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Good point. It should be a B.Sc. Indeed, the current undergraduate degree at Southampton IS a B.Sc.

So why wasn't my degree a B.Sc? Short answer: it was a while ago.

Psychology historically was less empirical--more about individuals articulating grand theories of their own, which were hard to test (e.g., Freud). Nowadays, however, nearly all academic psychologists are scientists who aim to produce piecemeal theories, or to effect adjustments to them, as members of a critical but interactive community. So it's nearly always B.Sc, not B.A., whereas that was less the case before.

Still, some aspects of psychology are a bit artsy. These include the more new-age spiritual part, and the postmodernist constructivist part. So, I think that psychology is never quite a science-like as STEM subjects.