Baker claims to provide an example of mathematical explanation of an empirical phenomenon which leads to ontological commitment to mathematical objects. This is meant to show that the positing of mathematical entities is necessary for satisfactory scientific explanations and thus that the application of mathematics to science can be used, at least in some cases, to support mathematical realism. In this paper I show that the example of explanation Baker considers can actually be given without postulating mathematical objects and thus (...) cannot be used by the mathematical realist. I also show that, despite this, mathematics keeps playing an important methodological role in the explanation and does not reduce to a merely computational or descriptive framework. (shrink)

In this article, I argue that mapping-based accounts of applications cannot be comprehensive and must be supplemented by analyses of other, qualitatively different, forms of application. I support these claims by providing a detailed discussion of the application of mathematics to a problem of election design that is prominent in social choice theory.

In a recent paper (Okasha, Mind 120:83–115, 2011), Samir Okasha uses Arrow’s theorem to raise a challenge for the rationality of theory choice. He argues that, as soon as one accepts the plausibility of the assumptions leading to Arrow’s theorem, one is compelled to conclude that there are no adequate theory choice algorithms. Okasha offers a partial way out of this predicament by diagnosing the source of Arrow’s theorem and using his diagnosis to deploy an approach that circumvents it. In (...) this paper I explain why, although Okasha is right to emphasise that Arrow’s result is the effect of an informational problem, he is not right to locate this problem at the level of the informational input of a theory choice rule. Once the informational problem is correctly located, Arrow’s theorem may be dismissed as a problem. (shrink)

Certain mathematical problems prove very hard to solve because some of their intuitive features have not been assimilated or cannot be assimilated by the available mathematical resources. This state of affairs triggers an interesting dynamic whereby the introduction of novel conceptual resources converts the intuitive features into further mathematical determinations in light of which a solution to the original problem is made accessible. I illustrate this phenomenon through a study of Bertrand’s paradox.

In this paper I introduce a novel strategy to deal with the indiscernibility problem for ante rem structuralism. The ante rem structuralist takes the ontology of mathematics to consist of abstract systems of pure relata. Many of such systems are totally symmetrical, in the sense that all of their elements are relationally indiscernible, so the ante rem structuralist seems committed to positing indiscernible yet distinct relata. If she decides to identify them, she falls into mathematical inconsistency while, accepting their distinctness, (...) she finds herself unable to account for it. I show that the ante rem structuralist has in fact the resources to account for the distinctness of indiscernibles and that these resources come from the very symmetry properties of the mathematical objects that seem to pose problems for her. (shrink)

Peano's axiomatizations of geometry are abstract and non-intuitive in character, whereas Peano stresses his appeal to concrete spatial intuition in the choice of the axioms. This poses the problem of understanding the interrelationship between abstraction and intuition in his geometrical works. In this article I argue that axiomatization is, for Peano, a methodology to restructure geometry and isolate its organizing principles. The restructuring produces a more abstract presentation of geometry, which does not contradict its intuitive content but only puts it (...) into a particular form. (shrink)

In this paper I study how divergent mathematical treatments affect mathematical modelling, with a special focus on utility theory. In particular I examine recent work on the ranking of information states and the discounting of future utilities, in order to show how, by replacing the standard analytical treatment of the models involved with one based on the framework of Nonstandard Analysis, diametrically opposite results are obtained. In both cases, the choice between the standard and nonstandard treatment amounts to a selection (...) of set-theoretical parameters that cannot be made on purely empirical grounds. The analysis of this phenomenon gives rise to a simple logical account of the relativity of impossibility theorems in economic theory, which concludes the paper. (shrink)

Throughout his work, John Dewey seeks to emancipate philosophical reflection from the influence of the classical tradition he traces back to Plato and Aristotle. For Dewey, this tradition rests upon a conception of knowledge based on the separation between theory and practice, which is incompatible with the structure of scientific inquiry. Philosophical work can make progress only if it is freed from its traditional heritage, i.e. only if it undergoes reconstruction. In this study I show that implicit appeals to the (...) classical tradition shape prominent debates in philosophy of mathematics, and I initiate a project of reconstruction within this field. (shrink)

