Sound and listening are intrinsically linked to how we experience and engage with places and communities. This guide invites landscape architects and urban designers to become soundscape architects and offers practical advice on sound and listening applicable to each stage of a design project: from reading the environment to intervening on it. This book foregrounds listening as an affective mediator between subjects and multispecies environments, and a vehicle to think and conceptualise environmental design beyond prevailing visual and human-centred modes. The (...) guide expands landscape architects' and urban designers' tools and skills to assess existing soundscapes, predict how those soundscapes will be altered through their designs, consider sound as a creative and active part of the design process, and envisage how users might perceive and be affected by those soundscapes as they evolve in time. The volume sits in the interface of research and practice, and incorporates theoretical, methodological and creative contributions from acoustic ecology, ecoacoustics, bioacoustics and sound art. Each of the design stages is illustrated through project examples that demonstrate the many advantages of incorporating attentive listening and sound into Landscape Architecture and Urban Design Practice. The book shows how incorporating listening and sounding as part of the design process promotes slow and subtle ways of practice, adds social and ecological value through the reduction of noise pollution and by monitoring the health of habitats, and enables the design of soundscapes that complement the character and design intent of a scheme and elicit joy and wonder. The book will be of interest to landscape architects, together with other design professionals such as urban designers, architects, geographers and engineers, who play a primary role in the composition of the soundscape. (shrink)

There are different disciplines that make use of reason as an essential element of its work. The most relevant are probably positive science, philosophy and theology. Opening a constructive dialogue between science and theology is very important because of the relevance that science has had in our culture. Unfortunately, the legitimately expected results in this field have not been achieved, mostly because the philosophy has not assumed the pertinent intermediary role as it was expected. In this article, the historic causes (...) of this fact are analyzed and some ways to help to resolve it are proposed. (shrink)

Desde la perspectiva de la investigación social partir de planteamientosfilosóficos se convierte en la tarea fundamental de construcción de sentido y en un reto constante al tratar de llevar a lapráctica desde la reflexión acciones útiles y coherentes. De estamanera llegamos a la propuesta hermenéutica desde planteamientospragmatistas que son el puente hacia un nuevo contexto paralas Ciencias Sociales. Este contexto supone pensarnos desde yen la contingencia y hacia y para la comprensión. Desde una visión antidualista y constitutivamente cooperativa del ser (...) humanonos entendemos poseedores de las herramientas necesarias paraabordar las infinitas posibilidades que nos ofrece la contingencia.Plantearemos un marco cooperativo desde el cual ser coherentesy potenciar nuestra predisposición a la comprensión. (shrink)

Traditional geometry concerns itself with planimetric and stereometric considerations, which are at the root of the division between plane and solid geometry. To raise the issue of the relation between these two areas brings with it a host of different problems that pertain to mathematical practice, epistemology, semantics, ontology, methodology, and logic. In addition, issues of psychology and pedagogy are also important here. To our knowledge there is no single contribution that studies in detail even one of the aforementioned areas.

In his 1978 paper “Mathematical Explanation”, Mark Steiner attempts to modernize the Aristotelian idea that to explain a mathematical statement is to deduce it from the essence of entities figuring in the statement, by replacing talk of essences with talk of “characterizing properties”. The language Steiner uses is reminiscent of language used for proofs deemed “pure”, such as Selberg and Erdős’ elementary proofs of the prime number theorem avoiding the complex analysis of earlier proofs. Hilbert characterized pure proofs as those (...) that use only “means that are suggested by the content of the theorem”, a characterization we have elsewhere called “topical purity”. In this paper we will examine the connection between Steiner’s account of mathematical explanation and topical purity. Are Steiner-explanatory proofs necessarily topically pure? Are topically pure proofs necessarily Steiner-explanatory? Answers to these questions will shed light on the general question of the relation between purity and explanatory power. (shrink)

