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)

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)

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)

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)

In this major study, Professor Kitching builds on recent scholarship on Marx and Wittgenstein to provide an incisive, readable account and critique of the whole of Marx's work. He presents the philosophical, economic, and political Marx as one thinker, and argues that the key to understanding Marx is his commitment to a 'philosophy of praxis'. This sees thought as just part of that purposive activity (or praxis) which distinguishes human beings from other creatures. This is the first book to analyse (...) all of Marx's thought from a Wittgenstein perspective; in doing so, it clarifies and deepens our understanding of Marx. (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)

A first in English, this book engages with the ways in which Hegel and Sartre answer the difficult questions: What is it to be human? What place do we have in the world? How should we live? What can we be?

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)

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)

In this collection of essays Gavin Kitching argues that the whole project of a 'science of society' is radically misconceived - the pursuit of an objective that ...

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)

Abstract: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)

" Although a historical organization is employed wherever a particular movement unfolds from earlier movements, the text's main organization is not motivated by ...

_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)

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)

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)

Big Data has been variously defined in the literature. In the main, definitions suggest that Big Data possess a suite of key traits: volume, velocity and variety, but also exhaustivity, resolution, indexicality, relationality, extensionality and scalability. However, these definitions lack ontological clarity, with the term acting as an amorphous, catch-all label for a wide selection of data. In this paper, we consider the question ‘what makes Big Data, Big Data?’, applying Kitchin’s taxonomy of seven Big Data traits to 26 datasets (...) drawn from seven domains, each of which is considered in the literature to constitute Big Data. The results demonstrate that only a handful of datasets possess all seven traits, and some do not possess either volume and/or variety. Instead, there are multiple forms of Big Data. Our analysis reveals that the key definitional boundary markers are the traits of velocity and exhaustivity. We contend that Big Data as an analytical category needs to be unpacked, with the genus of Big Data further delineated and its various species identified. It is only through such ontological work that we will gain conceptual clarity about what constitutes Big Data, formulate how best to make sense of it, and identify how it might be best used to make sense of the world. (shrink)

We give an overview of the practice of developing and using complex climate models, as seen from experiences in a major climate modelling center and through participation in the Coupled Model Intercomparison Project. We discuss the construction and calibration of models; their evaluation, especially through use of out-of-sample tests; and their exploitation in multi-model ensembles to identify biases and make predictions. We stress that adequacy or utility of climate models is best assessed via their skill against more naïve predictions. The (...) framework we use for making inferences about reality using simulations is naturally Bayesian, and has many points of contact with more familiar examples of scientific epistemology. While the use of complex simulations in science is a development that changes much in how science is done in practice, we argue that the concepts being applied fit very much into traditional practices of the scientific method, albeit those more often associated with laboratory work. (shrink)

Cohen’s (2023) mapping exercise of possible bioethical issues emerging from the use of ChatGPT in medicine provides an informative, useful, and thought-provoking trigger for discussions of AI ethic...

This paper explores the embedding of data producing technologies in people's everyday lives and practices. It traces how repeated encounters with digital data operate to naturalise these entities, while often blindsiding their agentive properties and the ways they get implicated in processes of exploitation and governance. I propose and develop the notion of ‘data doxa’ to conceptualise the way in which digital data – and the devices and platforms that stage data – have come to be perceived in Western societies (...) as normal, necessary and enabling. The ‘data doxa’ concept also accentuates the enculturation of many individuals into a data sharing habitus which frames digital technologies in simplistic terms as panaceas for the problems associated with contemporary life, figures of progress and convenience, and mediums of knowledge, pleasure and identity. I suggest that three types of data-based relations contribute to the formation of this doxic sensibility: fetishisation, habit and enchantment. Each of these relations come to mediate public understandings of digital devices and the data they generate, obscuring the multifaceted nature and hidden depths of data and their propensity to double up as technologies of exposure and discipline. As a result of this situation, imaginative educational programs and revamped regulatory frameworks are urgently needed to inform individuals about the contribution of data to the leveraging of value and power in today's digital economies, but also to protect them from experiencing data-based harms. (shrink)

This book explores the diverse understandings of the archaeological record in both historical and contemporary perspective, while also serving as a guide to reassessing current views. Gavin Lucas argues that archaeological theory has become both too fragmented and disconnected from the particular nature of archaeological evidence. The book examines three ways of understanding the archaeological record - as historical sources, through formation theory, and as material culture - then reveals ways to connect these three domains through a reconsideration of (...) archaeological entities and archaeological practice. Ultimately, Lucas calls for a rethinking of the nature of the archaeological record and the kind of history and narratives written from it. (shrink)

