"For neuroscientific findings of fetal pain to serve as a basis for permitting states to prohibit abortion prior to viability..."

".... they must tell us something about the nature of a fetus that makes the state’s interest in protecting it more compelling than its interest in protecting a woman’s right to make basic decisions about her own body. As pain sentience does not serve as a basis for legal prohibitions in general (or else mousetraps and deer hunting would be prohibited), the statutes’ real purpose is to use potential evidence of pain sentience in fetuses to indicate the presence of something far more compelling — namely, personhood."

From a NYT philosophy blog item written by William Egginton, a Humanities Professor the Johns Hopkins University.

The states are already allowed to prohibit abortion after viability (with exceptions for the life and health of the mother), but not because viability establishes that the fetus has turned into a person. In fact, the Supreme Court has never made much sense over why viability is the line. (I've taught the abortion cases many times, and the best I can say is that viability was chosen for the line because the Court wanted a place to draw a line and viability was a concept that existed within medicine.) The question of when the unborn is considered a "person" is reserved for the woman to answer for herself. That's the heart of the right that the Court has articulated. It was clearly stated in terms of autonomy to define life in Planned Parenthood v. Casey, when the Court revised Roe in the process of deciding not to overrule it:

At the heart of liberty is the right to define one's own concept of existence, of meaning, of the universe, and of the mystery of human life. Beliefs about these matters could not define the attributes of personhood were they formed under compulsion of the State.

It's interesting for Egginton to offer some philosophical analysis (and for neuroscientists to provide the information they have), but under Roe/Casey, it's for the individual pregnant woman to use that material as she sees fit in arriving at her own answer to the mystery of the value of the unborn entity. Pre-viability, anyway.