Annalisa Coliva (Int J Study Skept 10(3–4):346–366, 2020) asks, “Are there mathematical hinges?” I argue here, against Coliva’s own conclusion, that there are. I further claim that this affirmative answer allows a case to be made for taking the concept of a hinge to be a useful and general-purpose tool for studying mathematical practice in its real complexity. Seeing how Wittgenstein can, and why he would, countenance mathematical hinges additionally gives us a deeper understanding of some of his latest thoughts (...) on mathematics. For example, a view of how mathematical hinges relate to Wittgenstein’s well-known river-bed analogy enables us to see how his way of thinking about mathematics can account nicely for a “dynamics of change” within mathematical research—something his philosophy of mathematics has been accused of missing (e.g., by Robert Ackermann (Wittgenstein’s city, The University of Massachusetts Press, Amherst, 1988) and Mark Wilson (Wandering significance: an essay on conceptual behavior, Oxford University Press, Oxford, 2006). Finally, the perspective on mathematical hinges ultimately arrived at will be seen to provide us with illuminating examples of how our conceptual choices and theories can be ungrounded but nevertheless the right ones (in a sense to be explained). (shrink)

Far from being unwelcome or impossible in a mathematical setting, indeterminacy in various forms can be seen as playing an important role in driving mathematical research forward by providing “sources of newness” in the sense of Hutter and Farías :434–449, 2017). I argue here that mathematical coincidences, phenomena recently under discussion in the philosophy of mathematics, are usefully seen as inducers of indeterminacy and as put to work in guiding mathematical research. I suggest that to call a pair of mathematical (...) facts a coincidence is roughly to suggest that the investigation of connections between these facts isn’t worthwhile. To say of this pair, “That’s no coincidence!” is to suggest just the opposite. I further argue that this perspective on mathematical coincidence, which pays special attention to what mathematical coincidences do, may provide us with a better view of what mathematical coincidences are than extant accounts. I close by reflecting on how understanding mathematical coincidences as generating indeterminacy accords with a conception of mathematical research as ultimately aiming to reduce indeterminacy and complexity to triviality as proposed in Rota Indiscrete thoughts, Birkhäuser, 1997). (shrink)

In lieu of an abstract, here is a brief excerpt of the content:AQUINAS AS A COMMENTATOR ON DE ANIMA 3.5 JAMES T. H. MARTIN St. John's University Jamaica, New York DOES ST. THOMAS AQUINAS in his commentary on De Anima 3.5 provide an acceptable gloss on Aristotle 's cryptic remarks about active mind? That is, can one accept.that what Aquinas says about active mind is what Aristotle meant but for some reason did not say? Many modern commentators, among (...) them Franz Brentano, Marcel de Corte, Paul Siwek, and Francisco Peccorino, appear to think so and present an interpretation of active mind which agrees substantially with what Aquinas says in his Sententia Libri De Anima (Sent.).1 i Senteiitia Libri De Anima, opera omnia iussu Leonis XIII P.M. edita (Paris: Vrin, for the Leonine Commission, 1984). While he does criticize St. Thomas Aquinas for some statements which " seem to betray a certain lack of clarity concerning the nature of active intellect,'' Franz Brentano awards the first place among earlier commentators on Aristotle's doctrine of active mind to Aquinas : " Indeed, I am not sure whether I should not say that he correctly grasped Aristotle's entire doctrine" (The Psychology of Aristotle: In Particular His Doctrine of Active Intellect, ed. and trans. Rolf George [Berkeley: University of California Press, 1977], p. 155). De Corte holds that the originality of his study consists entirely in combining " all the technical means refined by modern criticism and which the thirteenth century did not have at its disposition " with the " Thomist interpretation of the Aristotelian theory of intelligence," an interpretation with which de Corte agrees, and which he presents as a necessary correction of the errors of modern commentators, who are "more or less instilled with an unconscious Averroism which radically vitiates their power of understanding" (La doctrine de l'intelligence chez Aristote [Paris: Vrin, 1934], p. 2). Siwek notes that "many of St. Thomas's explanations of Aristotelian psychology are altogether consonant with our own explanations,'' and warns his readers against undervaluing Aquinas's views (Aristotelis Tractatus de Anima Graece et Latine, editit, versione latina auxit, commentario illustravit [Rome: Desclee & C.i, 1965], p. 30). Peccorini com621 622 JAMES T. H. MARTIN Aristotle's text is concerned with two minds, "a mind which is such as matter by becoming all things, and another which is such as an active principle by making all things" (430a14-15). What are these minds, and what do they do? The central elements of Aquinas's exegesis of De Anima 3.5 consist in his answers to these questions. He holds that these two minds are " parts or potencies of the soul " (Sent. 3.4. 126). The role of passive mind, the "mind which is such as matter," is to apprehend the intelligible object (Sent. 3.4. 101-2), while that of active mind, the mind " which is such as an active principle by making all things," is to abstract the intelligibles (Sent. 3.4. 103-4), a role which he explains in this way: Active mind makes those things intelligible in act which previously were intelligible in potency. It does this by abstracting them from matter, for in this way they are intelligible in act, as has been said. Aristotle was led to posit an active mind to exclude the opinion of Plato, who held that the natures of sensible things are separated from matter and actually intelligible. Thus for Plato it was not necessary to posit an active mind. But because Aristotle holds that the natures of sensible things are in matter and not actually intelligible, it was necessary that he posit a certain intellect to abstract them from matter and so make them actually intelligible. (Sent. 3.4 50-63) Active mind on Aquinas's reading makes the potentially intelligible forms of sensible things actually intelligible, and in this way these sensible things become objects of thought. If one accepts this role for active mind, one is forced to accept as well, I think, that active mind is part of the soul rather than something separate from the knowing human subject. Aquinas argues this point at length in his commentary on De Anima 3.5. If thinking, the action of the passive mind, is in fact... (shrink)

