Predicativity, the Russell-Myhill Paradox, and Church's Intensional Logic

This paper sets out a predicative response to the Russell-Myhill paradox of propositions within the framework of Church's intensional logic. A predicative response places restrictions on the full comprehension schema, which asserts that every formula determines a higher-order entity. In addition to motivating the restriction on the comprehension schema from intuitions about the stability of reference, this paper contains a consistency proof for the predicative response to the Russell-Myhill paradox. The models used to establish this consistency also model other axioms of Church's intensional logic that have been criticized by Parsons and Klement: this, it turns out, is due to resources which also permit an interpretation of a fragment of Gallin's intensional logic. Finally, the relation between the predicative response to the Russell-Myhill paradox of propositions and the Russell paradox of sets is discussed, and it is shown that the predicative conception of set induced by this predicative intensional logic allows one to respond to the Wehmeier problem of many non-extensions.Comment: Forthcoming in The Journal of Philosophical Logi

MENCIUS\u27 JUN-ZI, ARISTOTLE\u27S MEGALOPSUCHOS, & MORAL DEMANDS TO HELP THE GLOBAL POOR

It is commonly believed that impartial utilitarian moral theories have significant demands that we help the global poor, and that the partial virtue ethics of Mencius and Aristotle do not. This ethical partiality found in these virtue ethicists has been criticized, and some have suggested that the partialistic virtue ethics of Mencius and Aristotle are parochial (i.e., overly narrow in their scope of concern). I believe, however, that the ethics of Mencius and Aristotle are both more cosmopolitan than many presume and also are very demanding. In this paper, I argue that the ethical requirements to help the poor and starving are very demanding for the quintessentially virtuous person in Mencius and Aristotle. The ethical demands to help even the global poor are demanding for Mencius jun-zi (君子chön-tzu / junzi) and Aristotle\u27s megalopsuchos. I argue that both the jun-zi and megalopsuchos have a wide scope of concern for the suffering of poor people. I argue that the relevant virtues of the jun-zi and megalopsuchos are also achievable for many people. The moral views of Mencius and Aristotle come with strong demands for many of us to work harder to alleviate global poverty

The Strength of Abstraction with Predicative Comprehension

Frege's theorem says that second-order Peano arithmetic is interpretable in Hume's Principle and full impredicative comprehension. Hume's Principle is one example of an abstraction principle, while another paradigmatic example is Basic Law V from Frege's Grundgesetze. In this paper we study the strength of abstraction principles in the presence of predicative restrictions on the comprehension schema, and in particular we study a predicative Fregean theory which contains all the abstraction principles whose underlying equivalence relations can be proven to be equivalence relations in a weak background second-order logic. We show that this predicative Fregean theory interprets second-order Peano arithmetic.Comment: Forthcoming in Bulletin of Symbolic Logic. Slight change in title from previous version, at request of referee

Fragments of Frege's Grundgesetze and G\"odel's Constructible Universe

Frege's Grundgesetze was one of the 19th century forerunners to contemporary set theory which was plagued by the Russell paradox. In recent years, it has been shown that subsystems of the Grundgesetze formed by restricting the comprehension schema are consistent. One aim of this paper is to ascertain how much set theory can be developed within these consistent fragments of the Grundgesetze, and our main theorem shows that there is a model of a fragment of the Grundgesetze which defines a model of all the axioms of Zermelo-Fraenkel set theory with the exception of the power set axiom. The proof of this result appeals to G\"odel's constructible universe of sets, which G\"odel famously used to show the relative consistency of the continuum hypothesis. More specifically, our proofs appeal to Kripke and Platek's idea of the projectum within the constructible universe as well as to a weak version of uniformization (which does not involve knowledge of Jensen's fine structure theory). The axioms of the Grundgesetze are examples of abstraction principles, and the other primary aim of this paper is to articulate a sufficient condition for the consistency of abstraction principles with limited amounts of comprehension. As an application, we resolve an analogue of the joint consistency problem in the predicative setting.Comment: Forthcoming in The Journal of Symbolic Logi

Bringing the Copenhagen Global Climate Change Negotiations to Conclusion

In this paper we discuss the global negotiations now underway and aimed at achieving new climate change mitigation and other arrangements after 2012 (the end of the Kyoto commitment period). These were initiated in Bali in December 2007 and are scheduled to conclude by the end of 2009 in Copenhagen. As such, this negotiation is effectively the second round in ongoing global negotiations on climate change and further rounds will almost certainly follow. We highlight both the vast scope and vagueness of the negotiating mandate, the many outstanding major issues to be accommodated between negotiating parties, the lack of a mechanism to force collective decision making in the negotiation, and their short time frame. The likely lack of compliance with prior Kyoto commitments by several OECD countries (some to a major degree), the effective absence in Kyoto of compliance/enforcement mechanisms, and growing linkage to non-climate change areas (principally trade) all further complicate the task of bringing the negotiation to conclusion. The major clearage we see that needs to be bridged in the negotiations is between OECD countries on the one hand, and lower wage, large population, rapidly growing countries (China, India, Russia, Brazil) on the other.climate change, global negotiation

