How does Paxos maintain the promise that future proposal will not break the current chosen value without knowing the future?
The bold section is saying that before proposing a value know if a value is accepted or if there is a higher proposal number that is chosen by one of the majority. If there is a higher proposal number, the proposer needs to propose a higher number than that is already proposed. If a value is already accepted then majority should know if a value is accepted. The proposer accepts the value. The majority is because two majorities always overlap.