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  Gastronomical Platonism

  Marco Panza

  The paper presents a Platonist approach to the art of cooking, based on a crucial distinction between taste and flavor. Being Platonist in cooking is surely not the same as being so in mathematics and logic. Göran is not so in these fields, but I'm confident, that as many mathematicians are spontaneously inclined to live in a Platonist heaven, the sophisticated cook and eater that Göran is will be pleased to imagine with me a Platonist realm of flavors.

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  Adam Smith and the Creative Role of Imagination

  Keith Hankins and Brennan McDavid

  That imagination plays a fundamental role in Smith’s accounts of both sympathy and scientific inquiry is well documented. Smith scholars have also long recognized that the accounts of these roles presented in The Theory of Moral Sentiments and the History of Astronomy are broadly Humean. In particular, the exercise of imagination in both the social and scientific domains is limited by the extent of our experience. Whether we are “changing places in fancy” with our fellows, thereby giving rise to that all-important sentiment of sympathy, or conjecturing relations between observed phenomena in an effort to quell the sentiments of wonder and surprise, acts of imagination draw on what is already familiar in order to fill in the gaps in our understanding of new phenomena we encounter. Hankins and McDavid extend the traditional analysis of Smith’s conception of imagination in three ways. First, they highlight the heretofore unappreciated role imagination plays in Smith’s account of technological invention. Second, they argue that close scrutiny of Smith’s discussion of invention reveals a distinction between two modes in which imagination is exercised: (i) a mimetic mode in which simple ideas from previous experience are faithfully applied to new circumstances and (ii) a creative mode in which much wider gaps are filled in with complex rearrangements of familiar ideas. Third, they argue that these two modes are operative in each of the domains in which imagination operates, and that exercises of imagination in one domain often help us overcome the limits on our imaginative capacities imposed in other domains.

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  Platonism, De Re, and (Philosophy of) Mathematical Practice

  Marco Panza

  The chapter advances a reformulation of the classical problem of the nature of mathematical objects (if any), here called “Plato’s problem,” in line with the program of a philosophy of mathematical practice. It then provides a sketch of a platonist solution, following the same perspective. This solution disregards as nonsensical the question of the existence of abstract, and specifically mathematical, objects, by rather focusing on the modalities of our access to them: objects (in general, both concrete and abstract) are regarded as individual contents that we have (or can have) a de re epistemic access to. The question of the existence of mathematical objects is then replaced by that of the modalities of our de re epistemic access to individual mathematical contents.

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  Permission, Prohibition, and Dynamism

  John Thrasher

  Modern, open societies are characterized by growth and dynamism. To many environmentalists, however, it is this very commitment to growth and change that put modern societies at odds with the values of environmental protection. Many argue that the uncertainty that comes from growth endangers the environment, with the implication being that we should adopt general prohibitions rules like the “Precautionary Principle,” which prohibits economic activity unless it can be proven to have no substantial environmental impact. I argue that this conclusion is largely mistaken. Dynamism is so important and in opposition to general prohibition rules that we should avoid them when possible. Instead, I argue that we should favor a general default permission rule. This rule, I argue, is not only more suited to most environmental domains but also compatible with a dynamic capitalist economy, which is crucial for raising standards of living and finding solutions to existing environmental problems.

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  L’applicabilité des Mathématiques

  Daniele Molinini and Marco Panza

  "Les mathématiques s'appliquent avec succès au monde qui nous entoure et nous aident à raisonner sur les phénomènes empiriques (tant naturels que sociaux), c'est-à-dire sur des faits qui font l'objet d'expéeriences par l'observation et l'expérimentation. Cela ne fait aucun doute."

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  Game Theory

  John Thrasher IV

  The formal study of strategic interaction known as game theory is one of the most important elements in the PPE toolbox. It is no exaggeration to say that game theory is the fundamental logic at the heart of the social and behavioral sciences, and it is crucial for understanding social and political life. Game theory is the core of modern economic theory, formal models in political science, and the most sophisticated and rigorous approaches to moral and political philosophy. Game theory is also important in many of the natural sciences, especially in theoretical biology. As Herbert Gintis (2009, xiii) puts it, “game theory is central to understanding the dynamics of life forms in general, and humans in particular.” As he goes on to argue, “disciplines that slight game theory are the worse – indeed much worse – for it” (Gintis, 2009, xiii). Because of this, any serious student of PPE should have at least some knowledge of and capacity to use game theory.

