Election years are always full of false claims and false beliefs. Candidates will tell you that some number — the deficit, unemployment, inflation — is going one way when it’s really going the other way. They’ll say that things are good when they’re bad, or bad when they’re good. They’ll invent scandals about their opponent and deny that their own scandals amount to anything. They’ll find imaginary disasters and injustices lurking in their opponent’s proposals, while making ridiculous claims about the benefits of their own.

That’s par for the course and a lot of it doesn’t matter. Americans are pretty skeptical of political claims, most of which go in one ear and out the other. Often the original disagreement gets lost in a subsequent argument about whether one or the other of the candidates is lying, or whether the media is holding one candidate to a higher standard than the other. Partisan voters find their own side’s case convincing, and the others tune out.

But there’s another kind of falsehood we should pay more attention to: the ones that slip past our filters and get woven into our fundamental image of who a candidate is and what he or she has to offer. Often they aren’t lies, exactly, or aren’t the clear fabrications that fact-checking columns like to expose. They’re more like the illusions and misdirections of stage magic: The card was never really in the deck, and the coin never left the magician’s hand. The magician may never say that it was or it did, while saying dozens of other false things of no particular significance to the illusion. The trick didn’t fool us so much as suggest ways that we could fool ourselves.

So in compiling this list, I completely ignored high-profile arguments like whether President Trump really can build his “big, beautiful wall” or make Mexico pay for it. I ignored all the insults and hyperbole, all the did-he-or-didn’t-he debates about his past, and the I-can’t-believe-he-said-that moments. Instead I looked for misconceptions that have gotten established in his public image, the kinds of things people take for granted while they argue about other things.

I found some. Whether you like Trump or not, your thinking is very likely influenced by one or more of these four false beliefs about him.

Donald Trump is one of America’s top businessmen. Trump himself makes this argument:

I’m running for office in a country that’s essentially bankrupt, and it needs a successful businessman

His critics claim to be appalled that somebody with no experience in public office could become president, but actually that’s fairly common in American history. Usually the outsider is a victorious general, like Eisenhower or Grant or Washington. Nobody has ever gone straight from academia to the presidency, but Democrats have been known to elevate university professors like Daniel Moynihan or Elizabeth Warren to the Senate. And maybe nobody has made the leap from the boardroom to the White House yet, but the idea of a businessman-president is not new. Ross Perot made the most credible third-party run in modern times. In the 1980s, Chrysler President Lee Iacocca was often the subject of presidential speculation. Mitt Romney didn’t like to talk much about his days as governor of Massachusetts (when he passed RomneyCare, the forerunner of ObamaCare) so he mostly ran on his record as a businessman. One of the candidates running against Trump in this year’s primaries, Carly Fiorina, was also coming from the business world.

So choosing one of our top businessmen or businesswomen to be president is actually not that radical a notion.

But is Trump in fact a top businessman? Not really. He’s a businessman, and he’s been OK at it, but he’s not at all the genius he’d like us to think he is.

To start with, he is rich, but not nearly as rich as he claims. He boasts of a $10 billion fortune, but Forbes estimates less than half that, $4.5 billion, and Bloomberg even less, $2.9 billion. Either estimate could be improved if Trump would ever release his tax returns, which is probably the reason he doesn’t. (For comparison, Forbes estimates that another businessman/politician, Mike Bloomberg, is nearly ten times as rich, worth an estimated $38 billion.)

Even $2.9 billion still seems like a lot of money, though, so let’s consider how he got it. Trump inherited a New York real estate empire from his father. The size of his inheritance (in 1974) is not a matter of public record, so estimates vary from $40 million to as high as $200 million. A few years later, in 1978, Business Week estimated Trump’s net worth at $100 million. Max Ehrenfreund observes that if Trump had cashed out then and stashed the money in an S&P 500 index fund, he’d be worth $6 billion today — considerably more than he probably has.

But even that’s not the full story. More than just money, Trump inherited a New York City real estate business and the corresponding connections. And although he talks a lot about his international properties and his diverse business ventures, New York real estate is still the center of his empire. The further he has gotten from his roots — whether it was his bankrupt Atlantic City casino, the Trump Tower Tampa project that collected deposits on luxury condos but went broke without building any of them, or non-real-estate failures like Trump Steaks, the Trump Shuttle, or Trump magazine — the less success he’s had. To the extent that he’s a successful businessman at all, he’s a successful NYC real estate developer.

Now look at the era that his career has spanned. Trump received his inheritance when New York City was bottoming out. In 1975 the city very nearly went bankrupt. Since then, the long-term trend has been dramatically upward. In retrospect, the last 40 years has been a very good time to be in New York City real estate. When the trend is on your side to that extent, you don’t have to be a that good to come out ahead.

For comparison, look at my father. He bought a 160-acre farm for $30,000 in 1950, and when I was dissolving his estate a few years ago, I sold it for $1 million. Did that significant increase reflect my Dad’s deep insight into real estate? Not to disparage my Dad’s intelligence, but no: His career as a farmer happened to fall during an era when the price of farmland went up.

On a larger scale, something similar happened to Trump. While he has engaged in a lot of impressive wheeling and dealing during his career, that activity is probably irrelevant to his wealth, and may even have kept him from being considerably more successful. He’s rich because his Dad was rich, and the business he inherited was destined to do well as long as he didn’t screw it up too badly.

He is financing his own campaign rather than selling out to special interests. Last September, Trump announced on Facebook:

Of course, Trump’s campaign was never completely funded out of his own pocket — there was always the money he collected by selling campaign hats and such, as well as small donations — but none of that invalidated his main point: Nobody bought a Make America Great Again hat or sent him $25 with the idea that they were buying a favor from the next president.

