More and more these days it is asked whether aesthetics is still possible. A question that, given the context and phrasing, seems to direct us towards its answer. Conferences and meetings, books and journal specials examine the issue of aesthetics, talk about rediscovery or return of aesthetics. Well known philosophers and aestheticians underscore the need to reconsider the foundations of aesthetics and set new directions for aesthetics today (Berleant, 2004) or attempt to expand aesthetics beyond aesthetics–like Welsch, for example who (...) tries to extend aesthetics beyond art to society and the life-world (Welsch, 1997). Others underline the need to revisit the aesthetic experience (Shusterman, 1999; Iseminger, 2002, Fenner, 1996) and examine the relevance or irrelevance of the aesthetic with art (Carroll, 2001). It seems that it is strongly recommended to turn to aesthetics on the condition however to carefully re-approach the meaning and import of the term in the present situation. The aesthetic that Passmore condemned as “dreary”(Passmore, 1954), the one Sparshott considered a formless conception, vague and loose in application (Sparshott, 1982), the same that Danto emphatically argues that has nothing to do with the definition of art or arts in general (Danto, 1981) returns to claim its rightful place in the fields of philosophy and critical theory (Levine, 1994, Michaud, 1999), as well as artistic creation. And one cannot but wonder: what does this return mean? What was the degree of aesthetics decline that we need to discuss about recovery or for new implementations of aesthetics? (shrink)

In this paper, I explore some parallels and dissimilarities between aesthetic appreciation that takes as its focus art objects and that which focuses on natural objects. I cover three areas. The first deals with general approach, whether a paradigm of engagement is more appropriate to environmental aesthetics than one of detachment and disinterest. The second theme is about preservation and whether the appropriate model is static or dynamic. The final theme is about environmental criticism and the application of aesthetic theory (...) to arguments for preservation. (shrink)

ABSTRACTIn this paper I investigate how conceptual engineering applies to mathematical concepts in particular. I begin with a discussion of Waismann’s notion of open texture, and compare it to Shapiro’s modern usage of the term. Next I set out the position taken by Lakatos which sees mathematical concepts as dynamic and open to improvement and development, arguing that Waismann’s open texture applies to mathematical concepts too. With the perspective of mathematics as open-textured, I make the case that this allows us (...) to deploy the tools of conceptual engineering in mathematics. I will examine Cappelen’s recent argument that there are no conceptual safe spaces and consider whether mathematics constitutes a counterexample. I argue that it does not, drawing on Haslanger’s distinction between manifest and operative concepts, and applying this in a novel way to set-theoretic foundations. I then set out some of the questions that need to be engaged with to establish mathematics as involving a kind of conceptual engineering. I finish with a case study of how the tools of conceptual engineering will give us a way to progress in the debate between advocates of the Universe view and the Multiverse view in set theory. (shrink)

Derivationists, those wishing to explain the correctness and rigour of informal proofs in terms of associated formal proofs, are generally held to be supported by the success of the project of translating informal proofs into computer-checkable formal counterparts. I argue, however, that this project is a false friend for the derivationists because there are too many different associated formal proofs for each informal proof, leading to a serious worry of overgeneration. I press this worry primarily against Azzouni's derivation-indicator account, but (...) conclude that overgeneration is a major obstacle to a successful account of informal proofs in this direction. (shrink)

Adult number representations can belong to either of two types. One is discrete, language-specific, and culturally-derived; the other is analog and language-independent. Quantitative evidence is presented to demonstrate that analog number representations are adult-like in young children. Five- to 7-year-olds accurately estimated rapidly presented groups of 5--11 items. Groups were presented in random order and random arrangements controlling for overall area. Children's data were qualitatively, and to some degree quantitatively, similar to adult data with one exception: the ratio of the (...) standard deviation of estimates to mean estimates decreased with age. (shrink)

