This discussion seems to be confusing reduction with prediction.
It's difficult to say whether perfect prediction is possible, even in principle, because of two reasons.
Firstly, we don't know if the universe is deterministic or not. The problem here is quantum mechanics (well, quantum field theory really). Whether we live in a deterministic universe depends on the
interpretation of quantum mechanics; and even if you choose the most popular deterministic version, 'Many Worlds', it doesn't actually mean that what we will observe will be deterministic. The macro world appears to be deterministic but it isn't difficult (as in Schrödinger's cat) to magnify single quantum events to the macro scale (I know the cat was a thought experiment but we are perfectly capable of doing something like that in practice - preferably without killing any cats).
Secondly, chaos also throws a bit of a spanner in the works, if the universe contains genuine continua (e.g. space-time). If it does, then perfect knowledge of the position of just one particle would require an infinite amount of data (it's not even just countable infinity, the infinity of a continuum is 'bigger'). Chaos means that you would need perfect knowledge because it can potentially magnify the tiniest of differences in the starting conditions, given enough time. I guess you could argue that an in principle argument could involve a truly infinite amount of starting data but you would need a
literally infinite computer, not just one with unlimited storage and processing power, i.e. 'as big and powerful as necessary'.
All of that is different from reduction. As I explained in
#21, you can deduce chemical properties of atoms from the basic quantum mechanics of the individual particles. Reduction would mean that, in principle, you can carry on up, explaining biology in terms of chemistry, then on up though behaviour and all the way up to tax arrangements. I don't see any problems with that in principle, and if you claim we can't, then it does call into question the laws of physics.