I argue against a prevailing view that the essence of Godis identical with the attributes. I show that given what Spinoza says in 2d2 – Spinoza'spurported definition of the essence of a thing – the attributes cannot be identical withthe essence of God (whether the essence of God is understood as the distinct attributesor as a totality of indistinct attributes). I argue that while the attributes do notsatisfy the stipulations of 2d2 relative to God, absolutely infinite and eternal power does (...) satisfythose stipulations. Hence, I conclude that absolutely infinite and eternal power is God'sessence and that the attributes are expressions of that power. (shrink)
Psychologists debate whether mental attributes can be quantified or whether they admit only qualitative comparisons of more and less. Their disagreement is not merely terminological, for it bears upon the permissibility of various statistical techniques. This article contributes to the discussion in two stages. First it explains how temperature, which was originally a qualitative concept, came to occupy its position as an unquestionably quantitative concept (§§1–4). Specifically, it lays out the circumstances in which thermometers, which register quantitative (or cardinal) differences, (...) became distinguishable from thermoscopes, which register merely qualitative (or ordinal) differences. I argue that this distinction became possible thanks to the work of Joseph Black, ca. 1760. Second, the article contends that the model implicit in temperature’s quantitative status offers a better way for thinking about the quantitative status of mental attributes than models from measurement theory (§§5–6). (shrink)
This paper assesses the claim that an agonistic model of democracy could foster greater accommodation of citizens' social, cultural and ethical differences than mainstream liberal theories. I address arguments in favor of agonistic conceptions of politics by a diverse group of democratic theorists, ranging from republican theorists - Hannah Arendt and Benjamin Barber - to postmodern democrats concerned with questions of identity and difference, such as William Connolly and Bonnie Honig. Neither Arendt's democratic agonism nor Barber's republican-inflected account of strong (...) democracy purports to include citizens' group-based cultural identities, and so cannot further the claim that agonistic politics is more inclusive of cultural and social differences. Postmodern agonistic democrats such as Connolly and Honig rely upon Arendt's account of the relationship between agonism and pluralism, and wrongly assume that her view of politics is compatible with formal respect and recognition for citizens' cultural group identities. While agonistic democracy helpfully directs us to attend to the importance of moral and political disagreement, I argue that the stronger claim that an agonistic model of democracy could more readily include culturally diverse citizens is simply unfounded. By contrast, recent liberal variants of agonistic democracy that conceive of legal and political institutions as tools for recognizing and mediating citizens' moral and cultural differences may suggest ways to deepen our democratic practices in plural societies. Key Words: agonism agonistic democracy Hannah Arendt citizenship cultural minorities pluralism republican theory. (shrink)
Recent accounts of the role of diagrams in mathematical reasoning take a Platonic line, according to which the proof depends on the similarity between the perceived shape of the diagram and the shape of the abstract object. This approach is unable to explain proofs which share the same diagram in spite of drawing conclusions about different figures. Saccheri’s use of the bi-rectangular isosceles quadrilateral in Euclides Vindicatus provides three such proofs. By forsaking abstract objects it is possible to give a (...) natural explanation of Saccheri’s proofs as well as standard geometric proofs and even number-theoretic proofs. (shrink)
Classical logic yields counterintuitive results for numerous propositional argument forms. The usual alternatives (modal logic, relevance logic, etc.) generate counterintuitive results of their own. The counterintuitive results create problems—especially pedagogical problems—for informal logicians who wish to use formal logic to analyze ordinary argumentation. This paper presents a system, PL– (propositional logic minus the funny business), based on the idea that paradigmatic valid argument forms arise from justificatory or explanatory discourse. PL– avoids the pedagogical difficulties without sacrificing insight into argument.
Hume describes the sciences as "noble entertainments" that are "proper food and nourishment" for reasonable beings (EHU 1.5-6; SBN 8).1 But mathematics, in particular, is more than noble entertainment; for millennia, agriculture, building, commerce, and other sciences have depended upon applying mathematics.2 In simpler cases, applied mathematics consists in inferring one matter of fact from another, say, the area of a floor from its length and width. In more sophisticated cases, applied mathematics consists in giving scientific theory a mathematical form (...) and then explaining and predicting matters of fact by means of mathematics and the theory. Since Hume holds that, "All inferences from experience are . . . .. (shrink)
Professor Grünbaum's much-discussed refutation of Zeno's metrical paradox turns out to be ad hoc upon close examination of the relevant portion of measure theory. Although the modern theory of measure is able to defuse Zeno's reasoning, it is not capable of refuting Zeno in the sense of showing his error. I explain why the paradox is not refutable and argue that it is consequently more than a mere sophism.
