In a 2022 paper, Hamami claimed that the orthodox view in mathematics is that a proof is rigorous if it can be translated into a derivation. Hamami then developed a descriptive account that explains how mathematicians check proofs for rigor in this sense and how they develop the capacity to do so. By exploring introductory texts in computability theory, we demonstrate that Hamami’s descriptive account does not accord with actual mathematical practice with respect to computability theory. We argue instead for (...) an alternative account in which imagination, anticipation, and interpretations of natural language play roles in establishing mathematical rigor. (shrink)

In this paper, we explore the role of syntactic representations in set theory. We highlight a common inferential scheme in set theory, which we call the Syntactic Representation Inferential Scheme, in which the set theorist infers information about a concept based on the way that concept can be represented syntactically. However, the actual syntactic representation is only indicated, not explicitly provided. We consider this phenomenon in relation to the derivation indicator position that asserts that the ordinary proofs given in mathematical (...) discourse indicate syntactic derivations in a formal logical system. In particular, we note that several of the arguments against the derivation indicator position would seem to imply that set theorists could gain no benefits from the syntactic representations of concepts indicated by their definitions, yet set theorists clearly do. (shrink)

In the mathematics education research literature, there is a growing body of scholarship on how mathematicians practice their craft. The purpose of this chapter is to survey some of this literature and explain how it can contribute to the philosophy of mathematical practice. We first describe how mathematics educators use empirical methodologies to investigate the behaviors of mathematicians and argue that findings from these studies can inform the philosophy of mathematical practice. We then illustrate this by summarizing research on mathematicians’ (...) understandings and mathematicians’ proof reading. (shrink)

Traditional models of mathematical proof describe proofs as sequences of assertion where each assertion is a claim about mathematical objects. However, Tanswell observed that in practice, many proofs do not follow these models. Proofs often contain imperatives, and other instructions for the reader to perform mathematical actions. The purpose of this paper is to examine the role of instructions in proofs by systematically analyzing how instructions are used in Kunen’s Set theory: An introduction to independence proofs, a widely used graduate (...) text in set theory. I use Kunen’s text to describe how instructions and constructions in proof work in mathematical practice and explore epistemic consequences of how proofs are read and understood. (shrink)

The issue of what constitutes a valid logical inference is a difficult question. At a minimum, we believe a permissible step in a proof must provide the reader with rational grounds to believe that the new step is a logically necessary consequence of previous assertions. However, this begs the question of what constitutes these rational grounds. Formalist accounts typically describe valid rules of inferences as those that can be found by applying one of the explicit rules of inference in the (...) formal system in which the proof is couched. However, philosophers of mathematics find such a description unhelpful because many inferences in the proofs that mathematicians actually produce cannot be expressed in a formal language, at least not without seriously distorting the semantic content of the inference (e.g., Larvor, 2012). In this chapter, we investigate mathematicians’ perceptions of a particular kind of inference in a particular setting. Specifically, we shed light on what types of graphical inferences mathematicians find permissible in a real analysis proof. Following Larvor (in press), we examine mathematicians’ reactions to metrical graphical inferences (i.e., inferences whose validity depends on the accuracy of the graph that was drawn and whose validity can be changed by minor deformations) and nonmetrical graphical inferences (i.e., inferences whose validity does not depend on a the accuracy of the graph and whose validity is not vulnerable to local deformations). The goal of this chapter is threefold. First, we demonstrate that most mathematicians reject metrical graphical inferences as impermissible in a real analysis proof. Second, we show that many mathematicians regard nonmetrical graphical inferences as permissible in a real analysis proofs. Third, we illustrate how mathematicians collectively disagree on the permissibility of nonmetrical inferences. (shrink)

In this article, we report a study in which 109 research-active mathematicians were asked to judge the validity of a purported proof in undergraduate calculus. Significant results from our study were as follows: (a) there was substantial disagreement among mathematicians regarding whether the argument was a valid proof, (b) applied mathematicians were more likely than pure mathematicians to judge the argument valid, (c) participants who judged the argument invalid were more confident in their judgments than those who judged it valid, (...) and (d) participants who judged the argument valid usually did not change their judgment when presented with a reason raised by other mathematicians for why the proof should be judged invalid. These findings suggest that, contrary to some claims in the literature, there is not a single standard of validity among contemporary mathematicians. (shrink)

