The Purpose in Life Test is a measure of purpose in life widely used in many cultures and countries; however, cross-cultural assessments are scarce. The present study aimed to evaluate the cross-cultural measurement invariance of the PIL in the general population of seven Latin American countries. A total of 4306 people participated, selected by non-probabilistic convenience sampling, where Uruguay has the highest mean age ; while Ecuador has the lowest mean age. Furthermore, in each country, there is a higher proportion (...) of women than men. Using Multi-Group Confirmatory Factor Analysis, the factorial structure does not show evidence of invariance among the included countries. However, based on the Multi-Group Factor Analysis Alignment, there is evidence that a three-dimensional structure of the PIL is the same in the participating countries. Results based on item response theory indicate that most PIL items can significantly differentiate responses according to the level of life purpose. In addition, people with low life purpose will tend to choose the lower response alternatives on the PIL; while people with higher life purpose will choose higher response alternatives. The findings indicate that the PIL has the potential to increase knowledge about how people conceive and experience their purpose in life in different countries. (shrink)

In this dialogue Plato shows the pretensions of the leading sophist, Protagoras, challenged by the critical arguments of Socrates. The dialogue broadens out to consider the nature of the good life and the role of intellect and pleasure.

Breathing fresh air into the philosophy of mathematics Content Type Journal Article DOI 10.1007/s11016-010-9470-8 Authors Marco Panza, IHPST, 13, rue du Four, 75006 Paris, France Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796.

What is mathematics about? And if it is about some sort of mathematical reality, how can we have access to it? This is the problem raised by Plato, which still today is the subject of lively philosophical disputes. This book traces the history of the problem, from its origins to its contemporary treatment. It discusses the answers given by Aristotle, Proclus and Kant, through Frege's and Russell's versions of logicism, Hilbert's formalism, Gödel's platonism, up to the the current debate on (...) Benacerraf's dilemma and the indispensability argument. Through the considerations of themes in the philosophy of language, ontology, and the philosophy of science, the book aims at offering an historically-informed introduction to the philosophy of mathematics, approached through the lenses of its most fundamental problem. (shrink)

The indispensability argument comes in many different versions that all reduce to a general valid schema. Providing a sound IA amounts to providing a full interpretation of the schema according to which all its premises are true. Hence, arguing whether IA is sound results in wondering whether the schema admits such an interpretation. We discuss in full details all the parameters on which the specification of the general schema may depend. In doing this, we consider how different versions of IA (...) can be obtained, also through different specifications of the notion of indispensability. We then distinguish between schematic and genuine IA, and argue that no genuine sound IA is available or easily forthcoming. We then submit that this holds also in the particularly relevant case in which indispensability is conceived as explanatory indispensability. (shrink)

Most of the arguments usually appealed to in order to support the view that some abstraction principles are analytic depend on ascribing to them some sort of existential parsimony or ontological neutrality, whereas the opposite arguments, aiming to deny this view, contend this ascription. As a result, other virtues that these principles might have are often overlooked. Among them, there is an epistemic virtue which I take these principles to have, when regarded in the appropriate settings, and which I suggest (...) to call ‘epistemic economy’. My purpose is to isolate and clarify this notion by appealing to some examples concerning the definition of natural and real numbers. (shrink)

Recent discussions on Fregean and neo-Fregean foundations for arithmetic and real analysis pay much attention to what is called either ‘Application Constraint’ ($AC$) or ‘Frege Constraint’ ($FC$), the requirement that a mathematical theory be so outlined that it immediately allows explaining for its applicability. We distinguish between two constraints, which we, respectively, denote by the latter of these two names, by showing how$AC$generalizes Frege’s views while$FC$comes closer to his original conceptions. Different authors diverge on the interpretation of$FC$and on whether it (...) applies to definitions of both natural and real numbers. Our aim is to trace the origins of$FC$and to explore how different understandings of it can be faithful to Frege’s views about such definitions and to his foundational program. After rehearsing the essential elements of the relevant debate (§1), we appropriately distinguish$AC$from$FC$(§2). We discuss six rationales which may motivate the adoption of different instances of$AC$and$FC$(§3). We turn to the possible interpretations of$FC$(§4), and advance a Semantic$FC$(§4.1), arguing that while it suits Frege’s definition of natural numbers (4.1.1), it cannot reasonably be imposed on definitions of real numbers (§4.1.2), for reasons only partly similar to those offered by Crispin Wright (§4.1.3). We then rehearse a recent exchange between Bob Hale and Vadim Batitzky to shed light on Frege’s conception of real numbers and magnitudes (§4.2). We argue that an Architectonic version of$FC$is indeed faithful to Frege’s definition of real numbers, and compatible with his views on natural ones. Finally, we consider how attributing different instances of$FC$to Frege and appreciating the role of the Architectonic$FC$can provide a more perspicuous understanding of his foundational program, by questioning common pictures of his logicism (§5). (shrink)

