Bruce Langtry's ‘God, the Best and Evil’ is a fine contribution to the literature. Here, I review the contents of the book, and then provide some critical remarks that, as fas as I know, have not been made elsewhere. In particular, I argue that his criticism of my formulations of logical arguments from evil (in my Arguing about Gods) is unsuccessful.

Although expected utility theory has proven a fruitful and elegant theory in the finite realm, attempts to generalize it to infinite values have resulted in many paradoxes. In this paper, we argue that the use of John Conway's surreal numbers shall provide a firm mathematical foundation for transfinite decision theory. To that end, we prove a surreal representation theorem and show that our surreal decision theory respects dominance reasoning even in the case of infinite values. We then bring our theory (...) to bear on one of the more venerable decision problems in the literature: Pascal's Wager. Analyzing the wager showcases our theory's virtues and advantages. To that end, we analyze two objections against the wager: Mixed Strategies and Many Gods. After formulating the two objections in the framework of surreal utilities and probabilities, our theory correctly predicts that (1) the pure Pascalian strategy beats all mixed strategies, and (2) what one should do in a Pascalian decision problem depends on what one's credence function is like. Our analysis therefore suggests that although Pascal's Wager is mathematically coherent, it does not deliver what it purports to, a rationally compelling argument that people should lead a religious life regardless of how confident they are in theism and its alternatives. (shrink)

Fechner's conception of psychophysics included both “outer psychophysics” the relation between stimulus intensity and the response reflecting sensation strength, and “inner psychophysics” the relation between neurelectric responses and sensation strength. In his own time outer psychophysics focussed on the form of the psychophysical law, with Fechner espousing a logarithmic law, Delboeuf a variant of the logarithmic law incorporating a resting level of neural activity, and Plateau a power law. One of the issues on which the dispute was focussed concerned the (...) appearance of contrasts if the overall illumination was increased or decreased; another issue was the question of whether a sensation of a “just noticeable difference” established for one value of a sensory dimension appeared the same for a value elsewhere on the dimension. The development of “inner psychophysics” led through the works of Delboeuf, Solomons, Jastrow, and Thurstone to modern signal detection theory. A third line of research, devoted to the question of what was meant by the “measurement” of sensation strength, stemmed from the criticism of Fechner's work by von Kries (1882) and others. Although a valid body of science could be built up without the intervening variable called “sensation strength,” such a science might be a cumbersome representation of reality. When an optical contrast is set up, and its overall illumination is increased or decreased, subjective contrasts involving medium levels of lightness vary little as illumination varies (as a power law based on sensation ratios or a logarithmic law based on sensation differences predict), but subjective contrasts involving extreme levels of lightness might be subject to the effects of other variables. (shrink)

In this paper I try to make as much sense aspossible of, first, the extensive philosophicalliterature concerned with the status of `Wateris H2O' and, second, the implications ofPutnam's invention of Twin Earth, anotherpossible world stipulated to be just like Earth, except that water is XYZ, notH2O.