Can there be mathematical explanations of physical phenomena? In this paper, I suggest an affirmative answer to this question. I outline a strategy to reconstruct several typical examples of such explanations, and I show that they fit a common model. The model reveals that the role of mathematics is explicatory. Isolating this role may help to re-focus the current debate on the more specific question as to whether this explicatory role is, as proposed here, also an explanatory one.

I identify and characterize a type of noncausal explanation in physics. I first introduce a distinction, between the physical properties of a system, and the representational properties of the mathematical expressions of the system’s physical properties. Then I introduce a novel kind of property, which I shall call a dual property. This is a special kind of representational property, one for which there is an interpretation as a physical property. It is these dual properties that, I claim, are amenable to (...) noncausal (mathematical, in fact) explanations. I discuss a typical example of such a dual property, and an example of an explanation as to why that dual property holds (the explanation of the quantization of the linear momentum). (shrink)

The articulation of an overarching account of scientific explanation has long been a central preoccupation for the philosophers of science. Although a while ago the literature was dominated by two approaches—a causal account and a unificationist account—today the consensus seems to be that the causal account has won. In this paper, I challenge this consensus and attempt to revive unificationism. More specifically, I aim to accomplish three goals. First, I add new criticisms to the standard anti-unificationist arguments, in order to (...) motivate the need for a revision of the doctrine. Second, and most importantly, I sketch such a revised version. Then I argue that, contrary to widespread belief, the causal account and this revised unificationist account of explanation are compatible. Moreover, I also maintain that the unificationist account has priority, since a most satisfactory theory of explanation can be obtained by incorporating the causal account, as a sub-component of the unificationist account. The driving force behind this reevaluation of the received view in the philosophy of explanation is a reconsideration of the role of scientific understanding. (shrink)

In spite of its dominance, there are well-known problems with Rawls’s method of reflective equilibrium (MRE), as a method of justification in meta-ethics. One issue in particular has preoccupied commentators, namely, the capacity of this method to provide a convincing account of the objectivity of our moral beliefs. Call this the Lack-of-Objectivity Charge. One aim of this article is to examine the charge within the context of Rawls’s later philosophy, and I claim that the lack-of-objectivity charge remains unanswered. A second (...) aim of this article is to examine the extent to which, despite Rawls’s express intention to avoid reliance on Kant’s moral philosophy, supplementing Rawls’s political constructivism with some Kantian elements, in particular Kant’s idea of a universal principle of right, not only addresses some of the issues raised by the lack-of-objectivity charge, but also does so without compromising the ability of the Rawlsian account to accommodate the pluralism of conceptions of the good, which he takes to be a fact of modern democracies. I argue for a revised justificatory methodology, which combines Rawls’s MRE and Kant’s Critical Method. (shrink)

I argue that a recent version of the doctrine of mathematical naturalism faces difficulties arising in connection with Wigner's old puzzle about the applicability of mathematics to natural science. I discuss the strategies to solve the puzzle and I show that they may not be available to the naturalist.

Steiner defines naturalism in opposition to anthropocentrism, the doctrine that the human mind holds a privileged place in the universe. He assumes the anthropocentric nature of mathematics and argues that physicists' employment of mathematically guided strategies in the discovery of quantum mechanics challenges scientists' naturalism. In this paper I show that Steiner's assumption about the anthropocentric character of mathematics is questionable. I draw attention to mathematicians' rejection of what Maddy calls ‘definabilism’, a methodological maxim governing the development of mathematics. I (...) contend that because definabilism is anthropocentric, its rejection casts doubts on Steiner's assumption. (shrink)

A critical approach on tolerance can be done as an endeavor to asset its rational arguments brought in its support or/and as a justification of its moral value within the process of human being completion. The commitment to such critical task is more necessary as it is unyieldingness summon in contemporary debates in political religious and, especially moral contexts, it has been equally valorized and contested. The most remarkable analyses of this rather summary rubric for many and often contradictory connotations, (...) then concept, underline the idea that a limit-matter is at stake: can be tolerated the intolerable? Because these boundaries are hard to be distinguished the critical position intellectually reasonable seems to be that of examining if is not more socially profitable and morally justifiable to be tolerant rather than intolerant.Developing possible arguments for and against the universal value of tolerance, critical discourse imposes a very meaningful statement: to uphold our humanity, even the demand for our right to intolerance must be done within the framework and with the means of tolerance. (shrink)

