Louis Narens

Written by one of the masters of the foundation of measurement, Louis Narens' new book thoroughly examines the basis for the measurement-theoretic concept of meaningfulness and presents a new theory about the role of numbers and invariance in science. The book associates with each portion of mathematical science a subject matter that the portion of science is intended to investigate or describe. It considers those quantitative or empirical assertions and relationships that belong to the subject matter to be meaningful (for that portion of science) and those that do not belong to be meaningless. The first two chapters of the Theories of Meaningfulness introduce meaningfulness concepts, their place in the history of science, and some of their traditional applications. The idea that meaningfulness will have different, but interrelated uses is then introduced. To provide formal descriptions of these, the author employs a powerful framework that incorporates pure mathematics, provides for qualitative objects and relations, and addresses the relationships between qualitative objects and pure mathematics. The framework is then applied to produce axiomatic theories of meaningfulness, including generalizations and a new foundation for the famous Erlanger Program of mathematics. The meaningfulness concept is further specialized with the introduction of intrinsicness, which deals with meaningful concepts and relations that are lawful and qualitativeness, which is concerned with qualitative concepts. The concept of empiricalness is then introduced to distinguish it from meaningfulness and qualitativeness. The failure to distinguish empiricalness from meaningfulness and qualitativeness has produced much confusion in the foundations of science literature and has generated many pseudo-controversies. This book suggests that many of these disappear when empiricalness is intersected with the other concepts to produce "meaningful and empirical relations," "empirical laws," and "qualitative and empirical concepts." A primary goal of this book is to show that the new theories of meaningfulness and intrinsicness developed in this book are not only descriptive but are also potent. Asserting that they do more than codify already existing concepts the book: *works out logical relationships between meaningfulness concepts that were previously unrecognized; *clarifies certain well-known and important debates by providing rich languages with new concepts and technical results (theorems) that yield insights into the debated issues and positions taken on them; and *provides new techniques and results in substantive scientific areas of inquiry. This book is about the role of mathematics in science. It will be useful to those concerned with the foundations of science in their respective fields. Various substantive examples from the behavioral sciences are presented.

Theories of Meaningfulness

Brian Skyrms

Utilitarianism began as a movement for social reform that changed the world, based on the ideal of maximizing pleasure and minimizing pain. There is a tendency to enter into debates for and against the ethical doctrine of Utilitarianism without a clear understanding of its basic concepts. The Pursuit of Happiness now offers a rigorous account of the foundations of Utilitarianism, and vividly sets out possible ways forward for its future development. To understand Utilitarianism, we must understand utility: how is it to be measured, and how the aggregate utility of a group can be understood. Louis Narens and Brian Skyrms, respectively a cognitive scientist and a philosopher, pursue these questions by adopting both formal and historical methods, examining theories of measuring utility from Jeremy Bentham, the founder of the Utilitarian movement, to the present day, taking in psychophysics, positivism, measurement theory, meaningfulness, neuropsychology, representation theorems, and the dynamics of formation of conventions. On this basis, Narens and Skyrms argue that a meaningful form of Utilitarianism that can coordinate action in social groups is possible through interpersonal comparison and the formation of conventions.

Philosophical and Psychological Foundations of Utility

The Pursuit of Happiness

There are many books on lattice theory in the field, but none interfaces with the foundations of probability. This book does. It also develops new probability theories with rigorous foundations for decision theory and applies them to specific well-known problematic examples. There is only one other book that attempts this. It uses quantum probability theory from physics. The new probability theories developed in this book are different; they are not borrowed from physics but are explicitly designed for decision theory. Contents:IntroductionBasic Lattice TheoryPseudo Complemented Distributive LatticesProbability and CoherenceRationality, Heuristics, and Human Judgments of ProbabilityOrthomodular Modeling of Psychological Paradigms Readership: Researchers in probability theory, logic and mathematical psychology. Key Features:Systematic, foundational development of probability theories based on Boolean and non-Boolean algebrasNew theoretical foundations for theories of belief that emphasize the logical structure of event spacesNew methods for modeling the Kahnemann and Tversky heuristics and other psychological paradigms based on intuitionistic logic and a generalization of quantum logicKeywords:Probability on Lattices;Decision Theory;Intuitionistic Logic;Lattice Theory

With Applications to Psychology

Probabilistic Lattices

Utilitarianism is one of the most famous ethical doctrines, based on the ideal of maximizing pleasure and minimizing pain. But Utilitarians and their opponents lack a clear scientific and philosophical understanding of its foundations, the measurement and aggregation of utility. This is what The Pursuit of Happiness now offers.

Louis Narens

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