Introduction -- Modernity, politics and Max Weber -- One-sided rationalization: Habermas on modernity, discourse and emancipation -- Critiquing Habermas: intersubjectivity, ethics and norm-free sociality -- The burden of our times: Arendt on modern oblivion and the promise of politics -- Judging Arendt: citizenship, action and the scope of politics -- The new dark age: MacIntyre on bureaucratic individualism and the hope for an ethical polity -- Engaging MacIntyre: flourishing, modernity and political struggle -- Closing reflections: ethics, politics and strategy (...) in the present. (shrink)

This article addresses the ability of Parallel Distributed Processing (PDP) networks to generate stagewise cognitive development in accordance with Piaget's theory of cognitive epigenesis. We carried out a replication study of the simulation experiments by McClelland (1989) and McClelland and Jenkins (1991) in which a PDP network learns to solve balance scale problems. In objective tests motivated from catastrophe theory, a mathematical theory of transitions in epigenetical systems, no evidence for stage transitions in network performance was found. It is concluded (...) that PDP networks lack the ability to recover the positive outcomes of analogous catastrophe analyses of real cognitive developmental data. In an attempt to further characterize the learning behaviour of PDP networks, we carried out a second simulation study using the discrimination‐shift paradigm. The results thus obtained indicate that PDP learning is compatible with the learning of stimulus‐response relationships, not with the acquisition of mediating rules such as conceived in (neo‐)Piagetian theory. In closing, we speculate about the feasibility of simulating stagewise development with alternative network architectures. (shrink)

If sociology is about society must it not also be about morality? In the nineteenth and early twentieth centuries, the identification between sociology and morality was clear cut; Marx, Durkheim, Weber, Spencer, and Veblen all dealt with moral issues and one might argue that they saw themselves as engaged in a moral vocation. Now, one might argue that the connections between sociology and moral currents have become more tenuous. Moral Culture examines what it means to be moral in contemporary (...) social and cultural life. Author Keith Tester takes the highly original and revealing step of exploring how violence today, and throughout history, affects the relatively safe and secure people who live in the west and who tend to know horror only through television and cinema screens. The book raises questions about the meaning and significance of massacres in the Balkans, Rwanda and, rather more historically, the Holocaust, and the slaughter of Vietnamese peasants by American soldiers in My Lai. It also discusses how Adolf Eichmann and the men of Charlie Company might be different from or similar to us. It answers questions about whether this is a time of moral decay or more seriously, the collapse of moral Civilization. Sociologists often claim that they make a virtue of being relevant and objective, but few have attacked these issues with the urgency and originality that Keith Tester displays in this work. Each chapter provides a historically aware account of a moral problem making it especially relevant reading for students of cultural studies, sociology, political science, and moral philosophy. (shrink)

The first four chapters of Max Weber's Economy and Society presented by Talcott Parsons in 1947 as Theory of Social and Economic Organization present a coherent and complete analysis of social, economic and political structures based upon a consistent theory of social action and its understanding. Parsons did not see them this way. His lengthy introduction sought to insert them into his own “action frame of reference”, and his rearrangement of the text made it difficult for a reader to (...) understand why it was constructed the way that it is. This essay describes how Parsons came to be principal translator and editor of the text, examines the changes that he made to it, and links his editorial practice to the analytical procedures that he followed in his Structure of Social Action. ☆ This essay is developed from a paper originally presented in June 2005 at a conference on Max Weber's Basic Sociological Concepts at ZiF, Bielefeld University; an earlier version of the present paper was published as “Talcott Parsons als Übersetzer der ‘Soziologischen Grundbegriffe’ Max Webers”. Max Webers ‘Grundbegriffe’. Kategorien der kultur- und sozialwissenschaftlichen Forschung. Ed. Klaus Lichtblau. (Wiesbaden: Verlag für Sozialwissenschaften, 2006) 337–366. (shrink)

