Sentence:  Essentially this imposed two <WSD>conditions</WSD> : First , international law had to recognize and be compatible with an international political system in which a number of states were competitive , suspicious , and opportunistic in their political alignments with one another ; second , it had to be compatible with the value system that they shared . 
Meaning of the word marked with <WSD> tags:  an assumption on which rests the validity or effect of something else