When a person wants to end an argument, one way to do so is to appeal to a higher authority with an oath. For example, some people do this by saying, "I am telling the truth so help me God." Even God used an oath to guarantee His promise to bless Abraham greatly ( Genesis 22:16; cf. Exodus 32:13; Isaiah 45:23; Jeremiah 22:5; Jeremiah 49:13). God swearing by Himself signifies that He binds His word to His character. Thus God gave Abraham double assurance that He would indeed deliver what He had promised. He gave him the assurance of the promise of the God who does not lie and the assurance that God specially guaranteed that particular promise. The two unchangeable things are God"s promise and His oath. God"s strong promise to Abraham then can be a great encouragement to us now because God has also promised us future blessings. Specifically, He has promised that we will receive rewards when we see Him if we persevere faithfully now (cf. 2 Timothy 2:12). [source][source][source]
The figure that closes Hebrews 6:18 is an Old Testament one. In our times of temptation to apostatize we can flee to the promises of God. We can take hold of them as a fearful person in Israel could flee to the altar of burnt offerings, take hold of its horns, and be safe from his assailants. The cities of refuge also provided safety for the Israelites ( Numbers 35:9-15; Joshua 20). We have a better refuge than the Israelites did in Judaism. [source][source][source]
"In Hebrews , the word "hope" never describes a subjective attitude (i.e, "our hope," or "hopefulness") but always denotes the objective content of hope, consisting of present and future salvation ..." [1][source]