SummaryDuring the 1950s at the latest, Max Weber became a ‘founding father’ of sociology, chiefly on the basis of a restricted set of canonical writings and without any consideration of his wider relationships to law, economics and politics. During the last ten years of his life he was responsible for a major collaborative work, the Grundriss der Sozialökonomik—Outline of Social Economics. The title was of his own choosing; and so it might well shed new light on his work if (...) we consider how this work was organised, and how Economy and Society, written as a contribution to this handbook, was intended to form part of it. (shrink)

In contrast to political realism's equation of the `political' with domination, Hannah Arendt understood the `political' as a relation of friendship utterly opposed to the use of violence. This article offers a critique of that understanding. It becomes clear that Arendt's challenge to realism, as exemplified by Max Weber, succeeds on account of a dubious redefinition of the `political' that is the reverse image of the one-sided vision of politics she had hoped to contest. Questioning this paradoxical turn leads (...) to a critique of Arendt's separation of violence and power and, consequently, her attempt to insulate a politics of friendship from one of hostility and coercion. However, political realism is not thereby affirmed. What is required, instead, is a view of the `political' that accepts the interwoven-ness of violence and power but also emphasizes the normative ideals of moderation and care. Key Words: Hannah Arendt • enmity • friendship • moderation • the `political' • power • realism • violence • Max Weber. (shrink)

Keith Ansell-Pearson, An Introduction to Nietzsche as Political Thinker (Cambridge: Cambridge University Press, 1994) hb: 0-521-41722-8. pb: 0-521-42721-5. Paul Patton, ed., Nietzsche, Feminism and Political Theory (London: Routledge. 1993) 0-4150-8256-0. Lester M. Hunt, Nietzsche and the Origin of Virtue (London: Routledge, 1993) 0-4150-9580-8. David Owen, Maturity and Modernity. Nietzsche, Weber, Foucault and the Ambivalence of Reason (London: Routledge, 1994) 0-4150-5398-6. Peter Lassmann and Ronald Spiers, eds., Weber: Political Writings (Cambridge: Cambridge University Press. 1994) hb: 0-521 -39312-4. pb: (...) 0-521 -39719-7. Friedrich Nietzsche, On the Genealogy of Morality and Other Writings, ed. Keith Ansell-Pearson, tr. Carol Diethe (Cambridge University Press, 1994) hb: 0-521-40459-2. pb: 0-521-40610-2. (shrink)