Polemos and Paideia: On the Weaponization of the School in Late Capitalism

A popular refrain in the politics of American education, often buttressed by a steady stream of studies, contends that ‘we are falling behind’ students from other countries. Sometimes this decline is specified in terms of discipline, but the general premise is that American students lag behind their foreign counterparts, with special dread attached to the notion of falling behind adversaries such as China. The failure to rectify our educational inadequacies apparently portends a genuine crisis, the loss of global dominance. The articulation of such fears is particularly instructive in discerning the political role of education in late capitalism, its conceptualization and uses within the context of politics. How do the fears of falling behind speak to the political role of education in late capitalism? I draw upon the ideas of the Herbert Marcuse and his Marxist intervention into Freudian psychoanalysis. Using Marcuse’s framework, I argue that in late capitalism the political role of education, formerly understood to serve life affirming value, has been reoriented to further the aims of the death drive. The fears of falling behind, and the policies that have followed, are symptomatic of a disposition toward education that has reconfigured the school as a means of conquest, subjugation, and war

Laser diagnostic method for plasma sheath potential mapping

2016 Summer.Includes bibliographical references.Electric propulsion systems are gaining popularity in the aerospace field as a viable option for long term positioning and thrusting applications. In particular, Hall thrusters have shown promise as the primary propulsion engine for space probes during interplanetary journeys. However, the interaction between propellant xenon ions and the ceramic channel wall continues to remain a complex issue. The most significant source of power loss in Hall thrusters is due to electron and ion currents through the sheath to the channel wall. A sheath is a region of high electric field that separates a plasma from a wall or surface in contact. Plasma electrons with enough energy to penetrate the sheath may result emission of a secondary electron from the wall. With significant secondary electron emission (SEE), the sheath voltage is reduced and so too is the electron retarding electric field. Therefore, a lower sheath voltage further increases the particle loss to the wall of a Hall thruster and leads to plasma cooling and lower efficiency. To further understand sheath dynamics, laser-induced fluorescence is employed to provide a non-invasive, in situ, and spatially resolved technique for measuring xenon ion velocity. By scanning the laser wavelength over an electronic transition of singly ionized xenon and collecting the resulting fluorescence, one can determine the ion velocity from the Doppler shifted absorption. Knowing the velocity at multiple points in the sheath, it can be converted to a relative electric potential profile which can reveal a lot about the plasma-wall interaction and the severity of SEE. The challenge of adequately measuring sheath potential profiles is optimizing the experiment to maximize the signal-to-noise ratio. A strong signal with low noise, enables high resolution measurements and increases the depth of measurement in the sheath, where the signal strength is lowest. Many improvements were made to reduce the background luminosity, increase the fluorescence intensity and collection efficiency, and optimize the signal processing equipment. Doing so has allowed for a spatial resolution of 60 microns and a maximum depth of measurement of ~2 mm depending on conditions. Sheaths surrounding common Hall thruster ceramics at various plasma conditions were measured in an attempt to determine the effect of SEE and a numerical analysis of the plasma-wall interactions was conducted to further understand the phenomena and compare against obtained data

Bringing the Copenhagen global climate change negotiations to conclusion

In this paper we discuss the global negotiations now underway and aimed at achieving new climate change mitigation and other arrangements after 2012 (the end of the Kyoto commitment period). These were initiated in Bali in December 2007 and are scheduled to conclude by the end of 2009 in Copenhagen. As such, this negotiation is effectively the second round in ongoing global negotiations on climate change and further rounds will almost certainly follow. We highlight both the vast scope and vagueness of the negotiating mandate, the many outstanding major issues to be accommodated between negotiating parties, the lack of a mechanism to force collective decision making in the negotiation, and their short time frame. The likely lack of compliance with prior Kyoto commitments by several OECD countries (some to a major degree), the effective absence in Kyoto of compliance/enforcement mechanisms, and growing linkage to non-climate change areas (principally trade) all further complicate the task of bringing the negotiation to conclusion. The major clearage we see that needs to be bridged in the negotiations is between OECD countries on the one hand, and lower wage, large population, rapidly growing countries (China, India, Russia, Brazil) on the other