IF LAST WEEK’S presidential debate was so restrained as to be soporific, the vice presidential debate was a rumble of cross talk and interruption that was much livelier — but similarly unilluminating.

The conversation Thursday night on domestic issues was both disappointingly narrow — issues such as education, immigration and climate change never came up — and infuriatingly dodgy.

Rep. Paul Ryan (R-Wis.), much like his running mate, Mitt Romney, repeatedly declined to identify any of the tax breaks that would be curtailed to pay for the proposed 20 percent reduction in tax rates. “Six studies have guaranteed this math will add up,” Mr. Ryan said. But the supposed studies offer no such assurance; indeed, the most reputable of them underscore the mathematical impossibility of simultaneously cutting the rates, avoiding greater debt, shielding the middle class and maintaining the current progressivity of the tax code. The unwillingness of the Republican ticket to offer specifics on how it would pay for the rate cuts remains nothing short of irresponsible. Mr. Ryan’s claim that the Bush tax cuts for the wealthy cannot be allowed to expire for fear of hurting small businesses that create jobs is similarly unconvincing; as Vice President Biden pointed out, a tiny sliver of small businesses earn enough to be affected by the higher rates.

But Mr. Biden, too, dodged and obfuscated, particularly on entitlement spending and the debt. “They haven’t put a credible solution on the table,” Mr. Ryan said of the Obama-Biden ticket on entitlement reform, and he was correct. “Their ideas are old and their ideas are bad, and they eliminate the guarantee of Medicare,” Mr.Biden said of the Republicans. But where is the Obama-Biden plan? Likewise, when moderator Martha Raddatz asked Mr. Biden, “What would you suggest beyond raising taxes on the wealthy that would substantially reduce the long-term debt,” his response was simply to repeat his vow to raise taxes on the wealthy. That is a non-answer; there’s no way to have the middle class pay less, as Mr. Biden promised, and leave entitlements unreformed yet not drown in debt.

For a campaign that has been dominated by talk of the economy, Thursday’s questioning had a powerful foreign policy focus. The most dramatic of a series of exchanges on foreign policy came on Afghanistan, after Mr. Biden declared, “We are leaving in 2014, period.” Mr. Ryan responded that such a categorical red line invited “our enemies to put a date on your calendar” and wait out the American withdrawal; Mr. Biden charged that a Romney administration was not truly committed to a withdrawal. Neither candidate mentioned that the Obama administration and Afghan government have agreed to negotiate the terms for a U.S. force of trainers and special forces to stay well beyond 2014.

The candidates sparred on Syria and Iran without spelling out substantial differences. Mr. Ryan scored the Obama administration for pursuing futile diplomatic initiatives on Syria, rather than building ties to the opposition, but offered no specifics when asked what a Romney administration would do differently. Both men disavowed any intention of sending U.S. troops to Syria. On Iran, Mr. Biden boasted that the Obama administration had applied the toughest sanctions in history; Mr. Ryan answered that Iran “is four years closer to a bomb.” Mr. Ryan charged that the Obama administration said “the military option is on the table, but it’s not credible.” Mr. Biden answered: “Do you want to go to war?” Without much justification, or evidence that the Romney policy differs from President Obama’s, he repeatedly suggested that a Romney administration would plunge the country into armed conflict.

At times Mr. Biden struck us as unduly condescending; Mr. Ryan, a touch unsure of his footing. But their performances both were fine; their weaknesses were less in presentation than in the failure of their tickets, in different ways, to offer an honest road map of their intentions for governing.