He notes in the first lecture that he thinks it is impossible to disprove determinism. A determined determinist can always resort to the argument: all of your senses are deceiving you and you are simply experiencing some predetermined script of qualia (he uses the analogy of watching a movie a second time).
I think the invulnerable argument for it is even simpler than that: whatever apparently non-determined behavior we observe may only appear that way because we don’t yet know the rules underlying it.
Any system will appear unsystematic until the precise rules governing it are known.
Since we can’t ever demonstrate that we’ve exhausted all possible theories of a system, the possibility always remains that tomorrow we would discover a perfectly effective one, and from that point the system would be as plainly deterministic as anything else.
In other words: we lack the capability to definitively distinguish between our own lacking knowledge and a system’s (potential) intrinsic non-determinism.
Right: if you are a brain-in-a-vat observing some powerful play, what can you say about the world in which the vat is embedded? (or for that matter, how is it that you can even be made aware of the vat’s existence?)