European Enlightenment thinkers like Emer de Vattel in his epic work The Laws of Nations argued that engaging in warfare should comply, as much as possible, with humane rules in the treatment of both combatants and noncombatants. Encapsulated by the phrase jus in bello, or justice in warfare, the question remains whether this idealist doctrine had application in military actions conducted during the Revolutionary War fought over the issue of American independence. This essay concludes that in such frontier regions as (...) the Mohawk Valley of New York, the doctrine of jus in bello had virtually no impact in restraining wartime cruelties. What actually occurred in such areas was vicious partisan warfare, or a contagion of violence characterized by brutal retribution and retaliation among combatants, along with merciless actions directed against civilian noncombatants. The Revolutionary War, at least in regions like frontier New York where partisan fighting predominated, had more in common wit.. (shrink)

It is thought that a valid inference to a logically necessary conclusion must proceed from entirely necessary premises. Counter-examples show this is false. Perhaps while the truth of a necessary proposition may follow from non-necessary premises, its necessity cannot so follow. Counter-examples show this to be mistaken. Must anyone who comes to know the non-necessary premises employed in the various counter-examples have prior knowledge of the necessity of the conclusions of the counter-examples? I argue against this. It is true that, (...) for any necessary proposition, there must be necessary premises from which it may validly be inferred; but no one need use these, or know these, or know how to use them, in order to know the necessity of any proposition. (shrink)

Additional theorizing about mathematical practice is needed in order to ground appeals to truly useful notions of the virtues in mathematics. This paper aims to contribute to this theorizing, first, by characterizing mathematical practice as being epistemic and “objectual” in the sense of Knorr Cetina The practice turn in contemporary theory, Routledge, London, 2001). Then, it elaborates a MacIntyrean framework for extracting conceptions of the virtues related to mathematical practice so understood. Finally, it makes the case that Wittgenstein’s methodology for (...) examining mathematics and its practice is the most appropriate one to use for the actual investigation of mathematical practice within this MacIntyrean framework. At each stage of thinking through mathematical practice by these means, places where new virtue-theoretic questions are opened up for investigation are noted and briefly explored. (shrink)

In the historical situation out of which Paul wrote, his kerygma offers the people of God, now reconstituted through Jesus Christ, a world-consciousness and calls them to a world-mission to bring about the obedience of faith among all nations.

This article contrasts Mark Bevir's approach to the history of ideas with a neo-Gramscian theory of discourse. Bevir puts the case for an ‘anti-foundationalist’ approach to understanding ideas, yet he defends a weak rationalism centred on individual intentions as the original source of all meanings. Discourse theorists—specifically Ernesto Laclau and Chantal Mouffe—also adopt an anti-foundationalist perspective but pursue its implications beyond any rationalism. The advantages of discourse theory are argued to lie in its emphasis on power and conflict in the (...) consitution and transformation of social meanings and identity. Laclau and Mouffe's work, it is claimed, alerts us to a political logic of discourse that Bevir's more rationalist approach to ‘ideas’ sidesteps. (shrink)