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  Property

  Bas van der Vossen

  "This chapter discusses the nature and value of property rights. It will explain (1) what property rights are, (2) the relationship between private property and economic development, and (3) some objections to structuring societies around such rights. This discussion throughout focuses on the decentralizing nature of private property rights, asking what implications it has from a philosophical, but also social and political, point of view."

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  Mindful Technology

  Mike W. Martin

  "Mindfulness has become a popular virtue. No longer just a fancy word for attentiveness, mindfulness denotes a wide-ranging excellence that promotes stress relief, emotional control, rational decision-making, concentration at work and at school and in sports, and-my interest-skills in developing and using technology. Although Buddhists have long celebrated mindfulness, recent health psychologists sing fuller-throated paeans. One therapist declares that "mindfulness frees us to act more wisely and skillfully in our everyday decisions" and provides "the solution' to countless daily difficulties (Siegel 2010, 34). Another prominent psychologist traces most problems to an absence of mindfulness: "Virtually all of our problems-personal, interpersonal, professional, and societal-either directly or indirectly stem from mindlessness" (Langer 2014, xiii). Such claims are overblown, but I agree that mindfulness warrants attention in thinking about technology."

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  Qué podría haber sido la universalidad para Euclides

  Marco Panza

  Las proposiciones geométricas de los Elementos de Euclides son universales. Pero, ¿en qué sentido lo son? ¿Tratan las proposiciones geométricas acerca de una cierta totalidad de ítems geométricos (posiblemente objetos)? Ello resultaría sugerido al leer tales proposiciones como sigue: 'Para todo segmento x, construir esto y esto'; 'Todos los triángulos son así y así'. ¿Tratan estas proposiciones de cualquier elemento de tal totalidad? Ello resultaría sugerido al leerlas del siguiente modo: 'Dado cualquier segmento, construir esto y esto'. 'Cualquier triángulo es así y así'. ¿Se refieren a esquemas (en el sentido lógico) de cualquier elemento de tal totalidad? Como parecería estar sugerido al leerlas de la siguiente manera: 'Dado el (un) segmento AB, construir esto y esto', 'El (un) triángulo ABC es así y así'. Considero que todas estas interpretaciones, estén ellas apoyadas o no en consideraciones filológicas, entran en conflicto con un hecho crucial: que no se proporciona ninguna condición global de identidad para los ítems relevantes, e incluso no hubiera podido proporcionarse en el entramado conceptual de la geometría de Euclides. Todo lo que se proporciona son condiciones locales de identidad, que dependen de representaciones diagramáticas de estos ítems. Luego, ningún sentido claro estaría disponible para las afirmaciones universales referidas, en un sentido u otro, a una totalidad fija de ítems geométricos. Posiblemente, el modo en que hoy concebimos a tal totalidad se encuentra condicionado, o al menos es diferente del modo en que lo griegos concebían una totalidad fija de ítems geométricos. Sin embargo, la pregunta que estoy planteando es una pregunta para nosotros, no para ellos. No estoy preguntando si Euclides concebía a una totalidad de ítems geométricos en algún sentido compatible con la ausencia de condiciones globales de identidad para sus elementos. Estoy preguntando si existe un modo para nosotros de comprender lo que él podría haber tomado como una afirmación universal, dado que no podemos adscribirle nuestra concepción de una totalidad fija de ítems geométricos. No quiero una respuesta desde la filología, simplemente porque esta es una pregunta que la filología no puede responder, puesto que no trata de lo que está escrito, sino de cómo nosotros entendemos lo que está escrito. Sin embargo,

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  The Ethics of Capitalism: An Introduction

  Daniel Halliday and John Thrasher

  "The textbook covers longstanding problems that are as old as the discussion of capitalism itself, such as wage inequality, global trade, and the connection between paid labor and human flourishing. It also addresses new challenges, such as climate change, the welfare state, and competitive consumption, and provides topical global case studies. Additionally, it includes study questions at the end of each chapter and an author-created companion website to help guide classroom discussion."