What sorts of epistemic virtues are required for effective mathematical practice? Should these be virtues of individual or collective agents? What sorts of corresponding epistemic vices might interfere with mathematical practice? How do these virtues and vices of mathematics relate to the virtue-theoretic terminology used by philosophers? We engage in these foundational questions, and explore how the richness of mathematical practices is enhanced by thinking in terms of virtues and vices, and how the philosophical picture is challenged by the complexity (...) of the case of mathematics. For example, within different social and interpersonal conditions, a trait often classified as a vice might be epistemically productive and vice versa. We illustrate that this occurs in mathematics by discussing Gerovitch’s historical study of the aggressive adversarialism of the Gelfand seminar in post-war Moscow. From this we conclude that virtue epistemologies of mathematics should avoid pre-emptive judgments about the sorts of epistemic character traits that ought to be promoted and criticised. (shrink)

We investigate how epistemic injustice can manifest itself in mathematical practices. We do this as both a social epistemological and virtue-theoretic investigation of mathematical practices. We delineate the concept both positively—we show that a certain type of folk theorem can be a source of epistemic injustice in mathematics—and negatively by exploring cases where the obstacles to participation in a mathematical practice do not amount to epistemic injustice. Having explored what epistemic injustice in mathematics can amount to, we use the concept (...) to highlight a potential danger of intellectual enculturation. (shrink)

This thesis is about the nature of proofs in mathematics as it is practiced, contrasting the informal proofs found in practice with formal proofs in formal systems. In the first chapter I present a new argument against the Formalist-Reductionist view that informal proofs are justified as rigorous and correct by corresponding to formal counterparts. The second chapter builds on this to reject arguments from Gödel's paradox and incompleteness theorems to the claim that mathematics is inherently inconsistent, basing my objections on (...) the complexities of the process of formalisation. Chapter 3 looks into the relationship between proofs and the development of the mathematical concepts that feature in them. I deploy Waismann's notion of open texture in the case of mathematical concepts, and discuss both Lakatos and Kneebone's dialectical philosophies of mathematics. I then argue that we can apply work from conceptual engineering to the relationship between formal and informal mathematics. The fourth chapter argues for the importance of mathematical knowledge-how and emphasises the primary role of the activity of proving in securing mathematical knowledge. In the final chapter I develop an account of mathematical knowledge based on virtue epistemology, which I argue provides a better view of proofs and mathematical rigour. (shrink)

In this paper we apply social epistemology to mathematical proofs and their role in mathematical knowledge. The most famous modern collaborative mathematical proof effort is the Classification of Finite Simple Groups. The history and sociology of this proof have been well-documented by Alma Steingart (2012), who highlights a number of surprising and unusual features of this collaborative endeavour that set it apart from smaller-scale pieces of mathematics. These features raise a number of interesting philosophical issues, but have received very little (...) attention. In this paper, we will consider the philosophical tensions that Steingart uncovers, and use them to argue that the best account of the epistemic status of the Classification Theorem will be essentially and ineliminably social. This forms part of the broader argument that in order to understand mathematical proofs, we must appreciate their social aspects. (shrink)

LEGO and math are both about what one do with the objects. In LEGO, he/she can build sets following the instructions, or alternatively dump a whole bunch of LEGO on the floor and build whatever he/she like. In math, he/she have a similar freedom to create new things, solve problems, and play around. Geometry makes far greater use of pictures and diagrams than tends to be the case for other areas of mathematics. This chapter focuses on diagrammatic proofs as a (...) key case where proofs guide him/her through a series of actions. If one accepts the LEGO account of diagrammatic proofs then he/she has strongly sided with the geometers against Plato. The main principle of departure from Plato is to focus on mathematical activities. The same thought is meant to apply to LEGO: the particular bricks are only important insofar as they facilitate the things we can practically do with them. (shrink)

A common description of a mathematical proof is as a logically structured sequence of assertions, beginning from accepted premises and proceeding by standard inference rules to a conclusion. Does this description match the language of proofs as mathematicians write them in their research articles? In this chapter, we use methods from corpus linguistics to look at the prevalence of imperatives and instructions in mathematical preprints from the arXiv repository. We find thirteen verbs that are used most often to form imperatives (...) in proofs, and that these show up significantly more often within proofs than in the surrounding mathematical writing. We also show that there are many more verbs used to form a diverse selection of instructions in proofs. These findings are at odds with the view of proofs as sequences of assertions. Instead, we argue in favour of the recipe model of proofs: that proofs are like recipes, giving instructions for mathematical actions to be carried out. (shrink)

