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A tour of the Bayesian perspective on pragmatics This is an introduction to the nested reasoning models (I think that you think that I think…) that I work on. I’ve tried to make this light on mathematical detail (barring the occasional technical digression) in favour of the big picture point, that Bayesian inference and nested reasoning are really great tools for thinking about language and meaning.
“Every block of stone has a statue inside it and it is the task of the sculptor to discover it.” - Michelangelo Borges inhabits a genre you could describe as ironic realism. His stories are liberally sprinkled with a trope where he takes some abstraction of his choice and makes it parochially literal in a deliberately absurd way. In the spirit of making up unwieldy words, I’ll call it:
This post definitely falls under philosophical miscellanea, but is a nice example of a commonality between ancient and modern philosophy. Sextus Empiricus, medieval skeptic, wrote a big (not Aquinas big, but definitely David Foster Wallace big) treatise on Pyrrhonism, a brand of radical skepticism which argues (more or less) that nothing is knowable. More specifically, Empiricus - aptly or inaptly named, I’m not sure - rejects dogma (roughly, scientific knowledge).
“There is strictly speaking no such thing as mathematical proof; we can, in the last analysis, do nothing but point; …proofs are rhetorical flourishes designed to affect psychology” - Hardy “Other thought experiments are less rigorous but often just as effective: little stories designed to provoke a heartfelt, table thumping intuition - “Yes of course, it has to be so” - about whatever thesis is being defended” - Dennett
Here is an elementary observation (I mean “elementary” in the sense mathematicians sometimes use it: i.e. straightforward if you already understand it, otherwise gibberish) that I talked about at MIT’s category theory seminar, relating Grice’s maxims of Quantity and Quality to the mathematical notion of a Galois connection. Inscrutable Summary: For a state space W, the left adjoint of a monotone map (i.e. a left Galois connection), \(L_0\), from a set of utterances U to the poset (ordered by inclusion) \(\mathcal{P}(W)\) is the monotone map \(S_1: \mathcal{P}(W)\to U\) which takes a set of states and returns the strongest true utterance with respect to \(L_0\).