WASHINGTON — (CNN) Five Supreme Court justices Tuesday seemed to agree with arguments that a Texas death row inmate should not be executed because he is intellectually disabled.

The challenge to the Texas death sentence is an opportunity for the court to further define standards states may use in determining intellectual disability.

Justices have previously ruled that the execution of the intellectually disabled violates the Constitution, but the court has largely left it up to the states to implement the ruling.

Tuesday, the four liberal justices — joined critically by Justice Anthony Kennedy — seemed to indicate that a Texas court had relied upon the wrong standards in ruling against the inmate, Bobby James Moore.

A lawyer for Moore argued that Texas had “adopted a unique approach” and urged the Supreme Court to reverse the decision.

Supporters of Moore hope that the court’s eventual ruling will bring Texas — a state that has executed more people than any other state since 1976 — in line with Supreme Court precedent.

“I think there is a conflict,” Kennedy said at one point, between the standards used by the lower court and current medical standards.

Moore was convicted of the 1980 murder of James McCarble, an employee at the Birdsall Super Market in Houston.

His lawyer, Clifford M. Sloan, argued that the Texas Court of Criminal Appeals was mistaken when it ruled that Moore was eligible for the death penalty because it based its decision on an outdated medical definition of intellectual disability.

Sloan pointed out that throughout his childhood Moore had “grave difficulties” with academic, social and conceptual issues.

In court papers Sloan said Moore’s own father called him “‘stupid’ for being slow to read and speak, and his teachers separated him from the rest of the class, often instructing him to draw pictures because he was unable to keep up with basic schoolwork.”

Moore was also hit in the head with a brick when he was 12 during an integration dispute that took place in his school.

The Texas court acknowledged that the position of the medical community on the diagnosis of intellectual disability has shifted in recent years, but said that “until the legislature acts” it is bound by its own precedent.

The lower court relied on a 1992 manual put out by the American Association on Mental Retardation that includes a three part test: significantly subaverage intellectual functioning, deficits in adaptive functioning (how one handles the demands of every day life,) and whether the disability was present in childhood.

But Sloan said the standard, fashioned in part on a fictional character in John Steinbeck’s novel “Of Mice and Men,” did not reflect current medical standards.

Sloan said that “refinements have occurred with regard to both intellectual function and adaptive behavior.”

He argued that “current standards place greatly reduced emphasis on IQ scores in the assessment of intellectual function and rely more on adaptive functioning” than earlier standards did.

In court papers Scott Keller, Texas’ Solicitor General, argued that the state is not required to “adhere precisely to a particular organization’s clinical definition of intellectual disability.”

He told the justices that the factors the lower court relied upon were “grounded in court precedent.”

But Justice Elena Kagan questioned whether the lower court’s rejection of the views of clinicians on some issues might mean “people with mild impairment can be executed, even though the clinicians would find those people to be intellectually disabled.”

Justice Samuel Alito appeared to be the most solid vote for Texas.

At one point he questioned whether the criteria used by the lower court was indeed outdated.

All eyes in court were on Justice Stephen Breyer who has urged the court to take on the larger question concerning the constitutionality of the death penalty in part because it can be applied arbitrarily nationwide.

While Moore’s case did not target the large constitutional question, Breyer expressed concern that the court might not be able to find a standard that would settle borderline intellectual disability cases nationwide.

“I don’t think there is a way to apply this kind of standard uniformly across the country, and therefore there will be disparities and uncertainties,” he said.