The aim of this paper is to put into context the historical, foundational and philosophical significance of category theory. We use our historical investigation to inform the various category-theoretic foundational debates and to point to some common elements found among those who advocate adopting a foundational stance. We then use these elements to argue for the philosophical position that category theory provides a framework for an algebraic in re interpretation of mathematical structuralism. In each context, what we aim to show (...) is that, whatever the significance of category theory, it need not rely upon any set-theoretic underpinning. (shrink)

This is the first volume on category theory for a broad philosophical readership. It is designed to show the interest and significance of category theory for a range of philosophical interests: mathematics, proof theory, computation, cognition, scientific modelling, physics, ontology, the structure of the world.

In this paper I argue that category theory ought to be seen as providing the language for mathematical discourse. Against foundational approaches, I argue that there is no need to reduce either the content or structure of mathematical concepts and theories to the constituents of either the universe of sets or the category of categories. I assign category theory the role of organizing what we say about the content and structure of both mathematical concepts and theories. Insofar, then, as the (...) structuralist sees mathematics as talking about structures and their morphology, I contend that category theory furnishes a framework for mathematical structuralism. (shrink)

This book is a meticulous argument for the contemporary value of Marx's democratic theory as an interpretive key for the postmodernism debates.

This paper considers the nature and role of axioms from the point of view of the current debates about the status of category theory and, in particular, in relation to the “algebraic” approach to mathematical structuralism. My aim is to show that category theory has as much to say about an algebraic consideration of meta-mathematical analyses of logical structure as it does about mathematical analyses of mathematical structure, without either requiring an assertory mathematical or meta-mathematical background theory as a “foundation”, (...) or turning meta-mathematical analyses of logical concepts into “philosophical” ones. Thus, we can use category theory to frame an interpretation of mathematics according to which we can be algebraic structuralists all the way down. (shrink)

In the present research, we validated a new scale developed from self-determination theory (SDT) to assess the functional meaning of cash rewards offered in the workplace. According to SDT, rewards can take on different meanings based on the way they are perceived by individuals. In a series of three studies in different socioeconomic contexts, we replicated the two-factorial structure of the scale measuring respectively workplace cash rewards’ informative and controlling meanings. In Study 1, we validated the English version of the (...) scale by exploring and then confirming its two-factor structure with two English-speaking employee samples. We further replicated its two-factor structure in a French-speaking employee sample of employees in Study 2 and in a Greek-speaking employee sample in Study 3, allowing us to validate its French and Greek version. Results from our three studies show how distinct meanings attributed to cash rewards, i.e., informative or controlling, relate differently to autonomous and controlled forms of motivation based on SDT. These findings suggest that workplace cash rewards differently influence employees’ motivation depending on whether they are perceived as informative or controlling, thus providing empirical evidence for the theoretical and practical implications of SDT’s concept of functional meaning of cash rewards. Our research contributes to the assessment and understanding of employees’ experience of workplace cash rewards and provides empirical evidence that the concept of the functional meaning of cash rewards is a distinct concept from other money-related concepts such as subjective pay satisfaction, performance-contingent rewards, and financially contingent self-worth. (shrink)

The four principles and consequentialism assist in teasing out moral dilemmas in medicine but often fail to account for the texture of our moral experience. In particular, these ethical approaches fail to account for the moral dilemma and the resultant distress. Conversely, by considering the relationships, emotionality, and motivations of human beings, Simone de Beauvoir's ethics of ambiguity furnishes a more robust ethical analysis and encourages a deeper understanding of how we actually negotiate relationships of care in medicine. I argue (...) that moral distress not only reveals our need for a fuller understanding of intersubjectivity—one not on offer by principalism or consequentialism—but also exposes the deeply ambiguous and agonizing nature inherent in our relationships with others. A case study is presented and analyzed via de Beauvoir's ethics so as to broaden our understanding of ethical decision-making in medicine. (shrink)

Structural realism has rapidly gained in popularity in recent years, but it has splintered into many distinct denominations, often underpinned by diverse motivations. There is, no monolithic position known as ‘structural realism,’ but there is a general convergence on the idea that a central role is to be played by relational aspects over object-based aspects of ontology. What becomes of causality in a world without fundamental objects? In this book, the foremost authorities on structural realism attempt to answer this and (...) related questions: ‘what is structure?’ and ‘what is an object?’ Also featured are the most recent advances in structural realism, including the intersection of mathematical structuralism and structural realism, and the latest treatments of laws and modality in the context of structural realism. The book will be of interest to philosophers of science, philosophers of physics, metaphysicians, and those interested in foundational aspects of science. (shrink)

I argue that recollection, in Plato's Meno , should not be taken as a method, and, if it is taken as a myth, it should not be taken as a mere myth. Neither should it be taken as a truth, a priori or metaphorical. In contrast to such views, I argue that recollection ought to be taken as an hypothesis for learning. Thus, the only methods demonstrated in the Meno are the elenchus and the hypothetical, or mathematical, method. What Plato's (...) Meno demonstrates, then, is that we cannot be philosophers if we fail to make use of the mathematician's hypothetical method. (shrink)

Delivered at the Collège de France between January and March 1980, the lectures entitled On the Government of the Living (Du gouvernement des vivants) seem to be the missing piece in the Foucauldian puzzle. Still unpublished, those eleven lectures were intended to set the theoretical foundation for the book announced as the fourth and last volume of the History of Sexuality, under the title Confessions of the Flesh (Les aveux de la chair). This book, however, was never published, despite the (...) fact that his editor described it as the keystone for the entire History of Sexuality.1 The value of Michel…. (shrink)