When a law court makes a decision based on the individual deliberation of each judge, a case of judgment aggregation occurs. The possibility that the aggregation's outcome be logically inconsistent, even though it is based on consistent individual judgments, arises relatively easily and has been the subject of several investigations. In this paper I show that this paradoxical behaviour is the effect of decision procedures that are unable to discriminate between logically consistent and logically inconsistent individual judgments. The paradoxes can (...) be resolved by selecting procedures that are not affected by this limitation. (shrink)

The Königsberg bridge problem has played a central role in recent philosophical discussions of mathematical explanation. In this paper I look at it from a novel perspective, which is independent of explanatory concerns. Instead of restricting attention to the solved Königsberg bridge problem, I consider Euler’s construction of a solution method for the problem and discuss two later integrations of Euler’s approach into a more structured methodology, arisen in operations research and genetics respectively. By examining Euler’s work and its later (...) developments, I achieve two main goals. First, I offer an analysis of the role played by mathematics as a problem-solving instrument within scientific enquiry. Second, I shed light on the broader significance of well known contributions to the debate on mathematical explanation. I suggest that these contributions, which are tied to a localised explanatory context, achieve a greater relevance and attain a sharper formulation when they are referred to scientific enquiry at large, as opposed to its possible explanatory outcomes alone. (shrink)

In this paper I defend mathematical nominalism by arguing that any reasonable account of scientific theories and scientific practice must make explicit the empirical non-mathematical grounds on which the application of mathematics is based. Once this is done, references to mathematical entities may be eliminated or explained away in terms of underlying empirical conditions. I provide evidence for this conclusion by presenting a detailed study of the applicability of mathematics to measurement. This study shows that mathematical nominalism may be regarded (...) as a methodological approach to applicability, illuminating the use of mathematics in science. (shrink)

In this paper I examine Field’s account of the applicability of mathematics from a measurementtheoretic perspective. Within this context, I object to Field’s instrumentalism, arguing that it depends on an incomplete analysis of applicability. I show in particular that, once the missing piece of analysis is provided, the role played by numerical entities in basic empirical theories must be revised: such revision implies that instrumentalism should be rejected and mathematical entities be regarded not merely as useful tools but also as (...) conceptual schemata by means of which we can articulate our understanding of experience. (shrink)

In this paper I study the activity of mathematical problem-solving in scientific practice, focussing on enquiries in mathematical social science. I identify three salient phases of mathematical problem-solving and adopt them as a reference frame to investigate aspects of applications that have not yet received extensive attention in the philosophical literature.

Using a basic theorem from mathematical logic, I show that there are field-extensions ofRon which a class of orderings that do not admit any real-valued utility functions can be represented by uncountably large families of utility functions. These are the lexicographically decomposable orderings studied in Beardon et al. (2002a). A corollary to this result yields an uncountably large family of very simple utility functions for the lexicographic ordering of the real Cartesian plane. I generalise these results to the lexicographic ordering (...) of \mathbb{R}^n, for every n > 2, and to lexicographic products of lexicographically decomposable chains. I conclude by showing how almost all of these results may be obtained without any appeal to the Axiom of Choice. (shrink)

In this paper I raise some objections to Field’s characterization of applied mathematics, showing, by means of three examples, that it is too restrictive. While doing so, I articulate a different and wider account of applicability. I conclude with an argument supporting its compatibility with an anti-realistic view on the existence of mathematical entities.

Highly idealized models, such as the Hawk-Dove game, are pervasive in biological theorizing. We argue that the process and motivation that leads to the introduction of various idealizations into these models is not adequately captured by Michael Weisberg’s taxonomy of three kinds of idealization. Consequently, a fourth kind of idealization is required, which we call hypothetical pattern idealization. This kind of idealization is used to construct models that aim to be explanatory but do not aim to be explanations.

From religion to philosophy to science, all human systems of definition are formed by human brains. The nature and limits of the human brain are the nature and limits of those systems. This essay shows how the human brain works normally then unusually, and what this reveals about the limits of human knowledge. There are many conditions and instances where the brain processes information unusually, including mental disorders, physical events, and drug use. This essay focuses on the neurological events called (...) mystical experiences. (shrink)

This short peer-reviewed text is a concise look at the psychology of how human beings make decisions, including how they form their worldviews and make arguments.

