developed. Wouldn't it be reasonable that they were developed by trial and error -- Feynman's "guess and test" -- that is to say that they were practising what we'd recognize as science?
[WS:] Obviously. This is how most people think. The crucial difference here is not whether modern science is rational and "traditional" knowledge is not, for both are rational in the meaning that you describe. The difference lies in the organizational capacity to pursue a systematic inquiry.
This makes the whole difference in the world, because knowledge is a cumulative process, and the speed at which experiences are accumulated matters. This speed is determined, for the most part, by the institutional capacity of producing and testing hypotheses storing the results, and retrieving them for future reference. There is a big difference between what modern science has at its disposal to "guess and test" its conjectures and what pre-modern medicine, many of which developed in the absence of written record keeping did.
Looking at this from a different angle - there is no reason to deny that traditional medicine used a "trial and error" approach and found a few good cures this way. So did modern science. The difference is that modern science found more good cures in hundred or so years than traditional medicine did in a few thousand years.
So even if we assume that modern science and traditional medicine use essentially the same trial-and-error reasoning process, modern science has significantly greater capacity to employ that reasoning process systematically. It is like a difference between a sickle and a lawn mower - both operate on the same mechanical principle, but the mower work much faster.
One more point. The key reason behind the modern capacity to accumulate knowledge is, well, "good old" capitalism, or rather its unprecedented capacity to produce and accumulate surplus. The more efficient surplus production, the greater the capacity to support people who can devote their lives to scientific pursuits, and thus the greater the output of scientific research work.
I think those who blame capitalism for woes of modern science or medicine (like Carrol or Doug who seconded his posting) confuse capitalism as understood by Karl Marx with the institutional framework existing in the United States. The essence of that framework is monopolistic control by organized groups of producers - which is more characteristic of the pre-capitalist guild system.
Wojtek