Este artículo tiene como propósito principal investigar la famosa sentencia derridiana “il n’y a pas de hors-texte”, que como sabemos entró a significar una especie de slogan de época. En función de este propósito, realizamos un examen del contexto de aparición más inmediato de la mentada frase, estudiamos sus condiciones de recepción y problematizamos el sentido de “texto” y “escritura” en el pensamiento derridiano. Como mostramos, estas nociones no se vinculan con ninguna “hiperbolización” del lenguaje, sino más bien su ruina.

The past three decades have witnessed the emergence, at the forefront of political thought, of several Kantian theories. Both the critical reaction to consequentialism inspired by Rawlsian constructivism and the universalism of more recent theories informed by Habermasian discourse ethics trace their main sources of inspiration back to Kant's writings. Yet much of what is Kantian in contemporary theory is formulated with more or less strict caveats concerning Kant's metaphysics. These range from radical claims that theories of justice must be (...) political, not metaphysical, to more cautious calls for replacing Kant's metaphysics with a more modest ontology, for instance, one informed by the relatively recent linguistic turn in philosophy. The volume will consist of thirteen state-of-the-art essays which explore the relationship between politics and metaphysics in Kant and Kantian political philosophy. All essays will be published for the first time in this volume and will be preceded by an Introduction from the editors. Given the current "legitimation crisis" of modern liberal democracies, the purpose of the collection as a whole is to revisit the question concerning the role of metaphysics in moral and political philosophy and to suggest new perspectives on the question of legitimation. (shrink)

I present a reconstruction of Eugene Wigner’s argument for the claim that mathematics is ‘unreasonable effective’, together with six objections to its soundness. I show that these objections are weaker than usually thought, and I sketch a new objection.

Constitutivism aims to justify substantial normative standards as constitutive of practical reason. In this way, it can defend the constructivist commitment to avoiding realism and anti-realism in normative disciplines. This metaphysical debate is the perspective from which the nature of the constitutivist justification is usually discussed. In this paper, I focus on a related, but distinct, debate. My concern will not be whether the substantial normative claims asserted by the constructivist have some elements, which are not constructed, but real, given (...) independently from us; instead, my concern will be more narrowly epistemic – whether those claims can be derived from premises, which are normatively less substantial than the normative conclusions themselves. I focus on Korsgaard’s transcendental articulation of the constitutivist argument. I conclude that more work would need to be done, in order for this argument to function as intended. (shrink)

Suppose we are asked to draw up a list of things we take to exist. Certain items seem unproblematic choices, while others (such as God) are likely to spark controversy. The book sets the grand theological theme aside and asks a less dramatic question: should mathematical objects (numbers, sets, functions, etc.) be on this list? In philosophical jargon this is the ‘ontological’ question for mathematics; it asks whether we ought to include mathematicalia in our ontology. The goal of this work (...) is to answer this question in the affirmative, by drawing on considerations on the the applicability of mathematics to natural science. (shrink)

The Principle of Indifference is a central element of the ‘classical’ conception of probability, but, for all its strong intuitive appeal, it is widely believed that it faces a devastating objection: the so-called (by Poincare´) ‘Bertrand paradoxes’ (in essence, cases in which the same probability question receives different answers). The puzzle has fascinated many since its discovery, and a series of clever solutions (followed promptly by equally clever rebuttals) have been proposed. However, despite the long-standing interest in this problem, an (...) important assumption, necessary for its generation, has been overlooked. My aim in this paper is to identify this assumption. Since what it claims turns out to be prima facie problematic, I will urge that the burden of proof now shifts to the objectors to PI; they have to provide reasons why this assumption holds. (shrink)

The paper rebuts a currently popular criticism against a certain take on the referential role of discontinuities and singularities in the physics of first-order phase transitions. It also elaborates on a proposal I made previously on how to understand this role within the framework provided by the distinction between data and phenomena.

