Ordination rites of the ancient churches of East and West

Reviewed Book: Bradshaw, Paul F. Ordination rites of the ancient churches of East and West. New York: Pueblo Pub, 1990

Measurement Theory and the Foundations of Utilitarianism

Harsanyi used expected utility theory to provide two axiomatizations of weighted utilitarian rules. Sen (and later, Weymark) has argued that Harsanyi has not, in fact, axiomatized utilitarianism because he has misapplied expected utility theory. Specifically, Sen and Weymark have argued that von Neumann-Morgenstern expected utility theory is an ordinal theory and, therefore, any increasing transform of a von Neumann-Morgenstern utility function is a satisfactory representation of a preference relation over lotteries satisfying the expected utility axioms. However, Harsanyi's version of utilitarianism requires a cardinal theory of utility in which only von Neumann-Morgenstern utility functions are acceptable representations of preferences. Broome has argued that von Neumann-Morgenstern expected utility theory is cardinal in the relevant sense needed to support Harsanyi's utilitarian conclusions. His basic point is that a preference binary relation is not a complete description of preferences in the von Neumann-Morgenstern theory. Rather, the preference relation needs to be supplemented by a binary operation, and it is this operation that makes the theory cardinal. Broome does not provide a formal argument in support of this conclusion. In this article, measurement theory is used to critically evaluate Broome's claims. It is shown that the criticisms of Harsanyi's theory by Sen and Weymark can be extended to the more complete description of expected utility theory that is obtained by using the mixture operators that appear in von Neumann and Morgenstern's original description of expected utility theory in addition to a preference relationexpected utility, utilitarianism, von Neumann-Morgenstern, Harsanyi

Second Quantization and the Spectral Action

We consider both the bosonic and fermionic second quantization of spectral triples in the presence of a chemical potential. We show that the von Neumann entropy and the average energy of the Gibbs state defined by the bosonic and fermionic grand partition function can be expressed as spectral actions. It turns out that all spectral action coefficients can be given in terms of the modified Bessel functions. In the fermionic case, we show that the spectral coefficients for the von Neumann entropy, in the limit when the chemical potential $\mu$ approaches $0,$ can be expressed in terms of the Riemann zeta function. This recovers a result of Chamseddine-Connes-van Suijlekom.Comment: Author list is expanded. The calculations in the new version are extended to two more Hamiltonians. New references adde