Gilles Deleuze (1925 - 1995) says that his interest for David Hume (1711 - 1776) is due to the fact that there are profound elements to a new image of thought in his philosophy. In a certain way, the theme of the image of thought is central in Deleuze's work, is characteristically deleuzean. It is about the problem of the rupture with the common sense and the problematization of the presuppositions. Deleuze inquiries it considering several philosophies, making use of the history of philosophy in a way of his own. He will take from some authors concepts that will aid him to find a new philosophical problem. We could say that Deleuze takes from Hume's philosophy some important originalities to think and express the problem of the presuppositions in philosophy. That is, besides exemplifying his philosophical method and style, the study of Hume would be an important source of ideas for Deleuze. Now, the preoccupation of being able to contribute with philosophy in a profound and new way is recurrent in Hume. His philosophical radicality would have been announced as a new scene of thought, being defined later as an attempt of introducing the experimental method of reasoning in the moral subjects, finally transforming itself in an easy style of reasoning. Hume will defend in all those instances some new medium to establish the truth - a conception that truth might be established by taste and sentiments. His philosophy will be drawn as a way to polish the taste and the sentiments, increasing their delicacy; as a way to relativize the search for truth in philosophy. Hume's radicalness can be appreciated in his own work, but the deleuzean critique of the image of the thought can also afford a penetrating view for the studying of that radicalness. Determined to research the link between these two philosophies, I have decided to study the question of Hume's radicalness in his own work and as it appears on Deleuze's writing too. I do not intend to reduce Deleuze to a mere commentator of Hume's philosophy, neither confine Hume's radicalness to Deleuze's philosophy; rather, my propose is to consider these two great philosophies simultaneously, feeling that they reinforce themselves. Thus, I hope to obtain from philosophy itself a view that takes into account the link between Hume and Deleuze.
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