Paine's argument begins from a simple observation: the people who made any given constitution, treaty, or law are, eventually, dead. Once dead, they have no more authority over the living than the living have over the unborn. It is therefore incoherent — not just unjust but logically impossible — for the dead to bind the living. When Burke appeals to the authority of the Glorious Revolution of 1688 as permanently settling the constitutional order of Britain, he is appealing to people who are no longer there to enforce their preference. The living generation is sovereign over its own affairs; the dead cannot be.
The legal doctrine of prescription — that a long-established practice acquires a kind of right by virtue of its age — is the principal target of this argument. For Burke, the age of an institution is evidence of its fitness: it has survived, it has been tested, it has the endorsement of countless generations who lived under it. For Paine, the age of an institution is morally irrelevant: a tyranny of a thousand years is still a tyranny. The mere fact that people have lived under a system — especially when they had no choice about it — tells us nothing about whether the system is just or whether the current generation is obliged to continue it.
The positive consequence of this argument is that every generation has not just the right but the duty to consider its own constitutional arrangements afresh — not because change is always good, but because no arrangement can claim legitimacy from the consent of people who did not exist when it was made. This is why Paine was enthusiastic about both the American and French constitutional moments: they were occasions when a living generation explicitly chose its own form of government rather than inheriting one. The constitutions they produced might themselves need revision in a generation or two — and that revision would be equally legitimate.
Jefferson expressed a very similar view in his famous letter to Madison (1789): "the earth belongs in usufruct to the living." There is evidence of mutual influence between Jefferson and Paine on this point, though Paine develops it more radically in Rights of Man.
