The 25th Amendment to the United States Constitution addresses the process of presidential succession, vacancy, and the disability of the President. It outlines the procedures for removing a President when they are unable to fulfill their duties due to physical or mental incapacity. The key section relevant to this question is Section 4 of the 25th Amendment.
Section 4 states that the Vice President, together with a majority of the Cabinet or another body as provided by law, can declare the President unable to discharge the powers and duties of their office. If such a declaration is made in writing and transmitted to the President pro tempore of the Senate and the Speaker of the House of Representatives, the Vice President immediately assumes the role of acting President.
The phrase "paranoia" as described in your question refers to a mental condition characterized by delusions of persecution, unwarranted jealousy, or exaggerated self-importance. It's essential to understand that the 25th Amendment does not specifically mention "paranoia" or any specific mental condition. Instead, it uses broader language, such as "unable to discharge the powers and duties of their office."
The amendment intentionally leaves the determination of the President's incapacity to a process involving the Vice President and the Cabinet (or another body as provided by law) rather than prescribing specific medical or psychological conditions. The intent is to provide a mechanism for handling situations where the President's ability to fulfill their responsibilities is in question due to any incapacity, be it physical or mental.
It's worth noting that invoking the 25th Amendment and declaring a President unable to fulfill their duties is an extraordinary measure and a decision of significant consequence. The process is politically sensitive and would require careful consideration by those involved to ensure it is not misused for political purposes.
Ultimately, the threshold for removing a President under the 25th Amendment depends on the circumstances and the judgment of those involved in the decision-making process. The framers of the Constitution deliberately left the determination somewhat flexible to allow for different situations that may arise over time.