During the last few months, several pioneer genome‐wide transcriptomic, proteomic and metabolomic studies have revolutionised the understanding of bacterial biological processes, leading to a picture that resembles eukaryotic complexity. Technological advances such as next‐generation high‐throughput sequencing and high‐density oligonucleotide microarrays have allowed the determination, in several bacteria, of the entire boundaries of all expressed transcripts. Consequently, novel RNA‐mediated regulatory mechanisms have been discovered including multifunctional RNAs. Moreover, resolution of bacterial proteome organisation (interactome) and global protein localisation (localizome) have unveiled an (...) unanticipated complexity that highlights the significance of protein multifunctionality and localisation in the cell. Also, analysis of a complete bacterial metabolic network has again revealed a high fraction of multifunctional enzymes and an unexpectedly high level of metabolic responses and adaptation. Altogether, these novel approaches have permitted the deciphering of the entire physiological landscape of one of the smallest bacteria, Mycoplasma pneumoniae. Here, we summarise and discuss recent findings aimed at defining the blueprint of any prokaryote. (shrink)

Over the years many mathematicians have voiced a preference for proofs that stay “close” to the statements being proved, avoiding “foreign”, “extraneous”, or “remote” considerations. Such proofs have come to be known as “pure”. Purity issues have arisen repeatedly in the practice of arithmetic; a famous instance is the question of complex-analytic considerations in the proof of the prime number theorem. This article surveys several such issues, and discusses ways in which logical considerations shed light on these issues.

No contexto da Guerra Fria, são analisados os relatórios das conferências relacionadas aos Huaqiao, ou chineses estrangeiros, entre 1951 e 1953. Esse foi um período inicial de políticas divididas entre as comunidades chinesas no exterior, entre o governo da República Popular da China e Guomindang, em Taiwan. Mais do que apoiar as populações chinesas no exterior, enfrentando dinâmicas de exclusão e discriminação nos países em que residiam, esses governos chineses encontraram nos compatriotas estrangeiros um cenário de luta por lealdade através (...) de discursos e estratégias políticas. (shrink)

In the Third Antinomy Kant exposes in a dramatically way the conflict between freedom and natural necessity. Kant uses denominations that they induce to confusion, because he resolves different problems than those we use to attribute to him. According to Kant, the new science opposes natural legality and freedom. This paper maintains that this false interpretation of the scientific epistemology depends on a slanted vision originated in the rationalistic metaphysics; among others reasons, because Kant takes the Physics from Wolff instead (...) of Newton. (shrink)

An interpretation of the “Parmenides” is proposed in base to the Plato’s “unwritten doctrines”. The greek author demonstrates in this dialogue that with the One only is impossible to think (hypothesis I), and this is why a principle of difference is required; that with the ontological conception of this difference neither, because contradictory conclusions would be followed (hypothesis II); and that without the One isimpossible to think, too (hypothesis III). These conclusions suggest the reader that the One is necessary to (...) think, but another or other principles must be searched to stablish a dialectic. Plato confirms this way the parenetic character of his dialogues respecting at the same time the selfconstrained taboo of the “unwritten doctrines” (he doesn’t mention the undefinite dyad). To come to these conclusions the author ofthis paper proposes a plan of the second part of this work, that divides it in three hypothesis, not in eight, like is usual today, and analyzes the categories that sustain the argumentatives subdivisions of each one of the hypotheses: the structure of all the hypotheses is the same. All this in critical discussion with the actual bibliography about the topics. (shrink)

Many mathematicians have sought ‘pure’ proofs of theorems. There are different takes on what a ‘pure’ proof is, though, and it’s important to be clear on their differences, because they can easily be conflated. In this paper I want to distinguish between two of them.

