In the opening verses of Parshat Nitzavim, Moshe Rabbeinu reminds the people that the covenant they are about to affirm binds not only the generation that is actually present, but also "those who are not here today" (Devarim 29:13)- all future generations as well. This statement raises a major philosophical issue that has troubled Jewish thinkers for many generations- how can a covenant made in the Sinai desert thousands of years ago still remain binding today?
The fact that a covenant, an agreement, was created between Hashem and Am Yisrael implies that the various obligations contained in the Torah are binding at least in part because of Am Yisrael's consent. The fact that they agreed to the covenant created the obligation. Yet, as many have pointed out, the Jews of future generations never agreed to accept the covenant in any kind of explicit or official way. If consent is necessary, then the Torah should not be automatically binding on the generations born after Sinai.
Many commentators phrase this question in language borrowed from the laws of shevuoth, oaths, or from the laws of monetary obligation. They note that a father's oath is not binding on his children (ein adam morish shevuah lebanav, Shevuoth 48a), and that a person cannot be obligated monetarily when they are not present (ein chavin la-adam she-lo be-fanav, Gittin 11b). Similarly, the oath taken by Am Yisrael at Sinai should not be binding on their children, and the obligations contained in the Torah should not apply to future generations.
The Abarbanel approaches this question by exploring other legal analogies. He notes that it is not true that children are never bound by their parent's obligations. For example, children who inherit their parents' assets may also inherit their debts and become debtors,ba'alei chov. An even more extreme example comes from the laws of Canaanite slaves. A Canaanite slave enters into a legal relationship with his master that requires the slave to follow the orders his master gives him, and gives the master ownership over the slave's body and his labor. In addition, the slave's status is inherited- all children born to the slave likewise become the property of the master. This type of legal relationship is one in which the legal obligations and status of the parents are indeed transferred to their children.
The Abarbanel argues that the covenant of Sinai went far beyond a normal oath or contract, creating a new master-slave relationship between Am Yisrael and Hashem. The generation of the desert, as it were, sold itself into Hashem's service. This created a new legal relationship between the people and their God, and this type of relationship is legally transferrable to all future generations of Jews.
A different type of answer is presented by the Akedat Yitzchak, the Abarbanel's older contemporary. Instead of trying to ground covenantal obligations in legal arguments, the Akedat Yitzchak claims that the Torah is binding on future generations of Jews for spiritual and metaphysical reasons. The Jewish people are connected to the Torah on such a deep level that they cannot survive without it. Just as is it is a law of nature that living things seek to live and avoid death, it is a metaphysical law that the Jewish people will not commit spiritual suicide by abandoning the Torah. The covenant with future generations that Moshe Rabbeinu references here is not a legal obligation, but a spiritual fact that Am Yisrael cannot thrive without following the Torah. The relationship between Hashem and the Jewish people goes beyond legal arguments.
It may be possible to blend the two approaches together and suggest that the Jewish people at Har Sinai did as the Abarbanel suggests; they created a relationship with God that legally obligates all future generations to follow all of the mitzvoth in the Torah. At the same time, as a result of this decision, the Jewish people forged a relationship with Hashem through the Torah that transcends any legal technicalities, as the Akedat Yitzchak suggests. This idea can also apply on an individual level. While building on the foundations of our official obligations, we can build a relationship with Hashem that is much deeper.