If Malthusian hypothesis was true, population would stay stable and slowly increasing with agricultural productivity increases, and most of all, it would very rapidly recover from population shocks like wars and diseases.
No, I don't think the Malthusian hypothesis says that; in particular, it doesn't talk about rapidity of recovery, only that population will keep growing in the face of any excess food.
no recovery during 400-1000 in spite of ample available land (against Malthusian hypothesis)
Yes, that would be evidence if there were truly available land. But the wikipedia article you cite seems to say that the land was not safe to farm. It took the shift from "mobile bandits" to "stationary bandits" to have a real supply of land. (Maybe this is what you say about slavery.) I don't see this complaint as very different from saying that the 400-600 population collapse disproves the malthusian hypothesis.
more or less doubling of population 1000-1350 ... and supposedly with increased quality of life, and increased wages etc. relative to previous period (against Malthusian hypothesis)
I think you are misreading wikipedia. I think that the establishment of law lead to higher quality of life, which lead to expansion, driving down the quality of life. That happens to fit the malthusian hypothesis. In particular, that article says that Europe had run out of food by 1350. This could be for malthusian reasons or it could be the exogenous shock of the end of the warm period. I think some people claim that the black death lead to higher per capita wealth than 1200, which suggests malthusian poverty after 1200. Wikipedia merely says higher wealth than 1300, which isn't saying much, since the climate was deteriorating by then.
The failure of Tuscany to return to its 1350 peak until 1850 is a serious problem for a malthusian hypothesis.
The faster climate, war, and disease change, the less important malthusian effects are. I think that they are visible in midieval european history, at least in the 1000-1300 expansion; others claim to see malthusian poverty in the following expansion. But perhaps they are not important; malthusian effects should probably not be blamed for the poverty of 600. China has a more stable history and, I am told, more visible malthusian effects, particularly the exploitation of poor land.
[My knowledge of High Medieval period is based mostly on listening to TTC's audiobook lecture series about it (highly recommended), not on Wikipedia.]
A few random thoughts:
I don't have one big mathematically pretty theory here. (Short-term) Malthusian theory seems to be widely accepted because it's mathematically pretty, and something like it works on many animal populations. It's not obvious from either theoretical or empirical point of view it makes sense for humans, at least after they stopped hunting and gathering own food.
Actual food production must c...
This is an attempt to list all of the possible ways in which humanity may avoid scenarios where the average standard of living is close to subsistence, in response to Robin Hanson's recent series of posts on Overcoming Bias, where he argues that such an outcome is likely in the long run.
I'll start with six, some suggested by myself, and others collected from comments on Overcoming Bias and Robin's own posts. If anyone provides additional ideas, I'll add them to the list.
(I have a more general point here, BTW, which is that predicting the far future is very difficult. Before thinking that some outcome is inevitable or highly likely, it's a good idea to repeatedly ask oneself "This is all the ways that I can think of why it may fail to come true. Am I sure that all of them have low probability and that I'm not missing anything?" There may be some scenario with a non-negligible probability that your brain simply overlooked when you first asked it.)
Singleton
A world government or superpower imposes a population control policy over the whole world.
Strong Security
Strong defensive technologies and doctrines (such as Mutually Assured Destruction) allow nations, communities, and maybe tribes and families to unilaterally limit their populations within their own borders, while holding off hordes of would-be invaders and immigrants.
Non-Human Capital
Maximizing the wealth and power of a nation requires an optimal mix of human and non-human capital. Nations that fail to adopt population controls find their relative wealth and power fade over time as their mixes deviate from the optimum (i.e., they find themselves spending too much resources on raising humans, and not enough on building machines), and either move to correct this or are taken over by stronger powers. (I believe that historically this was the reason China adopted its one-child policy.)
Unlimited Growth
We don't completely understand the laws of physics, nor the nature of value. There turns out to be some way for economic growth to continue without limit. (Robin himself once wrote "I know of no law limiting economic value per atom" but apparently changed his mind later.)
Selfish Memes
Memes that manage to divert people's resources away from biological reproduction and towards memetic reproduction will have an advantage over memes that don't. On the other hand, genes that manage to block such memes will have an advantage over genes that don't. Memes manage to keep the upper hand in this struggle (or periodically regain the upper hand).
Disease, Warfare, Natural Disasters, Aliens, Keeper of the Simulation
One or more of these come along regularly to keep the human population in check and per capita incomes above subsistence.