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The continuum gambit is a mathematical approach to eternalism—the denial of nebulosity. When it becomes obvious that things are not either this or that, but somewhat both and neither—a typical manifestation of nebulosity—the continuum gambit suggests that reality is a matter of shades of gray, corresponding to numbers on a continuous scale.
Often, modeling a phenomenon as a continuum works well. Often, it’s actively misleading instead. Even when it works well in practice, a continuum is rarely (if ever) how the phenomenon actually works.
The continuum gambit attempts to preserve eternalism in the face of nebulosity by confusing a mathematical model with reality.
For example, probability theory models uncertainty with a continuum, thereby attempting to regain certainty at a meta level, and to reassert optimal control with decision theory. As a practical tool, probability theory is sometimes extremely effective—and sometimes totally useless. (“Knightian uncertainty” is not amenable to probabilistic modeling.)
Bayesianism is the eternalistic insistence that probability theory is always applicable, and even that it is a complete account of rationality or epistemology. (“Probability theory does not extend logic” is a technical refutation of one of the sources of this delusion.)
Fuzzy set theory applies the continuum gambit to the problem of the nebulosity of categories. (Nebulous categories will be a major topic in the dualism chapter.) Whereas probability theory is often at least useful in practice, fuzzy set theory fails almost completely.
(I cover the failures of Bayesianism and of fuzzy set theory in detail in Part One of In The Cells of the Eggplant.)