How should liberal democratic states respond to cultural practices and arrangements that run afoul of liberal norms and laws? This article argues for a reframing of the challenges posed by traditional or nonliberal cultural minorities. The author suggests that viewed from up close, such dilemmas are revealed to be primarily intracultural rather than intercultural conflicts, and reflect the political and practical interests of factions of communities much more than deep moral differences. Using the example of the reform of customary marriage (...) laws in post-apartheid South Africa, this article makes the case for a more pragmatic, politically focused approach to resolving conflicts of culture that it is argued is both more democratic and effective than alternatives recently advanced by liberals and deliberative democracy theorists. (shrink)
Many historians of the calculus deny significant continuity between infinitesimal calculus of the seventeenth century and twentieth century developments such as Robinson’s theory. Robinson’s hyperreals, while providing a consistent theory of infinitesimals, require the resources of modern logic; thus many commentators are comfortable denying a historical continuity. A notable exception is Robinson himself, whose identification with the Leibnizian tradition inspired Lakatos, Laugwitz, and others to consider the history of the infinitesimal in a more favorable light. Inspite of his Leibnizian sympathies, (...) Robinson regards Berkeley’s criticisms of the infinitesimal calculus as aptly demonstrating the inconsistency of reasoning with historical infinitesimal magnitudes. We argue that Robinson, among others, overestimates the force of Berkeley’s criticisms, by underestimating the mathematical and philosophical resources available to Leibniz. Leibniz’s infinitesimals are fictions, not logical fictions, as Ishiguro proposed, but rather pure fictions, like imaginaries, which are not eliminable by some syncategorematic paraphrase. We argue that Leibniz’s defense of infinitesimals is more firmly grounded than Berkeley’s criticism thereof. We show, moreover, that Leibniz’s system for differential calculus was free of logical fallacies. Our argument strengthens the conception of modern infinitesimals as a development of Leibniz’s strategy of relating inassignable to assignable quantities by means of his transcendental law of homogeneity. (shrink)
A plausible and popular rule governing the scope of truth-functional logic is shown to be indequate. The argument appeals to the existence of truth-functional paraphrases which are logically independent of their natural language counterparts. A more adequate rule is proposed.
In formal logic there is a premium on clever paraphrase, for it subsumes troublesome inferences under a familiar theory. (A paradigm is Davidson's analysis 1967 of inferences like ?He buttered his toast with a knife; so, he buttered his toast?.) But the need for paraphrase in formal logic runs deeper than the odd recalcitrant inference, and thus, I shall argue, commits logicians to some interesting consequences. First, the thesis that arguments are valid in virtue of their form must be severely (...) qualified (?4). And second, it is misleading to view a formal logical theory as a standard for justifying and criticizing inference (?7). The latter point depends on the nature and role of paraphrase, which permit a range of conflicting logical theories. Conflicting logical theories arise from the conflicting goals of logical theorists and the promiscuous nature of paraphrase makes reconciliation impossible. (shrink)
The value and importance accorded to personal autonomy within liberalism would seem to suggest that cultural practices that severely constrain the choices of individuals through heavyhanded role socialization and restriction ought to be strongly discouraged in liberal societies. In this paper, I explore this claim in connection with the custom of arranged marriage, which has recently come under fire in some liberal democratic states, notably Britain. My aim is to try to complicate the liberal understanding of the relationship between cultural (...) traditions and personal autonomy. In the course of this discussion, I analyze and offer some criticisms of autonomy as a substantive ideal and requirement for flourishing. In revisiting and evaluating arguments in favor of a thick or substantive ideal of autonomy criticisms, I hope to show that a substantive ideal of autonomy as independence is culturally bounded in ways that are often overlooked by liberal philosophers. (shrink)
The widespread idea that infinitesimals were “eliminated” by the “great triumvirate” of Cantor, Dedekind, and Weierstrass is refuted by an uninterrupted chain of work on infinitesimal-enriched number systems. The elimination claim is an oversimplification created by triumvirate followers, who tend to view the history of analysis as a pre-ordained march toward the radiant future of Weierstrassian epsilontics. In the present text, we document distortions of the history of analysis stemming from the triumvirate ideology of ontological minimalism, which identified the continuum (...) with a single number system. Such anachronistic distortions characterize the received interpretation of Stevin, Leibniz, d’Alembert, Cauchy, and others. (shrink)
This article argues that liberal arguments for human rights minimalism, such as those of John Rawls and Michael Ignatieff, contain fundamental inconsistencies in their treatment of core rights to life and liberty. Insofar as their versions of minimalism foreground rights to physical security and basic freedom of movement, they cannot coherently exclude certain social and economic protections and liberties that directly support or are even partly constitutive of these rights. Nor do they have good grounds for putting the social and (...) private realms wholly beyond the purview of international law. “New” human rights that represent an expansion of civil rights in particular beyond the classic conception to encompass, for example, the right to freedom from sexual and gender-based violence, illustrate especially well the extent to which civil, social, and economic rights violations, and their remedies, are deeply interwoven. These emergent rights also directly challenge the dichotomy between public/political and private/social realms, and the corollary assumption that human rights violations occur mainly or exclusively in the former sphere. While the concerns that motivate arguments for human rights minimalism — considerations of pluralism and prudence — are legitimate, proponents would do best to reconsider the multiple roles that human rights in fact play, in spite of their essentially contested status. (shrink)
