In the 1960s, Woody Allen bemoaned the fact that it was impossible to get a divorce in New York unless one spouse could prove the other’s infidelity. “The Ten Commandments say, ‘Thou shalt not commit adultery,’ ” Allen quipped. “But New York state says you have to.”

A similar contradiction plagues American thinking — and American policy — on disability.

The Americans With Disabilities Act, passed with bipartisan support in 1990 at the urging of then-President George H.W. Bush, enshrines the notion that every American can and should hold a job regardless of physical or mental limitations.

Under the ADA, employers who refuse to hire or promote the disabled may be liable for money damages in federal court.

Social Security Disability Insurance, however, pays people who can show that they are too mentally or physically impaired to remain in the labor force. In short, for many workers, SSDI creates a quasi-right not to work.

This paradox is getting expensive. SSDI spending has doubled as a percentage of gross domestic product in the last 25 years, according to the Congressional Budget Office. The program paid $128.9 billion to 8.3 million beneficiaries in fiscal 2011, about one-fifth of all Social Security spending. The average monthly benefit is $1,100, slightly less than the average Social Security retirement check, but after two years on SSDI, beneficiaries also get Medicare. Indeed, SSDI added $80 billion to the cost of Medicare in fiscal 2011.

The disability trust fund, financed by a portion of the Social Security payroll tax, is set to run out of cash by 2016, though the government will undoubtedly borrow to meet its obligations.

What’s going on? Work certainly hasn’t gotten more physically demanding; quite the contrary. There’s no evidence that workers in general are substantially less healthy than they used to be.

The answers lie in SSDI’s haphazard history. When first adopted in 1956, the program applied only to workers older than 50 who were terminally ill or unable to work for the rest of their lives. It was essentially an early-retirement program for people with cancer, heart disease and other grave physical conditions.

In 1960, however, Congress removed the minimum age requirement, and in 1965, it allowed people to qualify if they suffered from a condition rendering them unable to “engage in substantial gainful activity” for a year or more, including mental and musculoskeletal ailments.

After that, the rolls swelled with people claiming crippling back aches and depression. Both the Carter and Reagan administrations tried to cull undeserving cases, but the resulting backlash was so strong that Congress actually liberalized the rules in 1984. In 2010, mental and musculoskeletal conditions accounted for 54 percent of all new SSDI cases, according to the CBO.

Though Washington pays benefits, states help decide who qualifies. Approval rates vary wildly across the country. Experience has been consistent in one respect, however: Applications spike during serious recessions, as laid-off workers turn to SSDI when unemployment benefits run out. Thanks to the Great Recession, applications spiked in 2010 to an all-time high of 2.94 million, before declining slightly last year.

I don’t mean to imply that all, or even most, SSDI beneficiaries are malingering. Indeed, some of the recent increase in enrollment would have occurred anyway due to the aging of the population.

It is nevertheless true that SSDI offers all the wrong incentives: Employers pay nothing when their workers go on SSDI. And for many workers, especially those with few skills, the alternative to a steady SSDI check (and, often, Medicare) would be a minimum-wage job, possibly one without insurance. Of course, the longer one stays out of work, the rustier one’s skills get. The program has no training or rehabilitation component.

Not surprisingly, only about 1 percent of SSDI beneficiaries have left the rolls annually since the mid-1980s, according to data compiled by MIT economist David Autor, a leading advocate of reform.

More than 6 percent of the U.S. working-age population is on SSDI. Does that statistic represent laudable social solidarity, a scandalous excess of the welfare state, or a tragic but unavoidable idling of human resources? Or is it an expression of this country’s understandable ambivalence about exactly what we should expect from the disabled, in an age when we know that depression really does disable some people — and that a man with two prosthetic legs can run in the Olympics?

We have no choice but to reconcile our conflicting goals and sentiments in a more cost-effective way than SSDI does now. Otherwise, SSDI’s growth will continue to erode productivity, swallow up scarce tax dollars, and make it that much harder to afford a sufficient safety net for everyone who needs it.