The last thirty years have seen a resurgence of interest in virtue among philosophers, psychologists, and educators. This co-authored book brings an interdisciplinary response to the study of virtue: it not only provides a framework for quantifying virtues, but also explores how we can understand virtue in a philosophically-informed way that is compatible with the best current thinking in personality psychology. The volume presents a major contribution to theemerging science of virtue and character measurement.

Quillen [17] introduced model categories as an abstract framework for homotopy theory which would apply to a wide range of mathematical settings. By all accounts this program has been a success and—as, e.g., the work of Voevodsky on the homotopy theory of schemes [15] or the work of Joyal [11, 12] and Lurie [13] on quasicategories seem to indicate—it will likely continue to facilitate mathematical advances. In this paper we present a novel connection between model categories and mathematical logic, inspired (...) by the groupoid model of (intensional) Martin–Löf type theory [14] due to Hofmann and Streicher [9]. In particular, we show that a form of Martin–Löf type theory can be soundly modelled in any model category. This result indicates moreover that any model category has an associated “internal language” which is itself a form of Martin-Löf type theory. This suggests applications both to type theory and to homotopy theory. Because Martin–Löf type theory is, in one form or another, the theoretical basis for many of the computer proof assistants currently in use, such as Coq and Agda (cf. [3] and [5]), this promise of applications is of a practical, as well as theoretical, nature. This paper provides a precise indication of this connection between homotopy theory and logic; a more detailed discussion of these and further results will be given in [20]. (shrink)

Our primary aim in this paper is to sketch the account of virtue that we think most amenable to virtue measurement. Our account integrates Whole Trait Theory from psychology with a broadly neo-Aristotelian approach to virtue. Our account is ‘ecumenical’ in that it has appeal for a wide range of virtue ethicists. According to WTT, a personality trait is composed of a set of situation-specific trait-appropriate responses, which are produced when certain “social-cognitive” mechanisms are triggered by the perception of trait-relevant (...) stimuli in a person’s external and/or internal environment. Moving from this starting point, we discuss our conception of a virtue and respects in which it both aligns with and diverges from Aristotle’s conception. We discuss roles for practical wisdom and motivation in our conception of virtue, and highlight respects in which WTT provides an amenable empirical framework into which key Aristotelian elements can be integrated. We conclude with brief remarks about our conception as an empirically adequate and measurable account. (shrink)

In this paper the machinery and results developed in [Awodey et al, 2004] are extended to the study of constructive set theories. Specifically, we introduce two constructive set theories BCST and CST and prove that they are sound and complete with respect to models in categories with certain structure. Specifically, basic categories of classes and categories of classes are axiomatized and shown to provide models of the aforementioned set theories. Finally, models of these theories are constructed in the category of (...) ideals. (shrink)

In this short note we give a glimpse of homotopy type theory, a new field of mathematics at the intersection of algebraic topology and mathematical logic, and we explain Vladimir Voevodsky’s univalent interpretation of it. This interpretation has given rise to the univalent foundations program, which is the topic of the current special year at the Institute for Advanced Study.

We introduce a new model construction for Martin-Löf intensional type theory, which is sound and complete for the 1-truncated version of the theory. The model formally combines, by gluing along the functor from the category of contexts to the category of groupoids, the syntactic model with a notion of realizability. As our main application, we use the model to analyse the syntactic groupoid associated to the type theory generated by a graph G, showing that it has the same homotopy type (...) as the free groupoid generated by G. (shrink)

As organizations take on grand challenges in gender equality, anti-racism, LGBTQ+ protections and workplace inclusion, many well-intentioned individuals from dominant groups (e.g., cisgender men, Caucasian, heterosexual) are stepping forward as allies toward underrepresented or marginalized group members (e.g., cisgender women, People of Color, LGBTQ+ identified employees). Past research and guidance assume an inevitable need for external motivation, reflected in the ‘business case’ for diversity and in top-down policies to drive equity and inclusion efforts. This qualitative study explored _internal_ motivations in (...) the form of morally motivated virtues of 25 peer-nominated exemplary allies serving in leadership positions. In-depth life/career story interviews were used to identify the virtues that supported their allyship journeys. Findings demonstrated that they tapped into several virtues that served distinct functions in a 4-stage allyship development process: Stage 1—Energizing psychological investment (compassion, fairness); Stage 2—Thinking through allyship-relevant complexities (intellectual humility, perspective-taking, wisdom); Stage 3—Initiating action (prudence, moral courage, honesty); Stage 4—Committing to allyship (perseverance, patience). We call this the ‘EThIC model of virtue-based allyship development.’ This study has implications for theory and research on a virtue-based approach to diversity, equity and inclusion. (shrink)

In this paper the familiar construction of the category of coalgebras for a cartesian comonad is extended to the setting of “algebraic set theory”. In particular, it is shown that, under suitable assumptions, several kinds of categories of classes are stable under the formation of coalgebras for a cartesian comonad, internal presheaves and comma categories.

We introduce a new sheaf-theoretic construction called the ideal completion of a category and investigate its logical properties. We show that it satisfies the axioms for a category of classes in the sense of Joyal and Moerdijk [17], so that the tools of algebraic set theory can be applied to produce models of various elementary set theories. These results are then used to prove the conservativity of different set theories over various classical and constructive type theories.

ABSTRACT We appreciate and respond to Cokelet’s thoughtful criticisms of our book. First, he points to deliberative forms of practical wisdom as objectionable to anti-rationalist’s. In response, we point to non-conscious (yet complex) forms of deliberation that occur as individuals automatically process and respond to virtue-relevant stimuli. Second, Cokelet states that reflecting upon one’s life as a whole may be unnecessary and ineffective for virtue development. We clarify that reflection is not the only means of virtue cultivation, and even flawed (...) reflection is likely helpful. Finally, Cokelet recommends aiming for ‘theoretical neutrality’ by recasting these core tenets as empirical hypotheses. We argue against a neutral perspective that accommodates antirationalist views that we think are on the wrong track. Non-neutral claims help generate testable empirical hypotheses that can move virtue science forward. (shrink)