vicious circle

from The American Heritage® Dictionary of the English Language, 5th Edition.

• noun A situation in which the apparent solution of one problem in a chain of circumstances creates a new problem and increases the difficulty of solving the original problem.
• noun A condition in which a disorder or disease gives rise to another that subsequently affects the first.
• noun Logic A fallacy in reasoning in which the premise is used to prove the conclusion, and the conclusion used to prove the premise.

from The Century Dictionary.

• noun See circle.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun A situation in which the solution to one problem creates a chain of problems, each making it more difficult to solve the original one.
• noun logic A fallacy in which the premise is used to prove a conclusion which is then used to prove the premise.

from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.

• noun one trouble leads to another that aggravates the first
• noun an argument that assumes that which is to be proved