This paper presents an overview on the concept of cardinal utility in its relations with the literature since the beginning of the XVIIIth century (Part I); an estimate of the cardinal utility function for its negative values, thus completing the estimate of this function for its positive values given in my 1984 Venice paper (Part II); and finally different applications to the theory of choices in the presence of risk and to the wealth transfer and tax (...) questions (Part III). (shrink)

We reexamine some of the classic problems connected with the use of cardinal utility functions in decision theory, and discuss Patrick Suppes's contributions to this field in light of a reinterpretation we propose for these problems. We analytically decompose the doctrine of ordinalism, which only accepts ordinal utility functions, and distinguish between several doctrines of cardinalism, depending on what components of ordinalism they specifically reject. We identify Suppes's doctrine with the major deviation from ordinalism that conceives of (...) utility functions as representing preference differences, while being non- etheless empirically related to choices. We highlight the originality, promises and limits of this choice-based cardinalism. (shrink)

Though the Random Utility Model (RUM) was conceived entirely in terms of ordinal utility, the apparatus through which it is widely practised exhibits properties of cardinal utility. The adoption of cardinal utility as a working operation of ordinal is perfectly valid, provided interpretations drawn from that operation remain faithful to ordinal utility. The article considers whether the latter requirement holds true for several measurements commonly derived from RUM. In particular it is found that (...) measurements of consumer surplus change may depart from ordinal utility, and exploit the cardinality inherent in the practical apparatus. (shrink)

Modern microeconomic theory is based on a foundation of ordinal preference relations. Good textbooks stress that cardinal utility functions are artificial constructions of convenience, and that economics does not attribute any meaning to “utils.” However, we argue that despite this official position, in practice mainstream economists rely on techniques that assume the validity of cardinal utility. Doing so has turned mainstream economic theorizing into an exercise of reductionism of objects down to the preferences of ‘ideal type’ (...) subjects. (shrink)

We establish a simple condition, based on the willingness to bet on events, under which two biseparable preferences have cardinally equivalent utilities.

It is widely held that under ordinal utility, utility differences are ill-defined. Allegedly, for these to be well-defined (without turning to choice under risk or the like), one should adopt as a new kind of primitive quaternary relations, instead of the traditional binary relations underlying ordinal utility functions. Correlatively, it is also widely held that the key structural properties of quaternary relations are entirely arbitrary from an ordinal point of view. These properties would be, in a nutshell, (...) the hallmark of cardinal utility. While much is obviously true in these two tenets, this note explains why, as stated, they should be abandoned. Any ordinal utility function induces a rich quaternary relation. There is such a thing as ordinal utility differences. Furthermore, this induced quaternary relation respects, apart from completeness, the most standard structural properties of quaternary relations. These properties are, from an ordinal point of view, anything but arbitrary; from a quaternary perspective only completeness should be considered the hallmark—if any—of cardinal utility. These facts are explained to be especially relevant to the critical appreciation of the ordinalist methodology. (shrink)

Maxmin Expected Utility was first axiomatized by Gilboa and Schmeidler in an Anscombe–Aumann setup Anscombe and Aumann which includes exogenous probabilities. The model was later axiomatized in a purely subjective setup, where no exogenous probabilities are assumed. The purpose of this note is to show that in all these axiomatizations, the only assumptions that are needed are the basic ones that are used to extract a cardinal utility function, together with the two typical Maxmin assumptions, Uncertainty Aversion (...) and Certainty Independence, applied only to 0.5:0.5 mixtures. For the purely subjective characterizations, this means that assumptions involving an unbounded number of variables can be replaced with assumptions that involve only a finite number thereof. (shrink)

The response mode bias, in which subjects exhibit different risk attitudes when assessing certainty equivalents versus indifference probabilities, is a well-known phenomenon in the assessment of utility functions. In this empirical study, we develop and apply a cardinal measure of risk attitudes to analyze not only the existence, but also the strength of this phenomenon. Since probability levels involved in decision problems are already known to have a strong impact on behavior, we use this approach to study the (...) impact of probabilities on the extent of the response mode bias. We find that the direction in which probabilities influence measured risk aversion is the opposite in the certainty equivalence (CE) method versus in the probability equivalence (PE) method. Utilizing the CE elicitation approach leads to an increase of risk seeking for gambles involving high probabilities. For the PE method, subjects tend to behave risk averse with gambles of high probabilities. This behavior is reversed in the gain domain. This “tailwhip” effect is consistently replicated in several experiments, involving both loss and gain domains of lotteries. (shrink)