The more interesting question was how that self-financing worked: Trump gave his campaign very little. Instead, he loaned money to his campaign. According to the Sunlight Foundation, as of late February, loans from Trump himself made up 68.7% of the campaign’s funding. Last week, the Wall Street Journal reported: “Mr. Trump lent his campaign $36 million of the $47 million he spent on the primaries through March, with the rest coming mostly from small donations.”

But now that he is heading towards a fall campaign that could cost a billion or more, self-financing is out the window. Trump now has a joint fund-raising agreement with the Republican National Committee, and is pursuing all the big-money donors who usually give to Republican campaigns. A Great America super PAC is also raising money to support Trump’s general-election campaign.

One possibility is that Trump could use big-donor money to pay back the loans he made to the campaign — a sort of retroactive de-self-financing. In other words, money collected from lobbyists and billionaires could go straight into Trump’s pocket. Campaign spokesmen say that won’t happen, but there has also been no move to officially turn the loans into contributions.

In the primary campaign, Trump frequently claimed that big donors own candidates. He said of Ted Cruz: “Goldman Sachs owns him. Remember that folks.” Now he’s looking for a billion dollars from the same people who funded his Republican rivals. To exactly the same extent that they were selling themselves then, he’s selling himself now.

He was against invading Iraq. Trump counters Hillary Clinton’s greater experience as First Lady, Senator, and Secretary of State by claiming to have better judgment. The foremost example he gives is that he spoke out against invading Iraq, while she voted to authorize the invasion.

In a February debate with the other Republican candidates in South Carolina, he said

I’m the only one on this stage that said, “Do not go into Iraq. Do not attack Iraq.” Nobody else on this stage said that. And I said it loud and strong. And I was in the private sector. I wasn’t a politician, fortunately. But I said it, and I said it loud and clear, “You’ll destabilize the Middle East.”

He may remember it that way, but that’s not how it happened. PolitiFact, the Washington Post Fact Checker, and FactCheck.Org have all looked at this claim. PolitiFact rates it False and the WaPo gives its lowest rating, four Pinocchios. FactCheck.Org does not give a simple rating, but provides a timeline of Trump’s statements on the war that begin with support and only come around to opposition later, at about the same time as the rest of the country.

The invasion didn’t begin until March, 2003, but the national debate about authorizing it happenedthe previous fall. Congress passed the authorization resolution (the one Hillary voted for) in October, 2002. In a September, 2002 radio interview, Howard Stern asked Trump “Are you for invading Iraq?” and Trump responded “Yeah, I guess so.”

Like most of the country (and Clinton), Trump eventually soured on the war. But it happened little by little, as is clear from this interview for the August 2004 edition of Esquire. By then, things had started going bad in Iraq: The first battle of Fallujah had been the previous April, and it was starting to be clear that we wouldn’t find the WMDs that had been the most impressive justification for the original invasion. But even this late, Trump didn’t say the invasion was a bad idea, just that he’d have done it better.

Look at the war in Iraq and the mess that we’re in. I would never have handled it that way. Does anybody really believe that Iraq is going to be a wonderful democracy where people are going to run down to the voting box and gently put in their ballot and the winner is happily going to step up to lead the county? C’mon. Two minutes after we leave, there’s going to be a revolution, and the meanest, toughest, smartest, most vicious guy will take over. And he’ll have weapons of mass destruction, which Saddam didn’t have. What was the purpose of this whole thing? Hundreds and hundreds of young people killed. And what about the people coming back with no arms and legs? Not to mention the other side. All those Iraqi kids who’ve been blown to pieces. And it turns out that all of the reasons for the war were blatantly wrong. All this for nothing!

In short, Trump’s trajectory on Iraq is similar to Clinton’s: At first he supports the war. Then he begins to have doubts about how the Bush administration is handling it. And eventually he comes to believe that it was a bad idea. The major difference between the two candidates is that Clinton admitted her mistake; Trump just replaced those memories with ones where he was right from the get-go.

His Muslim immigration ban is just temporary. A press release in December said Trump was

calling for a total and complete shutdown of Muslims entering the United States until our country’s representatives can figure out what is going on.

Subsequent statements have described the ban as “temporary”. This January TV ad, for example, talked about

a temporary shutdown of Muslims’ entering the United States until we can figure out what’s going on.

“Temporary” is a big part of the ban’s appeal. It’s dubious constitutionally to apply a religious test to immigrants and visitors, and it’s not at all clear how such a ban would work. (If I want to come to America, what proof can I offer that I’m not a Muslim?) But problems are easy to ignore if they’re just temporary.

However, calling something “temporary” doesn’t make it temporary. The Pentagon built gobs of “temporary” buildings during World War II, and so many of them were still in use forty years later that the Military Construction Act of 1983 had to specifically mandate their destruction.

If something is really temporary, it’s end is in sight. Either it has an explicit time limit, or it is tied to some other process that is clearly headed towards termination. (As in: “We’ll come straight home after the football game.”) Trump’s ban isn’t like that.

Picture it this way: Suppose you’re a ninth-grader and your parents are punishing you by taking away your video game access. If they tell you your access is gone for a week, that’s temporary. If they tell you it’s gone “until you start passing your math quizzes again”, that also is temporary (assuming that you can pass those quizzes if you start studying). But if it’s “until you shape up”, with no specifics given about what shape up means, that’s not temporary. They’ve opened the possibility that they may change their minds some time in the future, but that’s about all.

That’s all Trump has offered. Maybe at some point in the future, President Trump will go on TV to say, “OK, I’ve figured out what’s going on, so Muslims can start coming in again.” I have trouble picturing that happening at all, but even if I stretch my imagination, it’s not happening on any predictable schedule.