There are some things that escape me about the anti-Trump arguments, but in particular the notion of being "qualified" to be President.
In Britain, we are plagued by a class of career politicians at the moment, who study, for example, PPE at Oxbridge, graduate, segway into a job working for a politician, 10 years later get selected for election by the party in an unsafe seat. Tow the line, keep your mouth shut, don't make any enemies, next election cycle they put you in a safe seat and you're in parliament running the country. It's been this way for decades here and abroad, and I doubt there is a person in the western world who can say that these modern career politicians as a group, have not at some point made some catastrophic decisions and their collective lack of experience in anything outside of politics may well be a reason for that.
To me qualifications go hand in hand with the idea of seeing politics as a career, and that idea really irritates me. To not see politics as a calling or a grand instrument of change or a solemn duty, but as a source of income and status. It isn't how politics should be. It might be why Trump is doing as well as he is. Clinton is nothing special, vote for her, you get more of the same. Trump doesn't need the money, he is already more famous than many politicians can ever hope to be. I think Trump voters sense that on some level, even if they don't agree with everything he says.
Are qualifications for presidency really something to be concerned about? Or is this just a cheap shot that doesn't make sense if analysed? To work under a political party machine you have to be on board with 99% of that party's vision. Anyone who deviates from that vision is either excluded or controlled and will never see power. So to be qualified means to have worked in politics... but to work in politics you have be similar enough in thought, word and deed to the extant political class. That's how the system is right now, so any candidate offering real change, will be an enemy of the political class, will not have worked with or under them and will be "unqualified" by default.
Perhaps you mean qualified in the sense of foreign relations? To be able to take the lead in international affairs, to not make a joke about eating dogs in front of his Chinese counterpart. A valid concern you might think, but everyone's memory seems to be very short, you guys had an idiot for president quite recently. His endless gaffes, unthinking one-liners, ditsy behaviour and unintentional offence had the whole world in fits of laughter for years. A nuclear exchange didn't happen with the inept Mr. Bush at the helm. Trump may actually be better than Bush in this regard once his necessarily demagogic campaign comes to an end.
The shining example of Bush also works for the final point I would like to make: Even if there is such a thing as being qualified to be president, the president is not the government. The Bush administration was possibly the most Machiavellian government the US has ever seen, Bush the man was an empty headed teddy bear.
Trump, I think, is neither of the two seemingly contradictory personas the media have created for him, that of the hapless idiot and the closet racist evil visionary. He is not as dumb as Bush, but he's not the Dark Lord of Mordor either planning to sign Mexican internment orders with the blood of ISIS jihadis. He is smart enough to fill the government with people much smarter than he is to find solutions to the (very real) issues on which he is getting elected. And that I think is what you need in a president, someone to set the tone and find the right people to actually make things happen.
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Behold! we are not bound for ever to the circles of the world, and beyond them is more than memory, Farewell!