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That's a really restrictive and explicit demarcation of "formal language". I'd happily describe logic as formal language and then go hunting for places which se
by tel 12y ago
That's a really restrictive and explicit demarcation of "formal language". I'd happily describe logic as formal language and then go hunting for places which seem to have non-trivial interactions with logic.
- jordigh 12y agoWell, if you define it to be broad enough, then you are correct by definition. My point here is that there is a big, broad cultural gap between mathematics and programming that you are not going to breach merely by saying that a lot of mathematics is about formal languages (in the nontechnical sense of "formal language"). Far from it. Most of mathematics does not talk about formal languages and most of mathematics itself uses very informal language. It looks forbidding to outsiders, but there are many linguistic styles, fashions, abbreviations, shorthands, jokes, puns, and conventions in mathematical writing, very little of which is easy to algorithmically feed into a computer.
- tel 12y agoSure, and I'm not claiming that you must unify them. Or that you can't. I'm also not saying that the language of mathematics is a formal language, but instead that it shares structure with them. The very notion of the interplay between a theory and its model is not dissimilar. I'm not trying to absolve a cultural gap. Nor am I trying to claim that if you dropped a mathematician into a programming role they would thrive, or visa versa. I'm simply trying to claim that there is a whole lot of similarity between the two and refutations of that are silly. Seeking a clear-cut demarcation between fields is a little silly as an exercise. Finally, exploiting the similarity is powerful. Both fields benefit from this fact already and the more widespread the idea is the better.