It is long known that facial configurations play a critical role when inferring mental and emotional states from others. Nevertheless, there is still a scientific debate on how we infer emotions from facial configurations. The theory of constructed emotion (TCE) suggests that we may infer different emotions from the same facial configuration, depending on the context (e.g. provided by visual and lexical cues) in which they are perceived. For instance, a recent study found that participants were more accurate in inferring (...) mental and emotional states across three different datasets (i.e. RMET, static and dynamic emojis) when words were provided (i.e. forced-choice task), compared to when they were not (i.e. free-labelling task), suggesting that words serve as contexts that modulate the inference from facial configurations. The goal of the current within-subject study was to replicate and extend these findings by adding a fourth dataset (KDEF-dyn), consisting of morphed human faces (to increase the ecological validity). Replicating previous findings, we observed that words increased accuracy across the three (previously used) datasets, an effect that was also observed for the facial morphed stimuli. Our findings are in line with the TCE, providing support for the importance of contextual verbal cues in emotion perception. (shrink)

This study examined individual, task, and environmental constraints that influence the career progression of youth Brazilian elite basketball players and the probability of reaching Novo Basquete Brasil and to determine if the association of the relative age effect is a key factor in the career progression. The sample consisted of 4,692 male players who were registered to participate in at least one U15, U17, or U22 youth Brazilian basketball championship between 2004 and 2018. Athletes who reached a high-performance level were (...) coded like NBB players. The birthdates, height, body mass, playing position, geographic region, club, competition category, and team performance were retrieved from the official data archive of the Brazilian Basketball Confederation and the National Basketball League. The maturity status was estimated using the predicted age at peak height velocity. A binary logistic regression examined the influence of each characteristic on the probability of a youth Brazilian basketball player to reach the NBB. The receiver operating characteristic curves and the associated area under the curve were used to assess the discriminant ability of the model. The taller and younger players not selected early into national teams, without specialization by playing position, who participated in U22 national championship, migrated to the southeast region, and remained in the formation process over time have a greater chance to reach the NBB. The ROC curve demonstrated an AUC of 93%. A combination of individual, task, and environmental characteristics influences the sport career of a young Brazilian basketball player in reaching the NBB. Further, early-maturing athletes have a greater chance to reach higher performances. RAE influences lower-level categories, but not a “NBB player's” career progression. The coaches, stakeholders, and practitioners should perform a holistic evaluation of sport talent in terms of a constraint-based theoretical model with the aim of avoiding bias produced by the maturational status and RAE in the youth Brazilian elite basketball. (shrink)

