theory to see where it works and where it doesn’t, when it is applicable and when it isn’t. It shows you why knowing the difference can offer you a powerful way to transform your life from one driven by fear to one driven by love.

In two often neglected passages of the Critique of Pure Reason, Kant submits that the Critique is a 'treatise' or a 'doctrine of method'. These passages are puzzling because the Critique is only cursorily concerned with identifying adequate procedures of argument for philosophy. In this book, Gabriele Gava argues that these passages point out that the Critique is the doctrine of method of metaphysics. Doctrines of method have the task of showing that a given science is indeed a science because (...) it possesses 'architectonic unity' – which happens when it realizes the 'idea' of a science. According to Gava's novel approach, the Critique establishes that metaphysics is capable of this unity, and his reading of the Critique from this perspective not only illuminates the central role of the Transcendental Doctrine of Method within it, but also clarifies the relationship between the different parts of the work. (shrink)

The history of Pythagoreanism is littered with different and incompatible interpretations. This observation directs this book towards a fundamentally historiographical rather than philological approach, setting out to reconstruct the way in which the tradition established Pythagoreanism s image.".

The central theme of this important book is that we are paying the price of an arrogance that refuses to recognize mystery. The author invites the reader to enter into the argument that he holds with himself on a great number of problems. Written in the early 1950s, Marcel's discussion of these topics are remarkably contemporary, e.g.: * Our crisis is a metaphysical, not merely social, one. * What a man is depends partly on what he thinks he is, and (...) a materialistic philosophy turns men into things. * Can a man be free except in a free country? * Stoicism is no longer a workable philosophy because today pressure can be put on the mind as well as on the body. * Technical progress is not evil in itself, but a technique is a means that, regarded as an end, can become either an idol or an excuse for self-idolatry. State control of scientific research, leading to a concentration on new means of destruction, is a calamity. * Fanaticism is an opinion that refuses to argue, and so the fanatic is an enemy of truth. * The kind of unification that science is bringing about today is really an ironing out of differences, but the only valuable kind of unity is one that implies a respect for differences. * We must beware of thinking in terms of great numbers and so blinding ourselves to the reality of individual suffering. Our philosophical approach to being is made possible only by our practical approach to our neighbor. * We must encourage the spirit of fraternity and distrust the kind of egalitarianism that is based on envy and resentment. * No man however humble should feel that he cannot spread the light among his friends. No easy solution is offered, but the author conveys his own faith that ultimately love and intelligence will triumph. (shrink)

Saul Kripke once noted that there is a tight connection between computation and de re knowledge of whatever the computation acts upon. For example, the Euclidean algorithm can produce knowledge of which number is the greatest common divisor of two numbers. Arguably, algorithms operate directly on syntactic items, such as strings, and on numbers and the like only via how the numbers are represented. So we broach matters of notation. The purpose of this article is to explore the relationship between (...) the notations acceptable for computation, the usual idealizations involved in theories of computability, flowing from Alan Turing’s monumental work, and de re propositional attitudes toward numbers and other mathematical objects. (shrink)

We examine George Boolos's proposed abstraction principle for extensions based on the limitation-of-size conception, New V, from several perspectives. Crispin Wright once suggested that New V could serve as part of a neo-logicist development of real analysis. We show that it fails both of the conservativeness criteria for abstraction principles that Wright proposes. Thus, we support Boolos against Wright. We also show that, when combined with the axioms for Boolos's iterative notion of set, New V yields a system equivalent to (...) full Zermelo-Fraenkel set theory with a principle of global choice. This advances Boolos's longstanding interest in the foundations of set theory. (shrink)

Behind the dramas and conflicts, there exists a quiet inner place where meditation and mindfulness can help us reside. This book shares personal insights from visionary leaders -- the Dalai Lama, Jon Kabat-Zinn, and Marianne Williamson among them -- who discuss their methods of maintaining mental health and happiness. Their teaching can help you transform your life from the inside out and discover innate strength, kindness, and courage.

