Purifying applied mathematics and applying pure mathematics: how a late Wittgensteinian perspective sheds light onto the dichotomy

In this work we argue that there is no strong demarcation between pure and applied mathematics. We show this first by stressing non-deductive components within pure mathematics, like axiomatization and theory-building in general. We also stress the “purer” components of applied mathematics, like the theory of the models that are concerned with practical purposes. We further show that some mathematical theories can be viewed through either a pure or applied lens. These different lenses are tied to different communities, which endorse different evaluative standards for theories. We evaluate the distinction between pure and applied mathematics from a late Wittgensteinian perspective. We note that the classical exegesis of the later Wittgenstein’s philosophy of mathematics, due to Maddy, leads to a clear-cut but misguided demarcation. We then turn our attention to a more niche interpretation of Wittgenstein by Dawson, which captures aspects of the aforementioned distinction more accurately. Building on this newer, maverick interpretation of the later Wittgenstein’s philosophy of mathematics, and endorsing an extended notion of meaning as use which includes social, mundane uses, we elaborate a fuzzy, but more realistic, demarcation. This demarcation, relying on family resemblance, is based on how direct and intended technical applications are, the kind of evaluative standards featured, and the range of rhetorical purposes at stake.

Religious Disagreement Is Not Unique

Chapter 4 addresses the fact that in discussions of religious disagreement, some epistemologists have suggested that religious disagreement is distinctive. More specifically, they have argued that religious disagreement has certain features which make it possible for theists to resist conciliatory arguments that they must adjust their religious beliefs in response to finding that peers disagree with them. The chapter considers what its author takes to be the two most prominent features which are claimed to make religious disagreement distinct: religious evidence and evaluative standards in religious contexts. It argues that these two features fail to distinguish religious disagreement in the ways they have been taken to. However, it shows that the view that religious disagreement is not a unique form of disagreement makes religious disagreement less, rather than more, worrisome to the theist who would prefer to rationally remain steadfast in her religious beliefs.

Norms Require Not Just Technical Skill and Social Learning, but Real Cooperation

Birch’s account of the evolutionary origins of social norms is essentially individualistic. It begins with individuals regulating their own actions toward internally represented goals, as evaluative standards, and adds in a social dimension only secondarily. I argue that a better account begins at the outset with uniquely human collaborative activity in which individuals share evaluative standards about how anyone who would play a given role must behave both toward their joint goal and toward one another. This then scaled up to the shared normative standards for anyone who would be a member of ‘our’ social group.

Five paths to personality coherence: Integrative implications of the Knowledge-and-Appraisal Personality Architecture

The study of personality coherence can be grounded in an analysis of personality architecture, that is, the overall structure and dynamics of intra-individual personality systems. A personality architecture can identify, and organize the study of, interrelated phenomena that each are instances of personality coherence. It thereby can provide an integrative framework for understanding relations among distinct lines of research. This thesis is advanced by drawing on the Knowledge-and-Appraisal Personality Architecture, or KAPA model. KAPA model principles distinguish among three classes of social-cognitive knowledge structures: beliefs, goals, and evaluative standards. These distinctions, in turn, provide a foundation for understanding five aspects of personality coherence: 1) Belief-Based Coherence, 2) Goal-Based Coherence, 3) Evaluative Standards-Based Coherence, 4) Intra-Psychic Coherence (that is, coherent functional interrelations among personality systems), and 5) Phenomenological Coherence. Research documenting each of these five paths to personality coherence is reviewed. The paper also reviews the strengths and limitations of 20th-century social-cognitive formulations that provide key foundations for the KAPA model.

