Zellig Harris framed it as a correlation: if A and B differ more in meaning than A and C, their distributions will “often” differ more as well; “difference of meaning correlates with difference of distribution” (Harris, 1954, p. 156). His example: oculist and eye-doctor occur in almost the same environments; oculist and lawyer do not. J. R. Firth supplied the famous motto, “You shall know a word by the company it keeps!”, illustrated with the collocations of ass (you silly —, don't be such an —) (Firth, 1957, p. 11).
Tiny example. If in a corpus coffee occurs with cup, brew, bitter and beans, and tea with cup, brew, bitter and leaves, the hypothesis predicts that coffee and tea will be closer to each other than to screwdriver. That is what word2vec and embeddings do at scale (M. Mitchell, 2019, ch. 11).
Wittgenstein, with care. Firth quotes Wittgenstein in that very passage (“the meaning of words lies in their use”) and speaks of language games (1957, p. 11). But “meaning is use” is not “meaning is distribution”. First, Wittgenstein restricts it to a large class of cases, not all (Wittgenstein, 1953/2009, §43). Second, his “use” is an expression's place in human activities (language games, forms of life, rules followed and corrected), not the co-occurrence of strings in a corpus; Bender & Koller (2020) insist on precisely this (2020, p. 5191). Third, neither Harris nor Firth identified meaning with distribution: Harris stresses that meaning is not a property of language alone but “a general characteristic of human activity” (1954, p. 151), and Firth treats collocation as one mode of meaning among others, alongside the context of situation (1957, pp. 11–12). Brunila & LaViolette (2022) show that NLP tends to read the two as if they said the same thing.
For an inferentialist, moreover, what fixes a content is not which words an expression occurs with but what follows from it and what it rules out: a normative relation, not a statistical one. Whether distributional models capture any of that inferential profile, and how, is exactly what is under discussion (see form vs meaning).