Roughly, a proof of a theorem, is “pure” if it draws only on what is “close” or “intrinsic” to that theorem. Mathematicians employ a variety of terms to identify pure proofs, saying that a pure proof is one that avoids what is “extrinsic,” “extraneous,” “distant,” “remote,” “alien,” or “foreign” to the problem or theorem under investigation. In the background of these attributions is the view that there is a distance measure (or a variety of such measures) between mathematical statements and (...) proofs. Mathematicians have paid little attention to specifying such distance measures precisely because in practice certain methods of proof have seemed self- evidently impure by design: think for instance of analytic geometry and analytic number theory. By contrast, mathematicians have paid considerable attention to whether such impurities are a good thing or to be avoided, and some have claimed that they are valuable because generally impure proofs are simpler than pure proofs. This article is an investigation of this claim, formulated more precisely by proof- theoretic means. After assembling evidence from proof theory that may be thought to support this claim, we will argue that on the contrary this evidence does not support the claim. (shrink)

A bibliometric index is proposed that accounts for the differential contribution authors make to a joint paper published, the valuation of the number of publications, the quality of the journals in which the authors are published and which cite them, as well as the timeliness of the paper. This approach means the index can be used in selection processes for positions of employment or the award of research projects, as it abides by the premise of considering scientific merit based on (...) the quality and quantity of publications. The term weighted citability index is used to refer to a mathematical process that uses filters proportionally both to the degree of involvement in the joint research and to the values of number, quality, and timeliness of the research papers. (shrink)

Many mathematicians have cited depth as an important value in their research. However, there is no single widely accepted account of mathematical depth. This article is an attempt to bridge this gap. The strategy is to begin with a discussion of Szemerédi's theorem, which says that each subset of the natural numbers that is sufficiently dense contains an arithmetical progression of arbitrary length. This theorem has been judged deep by many mathematicians, and so makes for a good case on which (...) to focus in analyzing mathematical depth. After introducing the theorem, four accounts of mathematical depth will be considered. (shrink)

O artigo levanta questões que interessam ao tema do magistério filosófico: o sentido original do conceito de filosofia, sua realização peculiar no método pedagógico de Sócrates, a ideia da filosofia como saber e como ciência. É a filosofia, para o professor e para o aluno, principalmente busca ou aquisição? O artigo considera, neste contexto, a magnitude do empreendimento filosófico e, por outro lado, as possibilidades da razão humana, que as filosofias mesmas diversamente tematizam.El artículo plantea cuestiones que interesan al magisterio (...) filosófico: el sentido original del concepto de filosofía, su realización peculiar en el método de Sócrates, la idea de la filosofía como saber y como ciencia. Es la filosofía, para el profesor y para el alumno, principalmente búsqueda o adquisición? El artículo considera, en este contexto, la magnitud del emprendimiento filosóficoy, por otro lado, las posibilidades de la razón humana, que las mismas filosofías diversamente tematizan. (shrink)

This article will consider imagination in mathematics from a historical point of view, noting the key moments in its conception during the ancient, modern and contemporary eras.

El artículo expone la evolución de las expectativas acerca del futuro y destino final del hombre tanto a nivel individual como colectivo. Hasta el siglo XVIII predominaban las preocupaciones referidas al destino personal de cada hombre y el significado de la muerte. Tras las revoluciones que acabaron con el antiguo régimen, empezó a dominar el interés por el futuro de la humanidad en su conjunto. Desde mediados del siglo XX hay una preocupación creciente ante el peligro de que la especie (...) humana desaparezca y sea suplantada por otro tipo de entidades, tal vez desarrolladas por el propio hombre. El transhumanismo se ha presentado como una respuesta, basada en la ciencia, a las ansias de supervivencia y mejora del hombre. No obstante, sus propuestas adolecen de varias debilidades, algunas de ellas posiblemente irreparables. (shrink)

Many mathematicians and philosophers of mathematics believe some proofs contain elements extraneous to what is being proved. In this paper I discuss extraneousness generally, and then consider a specific proposal for measuring extraneousness syntactically. This specific proposal uses Gentzen's cut-elimination theorem. I argue that the proposal fails, and that we should be skeptical about the usefulness of syntactic extraneousness measures.