Altruism is a popular economic explanation for a wide range of pro-social decisions and actions. It has been applied frequently in several different streams of literature, and is a descriptively compelling model of behavior. This paper provides a theoretical framework for the existence of ordinal and cardinal altruistic value functions, as well as altruistic utility functions, based on an altruistic preference relation. Representation theorems are developed to specify relatively weak conditions under which altruistic value and utility functions (...) can be shown to exist. In addition, conditions that lead to additive forms of these functions are provided. (shrink)

Karol Wojtyła found phenomenology very helpful for the analysis of concrete human experience and for overcoming the ethical formalism ofKant. Phenomenology, he believed, could also enrich classical Thomism by exploring the lived experience of freedom, interiority, and self-governance. But phenomenology, in his opinion, needed to be supplemented by metaphysics in order to ground experiences such as the sense of duty in the real order. He criticized much modern philosophy for abandoning metaphysics and thus neglecting the sapiential dimension. Since his career (...) as a professor was very short, he did not have time to complete his project of a personalist Thomism in which phenomenology and metaphysics would be harmoniously combined. (shrink)

Cardinal Mercier’s Manual of Modern Scholastic Philosophy is a standard work, prepared at the Higher Institute of Philosophy, Louvain, mainly for the use of clerical students in Catholic Seminaries. Though undoubtedly elementary, it contains a clear, simple, and methodological exposition of the principles and problems of every department of philosophy, and its appeal is not to any particular class, but broadly human and universal. Volume I includes a general introduction to philosophy and sections on cosmology, psychology, criteriology, and metaphysics (...) or ontology. (shrink)

Rousseau’s political project consists in ensuring that the citizens of the social contract, in uniting with each other, preserve their ability to self-legislate, or be autonomous. For this to work, however, members of the social contract would need to feel intrinsically linked to the political whole. This essay investigates what that feeling might be and how it can be grown. I argue that Rousseau develops a model of the energy or character of the being capable of autonomy, capable of experiencing (...) themselves as part of the whole. That energy is a pathos of vigour, a strong sentiment and way of being that I develop from Rousseau’s educational precepts in Émile, which makes the citizen feel free and robust in dependence and boundedness. Autonomy, then, comes from the active exercise of oneself, physically and mentally, in an environment bounded by things, and this results in a sentiment of vigour, a vitality that produces confidence and poise, which then entices further activity. (shrink)

Real-life stories from teachers who share their passion for shaping the lives of young people today.

'ground-breaking anthology... wide array of perspectives on WW1, from both sides of the fighting' -B. Adler, Choice 'a very fine anthology' -Times Literary SupplementThe First World War inspired a huge outpouring of writing that, until recently, was thought to be almost the exclusive preserve of men. Yet the war also acted as a catalyst which enabled women writers to find a literary and political voice. This anthology bears witness to the great variety and scope of women's writing about the war. (...) Covering the years 1914-1930, the book brings together little-known writing from across the world, drawing on a wide spectrum of genres from letters and diary entries to essays, novels, and short stories. Among the celebrated writers featured in this anthology are: Radclyffe Hall, Sylvia Pankhurst, Maud Gonne, Rebecca West, May Sinclair, Olive Schreiner, Colette, Vera Brittain, Gertrude Stein, Katherine Mansfield, HD, and Virginia Woolf. (shrink)

The proposed heavy dependence on Pavlovian conditioning to account for social behavior confounds phylogenically and ontogenically selected behavior patterns and ignores the extension of the principle of selection by consequences from biological to learning theory. Instead of acknowledging operant relations, Domjan et al. construct vaguely specified mechanisms based upon anticipatory cost-benefit considerations that are not supported by the Pavlovian conditioning literature.

In Balcony in the Forest, Julien Gracq composes a soundscape in four dimensions: he establishes an undulating background by involving spatial events; he forms temporal figures by involving material affects—spatial events and material affects extracted from depths before being enveloped by a resonant place. Each of the four dimensions has a particular relationship to the sounds of power and the power of sound, and it is up to the reader to decide whether the soundscape composed in and by the writing (...) makes this double... (shrink)

This paper concerns late 1920 s attempts to construct unitary theories of gravity and electromagnetism. A first attempt using a non-standard connection—with torsion and zero-curvature—was carried out by Albert Einstein in a number of publications that appeared between 1928 and 1931. In 1929, Tullio Levi-Civita discussed Einstein’s geometric structure and deduced a new system of differential equations in a Riemannian manifold endowed with what is nowadays known as Levi-Civita connection. He attained an important result: Maxwell’s electromagnetic equations and the gravitational (...) equations were obtained exactly, while Einstein had deduced them only as a first order approximation. A main feature of Levi-Civita’s theory is the essential use of the Ricci’s rotation coefficients, introduced by Gregorio Ricci Curbastro many years before. We trace the history of Ricci’s coefficients that are still used today, and highlight their geometric and mechanical meaning. (shrink)