I dedicate this essay to the memory of the late Wolfgang Mommsen—the subject would have been congenial to him. It is one of a series of offshoots from a central project: a scholarly edition of Max Weber's Protestant Ethic with commentary. When I first told Prof. Mommsen of my plan in 1994 he looked me full in the face and gave a characteristic growl: “All that work!” Here was a man who knew what he was about. My thanks to (...) Ross McKibbin and Keith Tribe for reading this paper in draft. The article begins by examining Max Weber's relations with Lujo Brentano, much the most important “precursor” to Weber in the field of economics. In particular, Brentano conducted a form of parallel inquiry into the rise of ‘the spirit of capital’ in England 35 years before Weber looked for the origins of “spirit” of capitalism there, and the contrast between these two ideas casts much light both on Brentano and on Weber's Protestant Ethic. This personal history leads into a broader history of the transition in German economic thought between the 1860s – the formative decade for Brentano but also the era of Marx's Capital – and that of Weber's generation coming to maturity c.1890. Marx and Weber remain the two great canonical thinkers and original minds; but any authentic historical comparison between Marx and Weber must take in Brentano. The essence of the contrast between the generations is that between Weber's novel conception of an ethical ‘capitalism’, and the materialism and naturalism underpinning Brentano's and Marx's ‘capital’, although Weber and Brentano are alike as liberals, democrats and bourgeois. ☆ Some abbreviations for Weber: AfSS for Archiv für Sozialwissenschaft und Sozialpolitik; GARS for Gesammelte Aufsätze zur Religionssoziologie (Tübingen, 1920) vol. i; WL for Gesammelte Aufsätze zur Wissenschaftslehre (Tübingen, 1968); Grundriss for Grundriss zu den Vorlesungen über Allgemeine (“theoretische”) Nationalökonomie [1898], repr. Tübingen, 1990; MWG for Max Weber Gesamtausgabe ed. Horst Baier et al. (Tübingen, 1984); Briefe for letters by Weber in this edition; ‘Nachlaß Max Weber’ for unpublished letters from the Geheimes Staatsarchiv, Berlin-Dahlem, VI. HA Nachlaß Max Weber. Lebensbild for Marianne Weber, Max Weber: Ein Lebensbild (Tübingen, 1926); Zohn for idem, Max Weber. A Biography (New Brunswick, 1988) tr. Harry Zohn. For Brentano: Der wirtschaftende Mensch for Der wirtschaftende Mensch in der Geschichte (Leipzig, 1923); Konkrete Grundbedingungen for Konkrete Grundbedingungen der Volkswirtschaft (Leipzig, 1924); Der tätige Mensch for Der tätige Mensch und die Wissenschaft von der Wirtschaft (Marburg, 2006) ed. R. Bräu, H.G. Nutzinger. ‘Die Entwickelung der Wertlehre’ for ‘Die Entwickelung der Wertlehre’, Sitzungsberichte der Königlich Bayerischen Akademie der Wissenschaften. Philosophisch-philologische und historische Klassen. Jahrgang 1908, 3. Abhandlung (15 Feb. 1908), 1–84; ‘Theorie der Bedürfnisse’ for ‘Versuch einer Theorie der Bedürfmisse’, ibid., 10. Abhandlung (5 Dec. 1908), 1–79; ‘Die Malthussche Lehre’ for ‘Die Malthussche Lehre und die Bevölkerungsbewegung der letzten Decennien’ [1909], Abhandlungen der historischen Klasse der Königlich Bayerischen Akademie der Wissenschaften XXIV (1906–1909), 565–625, 1*–39*. (shrink)

The recent literature on causality has seen the introduction of several distinctions within causality, which are thought to be important for understanding the widespread scientific practice of focusing causal explanations on a subset of the factors that are causally relevant for a phenomenon. Concepts used to draw such distinctions include, among others, stability, specificity, proportionality, or actual-difference making. In this contribution, I propose a new distinction that picks out an explanatorily salient class of causes in biological systems. Some select causes (...) in complex biological systems, I argue, have the property of enabling coherent causal control of these systems. Examples of such control variables include hormones and other signaling molecules, e.g., TOR (target of rapamycin), morphogens or the products of homeotic selector genes in embryonic pattern formation. I propose an analysis of this notion based on concepts borrowed from causal graph theory. (shrink)

ABSTRACTDo truth tables—the ordinary sort that we use in teaching and explaining basic propositional logic—require an assumption of consistency for their construction? In this essay we show that truth tables can be built in a consistency-independent paraconsistent setting, without any appeal to classical logic. This is evidence for a more general claim—that when we write down the orthodox semantic clauses for a logic, whatever logic we presuppose in the background will be the logic that appears in the foreground. Rather than (...) any one logic being privileged, then, on this count partisans across the logical spectrum are in relatively similar dialectical positions. (shrink)

Methodological pluralism is advocated in this book, which takes students on an investigative tour of uncertainty in the social sciences, with particular emphasis on the scientific response to uncertainty. Much of the material is drawn from the disciplines of international relations and politics.

Addressing Merleau-Ponty's work Phenomenology of Perception, in dialogue with The Visible and the Invisible, his lectures at the Collège de France, and his reading of Proust, this book argues that at play in his thought is a philosophy of “ontological lateness”. This describes the manner in which philosophical reflection is fated to lag behind its objects; therefore an absolute grasp on being remains beyond its reach. Merleau-Ponty articulates this philosophy against the backdrop of what he calls “cruel thought”, a style (...) of reflecting that seeks resolution by limiting, circumscribing, and arresting its object. By contrast, the philosophy of ontological lateness seeks no such finality-no apocalypsis or unveiling-but is characterized by its ability to accept the veiling of being and its own constitutive lack of punctuality. To this extent, his thinking inaugurates a new relation to the becoming of sense that overcomes cruel thought. Merleau-Ponty's work gives voice to a wisdom of dispossession that allows for the withdrawal of being. Never before has anyone engaged with the theme of Merleau-Ponty's own understanding of philosophy in such a sustained way as Whitmoyer does in this volume. (shrink)

The author offers perspectives that can assist healthcare managers in achieving the highest ethical standards as they face their roles as healthcare providers, employers, and community service organizations. He also examines how to comply with relevant laws and regulations, provide high quality patient care with limited resources, and more.

