| TLP# | Wittgenstein | UM |
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The Tractatus assumes a closed world: what is not the case is thereby false. The UM's open-world epistemology corrects this: s = 0 is ignorance, not falsity.
The Tractatus assumes a closed world throughout: what is not the case is thereby false (2.05, 2.06). The UM's open-world epistemology corrects this at exactly one point: s = 0 is ignorance, not falsity. What is not observed is not thereby non-existent. "What we cannot speak about" is not "what is false" but "what we do not know."
This correction is Wittgenstein's own, made in the Investigations: the Tractatus's rigid logical form gives way to the plurality of language games, and the sharp true/false boundary gives way to the graded, context-dependent, open-world epistemology that the UM formalizes.
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In UM terms: the limits of my event space E mean the limits of what I can predict. Events outside E are not just unpredictable — they are unrepresentable.
This is the strawberry theorem: a token-level language model has token-level event spaces. The question "How many r's in strawberry?" requires character-level event spaces. The token-level model cannot answer — not because it lacks knowledge, but because the question is inexpressible in its event space.
The character-level model has different event spaces: each character is an atomic event. It can represent "s", "t", "r", "a", "w", "b", "e", "r", "r", "y" individually. The token-level model sees "straw" + "berry" — no individual characters, no way to count them.
Wittgenstein anticipated this exactly: what cannot be expressed in the language (event space) cannot be thought (predicted). The limits of the language ARE the limits of the world.