Questions on Federal Question Jurisdiction

1.  Keep in mind the scope of the judicial power of the United States under Art. III § 2. What does the phrase "arising under this Constitution, the Laws of the United States, and Treaties made" mean? In thinking about this matter, consider cases that the United States Supreme Court takes on appeal from state supreme courts. Taking such cases is an exercise of the judicial power of the United States. So there must be something under Article III giving the Supreme Court this power. With this in mind, how ought the scope of "arising under" in Art. III be interpreted?

2. According to the Mottley case, what does "arising under" in 28 U.S.C. § 1331 mean? How can the same phrase have such a radically different meaning in the Constitution and in a statute?

3. Does the interpretation of § 1331 in Mottley mean that there is no possibility of a federal court reviewing the federal defense at issue in the case?

4. Why should the Supreme Court dismiss the Mottley case for want of subject matter jurisdiction when the defendant did not make a motion to dismiss on that ground?

5. Is a suit by P against D for patent infringement a federal question action under 1331? Assume instead that P and D sign a contract allowing D to make use of P's patent for a fee. D breaks the contract by not paying the fee and P sues D for the breach. Is that a federal question action under 1331?

6. Imagine the state-law cause of action of a plaintiff rides upon the interpretation of some federal law. For example, I am the beneficiary of a trust and sue the trustee. My cause of action is that he violated his state-law fiduciary duties by investing in illegal securities. According to state-law, the fiduciary duty is violated if the securities are illegal under either federal or state law. In this case, the securities were illegal under federal law. Is there federal question jurisdiction for the case under 1331?

7. Imagine that a plaintiff sues in state court on a state law cause of action that he knows is preempted by federal law. Does the rule in Mottley mean the plaintiff has successfully defeated removal of what is essentially a federal cause of action?

8. You hit me in the face and I bring an action against you in federal court (using federal question jurisdiction as my source of subject matter jurisdiction) for a violation of federal securities laws. Failure to state a claim or failure of subject matter jurisdiction? Would it make a difference which it is characterized as?