Here’s a quick summary of the philosophical problems with Capital in the 21st Century, with links substantiating these claims.

Increasing inequalities of income and wealth are problematic from a moral point of view because these increasing inequalities are opaque to the public, unjust, and will generate social instability, all undermining the ability of democratic institutions to be sovereign over the economy. A global progressive annual tax on capital will solve these problems because it will compress these inequalities, restore stability, rectify unjust inequalities, and generate social stability. As a result, it will restore democratic control over the economy.

However, Piketty never defines instability or explains whether we’re in danger of reaching destabilizing inequality. He is unclear about which principle of distributive justice he endorses, so it is hard to know how much of present inequality is unjust. Depending on how he specifies his principle, Piketty either endorses a vague principle of promoting the common utility, which does not justify much redistribution, or he endorses something like the Difference Principle, in which case his conception of distributive justice is not grounded in the common commitments of members of liberal democratic societies, as he says. A global capital tax is not necessary to increase financial transparency because we can get transparency in other ways. Finally, Piketty never tells us what democratic control means or gives us reason to think that we will soon lose control due to instability and unjust inequalities.