Final answer:
Aleksandr Solzhenitsyn gave his speech during the Cold War to denounce censorship in the Soviet Union.
Step-by-step explanation:
Aleksandr Solzhenitsyn gave his speech during the Cold War, a period of intense rivalry between the United States and the Soviet Union. His intention for giving the speech was to denounce censorship in the Soviet Union. Solzhenitsyn was a critic of the Soviet government and used his speech as a platform to expose the oppressive nature of the regime and call for freedom of expression.