Acknowledgements. 1. Introduction. 2. Pooled Beneficence; G. Cullity. 3. Garrett Cullity's Response to an Imperceptibility Challenge; J.H. Sobel. 4. Perceiving Imperceptible Harms: With Other Thoughts on Transitivity, Cumulative Effects, and Consequentialism; D.H. Regan. 5. The Least Sub-noticeable Difference; T. Tannsjo. 6. Utility Pumps and the Value of Partial Compliance; M.J. Almeida. 7. Utilitarianism and Interpersonally Comparable Cardinal Utility: Some Implications of Just Perceivable Increments of Happiness; Y.-K. Ng. 8. Money Pump with Foresight; W. Rabinowicz. Index.

The papers collected here represent the most recent work on a much­ neglected problem in practical reasoning. It is the problem of imperceptible harms and benefits. It is perhaps better to characterize the problem as a collection of puzzles or paradoxes, since those who deny the existence (or possibility) of imperceptible decrements (or increments) face problems no less perplexing than those who affinn their existence. The puzzles and paradoxes combine very practical and pressing worries about our obligations to relieve starvation, mitigate suffering and conserve resources, with deep metaethical worries about the nature of practical rationality. I use these brief introductory pages to familiarize the reader with the basic set of problems examined in this collection. Most of us think that an action cannot be wrong if its effects are entirely and always imperceptible.· Jonathan Glover's fanciful example of the 100 armed bandits and the 100 Wlarmed tribesman clearly illustrates a deep worry with such moral reasoning.