If Descartes’s rationalism leaves us with despair, Hume’s empiricism doesn’t provide us with anything more compelling.
A purely rationalist model like Descartes’s that finds its basis in radical doubt first leaves us with despair because we cannot have certain knowledge if we affirm that as a basis for our understanding of the world. Hume’s empirical system (we gain “ideas” via “impressions,” or, to put it a little more simply, any knowledge we gain about reality is gained via sense experience) leaves us with an inability to reasonably believe in the transcendent or the existence of ethical norms. How we ought to act is simply a matter or custom and the social nature of human beings.
That’s why Kierkegaard’s claim, a little less than a hundred years later, that “subjectivity is truth” is necessary. Ethico-religious truth isn’t actually knowable rationally or empirically. That realm of human life is off-limits to objectivity, because objectivity necessarily is disembodied. It’s also important to note that Kierkegaard was approving of both a form of rationalism and empiricism (I think this was likely due to a Kantian influence). He understood that the form of rationalism that affirms abstract truth (mathematics and necessary, logical assertions) and an empiricism that seems to bestow approximate knowledge of how the world functions and historical fact are good, necessary things.
We just can’t submit ethical and religious truth to the same level of inquiry, because they are categorically different spheres. “Knowing” these kinds of truth necessarily implies embodiment of those truths. If we don’t embody selflessness, for example, we reveal that we don’t know that selflessness is a worthwhile virtue. If we don’t embody Jesus, the same can be said. Kierkegaard attacked philosophical abstraction, but only at the service of honesty about our current ethical and religious states. This is a different kind of epistemology — a religious one, and one that doesn’t allow the modernist assumptions about the superiority of human rationality to set the standards for truth in all spheres.