to question 1) I think that accidental connections include the ability of a pope to command acts of the state that has left them derelict, or for a gov. to seek counsel from a clergy member.
to your argument against state-church est. I think you give a good case but how does it mesh with the Syllabus of Errors?
I still cannot answer the first. I do not understand the question. I need specifics. In what case has a government (our government) sought the advice of the Catholic Church. Actually, I do know one here in NY. But I want to understand your question.
I’m not familiar with the Syllabus of Errors, but a quick look seems to me that it’s not a call to establish the Church as the religion of any government. It removed and corrected errors where there was too much secular involvement in the Church, calls for liberalism, and where there was actual persecution of the Church by governments. In fact, the Syllabus ends with a restatement of Jesus’ words on “render unto Cesar what is Cesar’s and render unto God what is God’s.” It acknowledges that there is secular authority and there is Church authority. Secular authority is not to be disrepected by this Syllabus of errors.
Look at #77. It says the error was that it is not expedient for the Church to be a state religion. We look at the word “expedient” which can mean that the document could be saying (in the original) that it would be “inconvenient”, “improper” or “immoral” for the Church to be a state religion, and it was removed. There’s no proof either way and the statement is too strong an assertion. That does not call for the establishment of a state sponsored religion - nor does it negate the idea that some countries, such as the U.S, prohibit the establishment of one.
However, John Henry Newman said the Syllabus of Errors was easily misinterpreted too unless the original document being challenged was checked. So, what we have are excerpts from documents, of which parts are considered in error. So, without full reading of the whole of the listed documents we cannot know the context in which each error was made. In fact, John Henry Newman said the Syllabus itself was misinterpreted.
Please read here the section on Catholics, where John Henry Newman is quoted:
en.wikipedia.org/wiki/Syllabus_of_Errors#Catholics
Finally, the document ends with:
“The faith teaches us and human reason demonstrates that a double order of things exists, and that we must therefore distinguish between the two earthly powers, the one of natural origin which provides for secular affairs and the tranquillity of human society, the other of supernatural origin, which presides over the City of God, that is to say the Church of Christ, which has been divinely instituted for the sake of souls and of eternal salvation… The duties of this twofold power are most wisely ordered in such a way that to God is given what is God’s (Matt. 22:21), and because of God to Caesar what is Caesar’s, who is great because he is smaller than heaven. Certainly the Church has never disobeyed this divine command, the Church which always and everywhere instructs the faithful to show the respect which they should inviolably have for the supreme authority and its secular rights…”