I put my bashfulness in my pocket, and plunge into a long conversation on the war, the weather, music, Carlyle, skating, genius, hoops, and the immortality of the soul.
Using the Latin root mort meaning death and the prefix im meaning not, the meaning of immortality as used in this sentence from the passage most likely means
1. being dead.
2. having morals.
3. ending in death.
4. unending existence.