The project of this Précis de philosophie de la logique et des mathématiques (vol. 1 under the direction of F. Poggiolesi and P. Wagner, vol. 2 under the direction of A. Arana and M. Panza) aims to offer a rich, systematic and clear introduction to the main contemporary debates in the philosophy of mathematics and logic. The two volumes bring together the contributions of thirty researchers (twelve for the philosophy of logic and eighteen for the philosophy of mathematics), specialists (...) in the history or philosophy of logic or mathematics. Each volume consists of ten chapters; each chapter is about forty pages, is independent from the others and deals with a particular philosophical question about logic or mathematics. The objective is to offer to the French-speaking reader a reference book. On many of the issues addressed, this Précis offers the first clear and thorough synthesis that is available in French. -/- This book is intended for third year / master's students, but also for teachers of philosophy in secondary or higher education, for logicians and mathematicians willing to take a philosophical look at the fundamental concepts of their discipline, and for any reader interested in the basic issues discussed in the philosophy of logic and mathematics. Each chapter is self-contained, although some basic training in logic (or in mathematics, as the case may be) is required. The book should be looked at as a comprehensive framework for contemporary discussions in the philosophy of logic and mathematics, while also giving some guidance on the disciplinary content required by these discussions. -/- The first three chapters of the present volume (on the philosophy of mathematics) are devoted to the history of the philosophy of mathematics: from antiquity to the modern era, and from this period to the foundational crisis of the nineteenth century, to the twentieth century. Next, four chapters deal with the crucial questions for the philosophy of mathematics of the twentieth century: the opposition and/or comparison of set theory and category theory as foundational frameworks for mathematics; mathematical constructivism; the analysis of calculability; and Benaceraff's problem. The two following chapters are focused on the philosophy of mathematical practice, by treating the notion of ideals of proof, in particular explanation and purity, and the notion of informal proof and the use of visual artifacts in mathematical argumentation. Finally the last chapter deals with the applicability of mathematics, including the role of probability. -/- In Chapter 1, Sébastien Maronne and David Rabouin present the history of the philosophy of mathematics from antiquity to the modern era. The goal is to show that the philosophy of mathematics has a history as ancient as mathematics and philosophy itself, a history largely continuous with the latter, often by staying out of sync with respect to the former. In Chapter 2, Sébastien Gandon discusses the question of the foundations of mathematics from Kant to the end of the nineteenth century. By tying this question to Kant, he is able to show that the discussion of the foundations of mathematics that occupied a large part of these two centuries has much older roots. Accent is placed on the differences between the framework proposed by Kant for making sense of classical mathematics and the use made by Frege and then Russell of logical tools for giving a different reading of arithmetic and real analysis. The link between between these different conceptions and the evolution of mathematics itself is also underlined. -/- Chapter 3, written by Hourya Benis-Sinaceur and Mirna Džamonja, deals with the evolution of mathematics in the twentieth century, notably the structuralist turn of Dedekind, E. Noether, and Bourbaki, and certain more recent developments. They devote themselves, among other things, to explaining how these developments can be understood as responses to and extensions of questions posed during the foundational debate of the immediately preceding era. -/- In Chapter 4, Jean-Pierre Marquis and Jean-Jacques Szczeciniarz discuss the different foundational options coming from set theory and category theory. They discuss, among other things, Lawvere's program to replace ZF with an axiomatization of the category of sets, the latter judged better adapted to the needs of contemporary mathematics. Different reactions, as much philosophical as technical, raised by this program are also taken into account. -/- Constructive mathematics are the object of Chapter 5, in which Gerhard Heinzmann and Mark van Atten examine in a critical and comparative manner a variety of constructivisms, including intuitionism, constructive type theory, predicativism, and finitism. -/- In Chapter 6, Guido Gherardi and Maël Pegny present computability theory, stressing its philosophical consequences. They discuss the basic concepts of this theory, for the computability of both the natural numbers and the real numbers. They then tackle the theory of computational complexity. -/- In Chapter 7, Andrea Sereni and Fabrice Pataut present Benacerraf's problem, opposing every possible account of mathematical knowledge to the availability of a theory of truth founded on an abstract ontology of mathematical objects. They give an overview of the original problem and its reformulation by Hartry Field, and reconstruct the debate that this problem has raised, by meeting at once the major opposing positions today of the analytic affiliation of the philosophy of mathematics, as much those on the platonist side as on that of nominalism. -/- In Chapter 8, Valeria Giardino and Yacin Hamami treat certain crucial aspects of the philosophy of mathematical practice. They deal in particular with the notion of an informal proof and on the role of artifacts in mathematical reasoning. They consider how such proofs, making use of these means, can contribute to the understanding of theorems and mathematical theories, thanks also to the role of visualisation and the aid of computer tools. -/- Why do mathematics often give several proofs of the same theorem? This is the question that Andrew Arana raises in Chapter 9, introducing the notion of an epistemic ideal and discuss two such ideals, the explanatoriness and purity of proof. -/- Chapter 10 is devoted to the applicability of mathematics in the study of empirical phenomena. After summarizing the history of this question, going back to Plato and Aristotle and passing by Mill and Kant, Daniele Molinini and Marco Panza reconstruct the contemporary debate, in relation, among other things, to questions raised in the philosophy of science. -/- Two appendices complete the volume. In the first Frédéric Patras treats the French tradition in philosophy of mathematics of the 20th century. In the second, Maria Carla Galavotti discusses the notion of probability and its use in science. (shrink)

Nam ibn M recently edited and translated in French by Roshdi Rashed and Christian Houzel bit ibn Qurras treatise is its large use of a form of inferences that can be said in a sense that will be explained. They occur both in proofs of theorems and in solutions of problems. In the latter case, they enter different sorts of problematic analyses that are mainly used to reduce the geometrical problems they are concerned with to al-Khw’s equations.

The Kiki-Bouba effect comprises a relation between two abstract figures and two non-words: the star-shaped figure is called 'Kiki' and the rounded figure 'Bouba'. The effect is explained by a sound-vision synaesthesia: certain sounds are associated with certain shapes in a non-arbitrary manner.When we asked the participants to decide which of the two figures, the star-shaped or the rounded one, to call yin and which yang, some 85% choose the star-shaped figure as yin. There are previous cases of synaesthesia where (...) personality is attributed to numbers or letters. In our results, the word Kiki is overall happy, clever, small, thin, young, unpleasant, and nervous. The starshaped figure is overall clever, tall, small, slim, nervous, unpleasant, and upper-class. That is, the correspondence above all concerns the qualifying adjectives clever, unpleasant, and nervous, as well as the physical appearance small and thin. This brings us to the fat-thin effect. Cinema, literature, comics, and children's programmes are full of contrasting figures: Don Quixote and Sancho Panza, Laurel and Hardy , Asterix and Obelix, Tintin and Captain Haddock, Bert and Ernie , or the Spanish comic about very naughty twin boys called Zipi and Zape . Our main conclusion is that first names and last names are not entirely arbitrary. There is a correspondence between names and physical characteristics and concepts . The Kiki-Bouba effect is a semantic one. (shrink)

Gennaro Chtjerchia, Dynamics of meaning: anaphora, presupposition, and the the of grammar. Chicago and London: The University of Chicago Press, 1995.xv+ 270 pp, £59.95, £31.95 G. Pr...

