Inhabitants of a Hume world are right to explain their world with this Hume-world theory. They just happen to live in a world where no prediction is possible.
Just because what you believe happens to be true, doesn't mean you're right to believe it. If I walk up to a roulette wheel, certain that the ball will land on black, and it does--then I still wasn't right to believe it would.
Hypothetical Hume-worlders, like us, do not have the luxury of access to reality's "source code": they have not been informed that they exist in a hypothetical Hume-world, any more than we can know the "true nature" of our world. Their Hume-world theory, like yours, cannot be based on reading reality's source code; the only way to justify Hume-world theory is by demonstrating that it makes accurate predictions.
Arguably, it does make at least one prediction: that any causal model of reality will eventually break down. This prediction, to put it mildly, does not hold up well to our investigation of our universe.
Alternatively, you could assert that if all possibilities are randomly realized, we might (with infinitesimal probability) be living in a world that just happened to exactly resemble a causal world. But without evidence to support such a belief, you would not be right to believe it, even if it turns out to be true. Not to mention that, as others have mentioned in this thread, unfalsifiable theories are a waste of valuable mental real estate.
David Hume called causation the “cement of the universe”, and he was convinced that psychologically and in our practices, we can’t do without it.
Yet he was famously sceptical of any attempt to analyze causation in terms of necessary connections. For him, causation can only be defined in terms of a constant conjunction in space and time, and that is, I would add, no causation at all, but correlation. For every two events that seem causally connected can also, and without loss of the phenomenon, be described as just the first event, followed by the second. It’s really “just one damn thing after another”. It seems to me we still cannot, will not and need not make sense of the notion of causation (virtually no progress has been made since Hume's time).
There seems no need for another sort connection besides the spatio-temporal one, nor do we perceive any. In philosophy, a Hume world is a possible world defined in this way. All the phenomena are the same, but no necessary connections hold between the supposed relata. Maybe one should best imagine such a world as a game of life-world, but without a fundamental level governed by laws and forces; or as a movie, made of frames that are not intrinsically connected to each other. So, however strong the psychological forces that drive humans to accept further mysterious connections: Shouldn't we just stop worrying and accept living in a Hume world? Or are there actual arguments in favour of "real" causation?
Yes. There's the problem of order. What accounts for all the order in the world?It is remarkably ordered. If no special connections hold between events, why isn’t the world pure chaos? Or at least much more disordered? When two billard balls collide, never does one turn into an pink elephant.To explain this, men came up with laws of nature (self-sustained or enforced by a higher being).
So, there's the paradox: On the one hand, we have to postulate special connections to account for an orderly world like ours; on the other, we cannot give a proper account of these connections.
Inflationary cosmology to the rescue.
I won't go into the details (but see the nontechnical explanation and some further philosophical implications here).
Suffice it to say that
1) inflationary cosmology is mainstream physics, and
2) it postulates a spatially infinite universe in which every event with nonzero probability is realized infinitely many times.
How does this help to solve our paradox? The solution seems straightforward:
In an infinite universe of the right kind, order can locally emerge out of random events. Our universe is of the right kind.
So, we can account for the order in our observed (local) part of the universe.
Random events just happen, one after another, there is no need for mysterious causal connections. We throw them out but keep the order.
Problem solved.
Q: But if this is true, it’s the end of the world. Thinking, action, science, biases and many, many more concepts are causal ones. How can we do without them?
A: life is hard, get over it.
Q: But the theory is untestable?!
A: Falsificationism is dead; we have other evidences in favour (see below).
Q: But isn’t the theory self-defeating?
A: It is certainly odd to have a theory informed by experiences and high-level physics that tells us that, strictly speaking, there are no experiences or sciences. But it doesn’t seem incoherent to me climb the ladder and then throw it away.
And, looking at the bright side:
In addition to being non-mysterious and conceptually sparse, this might allow to solve some additional (would-be?) hard problems:
qualia, clustering of tropes, time travel-paradoxes, indeterministic processes: All easy or trivial when a thouroughly indeterministic universe is considered.
So. What do you think – if you can?