Gaisi Takeuti extended Gentzen's work to higher-order case in 1950's–1960's and proved the consistency of impredicative subsystems of analysis. He has been chiefly known as a successor of Hilbert's school, but we pointed out in the previous paper that Takeuti's aimed to investigate the relationships between "minds" by carrying out his proof-theoretic project rather than proving the "reliability" of such impredicative subsystems of analysis. Moreover, as briefly explained there, his philosophical ideas can be traced back to Nishida's philosophy in Kyoto's (...) school. For the proving the consistency of such systems, it is crucial to prove the well-foundedness of ordinals called "ordinal diagrams" developed for it. Takeuti presented such arguments several times in order to show that they are admitted in his stand point. As a starting point of investigating his finitist stand point, we formulate the system of ordinal notations up to ε0 and reconstruct the well-foundedness arguments of them. (shrink)

l propósito de este trabajo es indagar la relación existente entre el fenóme-no de la ciencia, su eclosión y progreso, y la presencia de una atmósfera cultural cristiana. Se trata de dirimir si en la práctica han dominado más las voces que dentro del cristianismo han alentado a los investigadores o si han predominado más las que la han cohibido y reprimido. El autor se inclina por la primera alternativa. A través de una mirada histórica, constata las profundas raíces cristianas (...) de la ciencia moderna. (shrink)

Part of the task of doing moral philosophy is to strengthen our confidence in morality or to bring back the gravitas of morality. I argue that this cannot be done by a representational view of moral reality and by downplaying the importance of human sentiments that make our moral assertions more natural and authentic.

Octavio Paz se vio inmerso a lo largo de su vida en los acontecimientos más significativos del siglo XX. Este contacto directo con la historia le llevó a cuestionar repetidas veces los principios básicos de la acción política y los valores que deben sustentarla. En este trabajo se analizan las diversas fases de la evolución ideológica de Paz, que no estuvo subordinada a las urgencias de una ambición personal, lo que le permitió zafarse del oportunismo de tantos intelectuales latinoamericanos. En (...) lugar de ir a remolque de los tiempos, sus reflexiones responden a la lógica de un desarrollo interno, que profundiza progresivamente en el alcance y las consecuencias de la idea de libertad, una libertad que es concebida lejos del limbo de las abstracciones y se piensa cada vez más en función de las exigencias irrenunciables del hombre de carne y hueso. (shrink)

En la literatura referente al transhumanismo hay mucho espacio dedicado a descripciones y taxonomías, pero escasa discusión en profundidad de las bases y límites de los planteamientos teóricos subyacentes. Los críticos apostan en demasía por los argumentos ad hominem, mientras que los partidarios se entretienen más de lo conveniente en exaltar las futuras prestaciones de un progreso exponencialmente acelerado. En este texto se intenta llevar a cabo una reflexión más serena, centrada en las nociones de «esencia humana», «naturalización» y «autoconciencia».

Gaisi Takeuti (1926–2017) is one of the most distinguished logicians in proof theory after Hilbert and Gentzen. He extensively extended Hilbert's program in the sense that he formulated Gentzen's sequent calculus, conjectured that cut-elimination holds for it (Takeuti's conjecture), and obtained several stunning results in the 1950–60s towards the solution of his conjecture. Though he has been known chiefly as a great mathematician, he wrote many papers in English and Japanese where he expressed his philosophical thoughts. In particular, he used (...) several keywords such as "active intuition" and "self-reflection" from Nishida's philosophy. In this paper, we aim to describe a general outline of our project to investigate Takeuti's philosophy of mathematics. In particular, after reviewing Takeuti's proof-theoretic results briefly, we describe some key elements in Takeuti's texts. By explaining these texts, we point out the connection between Takeuti's proof theory and Nishida's philosophy and explain the future goals of our project. (shrink)

An account of mathematical understanding should account for the differences between theorems whose proofs are “easy” to discover, and those whose proofs are difficult to discover. Though Hilbert seems to have created proof theory with the idea that it would address this kind of “discovermental complexity”, much more attention has been paid to the lengths of proofs, a measure of the difficulty of _verifying_ of a _given_ formal object that it is a proof of a given formula in a given (...) formal system. In this paper we will shift attention back to discovermental complexity, by addressing a “topological” measure of proof complexity recently highlighted by Alessandra Carbone ( 2009 ). Though we will contend that Carbone’s measure fails as a measure of discovermental complexity, it forefronts numerous important formal and epistemological issues that we will discuss, including the structure of proofs and the question of whether impure proofs are systematically simpler than pure proofs. (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)