This paper aims to provide two abductive considerations adducing in favor of the thesis of Necessitism in modal ontology. I demonstrate how instances of the Barcan formula can be witnessed, when the modal operators are interpreted 'naturally' -- i.e., as including geometric possibilities -- and the quantifiers in the formula range over a domain of natural, or concrete, entities and their contingently non-concrete analogues. I argue that, because there are considerations within physics and metaphysical inquiry which corroborate modal relationalist claims (...) concerning the possible geometric structures of spacetime, and dispositional properties are actual possible entities, the condition of being grounded in the concrete is consistent with the Barcan formula; and thus -- in the geometric setting -- merits adoption by the Necessitist. (shrink)

Part of the appeal of the biological approach to personal identity is that it does not have to countenance spatially coincident entities. But if the termination thesis is correct and the organism ceases to exist at death, then it appears that the corpse is a dead body that earlier was a living body and distinct from but spatially coincident with the organism. If the organism is identified with the body, then the unwelcome spatial coincidence could perhaps be avoided. It is (...) argued that such an identification would be a mistake. A living organism has a different part/whole relationship and persistence conditions than the alleged body. A case will be made that the concept ‘human body’ is a conceptual mess, vague in an unprincipled manner, and that an eliminativist stance towards dead bodies is the appropriate response. CiteULike Connotea Del.icio.us What's this? (shrink)

Oxford Philosophical Texts Series Editor: John Cottingham The Oxford Philosophical Texts series consists of authoritative teaching editions of canonical texts in the history of philosophy from the ancient world down to modern times. Each volume provides a clear, well laid out text together with a comprehensive introduction by a leading specialist, giving the student detailed critical guidance on the intellectual context of the work and the structure and philosophical importance of the main arguments. Endnotes are supplied which provide further commentary (...) on the arguments and explain unfamiliar references and terminology, and a full bibliography and index are also included. The series aims to build up a definitive corpus of key texts in the Western philosophical tradition, which will form a reliable and enduring resource for students and teachers alike. David Hume's aim in writing An Enquiry concerning Human Understanding was to introduce his philosophy to a European culture in which many educated people read original works of philosophy. He gives an elegant and accessible presentation of strikingly original and challenging views about the limited powers of human understanding, the attractions of scepticism, the compatibility of free will and determinism, and weaknesses in the foundations of religion. Hume's philosophy was highly controversial in the eighteenth century and remains so today. The text printed in this edition is that of the Clarendon critical edition of Hume's works. A substantial introduction by the editor explains the intellectual background to the work and surveys its main themes. The volume also includes detailed explanatory notes on the text, a glossary of terms, a full list of references, and a section of supplementary readings. (shrink)

As a continuation of the work of the third author in [5], we make further observations on the features of Galois cohomology in the general model theoretic context. We make explicit the connection between forms of definable groups and first cohomology sets with coefficients in a suitable automorphism group. We then use a method of twisting cohomology (inspired by Serre’s algebraic twisting) to describe arbitrary fibres in cohomology sequences—yielding a useful “finiteness” result on cohomology sets. Applied to the special case (...) of differential fields and Kolchin’s constrained cohomology, we complete results from [3] by proving that the first constrained cohomology set of a differential algebraic group over a bounded, differentially large, field is countable. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

In this classic work David Bohm, writing clearly and without technical jargon, develops a theory of quantum physics which treats the totality of existence as an unbroken whole.

This volume is devoted to Lewis's work in metaphysics and epistemology. Topics covered include properties, ontology, possibility, truthmaking, probability, the mind-body problem, vision, belief, and knowledge. The purpose of this collection, and the volumes that precede and follow it, is to disseminate more widely the work of an eminent and influential contemporary philosopher. The volume will serve as a useful work of reference for teachers and students of philosophy.

