On the Reality of the Continuum Discussion Note: A Reply to Ormell, ‘Russell's Moment of Candour’, Philosophy: Anne Newstead and James Franklin

In a recent article, Christopher Ormell argues against the traditional mathematical view that the real numbers form an uncountably infinite set. He rejects the conclusion of Cantor’s diagonal argument for the higher, non-denumerable infinity of the real numbers. He does so on the basis that the classical conception of a real number is mys- terious, ineffable, and epistemically suspect. Instead, he urges that mathematics should admit only ‘well-defined’ real numbers as proper objects of study. In practice, this means excluding as inadmissible all those real numbers whose decimal expansions cannot be calculated in as much detail as one would like by some rule. We argue against Ormell that the classical realist account of the continuum has explanatory power in mathematics and should be accepted, much in the same way that "dark matter" is posited by physicists to explain observations in cosmology. In effect, the indefinable real numbers are like the "dark matter" of real analysi

Regional governmentality: neoliberalization and the Caribbean community single market and economy

Formally launched on 30 January 2006, the Caribbean Community (CARICOM) Single Market and Economy (CSME) is, like many other regional economic initiatives, designed to create an economic space in which the uninhibited flow of goods, capital and skills across the borders of member states is anticipated to generate competitive business opportunities and external investment. Despite the intensification of such regional programmes, promoters and critics alike continue to consider CARICOM to be an intergovernmental organization dependent on the political will of member states as they negotiate the pressures of neoliberal globalization. In this paper, I argue that such a framing of regional integration in the Caribbean misses some of the tangible ways that CARICOM works beyond the sovereign intent of member states to enable the encroachment of neoliberal-style economic orders across the space of the region. I adopt a Foucauldian analytics of governmentality to unhinge CARICOM from the governments of its member states. Once freed from a persistent statism it becomes possible to consider the technical competencies through which CARICOM initiatives increasingly connect and cohere with neoliberal rationalities. My goal in developing such an analytics is not to suggest CARICOM operates as a superstate but rather to broaden the sites considered relevant to understanding the encroachment of neoliberalism in the Caribbean

Indispensability Without Platonism

According to Quine’s indispensability argument, we ought to believe in just those mathematical entities that we quantify over in our best scientific theories. Quine’s criterion of ontological commitment is part of the standard indispensability argument. However, we suggest that a new indispensability argument can be run using Armstrong’s criterion of ontological commitment rather than Quine’s. According to Armstrong’s criterion, ‘to be is to be a truthmaker (or part of one)’. We supplement this criterion with our own brand of metaphysics, 'Aristotelian (...) realism', in order to identify the truthmakers of mathematics. We consider in particular as a case study the indispensability to physics of real analysis (the theory of the real numbers). We conclude that it is possible to run an indispensability argument without Quinean baggage

Nonprofits in Rural America: Overcoming the Resource Gap

Nonprofit organizations across the United States serve the needs of rural communities in critically important ways. Yet the conditions under which they operate, challenging in the best of times, become even more difficult under national economic stress. To help inspire discussion and additional research on the management of rural nonprofits, the Bridgespan Group undertook the research reported in this paper -- research that shines the spotlight on one particularly acute challenge, the resource gap