I'm wondering if there any way to obtain, for a specific Stack Exchange site such as Philosophy, how many questions exist that have 0 upvotes, 1 upvote, -1, etc.
You can do this easily with a SEDE query - this one uses the score of a question instead of upvotes only, as I think that's what you're looking for.
For reference, here is the query. Please note that SEDE is updated only once a week, on Sunday morning.
SELECT Score, COUNT(*) FROM Posts WHERE PostTypeId = 1 GROUP BY score ORDER BY score