Religion, science, and naturalism -- Perception and religious experience -- Panexperientialism, freedom, and the mind-body relation -- Naturalistic, dipolar theism -- Natural theology based on naturalistic theism -- Evolution, evil, and eschatology -- The two ultimates and the religions -- Religion, morality, and civilization -- Religious language and truth -- Religious knowledge and common sense.

In this innovative study, Lea David critically investigates the relationship between human rights and memory, suggesting that, instead of understanding human rights in a normative fashion, human rights should be treated as an ideology. Conceptualizing human rights as an ideology gives us useful theoretical and methodological tools to recognize the real impact human rights has on the ground. David traces the rise of the global phenomenon that is the human rights memorialization agenda, termed 'Moral Remembrance', and explores what happens once (...) this agenda becomes implemented. Based on evidence from the Western Balkans and Israel/Palestine, she argues that the human rights memorialization agenda does not lead to a better appreciation of human rights but, contrary to what would be expected, it merely serves to strengthen national sentiments, divisions and animosities along ethnic lines, and leads to the new forms of societal inequalities that are closely connected to different forms of corruptions. (shrink)

Liberal thinkers of the eighteenth and nineteenth centuries were alert to the political costs and human cruelties involved in European colonialism, but they also thought that European expansion held out progressive possibilities. In Progress, Pluralism, and Politics David Williams examines the colonial and anti-colonial arguments of Adam Smith, Immanuel Kant, Jeremy Bentham, and L.T. Hobhouse. Williams locates their ambivalent attitude towards European conquest and colonial rule in a set of tensions between the impact of colonialism on European states, the possibilities (...) of progress in distant and diverse places, and the relationship between universalism and cultural pluralism. In so doing he reveals some of the central ambiguities that characterize the ways that liberal thought has dealt with the reality of an illiberal world. Of particular importance are appeals to various forms of universal history, attempts to mediate between the claims of identity and the reality of difference, and the different ways of thinking about the achievement of liberal goods in other places. Pointing to key elements in still ongoing debates within liberal states about how they should relate to illiberal places, Progress, Pluralism, and Politics enriches the discussion on political thought and the relationship between liberalism and colonialism. (shrink)

Moral claims not only purport to be true, they also purport to guide our choices. This book presents a new theory of normative judgment, the "standard-based theory," which offers a schematic account of the truth conditions of normative propositions of all kinds, including moral propositions and propositions about reasons. The heart of Copp 's approach to moral propositions is a theory of the circumstances under which corresponding moral standards qualify as justified, the " society -centered theory." He argues that because (...) any society needs a social moral code in order to enable its members to live together successfully, and because it would be rational for a society to choose such a code, certain moral codes, and the standards they include, are justified. According to the standard-based theory then, if certain moral standards are indeed justified, corresponding moral propositions may be true. Copp 's approach to morality and explaining normativity and the truth conditions of moral claims, raises a number of important issues in moral theory, as well as in metaphysics and the philosophy of language. (shrink)

"My work has had nothing to do with gay liberation," Michel Foucault reportedly told an admirer in 1975. And indeed there is scarcely more than a passing mention of homosexuality in Foucault's scholarly writings. So why has Foucault, who died of AIDS in 1984, become a powerful source of both personal and political inspiration to an entire generation of gay activists? And why have his political philosophy and his personal life recently come under such withering, normalizing scrutiny by commentators as (...) diverse as Camille Paglia, Richard Mohr, Bruce Bawer, Roger Kimball, and biographer James Miller? David M. Halperin's Saint Foucault is an uncompromising and impassioned defense of the late French philosopher and historian as a galvanizing thinker whose career as a theorist and activist will continue to serve as a model for other gay intellectuals, activists, and scholars. A close reading of both Foucault and the increasing attacks on his life and work, it explains why straight liberals so often find in Foucault only counsels of despair on the subject of politics, whereas gay activists look to him not only for intellectual inspiration but also for a compelling example of political resistance. Halperin rescues Foucault from the endless nature-versus-nurture debate over the origins of homosexuality ("On this question I have absolutely nothing to say," Foucault himself once remarked) and argues that Foucault's decision to treat sexuality not as a biological or psychological drive but as an effect of discourse, as the product of modern systems of knowledge and power, represents a crucial political breakthrough for lesbians and gay men. Halperin explains how Foucault's radical vision of homosexuality as a strategic opportunity for self-transformation anticipated the new anti-assimilationist, anti-essentialist brand of sexual identity politics practiced by contemporary direct-action groups such as ACT UP. Halperin also offers the first synthetic account of Foucault's thinking about gay sex and the future of the lesbian and gay movement, as well as an up-to-the-minute summary of the most recent work in queer theory. "Where there is power, there is resistance," Michel Foucault wrote in The History of Sexuality, Volume I. Erudite, biting, and surprisingly moving, Saint Foucault represents Halperin's own resistance to what he views as the blatant and systematic misrepresentation of a crucial intellectual figure, a misrepresentation he sees as dramatic evidence of the continuing personal, professional, and scholarly vulnerability of all gay activists and intellectuals in the age of AIDS. (shrink)

