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Philosophical discussion of the continuous-discrete dichotomy often includes discussion of the so-called analog-digital dichotomy. Some work has gone into showing how these two pairs are actually quite different, and that the second is not even a proper dichotomy. Less attention has been paid to the continuous-discrete dichotomy on its own terms, which will be the focus of the present essay. First, I offer some clarity about the nature of the continuous that has been obscured in some of the literature on this topic. Next, I argue that while the continuous-discrete pair truly is dichotomous (in the sense that the terms are mutually exclusive), it is also best to consider the classification of something as either continuous or discrete as a relative, rather than absolute, matter.
Some authors, such as (Goodman, 1968), have identified the continuous with the analog, and the digital with the discrete. In Maley (2011), I argue that this identification is flawed. Goodman also identifies continuity with density. This is also flawed, and showing why helps to add some clarity to what continuity is, without getting too distracted by precise mathematical details.
After clarifying continuity, I argue that whether something is discrete or continuous is best answered relative to a particular scheme, theory, framework, or interest. If they are thought to be absolute properties, then two undesirable features follow: discreteness or continuity are beholden to fundamental physics, and everything is continuous or everything is discrete.