Although wonder is a response to what is extraordinary or regarded as such, this covers a variety of things. Hence, wonder covers a spectrum from mere surprise or puzzlement to stronger responses like dread or amazement; moreover, it is often linked to other powerful responses like fear or admiration, and it can lead people into many pursuits and areas of reflection. I look at the variety of the objects of wonder, and of the neighbouring responses and conceptual connections found here, (...) then I discuss the response of wonder itself, and its causes and effects. Finally, I ask why the sense of wonder can atrophy, and whether it can be suppressed deliberately. (shrink)
Gender and Justice in Multicultural Liberal States explores the challenges that culturally plural liberal states face when they hold competing political commitments to cultural rights and sexual equality, and advances an argument for resolving such dilemmas through democratic dialogue and negotiation. Exploring recent examples of gendered cultural conflicts in South Africa, Canada, and Britain, this book shows that there is an urgent need for workable strategies to mediate the antagonisms between the cultural practices and arrangements of certain ethno-cultural and religious (...) groups and the norms and constitutional rights endorsed by liberal states. Yet such strategies will be successful only insofar as they can resolve conflicts without either reinforcing women's subordination within cultural communities or unjustly dismissing calls for cultural recognition and forms of self-governance. To this end, the book develops an approach to mediating cultural tensions that takes seriously the demands of justice by cultural and religious minorities in liberal democratic states. Grounded in an argument for democratic legitimacy, this approach invokes norms of political inclusion and democratic dialogue, and highlights negotiation and compromise as the best vehicles for arriving at resolutions to conflicts of cultural value. However, it also reconceives the basis of democratic legitimacy so as to include not merely formal expressions of political consent, but also a range of non-formal democratic activity that occur in the private and social spheres, from acts of cultural reinvention and subversion to outright expressions of dissent and cultural refusal. (shrink)
Following the ideas of Poincaré, Reichenbach, and Grunbaum concerning the convention of setting up clock systems, we analyze clock systems and light propagation within the framework of four-dimensional symmetry. It is possible to construct a new four-dimensional symmetry framework incorporatingcommon time: observers in different inertial frames of reference use one and the same clock system, which is located in any one of the frames. Consequently, simultaneity has a meaning independent of position and independent of frame of reference. A further consequence (...) is that the two-way speeds of light alone are isotropic in any frame. By the choice of clock system there will be one frame in which the one-way speed of light is isotropic. This frame can be arbitrarily chosen. The difference between one-way speeds and two-way speeds of light signals is considered in detail. (shrink)
I discuss John Henry Newman's correspondence with William Froude, F.R.S., (1810–79) and his family. Froude remained an unbeliever, and I argue that Newman's disputes with him about the ethics of belief and the relationship between religion and science not only reveal important aspects of his thought, but also anticipate modern discussions on foundationalism, the ethics of beliefs and scientism.
I take up Richard Swinburne's point, in his "Responsibility and Atonement," Ch. 5, that although the past cannot be changed, wrongdoers may change its significance by 'disowning' their actions through atonement, just as their victims may do so through forgiveness. I argue that the point can and should be pressed much more strongly than it is by Swinburne within the terms of his own discussion; and that it has a much wider significance, transcending that discussion, for there is a constant (...) interplay between events, human actions, and our retrospective assessment of the past. Finally, I look tentatively at the question in an eschatological perspective. (shrink)
Anthropologists have long wrestled with their impact upon the people they study. Historically, the discipline has served and subverted colonial agendas, but views itself traditionally as an advocate for the disempowered and as an instrument of public policy. Marketing is now among the pre-eminent institutions of cultural stability and change at work on the planet. Currently, ethnography is assuming a growing importance in the marketer’s effort to influence the accommodation and resistance of consumers to the neocolonial forces of globalization. The (...) ethical consequences of market-oriented ethnography are explored in this essay. (shrink)
The following is an introduction to a roundtable panel of the American Political Science Association meeting (Normative Political Theory Division) held September 2, 1994, in New York City. I set out some main themes in the "care/justice debate," and suggest that the impasse between care proponents and liberal, neo-Kantian thinkers is perpetuated by caricatured construals of these theories; salient differences come into relief by addressing the ethical and political applications of these moral perspectives.
A new theory of four-dimensional symmetry introduced by Hsu has been criticized as logically inconsistent. We answer the criticisms that have been raised and show that in fact this theory is not logically inconsistent.