The question of the causality exercised by active mind cannot be dismissed as an attempt to go beyond what Aristotle explicitly says. One cannot say that Aristotle proves the existence of active mind but leaves the kind of causality it exercises an open question. Rather, if one accepts that Aristotle proves the existence of active mind, one must have an answer for the kind of causality it exercises. The analysis of De Anima, 3.5 shows that the principle on which the (...) argument for the existence of active mind rests cannot be read as arguing coherently for the existence of active mind as an efficient cause, but that the text is open to an interpretation along the lines of final causality. (shrink)

The rejection of a “characterless” moral self is central to some of Bernard Williams’ most important contributions to philosophy. By the time of Truth and Truthfulness, he works instead with a model of the self constituted and stabilized out of more primitive materials through deliberation and in concert with others that takes inspiration from Diderot. Although this view of the self raises some difficult questions, it serves as a useful starting point for thinking about the process of developing an authentic (...) moral point of view in the context of contemporary living. In what follows, I begin to fill out and extend this picture of the self and its related notion of authenticity by exploring some of the “technologies of the self” at play in Rachel Cusk’s recent work (primarily, the Outline trilogy, Coventry, Second Place, and “The Stuntman”) that ask us to rethink the possibility and importance of stability; seek a way of constituting oneself and one’s values outside the confining structures of traditional narrative (focusing instead on a framework that might be provided by the visual arts); and give a different role to the sort of internalized other Williams sees as being at work in the mechanisms of shame. (shrink)

In this broad historical and critical overview based on a lifetime of scholarship, James Alfred Martin, Jr., examines the development of the concepts of beauty and holiness as employed in theories of aesthetics and of religion. The injunction in the Book of Psalms to "worship the Lord in the beauty of holiness" addressed a tradition that has comprehended holiness primarily in terms of ethical righteousness--a conception that has strongly influenced Western understandings of religion. As the author points out, (...) however, the Greek forbears of Western thought, as well as many Eastern traditions, were and are more broadly concerned with the pursuit of beauty, truth, and goodness as ideals of human excellence, that is, with the "holiness of beauty." In this work Martin describes a philosophical stance that should prove to be most productive for the dialogue between aesthetics and religion. Beginning with the treatment of beauty and holiness in Hebrew, Greek, and classical Christian thought, the author traces the emergence of modern theories of aesthetics and religion in the Enlightenment. He then outlines the role of aesthetics in the theories of religion proposed by Otto, Eliade, van der Leeuw, and Tillich, in the cultural anthropology of Geertz, and in the thought of Santayana, Dewey, Whitehead, Heidegger, and Wittgenstein. In a global context Martin explores the relation of aesthetic theory to religious thought in the traditions of India, China, and Japan and concludes with reflections on the viability of modern aesthetic and religious theory in the light of contemporary cultural and methodological pluralism. Originally published in 1990. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. (shrink)

Gramsci's concept of hegemony is often believed to be a political account of legitimation. His Marxist critics go on to accuse him of failing to offer a properly structural account of bourgeois legitimation. I argue that Gramsci's theory attempted to straddle both economic and political accounts. In so doing, he presupposed the absence of effective authority in the Italian state. In such conditions, his project was to the orize the way in which economic classes became agents that would institute political (...) order. The difficulties in applying Gramsci's formu lation today lie in this combined economic and political account and the assumption of 'organic crisis' that supported it. (shrink)

"Chantal Mouffe's writings have been innovatory with respect to democratic theory, Marxism and feminism. Her work derives from, and has always been engaged with, contemporary political events and intellectual debates. This sense of conflict informs both the methodological and substantive propositions she offers. Determinisms, scientific or otherwise, and ideologies, Marxist or feminist, have failed to survive her excoriating critiques. In a sense she is the original post-Marxist, rejecting economisms and class-centric analyses, and the original post-feminist, more concerned with the varieties (...) of 'identity politics' than with any singularities of 'women's issues'. While Mouffe's concerns with power and discourse derive from her studies of Gramsci's theorisations of hegemony and the post-structuralisms of Derrida and Foucault, her reversal of the very terms through which political theory proceeds is very much her own. She centres conflict, not consensus, and disagreement, not finality. Whether philosophically perfectionist, or liberally reasonable, political theorists have been challenged by Mouffe to think again, and to engage with a new concept of 'the political' and a revived and refreshed notion of 'radical democracy'. The editor has focused on her work in three key areas: - Hegemony: From Gramsci to 'Post-Marxism' - Radical Democracy: Pluralism, Citizenship and Identity - The Political: A Politics Beyond Consensus The volume concludes with a new interview with Chantal Mouffe. James Martin is Professor of Politics at Goldsmiths, University of London, UK. He has published widely on Italian political thought, contemporary political theory and rhetoric."--. (shrink)

