In my paper I undertake an analysis of chosen short stories of Jorge Luis Borges in which the problem of mysticism occupies an important place. I claim that Borges, whose works are known for covering philosophical issues of most fundamental importance, is a writer who describes the impossibility of reaching a mystical experience in the modern world. As far as philosophical background of Borges is concerned there exists a well-spread opinion that Borges, who readily confessed his admiration for Berkeley and Hume, was an idealist himself. My point is that even though the Berkeleyan epistemology influenced Borges, there is a fundamental difference between those thinkers which consists of the fact that in the philosophy of Berkeley there is a place for God. As a result it can be claimed that the world as an object of God's experience has a stable existence. There is no place for such a privileged being neither in the ontology nor epistemology proposed by Borges. The world as described by him can be called a fiction because there is no privileged subject whose experience would not be accidental and private. For that reason the description of mystical experience is always a failure when it refers to modern times. I demonstrate it at length by the analysis of the short story entitled The Aleph, while taking into consideration other texts as well.