Arguing for mathematical realism on the basis of Field’s explanationist version of the Quine–Putnam Indispensability argument, Alan Baker has recently claimed to have found an instance of a genuine mathematical explanation of a physical phenomenon. While I agree that Baker presents a very interesting example in which mathematics plays an essential explanatory role, I show that this example, and the argument built upon it, begs the question against the mathematical nominalist.

What is the role of bridge laws in inter-theoretic relations? An assumption shared by many views about these relations is that bridge laws enable reductions. In this article, I acknowledge the naturalness of this assumption, but I question it by presenting a context within thermal physics (involving phase transitions) in which the bridge laws, puzzlingly, seem to contribute to blocking the reduction.

My main aim is to sketch a certain reading (‘genealogical’) of later Wittgenstein’s views on logical necessity. Along the way, I engage with the inferentialism currently debated in the literature on the epistemology of deductive logic.

The question as to whether there are mathematical explanations of physical phenomena has recently received a great deal of attention in the literature. The answer is potentially relevant for the ontology of mathematics; if affirmative, it would support a new version of the indispensability argument for mathematical realism. In this article, I first review critically a few examples of such explanations and advance a general analysis of the desiderata to be satisfied by them. Second, in an attempt to strengthen the (...) realist position, I propose a new type of example, drawing on probabilistic considerations. 1 Introduction2 Mathematical Explanations2.1 ‘Simplicity’3 An Average Story: The Banana Game3.1 Some clarifications3.2 Hopes and troubles for the nominalist3.3 New hopes?3.4 New troubles4 Conclusion. (shrink)

In this paper I reconstruct and critically examine the reasoning leading to the famous prediction of the ‘omega minus’ particle by M. Gell-Mann and Y. Ne’eman (in 1962) on the basis of a symmetry classification scheme. While the peculiarity of this prediction has occasionally been noticed in the literature, a detailed treatment of the methodological problems it poses has not been offered yet. By spelling out the characteristics of this type of prediction, I aim to underscore the challenges raised by (...) this episode to standard scientific methodology, especially to the traditional deductive-nomological account of prediction. (shrink)

In this paper I examine the fundamental views on the nature of logical and mathematical truth of both Frege and Carnap. I argue that their positions are much closer than is standardly assumed. I attempt to establish this point on two fronts. First, I argue that Frege is not attempting to defend metaphysical theses. Second, I argue that Carnap, where he does differ from Frege, can be seen to do so because of mathematical results proven in the early twentieth century. (...) The differences in their views are, then, not primarily philosophical differences. Also, it might be thought that Frege was interested in analyzing our ordinary mathematical notions, while Carnap was interested in the construction of arbitrary systems. I argue that this is not the case: our ordinary notions play, in a sense, an even more important role in Carnap’s philosophy of mathematics than they do in Frege’s. Finally, I address Tyler Burge’s interpretation of Frege which is in opposition to any Carnapian reading of Frege. (shrink)

The paper argues that the phenomenon of first-order phase transitions (e.g., freezing) has features that make it a candidate to be classified as 'emergent'. However, it cannot be described either as 'weakly emergent' or 'strongly emergent'; hence it escapes categorization in terms employed in the current literature on the metaphysics of science.

This book is meant as a part of the larger contemporary philosophical project of naturalizing logico-mathematical knowledge, and addresses the key question that motivates most of the work in this field: What is philosophically relevant about the nature of logico-mathematical knowledge in recent research in psychology and cognitive science? The question about this distinctive kind of knowledge is rooted in Plato’s dialogues, and virtually all major philosophers have expressed interest in it. The essays in this collection tackle this important philosophical (...) query from the perspective of the modern sciences of cognition, namely cognitive psychology and neuroscience. _Naturalizing Logico-Mathematical Knowledge _contributes to consolidating a new, emerging direction in the philosophy of mathematics, which, while keeping the traditional concerns of this sub-discipline in sight, aims to engage with them in a scientifically-informed manner. A subsequent aim is to signal the philosophers’ willingness to enter into a fruitful dialogue with the community of cognitive scientists and psychologists by examining their methods and interpretive strategies. (shrink)

In his Remarks on the Foundations of Mathematics, Wittgenstein claims, puzzlingly, that ‘the proof creates a new concept’ (RFM III-41). This paper aims to contribute to clarifying this idea, and to showing how it marks a major break with the traditional conception of proof. Moreover, since the most natural way to understand his claim is open to criticism, a secondary goal of what follows is to offer an interpretation of it that neutralizes the objection. The discussion proceeds by analysing a (...) well-known geometrical proof. (shrink)

The paper discuses whether the mathematical singularities characterizing first-order phase transitions are 'fictions'.