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  Measure and Continuity in Aristotle’s Physics V,3 (and Neighbourhoods)

  Marco Panza

  "As surprising as it might appear prima facie, it is not so much after a little reflexion. Whatever role measure could have played in Aristotle’s time in physics and mathematics, was depending on the content of the available mathematical theories, which is something Aristotle had less to say on, or even about which he never tried to say something. His attitude toward mathematics was always unequivocal: he certainly tried (without much success, by the way, as shown by the quite ambiguous claims of Metaphysics M 1-3) to understand its epistemic nature by so continuing, in a quite different direction, a reflexion already initiated by Plato, but he always took it as a datum, as an established portion of knowledge that is not to be contradicted. He never tried to improve or clarify it. What he says about measure seems to confirm this attitude. To clarify this point, a short survey of the mathematical conceptions of measure at his time, and of the way they differ from our present ones, is in order."

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  Note sull’evoluzione delle nozioni di continuità e di continuo in matematica

  Marco Panza

  Lo scopo di questo saggio è di fornire alcune linee direttive relative alla maniera in cui le nozioni matematiche di continuità e di continuo si sono gradualmente trasformate, a partire dalle concezioni di Aristotele, fino alle concezioni oggi in uso nelle presentazioni elementari dell'analisi reale, risalenti alla seconda metà dell'ottocento.

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  The Myths of the Self-Ownership Thesis

  Jason Brennan and Bas van der Vossen

  "As a result, every reasonable or remotely plausible theory of justice will have to recognize some role for the self-ownership thesis. And disputes between libertarians and left-liberals are not really about whether individuals are self-owners, but rather about which conception of self-ownership is the correct one. So, self-ownership is not a myth. But there are a number of myths about it, including A) that’s a foundational premise in libertarian, especially Robert Nozick’s, thought, and B) that left-liberals deny it while libertarians accept it."

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  Libertarianism

  Bas van der Vossen

  A regularly updated entry in the Stanford Encyclopedia of Philosophy about libertarianism.

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  Intellectual Disability, Sexual Assault, and Empowerment

  Virginia L. Warren

  Girls and women with intellectual disabilities, such as Down syndrome, have a shockingly high rate of rape and sexual assault -- 12 times the rates of persons without disabilities. The perpetrators are often caretakers, who repeatedly violate them. Empowerment is a better framework than autonomy to address this crisis. A conception of autonomy common in healthcare is individualistic and stresses rationality. It may disempower those deemed not competent to make autonomous decisions. By contrast, empowerment calls for changes that are nuanced, political, and far-reaching. An individual is empowered when some or all of the following occur: (a) one is involved in long-term projects (b) which make one feel energized and more confident in one's ability to make changes in one's life or society, (c) while developing traits and capacities which help to shape one's life, (d) often while being supported by -- and supporting -- others in a group or community effort with which one identifies, (e) thus enhancing one's particular skills, relationships, self-concept, and long-term well-being. Empowerment involves (f) seeking changes in laws, institutional policies, and the attitudes and behavior of other people. Here, the aim is transitioning to a more inclusive, caring and just society that values the "person first."

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  Asymptotic Quasi-completeness and ZFC

  Mirna Džamonja and Marco Panza

  The axioms ZFC of first order set theory are one of the best and most widely accepted, if not perfect, foundations used in mathematics. Just as the axioms of first order Peano Arithmetic, ZFC axioms form a recursively enumerable list of axioms, and are, then, subject to Gödel’s Incompleteness Theorems. Hence, if they are assumed to be consistent, they are necessarily incomplete. This can be witnessed by various concrete statements, including the celebrated Continuum Hypothesis CH. The independence results about the infinite cardinals are so abundant that it often appears that ZFC can basically prove very little about such cardinals. However, we put forward a thesis that ZFC is actually very powerful at some infinite cardinals, but not at all of them. We have to move away from the first few and to look at limits of uncountable cardinals, such as N_w. Specifically, we work with singular cardinals (which are necessarily limits) and we illustrate that at such cardinals there is a very serious limit to independence and that many statements which are known to be independent on regular cardinals become provable or refutable by ZFC at singulars. In a certain sense, which we explain, the behavior of the set-theoretic universe is asymptotically determined at singular cardinals by the behavior that the universe assumes at the smaller regular cardinals. Foundationally, ZFC provides an asymptotically univocal image of the universe of sets around the singular cardinals. We also give a philosophical view accounting for the relevance of these claims in a platonistic perspective which is different from traditional mathematical platonism.

