The article presents the elements of Hume's philosophy of politics present in his political essays. It analyses double meaning of 'politics' as Hume sometimes uses the term to describe the practise of ruling the state and sometimes to reflect on the state, its political order and government, meaning certain philosophy of politics. In both cases Hume demands scientific rules in politics. But in the first one Hume demands rational governance and in the other he seeks recognition of philosophical thesis concerning social world, its organisation and the rules governing it. In the latter, whether it is possible to build a theory according to the natural sciences' standards or not, it is possible to criticise already functioning philosophical solutions. It is possible to analyse it critically by applying the correctness standards set by theory of cognition for gaining and verifying knowledge. The elements of such analysis are presented in the example of the Hume's critics of social contract theory. The author discusses arguments used by Hume against this theory.