Shapiro knows there are totalitarians on the political Right. But statistically, they represent a fringe movement with little institutional clout. The authoritarian Left, meanwhile, is ascendant in nearly every area of American life. A small number of college-educated, coastal, and uncompromising leftists have not just taken over the Democratic Party but our corporations, our universities, our scientific establishment, our cultural institutions. And they have used their newfound power to silence their opposition. Shapiro lays bare the intolerance and rigidity (...) creeping into all American ideology, and prescribes the solution to ending the authoritarianism that threatens our future. -- adapted from jacket. (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)

This chapter contains sections titled: Geo‐Metrics: Man as the Measurer Thus Spoke Zarathustra: A Philosophical Landscape Poem Peoples and Fatherlands: Songs of the Earth Thinking with the Earth: Toward Geoaesthetics.

This chapter contains sections titled: The Invention of the Picturesque Style Olmsted and Central Park: Ethics, Politics, Aesthetics “The Gates” and the Meaning of the Park Notes.

Cells are cognitive entities possessing great computational power. DNA serves as a multivalent information storage medium for these computations at various time scales. Information is stored in sequences, epigenetic modifications, and rapidly changing nucleoprotein complexes. Because DNA must operate through complexes formed with other molecules in the cell, genome functions are inherently interactive and involve two-way communication with various cellular compartments. Both coding sequences and repetitive sequences contribute to the hierarchical systemic organization of the genome. By virtue of nucleoprotein complexes, (...) epigenetic modifications, and natural genetic engineering activities, the genome can serve as a read-write storage system. An interactive informatic conceptualization of the genome allows us to understand the functional importance of DNA that does not code for protein or RNA structure, clarifies the essential multidirectional and systemic nature of genomic information transfer, and emphasizes the need to investigate how cellular computation operates in reproduction and evolution. (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)

The purpose of the conference "On Pythagoreanism", held in Brasilia in 2011, was to bring together leading scholars from all over the world to define the status quaestionis for the ever-increasing interest and research on Pythagoreanism in the 21st century. The papers included in this volume exemplify the variety of topics and approaches now being used to understand the polyhedral image of one of the most fascinating and long-lasting intellectual phenomena in Western history. Cornelli's paper opens the volume by charting (...) the course of Pythagorean studies over the past two centuries. The remaining contributions range chronologically from Pythagoras and the early Pythagoreans of the archaic period (6th-5th centuries BCE) through the classical, hellenistic and late antique periods, to the eighteenth century. Thematically they treat the connections of Pythagoreanism with Orphism and religion, with mathematics, metaphysics and epistemology and with politics and the Pythagorean way of life. (shrink)

Building on recent work, I present sequent systems for the non-classical logics LP, K3, and FDE with two main virtues. First, derivations closely resemble those in standard Gentzen-style systems. Second, the systems can be obtained by reformulating a classical system using nonstandard sequent structure and simply removing certain structural rules (relatives of exchange and contraction). I clarify two senses in which these logics count as “substructural.”.

In this chapter, I investigate a problem for Kant’s claim that metaphysics can reach the status of science. The problem arises when one considers Kant’s account of the “architectonic unity” of metaphysics in the Architectonic of Pure Reason. Attaining architectonic unity is a condition for becoming a science for any body of cognitions that purports to be such. This is achieved when the cognitions belonging to a science are systematically organized according to the “idea of reason” which lies at the (...) basis of that science. However, Kant suggests that nobody can ever legitimately claim to have matched the idea of the philosopher, where this appears to imply that nobody can justifiably claim that she has fully grasped the idea of metaphysics. This generates a problem. I suggest that when Kant claims that the idea of the philosopher must remain an ideal or an archetype, he has a particular conception of philosophy in mind, that is, philosophy as a doctrine of wisdom. According to this understanding, philosophy must provide an example of how one can become virtuous. However, this is only a partial solution to our problem, for reasons that will be illustrated. (shrink)