Stanford Encyclopedia article surveying the life and work of D.C. Williams, notably in defending realism in metaphysics in the mid-twentieth century and in justifying induction by the logic of statistical inference.

Die Traume und Visionen aus der antiken Literatur, die die romischen Kaiser und ihr Umfeld betreffen, wurden bislang noch nicht auf ihre Bedeutung hin untersucht. Die vorliegende Arbeit schliesst diese Lucke, indem sie das Material von Caesar bis Maurikios analysiert. Dabei ergeben sich spezifische Motive, die besonders mit Traumen und Visionen verbunden sind: Geburt und Kindheit, Verheissung der Herrschaft, Erringung eines Sieges und gottliches Eingreifen, Ausubung der Herrschaft, besondere Befahigung und gottliche Begunstigung, nahendes Ende. Durch den breiten zeitlichen Ansatz gelingt (...) es, fur die Motive unterschiedliche Schwerpunkte auszumachen: Sie stehen alle in der Spannung zwischen einer gezielten Verbreitung zur Schaffung von Akzeptanz und der Literarisierung durch die antiken Autoren. Fur die Behandlung der Thematik waren nicht nur definitorische Vorarbeiten notwendig, sondern auch der mentale Horizont moglicher Rezipienten musste durch die Interpretation von Inschriften, Papyri und Selbstaussagen antiker Autoren in den Blick genommen werden. (shrink)

Definite descriptions, I shall argue, have two possible functions. 1] They are used to refer to what a speaker wishes to talk about, but they are also used quite differently. Moreover, a definite description occurring in one and the same sentence may, on different occasions of its use, function in either way. The failure to deal with this duality of function obscures the genuine referring use of definite descriptions. The best known theories of definite descriptions, those of Russell and Strawson, (...) I shall suggest, are both guilty of this. Before discussing this distinction in use, I will mention some features of these theories to which it is especially relevant. (shrink)

Darwin famously held that his use of the term "chance" in evolutionary theory merely "serves to acknowledge plainly our ignorance of the causes of each particular variation". Is this a tenable view today? Or should we revise our thinking about chance in evolution in light of the more advanced, quantitative models of Neo-Darwinian theory, which make substantial use of statistical reasoning and the concept of probability? Is determinism still a viable metaphysical doctrine about biological reality after the quantum revolution in (...) physics, or dowe have to abandon it in favor of an objective indeterminism? In light of such reflections, what is the relevant interpretation of probability in evolutionary theory? Do biologists use the concept of probability because they are finite cognitive agents or because the evolutionary process is fundamentally probabilistic? In this paper, I will show that we do not yet fully understand the nature of chance in evolution. (shrink)

Framed by social identity and cognitive moral reasoning theories, this paper assessed Gen Zs' level of principled moral reasoning, discovered during their undergraduate college years, and influences revealed by demographic variations using the Moral Reasoning Inventory. We discovered that Gen Zs' principled moral reasoning was lower than research reporting on Millennials, but not as dramatic a decline as scholars reported when investigating Baby Boomers, Generation Xers, and Millennials' Pscores. We found some differences within our sample based on business discipline (academic (...) major), the most powerful influence on Gen Zs' principled moral reasoning, followed by gender, work experience, and academic intelligence (GPA). Years in an academic program were not seen as influencing Gen Zs' principled moral reasoning. Overall, we conclude that Gen Zs may not exhibit a homogenous ethical identity as measured by their level of principled moral reasoning. Implications of these findings are discussed. (shrink)