The secular interpretation of Kant is widespread and Kant is viewed as the most prestigious founding father of liberal secularism. At the same time, however, commentators note that Kant’s position on secularism is in fact much more complex, and some go as far as to talk about an ambiguous secularism in his work. This paper defends a refined version of the secular interpretation. According to this refined version, Kant can offer a limited, political secularism on the basis of a simple (...) argument which focuses on the distinct epistemic statuses of political and religious claims; however, the paper argues, a more general secularism is unwarranted on the basis of the same argument. If my argument is correct, then it will account at least in part for the plurality of interpretations. Moreover, any further attempt to show that Kant’s relation to secularism is ambiguous or dismissive should take into consideration the argument from epistemic grounds presented here. (shrink)

The traditionalist interpretation of Kant's idealism reads his Critical philosophy as a version of traditional idealism, à la Berkeley. By contrast, a revolutionary account of Kant will assert the threefold distinction between states of mind, external objects of the world and things in themselves, and will reject the attempt to reduce external objects to states of mind. In this paper, I argue that, while Caird's interpretation is clearly not traditionalist, nor is it obviously revolutionary: he is critical of Kant's threefold (...) distinction, although he fully acknowledges Kant's attempt to uphold this distinction. While arguing for this claim, the paper will examine several classical objections to Kant's Critical philosophy, including the view that things in themselves should be rejected and that Kant's system lacks the unity necessary to account for the variety of distinctions he introduces, including the distinction between phenomena and noumena. (shrink)

Throughout the history of philosophical thinking, ethics has almost never been associated with ontology because the moral approach is about the action while the ontological approach is about the being. The prospective approach confers to moral philosophy a genuine ontological direction, an ontology of the human, since it aims at identifying the problems of (human) existence, which no longer describes “what should be” but mostly “what can be”, thus anticipating the ways of human existence in a future world.The challenges raised (...) by disruptive innovations and the environmental issue require the critical eye of moral philosophy regarding the impact of technological progress is having in redefining the human condition of tomorrow’s society; all the more so as we are facing a regrettable backwardness of moral progress, which does not seem to keep pace with the spectacular changes in science and technology. The wisdom of ethical reflection refers to a feeling of concern for both present and future humanity as a whole,relating not only to immediate reality but, especially, anticipating what might happen. (shrink)

The article comments upon the report written by the French captain Aubert about the Romanian space during the XIXth century. It analyses the richness of documentation data contained by the report, through the lenses of the historical anthropological categories of “the other’s image”. The author concludes that the report was elaborated in a period when French interests for the Romanian space was rising.

Derrida dice en más de una oportunidad que la cuestión de los demás vivientes, de lo otro que lo humano, ha inquietado siempre su escritura, aún cuando no fuera tema explícito de sus formulaciones. Este trabajo busca abordar esta aseveración como una ocasión para interrogar si tal inquietud se inscribió de manera semejante en todos los casos, o si acaso a los distintos tópicos, interlocutores y, en suma, texturas que atraviesa la escritura derridiana, no siguen impactos filosóficos relevantes para el (...) enfoque de tal problema. Para ello se reelerá _La voz y el fenómeno_ a la luz de las principales tesis del plantismo tal como lo desarrollan M. Marder y J. T. Nealon, a sabiendas no obstante que las plantas no suelen constituir los vivientes no humanos a los que se refiere Derrida. En este sentido, y sin pretender mostrar un supuesto solapamiento o develar lo que en verdad Derrida habría _querido-decir_, la presente investigación busca examinar una serie de herramientas que nos parecen particularmente interesantes para abordar la subjetividad desde una perspectiva postmetafísica. (shrink)

