Theory: The Logic of Science

Probability Theory: The Logic of Science


“Alan: Or, My Friend the Utility Monster”
Going beyond the conventional mathematics of probability theory, this study views the subject in a wider context. It discusses new results, along with applications of probability theory to a variety of problems. The book contains many exercises and is suitable for use as a textbook on graduate-level courses involving data analysis. Aimed at readers already familiar with applied mathematics at an advanced undergraduate level or higher, it is of interest to scientists concerned with inference f… more about book…

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“Alan: Or, My Friend the Utility Monster”(r/philosophy)

The weak point in the theory of utilitarianism being that, when one attempts to quantify utility and Bentham’s “sovereign masters of pain and pleasure”, you inevitably arrive at some aspect of expected utility theory. This yields, in some cases, an assumption that humans are fully rational actors capable of quantifying risk, uncertainty, and the future utility of their actions in an incomprehensibly complex world.

I don’t mean to imply that attempts to quantify subjective categories “ought” or “ought not” to be done, only that when people attempt to do so on the behalf of others instead of on an individual basis wherein one can rank one’s values ordinally, it invariably ends with the arbiter extrapolating and homogenizing the “wants and needs of the people”. This belongs in the fanciful cloud cuckoo lands of utopians and class-based theorists.

Additionally, the limitations placed on us by our philosophic views of probability and uncertainty can’t be emphasized enough. Does objective probability exist or are probabilities merely measures of man’s subjective uncertainty about the world à la Bayes? Personally, I’m an advocate of the later.

That said, I do enjoy and believe in many aspects of individualistic utilitarianism in which the ordinal ranking of values may occur. My favorite topic to read about is the von Mises brothers, their conceptions of uncertainty, and how they relate to Ludwig’s a priori economic theories. I recall Ludwig saying that he subscribed to Richard’s theory of “case probabilities” and aspects of the Frequentist method while still rejecting logical positivism. As a proponent of the subjective theory of value, I suspect he was a Bayesian at heart. Of course, if you read E.T. Jayne’s book, you’ll see that the two methods are one-and-the-same under the more general subjectivist interpretation of probability.


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E. T. Jaynes

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Cambridge University Press

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Probability Theory: The Logic of Science

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