Proposition I.1 is, by far, the most popular example used to justify the thesis that many of Euclid’s geometric arguments are diagram-based. Many scholars have recently articulated this thesis in different ways and argued for it. My purpose is to reformulate it in a quite general way, by describing what I take to be the twofold role that diagrams play in Euclid’s plane geometry (EPG). Euclid’s arguments are object-dependent. They are about geometric objects. Hence, they cannot be diagram-based unless diagrams (...) are supposed to have an appropriate relation with these objects. I take this relation to be a quite peculiar sort of representation. Its peculiarity depends on the two following claims that I shall argue for: ( i ) The identity conditions of EPG objects are provided by the identity conditions of the diagrams that represent them; ( ii ) EPG objects inherit some properties and relations from these diagrams. (shrink)

The aim I am pursuing here is to describe some general aspects of mathematical proofs. In my view, a mathematical proof is a warrant to assert a non-tautological statement which claims that certain objects (possibly a certain object) enjoy a certain property. Because it is proved, such a statement is a mathematical theorem. In my view, in order to understand the nature of a mathematical proof it is necessary to understand the nature of mathematical objects. If we understand them as (...) external entities whose 'existence' is independent of us and if we think that their enjoying certain properties is a fact, then we should argue that a theorem is a statement that claims that this fact occurs. If we also maintain that a mathematical proof is internal to a mathematical theory, then it becomes very difficult indeed to explain how a proof can be a warrant for such a statement. This is the essential content of a dilemma set forth by P. Benacerraf (cf. Benacerraf 1973). Such a dilemma, however, is dissolved if we understand mathematical objects as internal constructions of mathematical theories and think that they enjoy certain properties just because a mathematical theorem claims that they enjoy them. (shrink)

Greek ancient and early modern geometry necessarily uses diagrams. Among other things, these enter geometrical analysis. The paper distinguishes two sorts of geometrical analysis and shows that in one of them, dubbed “intra-confgurational” analysis, some diagrams necessarily enter as outcomes of a purely material gesture, namely not as result of a codifed constructive procedure, but as result of a free-hand drawing.

The book contains eight papers previously published in English—three of which also appeared in Mancosu's papers collection —and now translated into French (two of them are co-authored with J....

L'objectivité mathématique est le point de mire de nombreux débats logiques et philosophiques. L'opposition platonisme-nominalisme héritée de la tradition a évolué vers une discussion plus technique, qui conjugue des positions fines et complexes. Logiciens, mathématiciens et philosophes décrivent dans cet ouvrage le déplacement progressif de la question de l'objet non sensible vers celle, plus ancrée dans la pensée mathématique, de l'objet infinitaire ou de l'objet structural. Les compétences multiples mises ici à contribution font apparaître que les positions "platoniciennes" sont aujourd'hui (...) non seulement possibles, mais plurielles et, pour beaucoup d'entre elles, affranchies de tout ontologisme sommaire. La discussion confronte la pensée platonicienne aux enjeux logico-mathématiques contemporains et dégage ainsi la pertinence critique du platonisme mathématique. L'ouvrage aborde eh outre la question proprement dite des fondements des mathématiques. Les thèmes majeurs sont débattus sous des angles variables et opposés : finitarisme et constructivité, la portée et la légitimité des axiomes infinitisants de la théorie des ensembles, la valeur gnoséologique de la théorie des modèles... Les résultats les plus récents dans ces domaines sont mis en perspective au sein de nouvelles antinomies et d'une problématique qui évolue. (shrink)

Dans son intervention au colloque Koyré (Paris, 1986), Ernest Coumet a suggéré que le terme « révolution scientifique » ne désigne pas chez Koyré un événement historique, mais un idéaltype, au sens de Max Weber. L'auteur discute d'abord cette thèse de Coumet et expose les arguments que ce dernier apporte pour la soutenir. Dans la deuxième partie de l'article, il critique l'usage de la notion de révolution en histoire des sciences, en s'opposant en particulier à la possibilité de distinguer dans (...) les productions des savants une « pensée scientifique » qui serait influencée par la « pensée philosophique » et dont les bouleversements marqueraient l'avènement d'une révolution. (shrink)

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.

