Surreal decisions

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.     

制定诊疗规范--标准、指南和选择

制定一个诊疗规范,与对一个病人作出具体诊疗方案有相似性.在此两种情况中,人们必须鉴别可用的选择、评价不同选择的结果、确定这些结果是否合乎病人的意愿.诊疗规范可认定为一般的决定--是供给一组病人诊疗而不是一个病人诊疗的建议.     

Agency, authorship, and illusion

Daniel Wegner argues that conscious will is an illusion. I examine the adequacy of his theory of apparent mental causation and whether, if accurate, it suggests that our experience of agency and authorship should be considered illusory. I examine various interpretations of this claim and raise problems for each interpretation. I also distinguish between the experiences of agency and authorship.