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)

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)

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

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.

Frege's definition of the real numbers, as envisaged in the second volume of Grundgesetze der Arithmetik, is fatally flawed by the inconsistency of Frege's ill-fated Basic Law V. We restate Frege's definition in a consistent logical framework and investigate whether it can provide a logical foundation of real analysis. Our conclusion will deem it doubtful that such a foundation along the lines of Frege's own indications is possible at all.

In the Tractatus, it is stated that questions about logical formatting cannot be meaningfully formulated, since it is precisely the application of logical rules which enables the formulation of a question whatsoever; analogously, Wittgenstein’s celebrated infinite regress argument on rule-following seems to undermine any explanation of deduction, as relying on a logical argument. On the other hand, some recent mathematical developments of the Curry-Howard bridge between proof theory and type theory address the issue of describing the “subjective” side of logic, (...) that is, the concrete manipulation of rules and proofs in space and time. It is advocated that such developments can shed some light on the question of logical formatting and its apparently unintelligible paradoxes, thus reconsidering Wittgenstein’s verdict. (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 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)

Diagrams are ubiquitous in mathematics. From the most elementary class to the most advanced seminar, in both introductory textbooks and professional journals, diagrams are present, to introduce concepts, increase understanding, and prove results. They thus fulfill a variety of important roles in mathematical practice. Long overlooked by philosophers focused on foundational and ontological issues, these roles have come to receive attention in the past two decades, a trend in line with the growing philosophical interest in actual mathematical practice.

In this paper we argue that data science is a coherent and novel approach to empirical problems that, in its most general form, does not build understanding about phenomena. Within the new type of mathematization at work in data science, mathematical methods are not selected because of any relevance for a problem at hand; mathematical methods are applied to a specific problem only by `forcing’, i.e. on the basis of their ability to reorganize the data for further analysis and the (...) intrinsic richness of their mathematical structure. In particular, we argue that deep learning neural networks are best understood within the context of forcing optimization methods. We finally explore the broader question of the appropriateness of data science methods in solving problems. We argue that this question should not be interpreted as a search for a correspondence between phenomena and specific solutions found by data science methods; rather, it is the internal structure of data science methods that is open to precise forms of understanding. (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)

This book defends antitheodicism, arguing that theodicies, seeking to excuse God for evil and suffering in the world, fail to ethically acknowledge the victims of suffering. The authors argue for this view using literary and philosophical resources, commencing with Immanuel Kant's 1791 "Theodicy Essay" and its reading of the Book of Job. Three important twentieth century antitheodicist positions are explored, including "Jewish" post-Holocaust ethical antitheodicism, Wittgensteinian antitheodicism exemplified by D.Z. Phillips and pragmatist antitheodicism defended by William James. The authors argue (...) that these approaches to evil and suffering are fundamentally Kantian. Literary works such as Franz Kafka'sThe Trial, Samuel Beckett's Waiting for Godot, and George Orwell's Nineteen Eighty-Four, are examined in order to crucially advance the philosophical case for antitheodicism. (shrink)

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.

We argue that many optimization methods can be viewed as representatives of “forcing”, a methodological approach that attempts to bridge the gap between data and mathematics on the basis of an a priori trust in the power of a mathematical technique, even when detailed, credible models of a phenomenon are lacking or do not justify the use of this technique. In particular, we show that forcing is implied in particle swarms optimization methods, and in modeling image processing problems through optimization. (...) From these considerations, we extrapolate a principle for general data analysis methods, what we call ‘Brandt’s principle’, namely the assumption that an algorithm that approaches a steady state in its output has found a solution to a problem, or needs to be replaced. We finally propose that biological systems, and other phenomena that respect general rules of morphogenesis, are a natural setting for the application of this principle. (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.

This paper aims at clarifying the nature of Frege's system of logic, as presented in the first volume of the Grundgesetze. We undertake a rational reconstruction of this system, by distinguishing its propositional and predicate fragments. This allows us to emphasise the differences and similarities between this system and a modern system of classical second-order logic.

