I have posed what I’ve called, perhaps a bit over-dramatically, the ‘provocative’ thesis that the ideas Jung extracts from the Pauli dream series in Psychology & Alchemy (GW XII) have not the general validity he claims for them; that they’re really just an interpretation of a single subject’s psychological and narrative world. I have made a case for this thesis in one of my previous posts; I’m going to do the converse now and state the case against.
What, then, could we say in support of the idea that Jung’s ideas have general validity, after all?

1. We would start by conceding that the process of personal development that Jung traces, within the dream series, is an individual case; the materials are exclusively drawn from a single narrative and psychological world.
At this point, Jung’s careful arrangements that precluded influences come into play: to make the record of this individual subjectivity as pure as possible, he and his colleague abstained from interpretation, and merely guided the subject to collect and narrate the record of psychological contents on his own (§§ 45, 51). The upshot is not, then, that this was an “objective, natural process left to its own devices” (pace §§ 325, 328), but that this was a record of an individual’s narrative and psychological world, (comparatively) untouched by interpretive strategies as well as unusually well observed and recorded. It was the narration, not the ongoing psychological processes, which was kept uninfluenced.
What Jung’s own, subsequent interpretation in the book added to this was an inference to underlying dynamics (i.e. what he called the individuation process). Such inferences are not helped, but rather obscured by constant “amplification”, the practice of mentioning similar-looking or sometimes merely similarly named symbolisms elsewhere, in arbitrary cultural artifacts. Or perhaps they helped Jung, in the way heuristics or mnemonics can help with understanding complex or abstract relationships. But the value of the discussion lies not in those, but in what they helped find, namely, the psychological functions of what was going on in that individual subjective world: how the appearances of the Shadow or the Wise Man helped integrate unconscious contents into consciousness, how the emerging and self-regrouping shapes (mandalas) indicated progress or regress in centering the personality, and so on. These psychological dynamics are what connect the Pauli series interpretation with Jung’s other works, and what can help illuminate the theories in those works, such as in the Two Essays. (Pointers to other texts that just accumulate more pictures of mandalas don’t.)
The most important insight up to here is that we always have to interpret meaning, even numinous or “archetypal” meaning, within (or relative to) a given narrative and psychological world; that every such world is unique, and we can’t simply generalize from it.
Jedes Leben ist […] eine Verwirklichung eines Ganzen, das heißt eines Selbst, weshalb man die Verwirklichung auch als Individuation bezeichnen kann. Mit jedem Träger aber ist auch eine individuelle Bestimmtheit und Bestimmung gegeben […] (§ 330)
It follows that we must be careful in the question how we generalize: we cannot simply collect similar-looking symbols (such as characters like the Wise Old Man or shapes such as the mandala) and identify them with each other across individual narrative worlds. If indeed there is something that cuts across such worlds, as Jung generally assumes, it is likely less obvious than he made it seem: it might be something like functions in the individuation process (something underlying, abstract); there may be some motif connections, too, but these would not be simple similarities (“looks like a mandala in this world, looks like a mandala in that world, so it must be the same thing…”), and they certainly wouldn’t be demonstrated by merely enumerating them in pages after pages of “comparative” descriptions. They would be related more in the manner in which literary writers exert influence by reading each others’ books and taking up and transforming motifs from one another; perhaps more directly in the form of something like intertextual references and allusions. Their study would require a nuanced approach, and their theoretical import would likely be complex and indirect (rather than simply of the direct kind where some fixed symbols always have the same function, as Jung supposed; see GW XVI, § 339).
But we should insist, with Jung, that there is still something general here: that is the underlying dynamics, the psychological functions. And there is, in a sense, an illustration or exemplification to be extracted from the Pauli dream series. (It just doesn’t work via registering symbol similarities; it works by reading the unfolding narrative in a way that helps us further understand the underlying dynamics.) We should drop the false pretense, however, that this is an empirical generalization gathered from “many” samples.
2. Just as the case for the provocative hypothesis, the case against it is built entirely from elements of Jung’s own views. We don’t need a major reshaping of his ideas, or introduce any counterbalancing components into them. We do have to correct some ambiguities and errors, however, and possibly emphasize some of his notions more strongly than he himself did.
It is also true that Jung’s own tendency was the opposite. He framed his discussion in a way that suggests he wanted to make claims of quasi-empirical, scientific evidence, and that he tried to make his views appear as if he had provided such evidence for them. This has invited, and deservedly in my view, objections of pseudoscientific tendencies. And this must be taken seriously. Science is scientific because it follows a certain very rigorous method; it also works only within specific domains where empirical observation is possible. What Jung does — at least where he has produced his most interesting writings — does neither. It’s not itself science; it’s not anticipating new paradigms of science (be it relativity, quantum theory, chaos theory, or systems theory); it doesn’t need to be any of that to be either effective therapy, a path towards personal development and individuation, or a valuable philosophical theory. It does, however, need to be intellectually honest, willing to admit and correct mistakes; if it can achieve that, it will be possible to incorporate new thinking that has come up in the decades since Jung’s own writing: from logic, narratology, even the theories of meaning or the methods of inquiry (i.e. from philosophy). It’s true: none of these are very fashionable right now, and they won’t lend Jungian views the prestige that a perceived status as an objective science would have. (But then so won’t continuing along pseudoscientific rhetoric.) On the up side, though, they might inject fresh blood and update some of its ideational backbone. In the best of all possible scenarios, we might make some progress on a whole range of quite fascinating topics.