What is the main conflict in Sophie's World by Jostein Gaarder?

Fourteen year old Sophie opens her mail box to find philosophy questions and the first part of a written philosophy course. Instead of throwing them away, she begins to respond and finds herself immersed in a philosophical world via correspondence when everything is further complicated when she starts receiving letters addressed to another girl Hilde. To unravel the mystery, she must employ all her lessons and logic to answer questions that only seem to raise more questions.