Today’s bodies are akin to ‘walking sensor platforms’. Bodies either host, or are the subjects of, an array of sensing devices that act to convert bodily movements, actions and dynamics into circulative data. This article proposes the notions of ‘disembodied exhaust’ and ‘embodied exhaustion’ to conceptualise processes of bodily sensorisation and datafication. As the material body interfaces with networked sensor technologies and sensing infrastructures, it emits disembodied exhaust: gaseous flows of personal information that establish a representational data-proxy. It is this (...) networked actant that progressively structures how embodied subjects experience their daily lives. The significance of this symbiont medium in determining the outcome of interplays between networked individuals and audiences necessitates that it is carefully contrived. The article explores the nature and function of the data-proxy, and its impact on social relations. Drawing on examples that depict individuals engaging with their data-proxies, the article suggests that managing a virtual presence is analogous to a work relation, demanding diligence and investment. But it also shows how the data-proxy operates as a mode of affect that challenges conventional distinctions made between organic and inorganic bodies, agency and actancy, mortality and immortality, presence and absence. (shrink)

They use the language of ethics, but is it just a game?

Historians of science have often presented the inter-war period as a time when British scientific communities radically questioned existing scholarship on ‘race’. The ascendancy of genetics, and the perceived need to challenge Nazi ‘racial’ theory have been highlighted as pivotal issues in shaping this British revision of ‘racial’ ideas. This article offers a detailed analysis of British scientific thinking in the inter-war period. It questions whether historians have exaggerated or oversimplified the prevalence of anti-‘racial’ reform. It uses a wide range (...) of scientific writings to consider issues of continuity and change in ‘racial’ thinking in mainstream British scientific communities. The article probes the relationship between science and politics, focusing on the extent to which ideological factors affected both the scientific agenda and conclusions as regards ‘racial’ issues. Far from dismissing the idea that events in the inter-war period triggered changes in the way in which British scientists dealt with ‘race’, the article argues that the seeds of the post-Second World War international scientific rejection of ‘race’ were sown in inter-war Britain amid considerable ambivalence and discord.We must remember that the investigator, whether a biologist, an economist, or a sociologist, is himself a part of history, and that if he ever forgets he is a part of history he will deceive his audience and deceive himself.J. B. S. Haldane, Heredity and Politics, 1938. (shrink)

In the wake of two decades in which postmodern theory has become very popular in university humanities and social science departments around the world, Gavin Kitching claims that postmodernism is causing harm to students intellectually. Postmodern theory has engaged the hearts and heads of the brightest students because of its apparent political and social radicalism. Yet Kitching writes: “At the heart of postmodernism is very poor, deeply confused, and misbegotten philosophy. As a result even the very best students who (...) fall under its sway produce radically incoherent ideas about language, meaning, truth, and reality.” This is not another conservative attack on postmodern theory. Rather, it is a carefully considered analysis from a dedicated university teacher who is convinced that we have gone terribly astray. He analyzes why typical postmodern theoretical approaches simply aren’t effective tools for dealing with the realities of people and their activities, and he describes the philosophical confusion that lies at the heart of the problem. He also demonstrates the political implications for students, their universities, and society when students learn to use poorly constructed arguments as the basis of their writing. _The Trouble with Theory _is essential reading for all students writing a thesis in the humanities and the social sciences and for their teachers. (shrink)

This article examines the discourses that are used by the British press to represent obesity in its coverage of coronavirus disease 2019 (COVID-19). Obesity is understood to be a risk factor for COVID-19, with people with obesity being more likely to die from the virus. This study adopts a corpus-based approach to Critical Discourse Studies and utilises a novel approach to keyword analysis, based on comparing analysis corpora against two reference corpora in order to yield keywords that are, in this (...) case, characteristic compared to general coverage of both COVID-19 and obesity. It is argued that the context of the pandemic has produced a range of discourses around obesity that are more stigmatising than usual in both the tabloids and the broadsheets, with people with obesity being construed, for example, in especially fatalistic terms and as being responsible for the problems facing the country’s healthcare system. At the same time, the pandemic context also seems to have given rise to some more positive changes to press coverage of obesity, with race-related health disparities receiving more focus than usual and the right-leaning press being more likely to critique the Conservative Government than it usually is, resulting in an arguably more balanced style of reporting. (shrink)