Reviewed by: Luck Theory: A Philosophical Introduction to the Mathematics of Luck by Nicholas Rescher Steven D. Hales RESCHER, Nicholas. Luck Theory: A Philosophical Introduction to the Mathematics of Luck. Cham, Switzerland: Springer, 2021. xxxiii + 90 pp. Cloth, $70.00 Usually luck is thought of as something chancy, such as an unlikely occurrence, or something that might have easily not happened. Other kinds of luck seem like inexorable fate, like the bad luck of coming of age just in time for a wartime draft. In his latest book on luck, Nicholas Rescher focuses on the first kind, stochastic luck. In his first book on the topic, Luck: The Brilliant Randomness of Everyday Life (1995), Rescher defended a probability account of luck, one of the few contemporary philosophers to do so. Here he is back for more of the same, but centered on neither the philosophy nor the psychology of luck. Instead, his approach in his new book is mathematical and formal. He is convinced both that “virtually all consequences of the theory are intuitively acceptable” and also that “virtually all intuitively acceptable features of luck can be verified in the theory.” The claim that all the consequences of his theory are intuitively acceptable will come as a surprise to defenders of moral luck. In half a paragraph, Rescher dismisses the topic entirely: “[S]trictly speaking, there is no such thing as ‘moral luck’” (repeated twice). There is a long history of attempting to formalize and mathematize our understanding of luck. The origins of probability theory are due to Cardano, Pascal, Fermat, de Montmort, and others trying to solve gambling problems, quintessential examples of good and bad luck. By 1718 de Moivre had declared that good luck meant nothing more than chancy success (being “a Gainer at play”). Now, many of the early probability theorists took themselves to be eliminativists about luck: To understand the probability calculus was to recognize that luck is not a real thing. By contrast, Rescher thinks luck is real and is giving a theory of what it is. But what’s wrong with the eliminativist approach? If probability theory tells us all about chanciness, and luck is just chanciness, why hang on to an antiquated notion like luck? Rescher’s answer is familiar in the luck literature: Not everything improbable is a matter of luck. It is improbable that a coin toss would come up tails three times in a row, but unless you had a wager riding on it, it’s not a matter of luck. This feature is commonly known as a [End Page 152] significance condition, and Rescher endorses it. His mathematics of luck is built out of the probability calculus plus a calculus of value. The project of providing a mathematics of luck smacks of a solution in search of a problem. Providing a formal machinery lends an unjustified air of precision, as if at last we are reading the book of nature in its original language. For example, Rescher’s Basic Luck Equation is λ{O} =| O| – E. This equation means that the luck of an outcome (λ{O}) is equivalent to the difference between that outcome’s yield for an agent and the expectation of that yield. This equivalency sets up a linear relationship, but why think that’s how luck works? Maybe luck should be measured on a logarithmic scale, as the Richter scale measures the power of earthquakes, or luck could be a heteroscedastic variable that varies unequally as the result of yield and expectation. Or it could be that luck is something else altogether. Rescher writes that “lack of control is neither a sufficient nor a necessary condition for luck,” for instance, but he barely engages with the considerable literature on this idea. For Rescher, the inevitable cannot be lucky (Theorem 5). While initially appealing, that has some counterintuitive consequences. For example, if the world is deterministic and everything is inevitable, then nothing is lucky. Intuitively we are lucky that the constants of the universe hit the sweet spot of making life possible, but not for Rescher, given that those constants were nomologically necessary. We are neither lucky that God exists (since his existence would be necessary) nor unlucky...
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