Extinction is a concept of rapidly growing importance, with the world currently in the sixth mass extinction event and a biodiversity crisis. However, the concept of extinction has itself received surprisingly little attention from philosophers. I will first argue that in practice there is no single unified concept of extinction, but instead that its usage divides between descriptive, epistemic, and declarative concepts. I will then consider the epistemic challenges that arise in ascertaining whether a species has gone extinct, and how (...) these lead to serious limitations on responsibility and accountability for preventing extinctions. I will propose two conceptual engineering changes to our understanding of extinction. Firstly, to use twin epistemic concepts of extinction, corresponding to high and low epistemic demands. Secondly, to explicitly recognize that in many contexts extinction is a thick concept that contains an evaluative component, which therefore motivates explicit ethical considerations such as the use of precautionary principles. (shrink)

In this paper I shall consider two related avenues of argument that have been used to make the case for the inconsistency of mathematics: firstly, Gödel’s paradox which leads to a contradiction within mathematics and, secondly, the incompatibility of completeness and consistency established by Gödel’s incompleteness theorems. By bringing in considerations from the philosophy of mathematical practice on informal proofs, I suggest that we should add to the two axes of completeness and consistency a third axis of formality and informality. (...) I use this perspective to respond to the arguments for the inconsistency of mathematics made by Beall and Priest, presenting problems with the assumptions needed concerning formalisation, the unity of informal mathematics and the relation between the formal and informal. (shrink)

It seems to be the case that when we look at a flower in the way that the scientist does, we see the flower in one way, but when we look at the flower in a way as to view it as a thing of beauty, charm, elegance, we see it in a different way; we see it as an aesthetic object. Viewing the flower in such a way as to see it, or any object, as an aesthetic object, is (...) to be in the aesthetic attitude. What this work means to do is to formulate necessary and sufficient conditions for adoption of the aesthetic attitude. ;Analytically and traditionally, the aesthetic attitude is an attitude or state-of-perceiving that is entered into by an agent which serves to make the agent receptive to the having of an aesthetic experience, and transform the object of the agent's attention from an object-in-the-world into an aesthetic object. ;The aesthetic attitude has figured prominently in aesthetics from the Enlightenment until the present. Its most important formulations are disinterestedness , Psychical Distance , Aldrich's Impressionistic Viewing, Scruton's Empiricistic Account, and the naturalistic work of John Dewey and Monroe Beardsley. I conclude that a naturalistic formulation of the aesthetic attitude is correct. (shrink)

_Plain Aesthetics_ is an introduction to philosophical aesthetics and the philosophy of art written for all audiences. While students studying philosophy will find it informative, it is specifically constructed to be accessible to anyone, even those with no background in philosophy. It contains no jargon or technical language, except where such terms are defined at their point of use. Philosophers and theorists are discussed only where appropriate, and their views explained in context. _Plain Aesthetics_ is written as a conversation between (...) the author and the reader, and employs a great many examples of fascinating and influential artworks. Images and other works are presented to the reader both within the text and through an innovative interactive system. This book makes aesthetics accessible to everyone. (shrink)

How is modern psychotherapy impacted when it is approached from the presence and understanding of the unconditioned mind? What happens when therapists are able to function as a sacred mirror for their clients' essential nature, reflecting back not only the contents of awarenessùthoughts, feelings and sensationsùbut awareness itself? Informed by their direct experience as well as by nondual teachings from both eastern and western wisdom traditions, the authors take a fresh look at what psychotherapy can be. These seminal essays will (...) challenge and inspire readers to approach psychotherapy in a new wayùas a potential portal for experiencing their deepest nature as free and joyful beings.Seasoned clinicians, Dan Berkow, Stephan Bodian, Dorothy Hunt, Sheila Krystal, Lynn Marie Lumiere, Richard Miller, John Prendergast, John Welwood, Jennifer Welwood and Bryan Wittine, and innovative western spiritual teachers, Adyashanti and Peter Fenner, explore critical issues at the interface of psychology and spirituality from a nondual perspective. (shrink)

