Piketty has three objectives in presenting a brief history of equality. The first is to define equality, and describe its behavior over the past couple of centuries. The second is to determine the motivations and mechanisms supporting and opposing equality. And the third objective is to extrapolate supportive motivations and mechanisms into the future to extend and improve equality. There are a number of subsidiary objectives, the most important of which is to establish restorative justice for people and places ravaged by the economic and political systems set up to feed the growth of colonial and neocolonial empires.
The notion of equality shifts between equality of opportunity for intangibles, such as suffrage and education, and equality of outcome for tangibles, such as income and property. Measures of equality should be multidimensional (social, economic, environmental) to provide both broad determinations of equality and guidance for governance. The mechanisms are principally taxation, both progressive and confiscatory; a redistributive state, mainly in terms of welfare, but also for reparations and compensation; and democracy in social and corporate governance. The motivations, apart from the titular one, are the development of a transnational or global infrastructure to support continued progress, redressing past injustices and the downward and outward diffusion of power and resources.
A Brief History of Equality is a response, in part, to requests that Piketty write a concise summary of his other, more massive and detailed books (Capital in the Twenty-First Century, Capital and Ideology, Top Incomes in France in the Twentieth Century — none of which I've read). Given that motivation A Brief History of Equality is heavy on vision and light on details.
Piketty is a socialist, but not of the fire-breathing, smash capitalism kind. He's more of a social democrat, wanting to harness capitalism using taxes and democracy to evenly distribute capitalist benefits while ensuring that capitalist processes are always directed toward socially beneficial ends. Like Marxists, Piketty has a totalizing worldview, but one grounded in practical matters, such as finance and democracy, rather than in hypothetical armies (eventually) driven forward by metaphysical conceits. The grounding in practical matters adds weight and force to Piketty's ideas, as argued by the historical analysis in Equality. But even granting full credit to Piketty's analyses of cause and effect (which are light, and largely have the flavor of “after, therefore because” without further digging into the references), the scope of his worldview makes it hard to understand the mechanisms by which these matters are extrapolated into the future, and how they would work in the future to achieve their ends. The latter problem Equality handles by reference to democratic governance in corporate, transnational, and global scope; the former problem Equality does not handle at all.
