Well, not in a literal sense perhaps, but practically, if you are liable for a debt that was incurred before you were even born, let alone of voting age, how is that any different?
The question is: Who are you liable to? You are never liable to some dead person, but to some other living person.
If, in the future, there are people who are carrying some kind of burden because of the government debt established today, then there will also be, in the future, people who are benefiting from the government debt established today.
This is why I consider it a red herring to think of the debt as an inter-temporal issue. It is, if anything, at most an distributional fairness issue among the people living at any one point in time.
You might worry that in the future, the people won't have the tools at their disposal to fix those distributional fairness issues. However, since a monetarily sovereign government has the ultimate control over the interest rate that it pays on its debts (and the flows of interest payments are what is most relevant), this is not a concern.
I realize that this last part is very counter-intuitive if you're used to thinking only in terms of options available to the currency user. Read about how interest rates and liquidity operations of the central bank actually work: http://pragcap.com/resources/understanding-modern-monetary-s...
The bottom line is: If the political will to do it is there, those distributional issues can always be fixed in the medium term by manipulating the interest rate. One might have to switch over to using fiscal policy for inflation control, and capital constraints to limit runaway bank lending, but some economists argue that this is preferable anyway.