We reconstruct essential features of Lagrange’s theory of analytical functions by exhibiting its structure and basic assumptions, as well as its main shortcomings. We explain Lagrange’s notions of function and algebraic quantity, and we concentrate on power-series expansions, on the algorithm for derivative functions, and the remainder theorem—especially on the role this theorem has in solving geometric and mechanical problems. We thus aim to provide a better understanding of Enlightenment mathematics and to show that the foundations of mathematics did not, (...) for Lagrange, concern the solidity of its ultimate bases, but rather purity of method—the generality and internal organization of the discipline. (shrink)

Over the past thirty years, the doctrine of informed consent has become a focal point in discussions of medical ethics. The literature of informed consent explores the evolution of the principle of autonomy, purportedly emerging from the mists of 19th Century medical practice, and finding its earliest articulation in legal cases where wronged citizens asserted their rights against medical authority. A commonplace, if not obligatory, feature of that literature is a reference to the case of Mary Schloendorff and the opinion (...) written by Judge Benjamin Cardozo by which the case is remembered. Commentators today applaud the prescience of Cardozo for an early articulation of what eventually would become bioethical orthodoxy concerning informed consent and its place as a bulwark of patient autonomy. They inevitably quote Cardozo's famous statement, “Every human being of adult years and sound mind has a right to determine what shall be done with his own body.”. (shrink)

Since their birth, the views have not been just landscapes to contemplate. Vedutism solicited imagination through staging. The engravings of Giovan Battista Piranesi are a proof of this. Today, the photographic zooms allow a reading that reveals the presence of a continuous staging of characters and situations in them. These plates originated a spread of other works, especially in the lyric opera and cinematographic direction, becoming an emblematic case of artistic hermeneutics.

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. (shrink)

Part I of Frege’s Grundgesetze is devoted to the “exposition [Darlegung]” of his formal system.

Relativistic geometrical action for a quantum particle in the superspace is analyzed from theoretical group point of view. To this end an alternative technique of quantization outlined by the authors in a previous work and that is based in the correct interpretation of the square root Hamiltonian, is used. The obtained spectrum of physical states and the Fock construction consist of Squeezed States which correspond to the representations with the lowest weights $\lambda=\frac{1}{4}$ and $\lambda=\frac{3}{4}$ with four possible (non-trivial) fractional representations (...) for the group decomposition of the spin structure. From the theory of semigroups the analytical representation of the radical operator in the superspace is constructed, the conserved currents are computed and a new relativistic wave equation is proposed and explicitly solved for the time-dependent case. The relation with the Relativistic Schrödinger equation and the Time-dependent Harmonic Oscillator is analyzed and discussed. (shrink)

The Supreme Court decided Box v. Planned Parenthood of Indiana and Kentucky in 2019. Justice Clarence Thomas’s opinion in the case claimed there was a direct connection between the legalization of abortion, in the late 20th Century, and the beginnings of the birth control movement a full three quarters of a century earlier. “Many eugenicists,” Thomas argued, “supported legalizing abortion.”Justice Samuel Alito highlighted similar claims in Dobbs v. Jackson Women’s Health, citing a brief entitled “The Eugenic Era Lives on through (...) the Abortion Movement.” That brief was an echo of Justice Thomas’ misguided attempt at history in the Box opinion. Similar claims reoccur in Judge Matthew Kacsmaryk’s opinion in the Texas mifepristone case, Alliance for Hippocratic Medicine v. U.S. Food and Drug Administration.These false claims are the focus of this article. There is no evidence that early leaders of the eugenics movement supported abortion as part of the movement for birth control. It is accurate to describe those leaders as anti-abortion, and their followers as people who condemned abortion for moral, legal, and medical reasons. (shrink)

