The universal/particular distinction is fairly close to the universal/existential distinction. The latter constitutes a problem for empiricism – famously expressed by Russell’s problem of induction, where no existential statement can entail a universal statement.
The similarity comes when one realizes that universals are not given in experience (bracketing to the side for the moment the notion of the ‘given’). Universals do not follow from our experience of particulars in much the same way universal statements do not follow from existential statements.
To clarify what I take to be the similarity: just as no existential statement entails a universal statement, no universal follows from the experience of a particular.
But if all our experience is of particulars (we never experience a universal), how can we arrive at universal statements and universals? (I take a Gilson-ian view myself, where the intellect intuits or abstracts universals from the the experience of existing particulars).
The empiricists (Hume, for example) deny the existence of universals – which lands you with the problem of induction (as well as all the other sceptical problems which stem from the Humean tradition). All we have in experience or otherwise is particulars.Empiricism has the greatest problem with these issues, hence the focus on it.