[Review of] Carol Bruchac, Linda Hogan, Judith McDaniel, eds. The Stories We Hold Secret-Tales of Women\u27s Spiritual Development

The Stories We Hold Secret -- Tales of Women\u27s Spiritual Development is an anthology of thirty-one short fiction pieces written by and about women in America. These are not stories about extraterrestrial visits, enlightenment through gurus, or dramatic religious conversion; rather, these are stories of inner knowing, of our holy dailiness, as Linda Hogan says in the preface. The stories are as varied as women\u27s experience, from the quietness of a Native American woman cooking beans and cornbread in her kitchen to the tumult of a woman who for the first time becomes involved with a workers\u27 strike

On Sexual Lust as an Emotion

Sexual lust – understood as a feeling of sexual attraction towards another – has traditionally been viewed as a sort of desire or at least as an appetite akin to hunger. I argue here that this view is, at best, significantly incomplete. Further insights can be gained into certain occurrences of lust by noticing how strongly they resemble occurrences of “attitudinal” (“object-directed”) emotion. At least in humans, the analogy between the object-directed appetites and attitudinal emotions goes well beyond their psychological structure to include similar ways in which their occurrence can be introspectively recognized, resulting in similar extensions of their functionality and meaningfulness to the subject. I conclude that although further research is needed, given the strength of the analogy, the ability of lust to satisfy some general requirements for being an emotion, and perhaps certain neurological findings, lust may somewhat uniquely straddle the line between appetite and emotion

Judgment aggregation functions and ultraproducts

The relationship between propositional model theory and social decision making via premise-based procedures is explored. A one-to-one correspondence between ultrafilters on the population set and weakly universal, unanimity-respecting, systematic judgment aggregation functions is established. The proof constructs an ultraproduct of profiles, viewed as propositional structures, with respect to the ultrafilter of decisive coalitions. This representation theorem can be used to prove other properties of such judgment aggregation functions, in particular sovereignty and monotonicity, as well as an impossibility theorem for judgment aggregation in finite populations. As a corollary, Lauwers and Van Liedekerke's (1995) representation theorem for preference aggregation functions is derived.judgment aggregation function, ultraproduct, ultrafilter

Hyperfinite stochastic integration for Lévy processes with finite-variation jump part

This article links the hyperfinite theory of stochastic integration with respect to certain hyperfinite Lévy processes with the elementary theory of pathwise stochastic integration with respect to pure-jump Lévy processes with finite-variation jump part. Since the hyperfinite Itô integral is also defined pathwise, these results show that hyperfinite stochastic integration provides a pathwise definition of the stochastic integral with respect to Lévy jump-diffusions with finite-variation jump part. As an application, we provide a short and direct nonstandard proof of the generalized Itô formula for stochastic differentials of smooth functions of Lévy jump-diffusions whose jumps are bounded from below in norm.Lévy processes, stochastic integration, nonstandard analysis, Itô formula

A representative individual from Arrovian aggregation of parametric individual utilities

This article investigates the representative-agent hypothesis for an infinite population which has to make a social choice from a given finite-dimensional space of alternatives. It is assumed that some class of admissible strictly concave utility functions is exogenously given and that each individual's preference ordering can be represented cardinally through some admissible utility function. In addition, we assume that (i) the class of admissible utility functions allows for a smooth parametrization, and (ii) the social welfare function satisfies Arrovian rationality axioms. We prove that there exists an admissible utility function r, called representative utility function, such that any alternative which maximizes r also maximizes the social welfare function. The proof utilizes a special nonstandard model of the reals, viz. the ultraproduct of the reals with respect to the ultrafilter of decisive coalitions; this construction explicitly determines the parameter vector of the representative utility function.representative individual, Arrovian social choice, ultrafilter, ultraproduct, nonstandard analysis

On the foundations of Lévy finance: Equilibrium for a single-agent financial market with jumps

For a continuous-time financial market with a single agent, we establish equilibrium pricing formulae under the assumption that the dividends follow an exponential Lévy process. The agent is allowed to consume a lump at the terminal date; before, only flow consumption is allowed. The agent's utility function is assumed to be additive, defined via strictly increasing, strictly concave smooth felicity functions which are bounded below (thus, many CRRA and CARA utility functions are included). For technical reasons we require that only pathwise continuous trading strategies are permitted in the demand set. The resulting equilibrium prices depend on the agent's risk-aversion through the felicity functions. It turns out that these prices will be the (stochastic) exponential of a Lévy process essentially only if this process is geometric Brownian motion.financial equilibrium, asset pricing, representative agent models, Lévy processes, nonstandard analysis

An algebraic approach to general aggregation theory: Propositional-attitude aggregators as MV-homomorphisms

This paper continues Dietrich and List's [2010] work on propositional-attitude aggregation theory, which is a generalised unification of the judgment-aggregation and probabilistic opinion-pooling literatures. We first propose an algebraic framework for an analysis of (many-valued) propositional-attitude aggregation problems. Then we shall show that systematic propositional-attitude aggregators can be viewed as homomorphisms in the category of C.C. Chang's [1958] MV-algebras. Since the 2-element Boolean algebra as well as the real unit interval can be endowed with an MV-algebra structure, we obtain as natural corollaries two famous theorems: Arrow's theorem for judgment aggregation as well as McConway's [1981] characterisation of linear opinion pools.propositional attitude aggregation, judgment aggregation, linear opinion pooling, Arrow's impossibility theorem, many-valued logic, MV-algebra, homomorphism, Arrow's impossibility theorem, functional equation