re: Yes, it does.....in at least two of its amendments.
The 4th amendment says "The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized." It doesn't mention a general "right to privacy". It mentions a specific right against unreasonable search and seizure.
They are applying the right to privacy to abortions because that is the Constitutional provision that is the most appropriate when determining a woman's right to choose. It makes the most sense when looking at a woman's right to control what happens to her body. They are not supporting any general right to do whatever you want to or with your body, or a general right of privacy. They are specifically creating out of little more than thing air (and earlier court decisions but than they where created out of "thin air" more than anything in the constitution) a "constitutional right" to abortion. Earlier cases (primarily Griswald) invented such a constitutional right to contraception. The "right to control what happens to your body", is no more part of the constitution than the "right to an abortion".
But in the end, they must interpret the Constitution fairly and apply its provisions with even measure, or they will be overruled by a higher court. The USSC has no higher court to overturn its decisions.
Tim |