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Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: The Promise and Peril of Finite Sets, published by davidad on December 10, 2021 on The AI Alignment Forum. Has this ever happened to you? But how can we decide whether this {species/moral theory/consensus node/quantum world} is actually 2 different things, or just 1 thing? Or does it even count at all? The underlying cause of such dilemmas is that somebody, somewhere in the setup of your ontology and the framing of your problem statement, explicitly or implicitly, made the following move: For simplicity of analysis, we assume that X is a finite set. The Promise This is an incredibly popular simplifying assumption, easily competitive with "we assume this distribution is Gaussian" and "we neglect higher-order terms". It's plausibly the single most popular mathematical modeling assumption in the world, because one needs so little background knowledge to make use of it. It's also extremely powerful. Here's just some of the mathematical structure you get for free if you accept the assumption: Computable representation. Saying that X is a finite set can be formalized as ∃n:N.X≅{i:N|i