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  Enthymemathical Proofs and Canonical Proofs in Euclid’s Plane Geometry

  Abel Lassalle and Marco Panza

  Since the application of Postulate I.2 in Euclid’s Elements is not uniform, one could wonder in what way should it be applied in Euclid’s plane geometry. Besides legitimizing questions like this from the perspective of a philosophy of mathematical practice, we sketch a general perspective of conceptual analysis of mathematical texts, which involves an extended notion of mathematical theory as system of authorizations, and an audience-dependent notion of proof.

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  Was Frege a Logicist for Arithmetic?

  Marco Panza

  The paper argues that Frege’s primary foundational purpose concerning arithmetic was neither that of making natural numbers logical objects, nor that of making arithmetic a part of logic, but rather that of assigning to it an appropriate place in the architectonics of mathematics and knowledge, by immersing it in a theory of numbers of concepts and making truths about natural numbers, and/or knowledge of them transparent to reason without the medium of senses and intuition.

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  When Equality Matters

  John Thrasher

  Equality is at the heart of liberal, democratic political theory. Despite this, there is considerable disagreement about how we should understand equality in the context of liberal politics. Several different conceptions of equality (e.g., equality of opportunity, equality of welfare outcomes, and equality of basic rights) will recommend different and often conflicting policies and institutions. Further, we can expect, in democratic societies, that citizens will disagree on the correct conception of equality. This leads to the diversity problem of equality— there is no one conception of equality that will be acceptable to all citizens. This is compounded by the complexity problem of generating determinate and predictable results in the institutional application of any particular conception of equality. After identifying these problems and looking at G.A. Cohen’s defense of a thoroughly egalitarian conception of politics, I argue in favor of “democratic equality” as a political ideal.

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  Property and Business

  Bas van der Vossen

  "This chapter gives an overview of the main foundational theories of property. As I will show, there are two major families of justification for property (with each family, of course, having many different members). After laying out those two families and their potential problems, I will then consider some of the issues that reside in intellectual property, turning subsequently to explore one way in which a theory of business ethics may either be in tension or fit with such a justification of property. In particular, I will look at the tensions that stakeholder theory, on at least one version of that theory, might create."

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  In Defense of Openness

  Bas van der Vossen and Jason Brennan

  "The topic of global justice has long been a central concern within political philosophy and political theory, and there is no doubt that it will remain significant given the persistence of poverty on a massive scale and soaring global inequality. Yet, virtually every analysis in the vast literature of the subject seems ignorant of what developmental economists, both left and right, have to say about the issue. In Defense of Openness illuminates the problem by stressing that that there is overwhelming evidence that economic rights and freedom are necessary for development, and that global redistribution tends to hurt more than it helps. Bas van der Vossen and Jason Brennan instead ask what a theory of global justice would look like if it were informed by the facts that mainstream development and institutional economics have brought to light."

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  Contemporary Approaches to the Social Contract

  Fred D'Agostino, John Thrasher, and Gerald Gaus

  "To explicate the idea of the social contract we analyze contractual approaches into five elements: (1) the role of the social contract (2) the parties (3) agreement (4) the object of agreement (5) what the agreement is supposed to show."

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  Euler’s Introductio in analysin infinitorum and the Program of Algebraic Analysis: Quantities, Functions and Numerical Partitions

  Marco Panza

  After discussing in general Euler's program of algebraic analysis, as it is presented in the Introductio (1748), two particular topics are taken into account: Euler's notion of function and his analytic theory of numerical partitions.

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  On Benacerraf’s Dilemma, Again

  Marco Panza

  In spite of its enormous influence, Benacerraf’s dilemma admits no standard unanimously accepted formulation. This mainly depends on Benacerraf’s having originally presented it in a quite colloquial way, by avoiding any compact, somehow codified, but purportedly comprehensive formulation (Benacerraf 1973 cf. p. 29).

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  Debating Humanitarian Intervention: Should We Try to Save Strangers?

  Fernando R. Tesón and Bas van der Vossen

  "When violence breaks out in a country, foreign governments face a difficult dilemma: should they intervene on behalf of the victims, or should they remain spectators? Each choice offers its own perils, and philosophers Fernando R. Tesón and Bas van der Vossen offer contrasting views of intervention by employing modern analytic philosophy, particularly just war theory. Tesón and van der Vossen refer to and weigh the consequences of past, present, and future interventions in Syria, Somalia, Rwanda, Bosnia, Iraq, Lybia, Egypt, and more."