Die vorliegende Arbeit beschaftigt sich mit einem theoretischen Ansatz innerhalb der Semantik, der bisher in Europa wenig Zuspruch fand: die Prototypensemantik. Die Autorin weist nach, dass metaphorische Redewendungen sehr wohl strukturiert und vollstandig mit Mitteln moderner empirischer Forschung analysiert werden konnen. Vor allem soll diese Arbeit als Anstoss verstanden werden, neue Wege in der Semantik zu gehen. Diese ist eine Disziplin, in der eben nicht nur rein sprachwissenschaftliche Erkenntnisse und Methoden Verwendung finden sollten, da sie die Verbindung zwischen Sprache, Mensch (...) und Welt darstellt. Es ist daher notwendig, die Sprache in ihrem 'naturlichen' Zusammenhang zu betrachten.". (shrink)

Aphorismen-Bücher sind nicht systematisch und widersprechen eigentlich der Konsequenz des Denkens. Nietzsche indes fordert das «rück- und vorsichtige» Lesen der seinen, und in der Tat: In der Morgenröthe erschließen sich mehrere Gewebe von Verweisen. Hervor tritt eine Technik: mögliche Strukturen anzubieten, wie zum Beispiel Bildfolgen und Zahlenkomposition. Kontexte finden sich, die erstens alles Reden, selbst das philosophische, von den lästigen Verpflichtungen auf logische und empirische Sachverhalte und zu anderen, etwa ästhetischen Möglichkeiten des Denkens befreien, und die zweitens anbieten, den Kalkül (...) durch Zahlen- oder Bilderspiel zu ersetzen. Die kaleidoskopisch wechselnden Sinn-Angebote lassen die Wahrheitsfrage überflüssig und poetische Ideen sichtbar werden. (shrink)

The recently offered, Purported counter-Examples to justified, True belief analyses of knowledge are looked at with some care and all found to be either incoherent or inconclusive. It is argued that justified, True belief analyses are based on sound insight into the concept of knowledge. The distinction between having been justified in claiming to know something and actually having known it is used in an effort to get the discussion of knowledge back on the right track.

A commonly neglected feature of the so-called Equal Weight View, according to which we should give our peers’ opinions the same weight we give our own, is its prima facie incompatibility with the common picture of philosophy as an armchair activity: an intellectual effort to seek a priori knowledge. This view seems to imply that our beliefs are more likely to be true if we leave our armchair in order to find out whether there actually are peers who, by disagreeing (...) with us, force us to revise our beliefs. This article argues that the Equal Weight View should be spelled out in such a way that not only actual peer disagreement requires us to revise our beliefs, but also merely possible peer disagreement. This result is not a reductio ad absurdum of the view. Quite the opposite: it shows that the view is, contrary to appearance, compatible with our common way of doing philosophy. (shrink)

De se attitudes seem to play a special role in action and cognition. This raises a challenge to the traditional way in which mental attitudes have been understood. In this chapter, we review the case for thinking that de se attitudes require special theoretical treatment and discuss various ways in which the traditional theory can be modified to accommodate de se attitudes.

This book is available either individually, or as part of the specially-priced Arguments of the Philosphers Collection.

Indigenous peoples are disproportionally vulnerable to climate change. At the same time, they possess valuable knowledge for fair and sustainable climate adaptation planning and policymaking. Yet Indigenous peoples and knowledges are often excluded from or underrepresented within adaptation plans and policies. In this paper we ask whether the concept of epistemic injustice can be applied to the context of climate adaptation and the underrepresentation of Indigenous knowledges within adaptation policies and strategies. In recent years, the concept of epistemic injustice has (...) gained prominence, indicating that someone has been unfairly discriminated against in their capacity as a knower. We argue that many climate adaptation policies are epistemically unjust towards Indigenous peoples because of the underrepresentation of Indigenous knowledges by showing how the case of Indigenous knowledges in climate adaptation planning and policy satisfies five conditions of epistemic injustice. We further consider what challenges there are to integrating local and Indigenous knowledges within development in general, and climate adaptation strategies in particular and how these can be addressed. Whether the lack of Indigenous knowledges in climate adaptation policies constitutes an epistemic injustice matters because an injustice denotes an unfair advantage to one group – whether by design or default – that ought to be remedied and redressed. (shrink)