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Culture War Roundup for the week of January 15, 2024

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The idea that you can have a prior on bloxors being greeblic strikes me as a type error. The domain of priors are propositions, that is, assignments of truth values to possible world-states, not strings of words; to the extent that we pretend assign a probability to a string of words, this is only enabled by us having an understanding that the string encodes a world->bool map (or at least a distribution on such maps, to allow for linguistic uncertainty). Without knowing the definition of "bloxors" and "greeblic", I'm not aware of any canonical interpretation this sequence of words has that yields a truth value; and it does not seem reasonable to expect that any string actually encodes a valid map, any more than it is to expect that any line noise encodes a valid polynomial.

In fact, my prior on strings of Latin characters tells me that the bloxors statement is very likely to not encode a map/proposition, and therefore to not have a probability.

The domain of priors are propositions, that is, assignments of truth values to possible world-states, not strings of words

From a mathematical point of view, you can have a probability function defined over all sorts of domains. IIRC, Rudolf Carnap initially defined probability functions over sentences (in the sense of strings of symbols in an artificial language) while John Maynard Keynes and Harold Jeffreys did so over propositions (meanings of sentences) and later Carnap over models (in the formal logic sense). Then there's frequentism and other event-based definitions...

However, I agree with your comment, as we are thinking from the point of view of probability as an epistemologically meaningful magnitude, e.g. a measure of degrees of belief or evidential support. "Bloxers are greeblic" is not part of my languages. In general, I shall have at least some background evidence about any proposition in a language I speak, and thus not have pure uncertainty.

I mean, of course I'm not saying it's impossible to define a distribution on arbitrary strings or anything; but I don't think that this is the intended interpretation of any putative "anything has a probability" maxim one would ascribe to LW-style Bayesianism.