The philosophy of mathematical practice is not only a research topic, but overall a disciplinary field that is extending its importance and attracting the interest of an increasing number of scholars from different communities. The book edited by Paolo Mancosu provides a comprehensive and vivid account of the philosophy of mathematical practice, by showing it at work on different and multifarious topics, and by suggesting a substantial agenda for its development. This is also a momentous programme for the philosophy of (...) mathematics as a whole, aiming at "bringing some fresh air" into it. Furthermore, Mancosu's book gives voice to a community of scholars working in this area that does not only include the authors of the essays contained in it, but also a large group of scholars sharing their approach and often collaborating with them. (shrink)

Austerity politics, war in the Middle East and at other borders of the European Union, the rise of nationalisms, the emergence of populist parties and politicians, Islamophobia and the refugee crisis are amongst the recent developments suggesting the need for discussions about the theories and concepts that academic disciplines provide for making sense of societal, cultural and political transformations. In this article, we focus on the capacities of feminist political theories to undertake this task. By assessing different feminist approaches to (...) political analysis that range from focusing on women and men, to analysing gender, to doing intersectionality and to adopting post-structural and new materialist approaches, we explore the contributions and the limitations of each framework. This allows us to consider where feminist theoretical debates on gender and politics currently are, to assess old and new developments and to address lacunae in the debate. Our argument is that dominant approaches in political science influence the emergence and marginalisation of particular feminist frameworks for political analysis, but also that feminist theorising of gender and politics, in striving for recognition within mainstream political science, reproduces its own hegemonies and marginalisations. (shrink)

Since its inception the ‘mindblindness’ theory of autism has greatly furthered our understanding of the core social-communication impairments in autism spectrum conditions . However, one of the more subtle issues within the theory that needs to be elaborated is the role of the ‘self’. In this article, we expand on mindblindness in ASC by addressing topics related to the self and its central role in the social world and then review recent research in ASC that has yielded important insights by (...) contrasting processes relating to both self and other. We suggest that new discoveries lie ahead in understanding how self and other are interrelated and/or distinct, and how understanding atypical self-referential and social-cognitive mechanisms may lead to novel ideas as to how to facilitate social-communicative abilities in ASC. (shrink)

This study presents some observations related to a phenomenological-based research aimed to document the influence of the home environment on the human creative sphere. The main objective is to study the links between literary creation and housing of the individual who is generating it, with the aim to highlight some recurrences which make it possible to show how the relationship of writers and “creative people” with their own homes reveals the presence of special “psychological types”. We are presenting here only (...) one example for each of these main “types”. The phenomenological discipline records every single experience as irreducible to a objectified science, but does not deny that it could establish a set of examples from which to draw intersubjective considerations. We studied, therefore, a large number (cases) of experiential reports, without, as claimed by Brentano and Husserl in Crisis of European Sciences, abstracting an objective fact, but recurrences of experience. The research has been carried out with some students of the Polytechnic of Milan in recent years. The purpose of this analysis is also to record the ways in which a place is influencing individual sensibility (mainly of writers) through the analysis of his works, and to highlight “recurrent types” in relation to this connection. (shrink)

Patrizia Lombardo | : Stendhal et Musil sont les deux écrivains par excellence qui se sont interrogés sur le type de connaissance qui vient de la littérature. Avant Musil et comme Musil, Stendhal répond à cette question fondamentale en montrant que le roman offre une connaissance des émotions humaines et de leur lien avec les valeurs. Il s’agit à la fois de valeurs éthiques — les situations morales dans lesquelles se trouvent les personnages — et des valeurs esthétiques et (...) proprement littéraires — le tragique, le comique, le tragi-comique, le sublime, etc. Surtout, le roman n’est pas simple représentation du réel, mais aussi du possible. L’analyse de quelques phrases hypothétiques, conjectures et expériences de pensée dans Le Rouge et le Noir, confirme la thèse que la littérature propose une connaissance du possible à travers le travail de l’imagination. | : Stendhal and Musil are deeply concerned with the question of theknowledge value of literature. Like Musil and before him, Stendhalanswered this question by showing the potential of the novel :this literary form presents human emotions and their connection tovalues. The characters deal with various situations, therefore conveyethical values, while aesthetic values —such as the comic, thetragic, the tragic-comic, the sublime- emerge from the way in whichhuman actions and emotions are represented. All these values arebrought about by the style of Stendhal, which is both form and content,both ethical and aesthetic. The analysis of some hypotheticalsentences, conjectures and thought experiments in The Red and the Blackconfirms the thesis later endorsed by Musil, that literature allows forthe knowledge of the possible, thanks to the exercise of theimagination. (shrink)