This study described the relationships between academic class and student moral sensitivity and reasoning and between curriculum design components for ethics education and student moral sensitivity and reasoning. The data were collected from freshman (n = 506) and senior students (n = 440) in eight baccalaureate nursing programs in South Korea by survey; the survey consisted of the Korean Moral Sensitivity Questionnaire and the Korean Defining Issues Test. The results showed that moral sensitivity scores in patient-oriented care and conflict were (...) higher in senior students than in freshman students. Furthermore, more hours of ethics content were associated with higher principled thinking scores of senior students. Nursing education in South Korea may have an impact on developing student moral sensitivity. Planned ethics content in nursing curricula is necessary to improve moral sensitivity and moral reasoning of students. (shrink)

Until recently, discussion of virtues in the philosophy of mathematics has been fleeting and fragmentary at best. But in the last few years this has begun to change. As virtue theory has grown ever more influential, not just in ethics where virtues may seem most at home, but particularly in epistemology and the philosophy of science, some philosophers have sought to push virtues out into unexpected areas, including mathematics and its philosophy. But there are some mathematicians already there, ready to (...) meet them, who have explicitly invoked virtues in discussing what is necessary for a mathematician to succeed. In both ethics and epistemology, virtue theory tends to emphasize character virtues, the acquired excellences of people. But people are not the only sort of thing whose excellences may be identified as virtues. Theoretical virtues have attracted attention in the philosophy of science as components of an account of theory choice. Within the philosophy of mathematics, and mathematics itself, attention to virtues has emerged from a variety of disparate sources. Theoretical virtues have been put forward both to analyse the practice of proof and to justify axioms; intellectual virtues have found multiple applications in the epistemology of mathematics; and ethical virtues have been offered as a basis for understanding the social utility of mathematical practice. Indeed, some authors have advocated virtue epistemology as the correct epistemology for mathematics (and perhaps even as the basis for progress in the metaphysics of mathematics). This topical collection brings together several of the researchers who have begun to study mathematical practices from a virtue perspective with the intention of consolidating and encouraging this trend. (shrink)

This Element looks at the contemporary debate on the nature of mathematical rigour and informal proofs as found in mathematical practice. The central argument is for rigour pluralism: that multiple different models of informal proof are good at accounting for different features and functions of the concept of rigour. To illustrate this pluralism, the Element surveys some of the main options in the literature: the 'standard view' that rigour is just formal, logical rigour; the models of proofs as arguments and (...) dialogues; the recipe model of proofs as guiding actions and activities; and the idea of mathematical rigour as an intellectual virtue. The strengths and weaknesses of each are assessed, thereby providing an accessible and empirically-informed introduction to the key issues and ideas found in the current discussion. (shrink)

The attribution of perceptually based aesthetic properties to a garden should be indexed to whether that attribution is (1) to the ever-changing dynamic garden or (2) to some phenomenal capture of the garden in one’s experience, frozen like a photograph. Perceptually based aesthetic properties are used to identify objects, to compare them to others, to evaluate them, and to describe them as we seek to interpret or find meaning in them. This set of activities requires aesthetic properties that do not (...) change, or at least not much, if any degree of normativity is to be maintained. But those aesthetic properties that are derived from our immediate sensations of a garden only describe a garden at a certain time, under certain conditions, in certain states—all of which change constantly. Both descriptions are useful, and perhaps necessary, for appreciating gardens. (shrink)

Mathematicians often conduct aesthetic judgements to evaluate mathematical objects such as equations or proofs. But is there a consensus about which mathematical objects are beautiful? We used a comparative judgement technique to measure aesthetic intuitions among British mathematicians, Chinese mathematicians, and British mathematics undergraduates, with the aim of assessing whether judgements of mathematical beauty are influenced by cultural differences or levels of expertise. We found aesthetic agreement both within and across these demographic groups. We conclude that judgements of mathematical beauty (...) are not strongly influenced by cultural difference, levels of expertise, and types of mathematical objects. Our findings contrast with recent studies that found mathematicians often disagree with each other about mathematical beauty. (shrink)

Once a group of physicists at my university invited me to a physics colloquium. They were certain that I would get a great deal out of it. I love theoretical physics, although my preparation for understanding the "real stuff" is extremely modest. After the first ten minutes of the lecture, I realized I was in way over my head; though I understood the topic and the trajectory, I was not able to follow the path. But I stayed and continued to (...) enjoy the lecture. No longer was I understanding the lecture as a physics lecture—that is, as a lecture the contents of which was the articulation of a case for understanding a physical phenomenon or the application of a physical theory for understanding a physical phenomenon.... (shrink)

This work presents the concepts of translation and conservative translation between logics. By using algebraic semantics we introduce several conservative translations involving the classical propositional calculus and the many-valued calculi of Post and Lukasiewicz.