Current conceptions of the integration of computers into society often depend on the view that the human mind, as well as the computer, is a computational system. This view is widely taken to have broad implications for educational policy. We present a critique of the premise and some of the conclusions of the above argument. It is here shown that the thesis that the human mind is a computational system is, in principle, not scientifically supportable. It is also shown that, (...) even if the computational theory of mind were held for non-scientific reasons, the educational implications often derived from it do not follow. (shrink)

This article examines the anti-fascist rhetoric of the self-proclaimed `revolutionary liberal', Piero Gobetti, in Italy in the early 1920s. Gobetti is interesting from a rhetorical perspective for two reasons: first, for his efforts to redefine liberalism as an emancipatory ethic of struggle that extended to the revolutionary worker's movement; and second, for his rejection of fascism as essentially continuous with the anti-conflictual tendencies of the liberal parliamentary regime. An exemplary `ideological innovator', Gobetti's `paradiastolic' redescription of liberalism and his metaphorical reading (...) of fascism underscored a commitment to the value of rhetorical disputation over the meaning and form of liberty. This contrasts with contemporary approaches to fascism — and purportedly similar ideologies — which demonize or objectify in a way that forestalls such a debate. Yet, paradoxically, the cost of Gobetti's innovations was an inability to secure what Perelman calls the `universal audience', a task that preoccupied Gobetti's Marxist friend, Gramsci. (shrink)

Modern Italy is frequently diagnosed with having suffered an excess of ideological antagonism. However, poststructuralist political theory implies that, as a form of negative exclusion, antagonism serves a crucial purpose in shaping political discourse and delimiting social and political identities. This essay outlines the poststructuralist argument and sets out an agenda for rethinking ideological conflict in the Italian context. Taking the rise and decline of Italian Anti?Fascism as an example, it argues that antagonism is as important to ideological coherence as (...) is the positive content of political ideology itself. (shrink)

This article reviews the little examined early work of the Greek Marxist and state theorist, Nicos Poulantzas (1936–1979). In his first book, Nature du choses et droit of 1965, the young scholar developed a sociology of law culled from the insights of philosophical ontology. The article sets out the central claims of that book and reflects on its place in Poulantzas's intellectual development. Drawing on Heidegger, Sartre and Marx, Poulantzas proposed a species of Natural Law theory that unified ‘facts’ and (...) ‘values’ by grounding legal concepts in a theory of social praxis centred on material labour. Legal categories were thus irreducible to ahistorical essences but were, rather, expressions of mankind's struggle to realize its intrinsic freedom. As we shall see, although flawed and in key respects radically at odds with his later anti-humanism, Poulantzas's legal ontology nevertheless anticipated his mature theory of the state by setting out a philosophical sociology of the political order rooted in an anti-essentialist mode of inquiry. (shrink)

Poulantzas began his intellectual career as a scholar of law but eventually shifted his focus onto the theorization of the capitalist state. In his early publications, he explored legal concepts from the perspective of Phenomenology, inspired in particular by the Marxism of Jean-Paul Sartre and Lucien Goldmann. This chapter explores the logic of Poulantzas’s early legal thinking and the shift in his work under the influence of Louis Althusser’s ‘structural’ Marxism, which accompanied his new focus on the state in the (...) mid-to-late 1960s. This shift in his thought permitted Poulantzas a uniquely complex view of the state as a contingent, ‘material condensation’ of class forces. But his new insights were not fully extended to the exploration of legal subjectivities or the law as a site of socio-political contestation, which had been features of his earlier work. (shrink)

This article develops a view of collective memory as a rhetorical practice with an intimate connection to death. Drawing on the philosophy of Jacques Derrida, I argue that memory is inhabited by death – the loss of a living presence which, nonetheless, is the very condition for recollection and communication. Memory can never retrieve presence, for time is discontinuous, disjointed rather than linear. Instead, memory is presented as an ‘impossible gift’, a form of inheritance that charges us to remember anew. (...) These motifs, I argue, are central in epideictic rhetoric which, by dwelling on the present, invites collective recognition and affirmation concerning what fundamentally is. In the genre of the eulogy, especially, the event of death is encountered by reference to the fracturing of time, the experience of the gift, and the question of inheritance. Eulogy rhetoric, I suggest, is a powerful mode of collective memory that captures much of how we remember. (shrink)