Thus, Meyers provides a valuable account, not only of current medical attitudes, but also of relevant case and statute law as it stands at present.

*[[This paper appears in _Toward a Science of Consciousness II: The Second Tucson Discussions and Debates_ (S. Hameroff, A. Kaszniak, and A.Scott, eds), published with MIT Press in 1998. It is a transcript of my talk at the second Tucson conference in April 1996, lightly edited to include the contents of overheads and to exclude some diversions with a consciousness meter. A more in-depth argument for some of the claims in this paper can be found in Chapter 6 of my (...) book _The Conscious Mind_ (Chalmers, 1996). ]]. (shrink)

David Charles presents a major new study of Aristotle's views on meaning, essence, necessity, and related topics. These interconnected views are central to Aristotle's metaphysics, philosophy of language, and philosophy of science, and are also highly relevant to current philosophical debates. Charles aims to reach a clear understanding of Aristotle's claims and arguments, to assess their truth, and to evaluate their importance to ancient and modern philosophy.

Confronted with the apparent explanatory gap between physical processes and consciousness, there are many possible reactions. Some deny that any explanatory gap exists at all. Some hold that there is an explanatory gap for now, but that it will eventually be closed. Some hold that the explanatory gap corresponds to an ontological gap in nature.

In Phenomenology and the Problem of History. David Carr examines the paradox involving Husserl's transcendental philosophy and his later historicist theory.

This Introduction introduces readers to the concepts of political philosophy: authority, democracy, freedom and its limits, justice, feminism, multiculturalism, and nationality. Accessibly written and assuming no previous knowledge of the subject, it encourages the reader to think clearly and critically about the leading political questions of our time. THe book first investigates how politcial philosophy tackles basic ethical questions such as 'how should we live together in society?' It furthermore looks at political authority, discusses the reasons society needs politics in (...) the first place, explores the limitations of politics, and asks if there are areas of life that shouldn't be governed by politics. Moreover, the book explores the connections between political authority and justice, a constant theme in political philosophy, and the ways in which social justice can be used to regulate rather than destroy a market economy. In his travels through this realm, Miller covers why nations ar the natural units of government and wonders if the rise of multiculturalism and transnational co-operation will change all this, and asks in the end if we will ever see the formation of a world government. (shrink)

Beneath the stylized violence and thrilling car crashes, the Mad Max films consider universal questions about the nature of human life, order and anarchy, justice and moral responsibility, society and technology, and ultimately, human redemption. In Mad Max and Philosophy, a diverse team of political scientists, historians, and philosophers investigates the underlying themes of the blockbuster movie franchise, following Max as he attempts to rebuild himself and the world. -/- This book guides you through the barren wastelands of a post-apocalyptic (...) future as you explore ethics and politics in The Wasteland, the importance of costumes and music, humankind's relationship with nature, commerce, gender, religion, madness, and more. (shrink)

In this paper I examine some difficulties with the argument presented as a topological sorites in Z. Weber and M. Colyvan, ‘A topological sorites’, Journal of Philosophy 107, 311–325. In particular, I suggest that the argument may be used to support the claim that sorites-type paradoxes cannot arise in a cohesive environment.