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)

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)

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)

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 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)

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)

Cet article traite la problématique du facteur humain dans la société en réseau en mettant en évidence que les TIC sont à la fois créatrices et destructrices de lien social. Il propose une approche de la fracture numérique selon deux niveaux: - un accès inégalitaire à Internet et aux TIC; - des savoirs et savoir-faire insuffisants pour communiquer dans une société désormais régie par la manipulation et les mécanismes de génération de la connaissance. Il prend comme exemple référentiel la génération (...) Internet née de la double médiation technique et sociale caractéristique du lien social engendré par l'usage des TIC. Et, il situe ainsi la véritable origine de la fracture numérique dans les inégalités socio-économiques et culturelles qui existaient pour la plupart avant l'introduction des TIC et la mise en réseau de la société.This paper addresses the problem of the human factor in the network society by highlighting that ICTs are both creative and destructive social links. It proposes an approach to the digital divide in two levels: - unequal access to the Internet and ICT - knowledge and skills sufficient to communicate in a society now governed by the manipulation and generation mechanisms of knowledge. He takes as an example the Internet generation born repository of double mediation technical and social characteristics of social ties generated by the use of ICT. And it is thus the true origin of the digital divide in the socio-economic and cultural existed mostly before the introduction of ICT and networking company. (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 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.

This particular roundtable falls at the end of a four-year networking project (COST Action IS1307 New Materialism: Networking European Scholarship on ‘How Matter Comes to Matter’) and reflects upon the genealogies of new materialism and how these flow into the individual working practices of participants. The texts below were contributed remotely via email by members of the group, following face-to-face meetings in Barcelona, Maribor, Warsaw, Liverpool, Paris and Utrecht. Authors were unaware of each other’s responses and in this way the (...) dialogue has unfolded a little like a game of Exquisite Corpse or Consequences, with questions acting like a trail of breadcrumbs to follow. Accordingly, the text is the product of a partially bounded experimental system ‘designed to give unknown answers to questions that the experimenters themselves are not yet able to clearly ask’ (Rheinberger 1997: 28). Thus, it both ruminates upon work to date and is intended to generate novel responses from authors and readers alike. (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)

There are very few (published) accounts of editorial misconduct, and those that do exist are almost exclusively focused on medicine-related areas. In the present article we detail a case of editorial misconduct in a rather underexplored domain, the social sciences. This case demonstrates that although legal systems provide different instruments of protection to avoid, compensate for, and punish misconduct on the part of journal editors, the social and economic power unbalance between authors and publishers suggests the importance of alternative solutions (...) before or instead of bringing a lawsuit to court. It puts forward strong arguments in favour of the need for effective regulatory bodies so as to achieve and maintain a culture of research integrity by all involved in the process. (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)

Postmodern alienation -- Jameson's dialectical levels -- Baudrillard's hostile worlds -- Foucault's system of thought.

Aurora P. Jackson and Richard Scheines. Single Mother's Efficacy, Parenting in the Home Environment, and Children's Development in a Two-Wave Study.

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)

In this position paper, we would like to promote the alternative approach positioned between the two extreme positions consisting in refusing any innovation or in adopting technology without questioning it. This approach proposes a reflexive and responsible innovation based on a compromise between industrial and economic potentialities and a common respect of our human rights and values. We argue that the “silence of the chips right” is timely, relevant and sustainable to face ethical challenges raised by IoT such as protecting (...) privacy, trust, social justice, autonomy or human agency. We believe this technical solution may support establishing an ethics of IoT embedded in the technology itself. Our position is not ‘technocratic’: we do not agree with discourses arguing technology can fix problems. Through the responsible research and innovation approach we promote the idea that only human agency and user empowerment constitute a valid answer to the ethical, legal and social issues raised by IoT. (shrink)

This book examines the controversies surrounding biomedical research in the twenty-first century from a human rights perspective, analyzing the evolution and ...

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.

The introduction of information technology in the society and its pervasiveness in every aspect of citizens' daily life highlight societal stakes related to the goals regarding the uses IT, such as social networks. This paper examines two cases that lack a straightforward link with privacy as addressed and protected by existing law in Europe and the United-States , but whose characteristics, we believe fall on other privacy function and properties. In Western societies, individuals rely on normative discourses, such as the (...) legal one, in order to ensure protection. Hence, the paper argues that other functions of privacy need either further framing into legislation or they need to constitute in themselves normative commitments of an ethical nature for technology development and use. Some initiatives at the EU level recall such commitments, namely by developing a normative discourse based on ethics and human values. We argue that we need to interrogate society about those normative discourses because the values we once cherished in a non-digital society are seriously being questioned. (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 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.

(2002). Missing twins. Philosophy & Geography: Vol. 5, No. 1, pp. 13-17.

In appearance, Husserl’s writings seem not to have had any influence on linguistic research, nor does what the German philosopher wrote about language seem to be worth a place in the history of linguistics. The purpose of the paper is exactly to contrast this view, by reassessing both the position and the role of Husserl’s early masterpiece — the Logical Investigations — within the history of linguistics. To this end, I will focus mainly on the third (On the theory of (...) wholes and parts) and fourth (The distinction between independent and non-independent meanings) Investigations, paying special attention to Husserl’s mereology and to the idea of a general pure grammar. The paper tries to situate the third and fourth Logical Investigation within the general context of late nineteenth-century and early twentieth-century linguistics and furthermore attempts to show the historical and theoretical importance of the Logical Investigations for the birth and the development of one of the most important linguistic “schools” of the twentieth century, namely structural linguistics. (shrink)

This paper aims to consider the main features of the philosophy of linguistics proposed by Deleuze and Guattari, which emerges from the criticisms directed at what in A Thousand Plateaus they call ‘postulates of linguistics’. The paper focuses on the transition from the Saussurean concept of system and from the connected notion of structure to Deleuze and Guattari's concept of machine. More precisely, the purpose of the paper lies, on the one hand, in showing in which sense Deleuze and Guattari (...) claim that language is not a ‘structure’ but a ‘machine’ and why, accordingly, they maintain that the mentioned ‘postulates of linguistics’ must be refused; on the other hand, the paper represents an attempt at placing Deleuze and Guattari's position in the context of contemporary linguistics. (shrink)

The aim of the paper is to show the relevancy of Aron Gurwitsch’s transcendental-phenomenological theory of the field of consciousness for semiotics and the theory of meaning. After a brief biographical introduction, the paper will focus upon the key theoretical points that define Gurwitsch’s theory of the field of consciousness and will consider some of Gurwitsch’s reflections on linguistic and semiotic issues. Finally, it will be shown that the latter are strictly connected with Gurwitsch’s general philosophical framework and, accordingly, that (...) it is possible (and fruitful) to provide a semiotic understanding of Gurwitsch’s phenomenology. (shrink)