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)

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)

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)

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)

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)

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)

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)

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)

A substantial guide providing an overview of both physicalism and metaphysical naturalism, reviewing both questions of formulation and justification for both doctrines. Includes a diagnostic strategy for understanding talk of naturalism as a metaphysical thesis.

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)

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)

Inside What Would Plato Do?, you'll find the basics of philosophy, written in an easy, digestible way we can all understand, along with questions to help you apply these important theories to your own life. So, after you've learned about a philosophical concept, you'll then be challenged to test yourself and see how the results can impact your daily life. For instance, after learning about Kant's theory of morality and the importance of intention you're challenged with questions like: Can good (...) people do bad things? Was there a time when you intended to do something helpful that ended up being hurtful? Does that make you a good person (because you intended to do good) or a bad person (because the results were bad)? What Would Plato Do? will not only help you better understand some of the greatest thinkers ever but will also help you think of the world around you in a whole new way! (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)

In this article, I will try to show that (1) one of the more compelling reasons for advocating for aesthetic normativity comes from an axiom that suppositionally underlies aesthetic educational endeavors and (2) by framing aesthetic judgments contextually and hypothetically we may be able to deal effectively with one of the more compelling reasons for antinormativity, namely the fact of irreconcilable differences between judgments of two equally competent judges. I will try to show that framing judgments contextually is common practice (...) in aesthetic education. (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)

Ne vers 1180 a Aurillac, mort le 30 mars 1249, Guillaume d'Auvergne est nomme eveque de Paris des 1228. Son oeuvre est contemporaine de la querelle de l'aristotelisme qui gagne la faculte de theologie, et du bouleversement de l'histoire theorique qui l'accompagne. Quelle est la cause efficiente de la pensee? D'ou vient l'intelligible necessairement present dans l'ame qui pense? C'est a cela que repondent les neuf premieres parties du chapitre sept du De anima, ecrit vers 1240. La noetique de Guillaume (...) d'Auvergne, complexe, s'y deploie et sensiblement se demarque de l' augustinisme avicennisant qui traditionnellement la caracterise. L'ame, dans son rapport au sensible, est principium agens, lectrice, en tant qu'elle pense, d'un livre dont elle-meme est l'auteur, et dont la verite se passe en partie de l'illumination divine. (shrink)

We are immersed within an odorous sea of chemical currents that we parse into individual odors with complex structures. Odors have been posited as determined by the structural relation between the molecules that compose the chemical compounds and their interactions with the receptor site. But, naturally occurring smells are parsed from gaseous odor plumes. To give a comprehensive account of the nature of odors the chemosciences must account for these large distributed entities as well. We offer a focused review of (...) what is known about the perception of odor plumes for olfactory navigation and tracking, which we then connect to what is known about the role odorants play as properties of the plume in determining odor identity with respect to odor quality. We end by motivating our central claim that more research needs to be conducted on the role that odorants play within the odor plume in determining odor identity. (shrink)

We perceive smells as perduring complex entities within a distal array that might be conceived of as smellscapes. However, the philosophical orthodoxy of Odor Theories has been to deny that smells are perceived as having a distal location. Recent challenges have been mounted to Odor Theories’ veracity in handling the timescale of olfactory perception, how it individuates odors as a distal entities, and their claim that olfactory perception is not spatial. The paper does not aim to dispute these criticisms. Rather, (...) what will be shown is that Molecular Structure Theory, a refinement of Odor Theory, can be further developed to handle these challenges. The theory is further refined by focusing on distal perception that requires considering the perceptual object as mereologically complex persisting odor against a background scene conceived of as a smellscape. What will be offered is an expansion of Molecular Structure Theory to account for distal smell perception within natural environments. (shrink)

This is a book grounded in the real ethical challenges of modern business practice, with a world-religious perspective so necessary in an era of globalization.

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)

When it originated in the late 19th century, psychometrics was a field with both a scientific and a social mission: psychometrics provided new methods for research into individual differences, and at the same time, these psychometric instruments were considered a means to create a new social order. In contrast, contemporary psychometrics - due to its highly technical nature and its limited involvement in substantive psychological research - has created the impression of being a value-free discipline. In this article, we develop (...) a contrasting characterization of contemporary psychometrics as a value-laden discipline. We expose four such values: that individual differences are quantitative (rather than qualitative), that measurement should be objective in a specific sense, that test items should be fair, and that utility of a model is more important than its truth. Our goal is not to criticize psychometrics for employing these values, but rather to bring them into the open and to show that these values are not inevitable and are in need of systematic evaluation. (shrink)

Reflection Principles are commonly thought to produce only strong axioms of infinity consistent with V = L. It would be desirable to have some notion of strong reflection to remedy this, and we have proposed Global Reflection Principles based on a somewhat Cantorian view of the universe. Such principles justify the kind of cardinals needed for, inter alia , Woodin’s Ω-Logic.

First collected in Italy in 1985, _Art's Claim to Truth_ is considered by many philosophers to be one of Gianni Vattimo's most important works. Newly revised for English readers, the book begins with a challenge to Plato, Aristotle, Kant, and Hegel, who viewed art as a metaphysical aspect of reality rather than a futuristic anticipation of it. Following Martin Heidegger's interpretation of the history of philosophy, Vattimo outlines the existential ontological conditions of aesthetics, paying particular attention to the works of (...) Kandinsky, which reaffirm the ontological implications of art. Vattimo then builds on Hans-Georg Gadamer's theory of aesthetics and provides an alternative to a rationalistic-positivistic criticism of art. This is the heart of Vattimo's argument, and with it he demonstrates how hermeneutical philosophy reaffirms art's ontological status and makes clear the importance of hermeneutics for aesthetic studies. In the book's final section, Vattimo articulates the consequences of reclaiming the ontological status of aesthetics without its metaphysical implications, holding Aristotle's concept of beauty responsible for the dissolution of metaphysics itself. In its direct engagement with the works of Gadamer, Heidegger, and Luigi Pareyson, _Art's Claim to Truth_ offers a better understanding of the work of Vattimo and a deeper knowledge of ontology, hermeneutics, and the philosophical examination of truth. (shrink)