The idea of self-knowledge divides naturally into two parts in accordance with the distinction between knowledge by acquaintance and knowledge by description. I know myself and I know things about myself. The latter I know partly from self-acquaintance, partly from the behavior, especially linguistic, of others, and partly from each of these. All aspects of self-knowledge are controversial, so I shall concentrate in this paper on the question of self-acquaintance. My purpose is both philosophical and historical. It is commonly believed that Hume and Descartes held diametrically opposed, or at least strongly contrasting, views regarding self-acquaintance since Hume is regularly ridiculed for his denial of ability to discover his own Self whereas it would occur to no one to ascribe that same view to the author of the Meditations. In this paper I shall argue that contrary to appearances these two philosophers either held the same position or Descartes occupied the more agnostic extreme; and also that the position usually ascribed to Hume is, when properly understood, both correct and of fundamental philosophical significance. Part of my reason for selecting Hume and Descartes for analysis and comparison is to show thereby that the thesis of this paper is true independently of the rationalist/empiricist schism in philosophy.