I'm told that empirical data shows that social mobility has been declining, that life expectancy is inversely related to inequality, and that mental illness is more prevalent where there is higher inequality. I do not know whether these statistics are true or not.
Empirical evidence itself is of no use for understanding the effects of different norms relating to how resources are used – for that we need economics, and economics is a strictly axiomatic-deductive, i.e. non-empirical, science, as explained by Austrian economists such as Ludwig von Mises, Murray Rothbard and Hans Hoppe.
With regard to social mobility, we know from economic analysis that social mobility is maximised in a free market system, since any socialist or interventionist policies can only prevent people with less wealth from becoming someone with relatively high wealth. In a voluntary system, if a relatively poor person can successfully add value to society and satisfy the needs of his fellow man, there is nothing to stop him becoming a wealthy person.
As for inequality, it is difficult to see what the problem is. For most of human history, humans led lives that were poor, nasty, brutish and short. No one was wealthy; there was a great deal of equality. Then some individuals started breaking this situation of high equality by saving and implementing good new ideas – like creating wheelbarrows, ploughs and pots, which enabled them to produce more with less effort. Individuals with wheelbarrows were now wealthier than the “have-nots” who didn’t have them. The consistent opponent of inequality would have to denounce this improvement to the material conditions of man on account that it creates a two-class society and breaks the condition of high equality.
Yes, there is a high level of inequality in the world. The life of the poorest in Africa is not much different to the condition that once prevailed upon all humanity. But most people on Earth do not live in such conditions anymore, thanks to continued saving, and continued implementation of good new ideas: like cars, computers and iPods. It is a testament to the great strides we have made as a species that some individuals now have these “luxury” goods; production of basic necessities like food is so efficient that most people in the world - billions of us - do not need to worry about starving to death, which preoccupied almost all of the time of all humans throughout almost all of history.
Being concerned with inequality usually means being concerned about the existence of many people who unfortunately today who are poor by the standards of the average in developed societies. The implicit assumption – the critical error made by enemies of inequality – is that the only way to elevate the poorest in society to a decent standard of living is by the wealthiest in society giving up their high standard of living. This is plainly not the case, since if it were, no humans would ever have risen above the poverty our ancestors lived under.
Take the following hypothetical. We have two choices for what kind of society we want. 1) Everyone in the world has the same standard of living as the average American today. 2) Everyone in the world has at least the same standard of living as the average American today, with many people having a considerably higher standard of living than the average American today. The consistent opponent of inequality would have to prefer the first option, which is clearly barbaric in that it is supporting the lowering of the standard of living of a large number of people.
The goal of raising the standard of living of the poorest in society is a noble one. Praxeologically and empirically it can be shown that this is best achieved by free markets. If the restrictions on capital accumulation and investment in Africa were removed, productivity would increase and the poorest in society will be lifted to a higher standard of living. As a consequence of this, like all voluntary trades, the people who are already at a high standard of living benefit from an even higher standard of living. Any attempt to prevent such voluntary trade on the basis that it increases inequality harms both parties and prevents the mutual benefits of trade from being realised.