What was the goal of Enlightenment writers such as Hobbes and Locke? Ex. Thomas Hobbes and John Locke
From the most fundamental of standpoints, Enlightenment political thinkers sought to integrate scientific principles or ideas into governing policy and practice. Enlightenment writers felt that reasonability and rationality were elements that can be integrated into political practice. Thinkers like Hobbes and Locke were important in this process as both sought to inject reason and understanding in how individuals should rule or govern. Thinkers like Hobbes and Locke had fundamental principles that helped to guide their thinking. For Hobbes, the belief of man's nature being one that was predisposed to conflict and antagonism compelled him to embrace the idea of the Leviathan ruler that would subjugate these harmful tendencies in creating an autocratic political rule. For Locke, the belief that man's nature was a blank slate, capable of forming judgments based on experiences helped him form the idea of inalienable rights for citizens, social contracts between rulers and their ruled, and helped to establish the principle of limited government. The Empiricist thought both thinkers reflected was an application of the Age of Reason or the Enlightenment.
Although Hobbes and Locke were arguing for very different ideas, they had a major thing in common -- both were using the idea of rationality and experience as opposed to arguing from authority. This, as you can see in the wsu.edu link, was one of the major ideas of the Enlightenment. Their goal, therefore, was to use rational argument and human experience to explain how the world is and how the world should be.
In previous times, a thinker might argue for monarchy (as Hobbes did), but they would have done so on the basis of the divine right of kings, not on the basis of logic as Hobbes did. So what these two men have in common (their common goal) was to explain how things came to be (and what they should be like) on the basis of reason and experience, not on the basis of faith and authority.