Why do so many Anglo-American philosophy departments still prefer to teach ideas that depend on symbolic logic? Or in another light, why is so much contemporary philosophy in America still dedicated to analysis and ideals of "clarity" that depend on "higher order" languages?

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I'm not sure what is meant by "prefer to teach ideas that depend on symbolic logic". Most departments teach e.g. aesthetics, political philosophy, the history of early modern philosophy, the philosophy of mind, and so on and so forth -- and symbolic logic features little if at all in those courses. (When did you last see a quantifier when discussing how it is that we can apply emotion terms to music, or discussing whether we can justify more than a minimal state, etc., etc.?)

And a concern for clarity has little to do with symbolic logic (and nothing at all to do with 'higher order' languages). Clarity matters because we want to seek the truth co-operating with other enquirers. And we can't co-operate with other enquirers by together subjecting our conjectures to stern test and criticism and proposing revisions if we can't manage to make ourselves very plainly understood to each other.

Of course there are always intellectual pseuds who get off on talking to themselves with willful obscurity -- but do you really want to go in for that kind of intellectual masturbation?

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