The relationship between contingent self-esteem and trait self-esteem

Psychology researchers have suggested that in addition to its level, self-esteem is also manifested by other psychological components. One such component is contingency, which is the degree to which one’s feeling of self-worth is influenced by evaluative standards. I investigated how contingent self-esteem is related to trait self-esteem using Paradise and Kernis’ Contingent Self-Esteem Scale and Rosenberg’s (trait) Self-Esteem Scale. Data collected from classroom (N = 898) and Internet (N = 655) groups rendered a significant and consistent negative relationship between contingent and trait self-esteem. In addition, higher contingent self-esteem individuals tend to have a greater variability with their trait self-esteem levels; as individuals age, their contingent self-esteem tends to decrease; psychological sensitivity to evaluations is the contingent component most strongly associated with the level of self-esteem; and some evaluative resources, such as appearance, performance, and relationship, can be used by some individuals to boost their self-esteem. Future researchers should consider that the contingency of self-esteem is the psychological component not only related to the stability of self-esteem but also to the level of self-esteem.

Making the implicit quality standards and performance expectations for traditional legal scholarship explicit

Scholars in search of quality standards for traditional legal scholarship could well end up disappointed. By answering the question concerning what standards legal academics use for evaluating such works—through reviewing the international literature on evaluative standards and interviews with forty law professors—this Article aims at filling this gap. This Article recommends that traditional legal scholarship is judged by using the following criteria: (1) the conceptual design—a clearly formulated research question that is both original and significant and the adequacy of the methods proposed to answer that question; (2) the composition of a particular line of reasoning—does the researcher adhere to principles of accountability, accuracy, balance, and credibility?; and (3) the overall characteristics of a work of scholarship—the readability and persuasiveness of the whole and the extent to which the researcher managed to identify and clarify the presuppositions that may have potentially affected her inquiry.

Public reason, non-public reasons, and the accessibility requirement

In Liberalism without Perfection, Jonathan Quong develops what is perhaps the most comprehensive defense of the consensus model of public reason – a model which incorporates both a public-reasons-only requirement and an accessibility requirement framed in terms of shared evaluative standards. While the consensus model arguably predominates amongst public reason liberals, it is criticized by convergence theorists who reject both the public-reasons-only requirement and the accessibility requirement. In this paper, I argue that while we have good reason to reject Quong’s call for a public-reasons-only requirement, all public reason liberals should endorse at least some shared evaluative standards and, hence, an accessibility requirement.

The Elusive Ideal

This chapter discusses the concept of an evaluative perspective, which has been more thoroughly explored and formally modeled in the last decade. An evaluative perspective, Σ‎, includes three fundamental elements: (ES) a set of evaluative standards or criteria by which alternative social worlds in a domain {X} are to be evaluated; (WF) for all worlds i in the domain {X}, a specification of the world features of i that are relevant to evaluation according to ES, the evaluative standards; and (MP) a mapping function takes the evaluative standards (ES) and applies them to a social world, i, as specified by WF, yielding a so-called justice score for world i, the social world described by world features WFi. A theory meeting ES, WF, and MP evaluates a set (or domain) of social worlds {X} in terms of their realization of justice.

Pluralism

‘Pluralism’ is a broad term, applicable to any doctrine which maintains that there are ultimately many things, or many kinds of thing; in both these senses it is opposed to ‘monism’. Its commonest use in late twentieth-century philosophy is to describe views which recognize many sets of equally correct beliefs or evaluative standards; and in this sense it is akin to ‘relativism’. Societies are sometimes called ‘pluralistic’, meaning that they incorporate a variety of ways of life, moral standards and religions; one who sees this not as undesirable confusion but a proper state of things, espouses pluralism.

Discussion and Evaluation

Chapter 5 begins with a general discussion of the central research paradigms that ethnographers claim and/or move between. The remainder of the chapter is organized according to the evaluative standards used by the various stakeholders who surround the ethnographic enterprise—namely, researchers, members of researched communities, and readers. The section on researchers is centered on their aspirations to do “good work,” which the author proposes involves reflexivity, transparency, and sincerity. It also elaborates on the moral principles and ethical regulations that ethnographic researchers observe. In discussing members of researched communities, the author highlights their recent ability to speak back against the research, explaining how it has fostered more accountable and collaborative modes of ethnography. Finally, in discussing readers of ethnography, the author makes a distinction between “everyday” and “professional” readers, proposing a handful of criteria—credibility, coherence, impact, and worthiness—used by the latter in making their professional assessments.