That cynicism is often expressed in a lack of faith in government’s ability to do anything about the problem. This view ignores how much inequality has been made worse in the past few decades by government decisions. The emphasis on cutting taxes and spending that began in the Reagan years is a direct cause of economic insecurity now. It has led, for example, to education cuts that have harmed children in low-income school districts. Reversing those decisions can still have an enormous impact.

Mr. Obama did not reveal a sheaf of new ideas in his speech. But he did remind listeners of the many good ideas he has proposed about inequality over the years, most of which have been blocked by Republican opposition. A higher minimum wage would have an immediate effect on the buying power of millions of workers, stimulating growth and employment. Greater spending on high-quality preschool, a new emphasis on career and technical education and affordable higher education would all help to lower the barriers to economic mobility. Stronger collective-bargaining laws and nondiscrimination protections would help restore a balance in workplaces now tilted strongly toward employers.

And the Affordable Care Act, as Mr. Obama said forcefully, has enhanced security for millions of people who were previously uninsured or who lived in fear of losing their policies because of illness. “This law is going to work,” he said, “and for the sake of our economic security, it needs to work.” It will reduce personal bankruptcies, he said, cut sick time and keep children healthier and performing better in school.

What he should have added was the need to raise tax revenue, which is crucial to making the kinds of investments big enough to have a real effect on growth. The tax code must be overhauled to eliminate the absurdly generous breaks given to those at the very top — an idea that Mr. Obama has campaigned on but rarely brings up, given the implacable Republican opposition. But the president did issue a clear challenge to his opponents. Where are the Republican ideas for reducing the income gap? Most in the party don’t even recognize it as a problem. “You owe it to the American people to tell us what you are for,” he said, “not just what you’re against.” The silence from Republicans explains why economic inequality is rising.