Der Beitrag befasst sich mit den Chancen und Risiken einer allfälligen gesetzlichen Legalisierung der Suizidbeihilfe. Die Argumente, die gegen eine solche Legalisierung sprechen, werden zu drei thematischen Gruppen zusammengefasst und erörtert: „Slippery-Slope“-Argumente, Argumente vom „moralischen Druck“, und die Furcht vor einer „Entsolidarisierung der Gesellschaft“ sowie die „Gefährdung des Arzt-Patient-Verhältnisses“. Diese Gegenargumente erweisen sich als nicht zwingend, sofern Kriterien und Richtlinien für eine legitime Form der Suizidbeihilfe entwickelt und staatlich kontrolliert werden könnten.

We define and study a new notion called k-immunity that lies between immunity and hyperimmunity in strength. Our interest in k-immunity is justified by the result that θ does not k-tt reduce to a k-immune set, which improves a previous result by Kobzev [7]. We apply the result to show that Φ′ does not btt-reduce to MIN, the set of minimal programs. Other applications include the set of Kolmogorov random strings, and retraceable and regressive sets. We also give a new (...) characterization of effectively simple sets and show that simple sets are not btt-cuppable. (shrink)

In this paper, I lay out a case for why those objects of aesthetic attention which are principally characterized as natural objects should be understood not statically, as existing in merely a three-dimensional fixed state, but as dynamic, as existing in a space-time context, complete with change, movement, and flux. After this, I explain why this is important, how the dynamic nature of natural objects raises a concern for aesthetically evaluating natural objects, and how that concern may be addressed.

A record of the words and teachings of Confucius, _The Analects_ is considered the most reliable expression of Confucian thought. However, the original meaning of Confucius's teachings have been filtered and interpreted by the commentaries of Confucianists of later ages, particularly the Neo-Confucianists of the Song dynasty, not altogether without distortion.In this monumental translation by Professor D. C. Lau, an attempt has been made to interpret the sayings as they stand. The corpus of the sayings is taken as an organic (...) whole and the final test of the interpretation rests on the internal consistency it exhibits. In other words, _The Analects_ is read in the light of _The Analects._This results in a truer understanding of Confucius' thought than the traditional interpretation and paves the way for a re-assessment of its importance in the history of Chinese thought and its relevance to the present day world.This volume also contains an introduction to the life and teachings of Confucius, and three appendices on the events in the life of Confucius, on his disciples, and on the composition of _The Analects._. (shrink)

RésuméLa croyance que l'on est (ou pas) dans un état de douleur est singulière en ceci qu'elle semble pouvoir être qualifiée d'infaillibilité ou d'incorrigibilité logique, de même que le cogito. Mais comment se peut-il que l'existence d'une croyance (vraie) et l'existence du fait qui est l'objet de cette croyance puisssent constituer la même existence? Je propose ici une réponse à cette question. Parfois, une croyance peut être un désir.

Offering aesthetic judgments of gardens is common. These judgments follow an evidentiary structure that is common to the evaluation of other aesthetic objects: summary judgments evidenced by the attribution of narrow formal aesthetic properties, “formal-adjacent” aesthetic properties, and relevant contextual relations. Yet, in a garden, these evidencing properties and relations take on forms that are different from those of other aesthetic and/or art objects. In this article, I consider these differences and consider whether aesthetic analyses of gardens rest on one (...) or more conceptual mistakes. In the end, I conclude that we can meet all challenges. (shrink)

