What are some of the theoretical foundations for recognizing and adopting the exclusionary rule under the Fourth Amendment?
The major theoretical foundation of the exclusionary rule is the idea that the Fourth Amendment would have no meaning in the absence of such a rule.
In Weeks v. United States, the Supreme Court ruled that evidence seized in violation of the 4th Amendment could not be used in court. The Court held that there would be no point to having a 4th Amendment if the police could search for and seize evidence without a warrant and then use it even though it had been gotten illegally. As Justice Day said in his opinion in this case,
If letters and private documents can thus be seized and held and used in evidence against a citizen accused of an offense, the protection of the Fourth Amendment declaring his right to be secured against such searches and seizures is of no value, and, so far as those thus placed are concerned, might as well be stricken from the Constitution...
By this way of thinking, the point of the 4th Amendment is to prevent government authorities from infringing on the rights of the people to be "secure" in their homes and persons. If the government can violate this amendment and still use the evidence gained by doing so, the amendment has no meaning.