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)

As a reply to the commentary (Humphreys in Found Sci, 2012), we explore the methodological implications of seeing artificial neural networks as generic classification tools, we show in which sense the use of descriptions and models in data analysis is not equivalent to the original empirical use of epicycles in describing planetary motion, and we argue that agnostic science is essentially related to the type of problems we ask about a phenomenon and to the processes used to find answers.

Is consciousness a purely physical phenomenon? Most contemporary philosophers and theorists hold that it is, and take this to be supported by modern science. But a significant minority endorse non-physicalist theories such as dualism, idealism and panpsychism, among other reasons because it may seem impossible to fully explain consciousness, or capture what it's like to be in conscious states (such as seeing red, or being in pain), in physical terms. This Element will introduce the main non-physicalist theories of consciousness and (...) explain the most important arguments for them, and consider how they each respond to the scientific and other arguments in support of physicalism. This title is also available as Open Access on Cambridge Core. (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)

The phenomenal powers view claims that phenomenal properties metaphysically necessitate their effects in virtue of how they feel, and thereby constitute non-Humean causal powers. For example, pain necessitates that subjects who experience it try to avoid it in virtue of feeling bad. I argue for this view based on the inconceivability of certain phenomenal properties necessitating different effects than their actual ones, their ability to predict their effects without induction, and their ability to explain their effects without appeal to laws (...) or regularities. I also offer a harmony argument according to which the view offers the best explanation for otherwise seemingly fortunate psychophysical regularities. I then outline the view’s main implications for the metaphysics of causation and philosophy of mind. (shrink)

The ideal introduction for students of semantics, Lexical Meaning fills the gap left by more general semantics textbooks, providing the teacher and the student with insights into word meaning beyond the traditional overviews of lexical relations. The book explores the relationship between word meanings and syntax and semantics more generally. It provides a balanced overview of the main theoretical approaches, along with a lucid explanation of their relative strengths and weaknesses. After covering the main topics in lexical meaning, such as (...) polysemy and sense relations, the textbook surveys the types of meanings represented by different word classes. It explains abstract concepts in clear language, using a wide range of examples, and includes linguistic puzzles in each chapter to encourage the student to practise using the concepts. 'Adopt-a-Word' exercises give students the chance to research a particular word, building a portfolio of specialist work on a single word. (shrink)

In this book Daniel Wegner offers a novel understanding of the relation of consciousness, the will, and our intentional and voluntary actions. Wegner claims that our experience and common sense view according to which we can influence our behavior roughly the way we experience that we do it is an illusion.

As a reply to the commentary (Lenhard in Found Sci, 2012), we stress here that structural understanding of data analysis techniques is the natural counterpart to the lack of understanding of phenomena in agnostic science. We suggest moreover that the dynamics of computational processes, and their parallels with the dynamics of natural processes, will increasingly be, possibly, the driving force of the development of data analysis.

Generating group interaction is a necessary part of teaching philosophy, but there are many obstacles to creating it in a traditional classroom. We propose that philosophy courses can be improved by turning to hybrid models that integrate classroom discussion with online message boards, or forums. Using anecdotes and a comprehensive survey, we argue that using forums helps instructors overcome time constraints in the classroom, helps some students overcome anxiety over contributing, improves discussion, reduces the need to review, and gives instructors (...) a better view of how their students encounter philosophy. We also provide examples of how to use forums and forum assignments. (shrink)

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.

The socialist construction in Vietnam, aspect of human role.

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)

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)

In this paper we would like to attempt to shed some light on the way in which diagrams enter into the practice of ancient Greek geometrical analysis. To this end, we will first distinguish two main forms of this practice, i.e., trans-configurational and intra-configurational. We will then argue that, while in the former diagrams enter in the proof essentially in the same way they enter in canonical synthetic demonstrations, in the latter, they take part in the analytic argument in a (...) specific way, which has no correlation in other aspects of classical geometry. In intra-configurational analysis, diagrams represent in fact the result of a purely material gesture, which is not codified by any construction canon, but permitted only by the practice of the method of analysis and synthesis. (shrink)

Editorial NoteThe following Discussion Note is an edited transcription of the discussion on G. Aldo Antonelli’s paper “Semantic Nominalism: How I Learned to Stop Worrying and Love Universals”, held among participants at the IHPST-UC Davis Workshop Ontological Commitment in Mathematics which took place, in memoriam of Aldo Antonelli, at IHPST in Paris on December, 14–15, 2015. The note’s and volume’s editors would like to thank all participants in the discussion for their contributions, and Alberto Naibo, Michael Wright and the personnel (...) at IHPST for their technical support. (shrink)