Philosophie ist der Versuch, durch überzeugendes und durchsichtiges Argumentieren bestimmte Fragen zu lösen. Philosophische Grundthemen sind Fragen nach dem Verständnis der Welt im Ganzen und unserer Stellung in ihr. Diese Fragen können prinzipiell nur kontrovers beantwortet werden. Die Reihe Grundthemen Philosophie möchte der Diskussion solcher philosophischen Grundthemen einen Ort geben. Anstelle einer umfassenden einführenden Darstellung werden in den einzelnen Bänden in Auseinandersetzung mit ausgewählten historischen Positionen die jeweiligen Probleme analysiert und Lösungsmöglichkeiten diskutiert. Dabei setzt der Verfasser/die Verfasserin eigene Akzente und (...) bezieht Stellung, so dass sich nicht bloß ein Blick auf die Geschichte der Philosophie, sondern zugleich auch ein systematischer Beitrag zur Problemdiskussion ergibt. Zur Zeit sind weitere Bände zu den Themen Beziehungen, Kultur, Wissenschaft und Moralbegründung geplant. Die Bände der Reihe richten sich gleichermaßen an Studierende der Philosophie und anderer Fächer sowie an professionelle Philosophen. Außerdem wendet sich die Reihe an alle, die an Grundthemen der Philosophie interessiert sind. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Journal of Aesthetic Education 37.1 (2003) 40-53 [Access article in PDF] Aesthetic Experience and Aesthetic Analysis David E. W. Fenner The "raw data" that aesthetics is meant to explain is the aesthetic experience. People have experiences that they class off from other experiences and label, as a class, the aesthetic ones. Aesthetic experience is basic, and allother things aesthetic — aesthetic properties, aesthetic objects, aesthetic attitudes — (...) are secondary in their importance to aesthetic experiences. 1Considering aesthetic experience as the raw data that philosophical aesthetics seeks to explain is a relatively recent phenomenon. This was certainly not the focus in the seventeenth and eighteenth centuries. Aesthetic judgment was the focus of Shaftesbury, Hutcheson, Hume, and Kant: "How do we make meaningful judgments (hopefully real ones) about the aesthetic quality of (certain) objects and events?" But with George Santayana, John Dewey, and Jerome Stolnitz, the focus changes. Now the interest is in the aesthetic experience: what makes those experiences we label "aesthetic" special? Why do we separate those experiences from others?The movement from the Taste Theories to those focused on aesthetic experience is not a movement that is over and done with — far from it. There is still (and I think there will always be) a tension between these two very basic aspects of philosophical aesthetics. And, although I claim that aesthetic experience is the most basic thing that aesthetics studies, I recognize that this is challengeable and only true from a certain temporal viewpoint.I recently taught the most rewarding undergraduate course in aesthetics. The reason that it was so rewarding was that the students carried the class with deep and insightful discussions, and they were not shy about challenging what was coming out of my mouth. One of the challenges that informed our entire semester focused on the tension between experience and judgment. I lectured comfortably about aesthetic experience as our "raw data," and I lectured equally comfortably about how taking an aesthetic view of an object or event meant focusing primarily, if not exclusively, on [End Page 40] what is available to us through simple sensory acquaintanceship with the object. "Aesthetics," I said, "is about the sensuous aspects of our experiences." And so we could, for instance, take an aesthetic view of a Robert Mapplethorpe photograph which precluded our experiences being mired in the themes that the more famous Mapplethorpe photos take as their content. "Mapplethorpe is a great photographer," I argued, "and one can see this if one is willing to focus strictly on what meets your eye when you look at the picture." In short, I held the position that the aesthetic view is the formal one.Without saying more, what I did was conflate two different things. On the one hand, I argued that aesthetic experience is a natural part of life that aesthetics seeks to explore. On the other, I argued that appreciating something aesthetically was to appreciate its formal qualities, those qualities that one could access simply through looking, hearing, touching, for example. But these really are two different things.Aesthetic experiences, if we are to treat them as "raw data," must be explored without pre-conception, prejudice, or limitation. And, truly enough, the vast majority of aesthetic experiences are not focused exclusively, in terms of their contents, on formal or simple-sensory matters. Aesthetic experiences are, first, experiences. They are complex things, having to do with things as tidy as the formal qualities of the object under consideration and with things as messy as whether one had enough sleep the night before, whether one just had a fight with his roommate, whether one is carrying psychological baggage that is brought to consciousness by this particular aesthetic object. Later in this essay, I want to explore some of this complexity.The other side of what was happening in my class, the formal focus on the sensory as the basis for an aesthetic viewing, is not the substance of "aesthetic experience" per se. It is rather the basis of what we might call "aesthetic analysis." Aesthetic analysis has to do with separating out from our... (shrink)