I argue that if we distinguish between ontological realism and semantic realism, then we no longer have to choose between platonism and formalism. If we take category theory as the language of mathematics, then a linguistic analysis of the content and structure of what we say in and about mathematical theories allows us to justify the inclusion of mathematical concepts and theories as legitimate objects of philosophical study. Insofar as this analysis relies on a distinction between ontological and semantic realism, (...) it relies also on an implicit distinction between mathematics as a descriptive science and mathematics as a descriptive discourse. It is this latter distinction which gives rise to the tension between the mathematician qua philosopher. In conclusion, I argue that the tensions between formalism and platonism, indeed between mathematician and philosopher, arise because of an assumption that there is an analogy between mathematical talk and talk in the physical sciences. (shrink)

The concept of guardianship, its associated principles, distinctions, and articulation of the legal needs of the elderly are introduced via a review of well-canvassed criticisms of Canadian guardianship legislation. Claims that the reformed legislation of Alberta, Quebec, and British Columbia represent models of adequate adult guardianship compared with traditional (archaic lunacy) law are examined. This paper argues that these renovated models exhibit a dubious normative advance over traditional legislation. Specifically, the normative presuppositions of the reformed legislation, such as, restriction to (...) an autonomy-paternalism framework, and the norms of the liberal individual and state, obscure important issues in at least two key areas which challenge the models' assumptions; namely, assessment and legal competence and assessment and need. The development of guardianship laws and of social arrangements that are more responsive to the life experiences of the elderly requires critical re-articulation of the nature of individuals and their communities. (shrink)

We will argue that Sartre’s failure and Beauvoir’s success in formulating a successful existential ethics lie in their distinct understandings of transcendence. Sartre’s struggle between transcendent consciousness and immanent body undermines being-in-the-world and being-with-others (what is, in Sartre’s language, only a being-for-others) as a way to enrich the self. Contra Sartre, Beauvoir’s notion of transcendence is an upsurge of being which originates in and necessitates bodily immanence. For Beauvoir, transcendence is to be gained only by revelling in immanence, a gesture (...) that puts oneself at risk toward the Other. This putting oneself at risk is, however, the only way to generate an authentic and no longer conflictual encounter with the Other. (shrink)

Recent semantic approaches to scientific structuralism, aiming to make precise the concept of shared structure between models, formally frame a model as a type of set-structure. This framework is then used to provide a semantic account of (a) the structure of a scientific theory, (b) the applicability of a mathematical theory to a physical theory, and (c) the structural realist’s appeal to the structural continuity between successive physical theories. In this paper, I challenge the idea that, to be so used, (...) the concept of a model and so the concept of shared structure between models must be formally framed within a single unified framework, set-theoretic or other. I first investigate the Bourbaki-inspired assumption that structures are types of set-structured systems and next consider the extent to which this problematic assumption underpins both Suppes’ and recent semantic views of the structure of a scientific theory. I then use this investigation to show that, when it comes to using the concept of shared structure, there is no need to agree with French that “without a formal framework for explicating this concept of ‘structure-similarity’ it remains vague, just as Giere’s concept of similarity between models does ...” (French, 2000, Synthese, 125, pp. 103–120, p. 114). Neither concept is vague; either can be made precise by appealing to the concept of a morphism, but it is the context (and not any set-theoretic type) that determines the appropriate kind of morphism. I make use of French’s (1999, From physics to philosophy (pp. 187–207). Cambridge: Cambridge University Press) own example from the development of quantum theory to show that, for both Weyl and Wigner’s programmes, it was the context of considering the ‘relevant symmetries’ that determined that the appropriate kind of morphism was the one that preserved the shared Lie-group structure of both the theoretical and phenomenological models. (shrink)

This article explores the 2020 Turkish Netflix series Bir Başkadır (Ethos) written and directed by Berkun Oya about contemporary Turkey through its objects. With objects surge memories, which are both personal and collective. From the charged objects that convey private attachments, traumas, and histories to ordinary household trinkets and finally archival audiovisual material, this series assumes the status of museum in its drive to carefully exhibit the material world on screen. As the Turkish title of the series indicates, these objects (...) are “bir başkadır”: one of a kind. Through themes and practices of lost innocence, counter-archives, and archiveology, I sift through the quotidian objects, miniatures, old photos, souvenirs, and analogue film footage re-presented and re-collected in this series with an eye to their new scope and allure. The past and present rest adjacent to one another in the mise-en-scène of this series. In engagement with the philosophical writings of Walter Benjamin on the collector, the archive, and memory, Andreas Huyssen's concept of the “museal gaze,” Jennifer Culbert's “counter-archival sensibility,” and finally Catherine Russell's practice of “archiveology,” this article examines how the objects that fashion the on-screen world acquire depth and meaning and the film as museum comes to form. (shrink)

This paper considers the nature and role of axioms from the point of view of the current debates about the status of category theory and, in particular, in relation to the "algebraic" approach to mathematical structuralism. My aim is to show that category theory has as much to say about an algebraic consideration of meta-mathematical analyses of logical structure as it does about mathematical analyses of mathematical structure, without either requiring an assertory mathematical or meta-mathematical background theory as a "foundation", (...) or turning meta-mathematical analyses of logical concepts into "philosophical" ones. Thus, we can use category theory to frame an interpretation of mathematics according to which we can be structuralists all the way down. (shrink)

This paper explores varieties of scientific structuralism. Central to our investigation is the notion of `shared structure'. We begin with a description of mathematical structuralism and use this to point out analogies and disanalogies with scientific structuralism. Our particular focus is the semantic structuralist's attempt to use the notion of shared structure to account for the theory-world connection, this use being crucially important to both the contemporary structural empiricist and realist. We show why minimal scientific structuralism is, at the very (...) least, a powerful methodological standpoint. Our investigation also makes explicit what more must be added to this minimal structuralist position in order to address the theory-world connection, namely, an account of representation. (shrink)