: Some of the great physicists' belief in the existence of a connection between the aesthetical features of a theory (such as beauty and simplicity) and its truth is still one of the most intriguing issues in the aesthetics of science. In this paper I explore the philosophical credibility of a version of this thesis, focusing on the connection between the mathematical beauty and simplicity of a theory and its truth. I discuss a heuristic interpretation of this thesis, attempting to (...) clarify where the appeal of this Pythagorean view comes from and what are the arguments favoring its acceptance or rejection. Along the way, I sketch the historical context in which this heuristic interpretation gained credibility (the quantum crisis in physics in the 1920s), as well as the more general implications of this thesis for physicists' metaphysical outlook. (shrink)

This paper explores the connections between K. Wynn's well-known experiments in cognitive psychology and later Wittgenstein's views on the philosophy of mathematics.

A survey of the main themes and arguments concerning symmetry and invariance in physics and philosophy of physics.

The paper discusses the emergence of Frege's puzzle and the introduction of the celebrated distinction between sense and reference in the context of Frege's logicist project. The main aim of the paper is to show that not logicism per se is mainly responsible for this introduction, but Frege's constant struggle against formalism. Thus, the paper enlarges the historical context, and provides a reconstruction of Frege's philosophical development from this broader perspective.

The Dignity of the Children according to the New Testament teaching should be a landmark for modern era. New Testament raised the dignity of the unborn child, from a simple mass of cells to a child who has the right to be born and live. The child born has the value of a person that to enjoy family and society not only for economic potential but for the soul value as they bear the image of God. Children of different ages (...) have the right to be baptized, have access to the grace of the Sacraments and become saints. In fact the true dignity of man is his power to become a saint. And the child is the image of the saint, heir of the Heaven. (shrink)

Some of the post-socialist countries of Europe experienced after the fall of communism what some called a religious revival. Anthropologists and sociologists alike were sure that they discovered serious evidence against the case of secularization theory. What unfortunately most of them failed to observe was the particular shape and form of this religious growth and the structural changes of the religious mentalities occurred in the process of transition from a closed, ideologically monopolized society, to a pluralistic one. After more than (...) half of a century of atheistic ideologization of the public sphere, Romania remains one of the most religious countries of both Eastern and Western Europe. The thesis of this article is that this fact is due to the lack of modernization of the Romanian social system both before and during the post-socialist period. (shrink)

Immanuel Kant's work continues to be a main focus of attention in almost all areas of philosophy. The significance of Kant's work for the so-called continental philosophy cannot be exaggerated, although work in this area is relatively scant. The book includes eight chapters, a substantial introduction and a postscript, all newly written by an international cast of well-known authors. Each chapter focuses on particular aspects of a fundamental problem in Kant's and post-Kantian philosophy, the problem of the relation between the (...) world and transcendence. Chapters fall thematically into three parts: sensibility, nature and religion. Each part starts with a more interpretative chapter focusing on Kant's relevant work, and continues with comparative chapters which stage dialogues between Kant and post-Kantian philosophers, including Martin Heidegger, Hannah Arendt, Jean-François Lyotard, Luce Irigaray and Jacques Derrida. A special feature of this volume is the engagement of each chapter with the work of the late British philosopher Gary Banham. The Postscript offers a subtle and erudite analysis of his intellectual trajectory, philosophy and mode of working. The volume is dedicated to his memory. (shrink)

According to standard (quantum) statistical mechanics, the phenomenon of a phase transition, as described in classical thermodynamics, cannot be derived unless one assumes that the system under study is infinite. This is naturally puzzling since real systems are composed of a finite number of particles; consequently, a well‐known reaction to this problem was to urge that the thermodynamic definition of phase transitions (in terms of singularities) should not be “taken seriously.” This article takes singularities seriously and analyzes their role by (...) using the well‐known distinction between data and phenomena , in an attempt to better understand the origin of the puzzle. *Received April 2009; revised July 2009. †To contact the author, please write to: University of Cambridge, Department of History and Philosophy of Science, Free School Lane, Cambridge CB2 3RH, United Kingdom; e‐mail: [email protected]. (shrink)