Our visual experience seems to suggest that no continuous curve can cover every point of the unit square, yet in the late 19th century Giuseppe Peano proved that such a curve exists. Examples like this, particularly in analysis received much attention in the 19th century. They helped to instigate what Hans Hahn called a ‘crisis of intuition’, wherein visual reasoning in mathematics came to be thought to be epistemically problematic. Hahn described this ‘crisis’ as follows : " Mathematicians had for (...) a long time made use of supposedly geometric evidence as a means of proof in much too naive and much too uncritical a way, till the unclarities and mistakes that arose as a result forced a turnabout. Geometrical intuition was now declared to be inadmissible as a means of proof … "Avoiding geometrical evidence, Hahn continued, mathematicians aware of this crisis pursued what he called ‘logicization’, ‘when the discipline requires nothing but purely logical fundamental concepts and propositions for its development’. On this view, an epistemically ideal mathematics would minimize, or avoid altogether, appeals …. (shrink)

In this paper we consider three potential simplifications to a result of Solovay’s concerning the Turing degrees of nonstandard models of arbitrary completions of first-order Peano Arithmetic (PA). Solovay characterized the degrees of nonstandard models of completions T of PA, showing that they are the degrees of sets X such that there is an enumeration R ≤T X of an “appropriate” Scott set and there is a family of functions (tn)n∈ω, ∆0 n(X) uniformly in n, such that lim tn(s) s→∞.

Une preuve est pure si, en gros, elle ne réfère dans son développement qu’à ce qui est « proche » de, ou « intrinsèque » à l’énoncé à prouver. L’infinité des nombres premiers, un théorème classique de l’arithmétique, est un cas d’étude particulièrement riche pour les recherches philosophiques sur la pureté. Deux preuves différentes de ce résultat sont ici considérées, à savoir la preuve euclidienne classique et une preuve « topologique » plus récente proposée par Furstenberg. D’un point de vue (...) naïf, il semblerait que la première soit pure et la seconde impure. Des objections à cette vue naïve sont ici considérées et réfutées. Concernant la preuve euclidienne, la question relève de la logique, notamment de la définissabilité arithmétique de l’addition en termes de successeur et de divisibilité telle que démontrée par Julia Robinson, tandis qu’en ce qui concerne la preuve topologique, la question relève de la sémantique, notamment pour tout ce qui touche au problème de savoir ce qui est « inclus » dans le contenu d’énoncés particuliers.A proof is pure, roughly, if it draws only on what is « close » or « intrinsic » to the statement being proved. The infinitude of prime numbers, a classical theorem of arithmetic, is a rich case study for philosophical investigation of purity. Two different proofs of this result are considered, namely the classical Euclidean proof and a more recent « topological » proof by Furstenberg. Naively the former would seem to be pure and the latter to be impure. Objections to these naive views are considered and met. In the case of the former the issue rests on logical matters, specifically the arithmetic definability of addition in terms of successor and divisibility shown by Julia Robinson, while in the case of the latter the issue rests on semantic matters, specifically with respect to what is « contained » in the content of particular statements. (shrink)

A variety of projects in proof theory of relevance to the philosophy of mathematics are surveyed, including Gödel's incompleteness theorems, conservation results, independence results, ordinal analysis, predicativity, reverse mathematics, speed-up results, and provability logics.

A proof of a theorem can be said to be pure if it draws only on what is 'close' or 'intrinsic' to that theorem. In this Element we will investigate the apparent preference for pure proofs that has persisted in mathematics since antiquity, alongside a competing preference for impurity. In Section 1, we present two examples of purity, from geometry and number theory. In Section 2, we give a brief history of purity in mathematics. In Section 3, we discuss several (...) different types of purity, based on different measures of distance between theorem and proof. In Section 4 we discuss reasons for preferring pure proofs, for the varieties of purity constraints presented in Section 3. In Section 5 we conclude by reflecting briefly on purity as a preference for the local and how issues of translation intersect with the considerations we have raised throughout this work. (shrink)

