Sometimes in baseball, the batter hits a pop fly up and over towards the outfield, about 1/2 way between two of the outfielders. They both prepare to catch the ball and then both leave it to the other fielder, and the ball drops between them. This is called a blooper. The same thing happens in doubles tennis, when a ball comes down the center of the court and each of the players on the receiving side leave it to the other player - and the ball goes between them. With a bit of a stretch, here goes an analogy....
Something similar has happened in the gap between the fields of language and mathematics. On one side of the gap, mathematicians think they have gotten all they need from language and that linguists have the rest covered. After all, the parts of speech have been identified and sentence structure has been completely understood. Meanwhile linguists think they have gotten all they need from language and that mathematicians have the rest covered. After all, the workings of logic have been extracted from language and are completely understood.
I claim there is an important "ball" of content being dropped between these two fields of study: the central topic of meaning. Both mathematicians and linguists seem incapable of coming to grips with a good definition of "meaning" or "truth" and I wonder if any current practitioners think the other team has it figured out?
The whole point of having a crisply defined data structure to store the content of external expressions is that it implements meaning. You can argue about the proper data structure but the conversation moves way from vagueness in important details.
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