In this paper I begin by extending two results of Solovay; the first characterizes the possible Turing degrees of models of True Arithmetic (TA), the complete first-order theory of the standard model of PA, while the second characterizes the possible Turing degrees of arbitrary completions of P. I extend these two results to characterize the possible Turing degrees of m-diagrams of models of TA and of arbitrary complete extensions of PA. I next give a construction showing that the conditions Solovay (...) identified for his characterization of degrees of models of arbitrary completions of PA cannot be dropped (I showed that these conditions cannot be simplified in the paper. (shrink)

According to contemporary moral realism a moral property, like goodness or badness, is either a natural property or a non-natural property of actions or situations. Contemporary moral naturalists like Richard Boyd, Nicholas Sturgeon, and David Brink are a group of philosophers who are often referred to as Cornell realists because of their connection with Cornell University. Frank Jackson is another contemporary moral naturalist who is one of the leaders of The Canberra Planners at the Australian National University with which he (...) is connected. Jackson defends “the most extreme form of naturalism.” Jackson’s view is considered extremeby those who disagree with him because he believes that moral properties are reducible or identical to natural properties. This view of Jackson is opposed by contemporary non-naturalists like Jonathan Dancy, Derek Parfit, and Russ Shafer-Landau for reasons which in my view are not successful. Despite Jackson’s reductionism about the ethical, the Cornell realists, nevertheless, agree with him that moral properties are natural properties. (shrink)

William Blake and Zadie Smith reached strikingly similar critical positions towards philosophical trends current in their respective eras. Both excoriate those who, for selfish ends, disparage beauty and in so doing sabotage justice, love, joy and genuine freedom. Smith’s On Beauty, like Blake’s America: A Prophecy and Visions of the Daughters of Albion, indicts the reprehensible intellectual discourses of the day that undermine human happiness and corrupt the social order. Whereas Blake critiqued the rights revolutions set in motion by Thomas (...) Paine, William Godwin, Mary Wollstonecraft and others from a more broadly moral and future-oriented angle than has generally been recognized (as Saree Makdisi has shown), Smith wittily dramatizes that same vision through a huge range of up-to-date ideological discourses and antagonisms–many of them descended from Paine et al.–to refurbish Blake’s particular brand of radical antinomianism and to celebrate much the same optimistic spirit that Blake invested in America and Visions. Indeed, Smith’s novel anticipates and critiques ab ovo the sweepingenthusiasms that are animating current uprisings worldwide. (shrink)

Este trabajo analiza la presencia de la química en el pensamiento leibniciano. Se valora su contribución al nacimiento de la nueva química y la superación de la vieja alquimia. Se analizan los principales escritos consagrados por el filósofo a esta problemática, para establecer cómo evoluciona y qué relaciones tiene con sus trabajos en otras disciplinas.

This paper aims to bring together the study of normative judgments in mathematics as studied by the philosophy of mathematics and verbal hygiene as studied by sociolinguistics. Verbal hygiene (Cameron 1995) refers to the set of normative ideas that language users have about which linguistic practices should be preferred, and the ways in which they go about encouraging or forcing others to adopt their preference. We introduce the notion of mathematical hygiene, which we define in a parallel way as the (...) set of normative discourses regulating mathematical practices and the ways in which mathematicians promote those practices. To clarify our proposal, we present two case studies from 17th century France. First, we exemplify a case of mathematical hygiene proper: Descartes' algebraic geometry and Newton's subsequent criticism of it, a case of (im)purity in mathematics. Then, we compare Descartes' and Newton's mathematical hygiene with verbal hygiene from this period, as exemplified by the work of the grammarian Claude Favre de Vaugelas (Ayres-Bennett 1987). We argue that these early modern normative discourses on mathematics and language respectively can be seen as emanating from a common socio-political program: the development of a new bourgeois intellectual class. We conclude that the study of mathematical hygiene has the potential to yield new understandings of the social aspects of mathematical practice, and that similarities between mathematical and verbal hygiene at certain time periods, such as 17th century France, open up a new area of inquiry at the borders of linguistics and the philosophy of mathematics. (shrink)