“Think just how different the world would be,” said Senator Ted Cruz on Monday, in a speech so packed with vision-spinning and the word “imagine” that it seemed as if John Lennon had returned, as a Hispanic Texan running a hard-right, anti-establishment, Christian-themed campaign for the White House. Weird. But weird is the essence of Mr. Cruz, who is now the first major Republican in the 2016 race. Let the fund-raising begin. Commence the swelling of the Cruz coffers, and of Mr. Cruz’s public profile beyond the gated confines of C-Span and Fox News.

The “imagines” that Mr. Cruz doled out were chosen for his audience, students at Liberty University in Lynchburg, Va. Robust cheers greeted one of the first: “Imagine young people coming out of school with four, five, six job offers.” He summoned many images that would be hard to argue with. “Imagine instead of economic stagnation, booming economic growth.” “Imagine innovation thriving on the Internet.” “Imagine America finally becoming energy self-sufficient.” “Imagine a federal government that protected the privacy rights of every American.”

Of course, if you know Mr. Cruz, or are familiar with how government is supposed to work, or with reality in general, you’ll find some of his imaginaries problematic, like abolishing the Internal Revenue Service, sealing the border, or “repealing every word of Obamacare.”

“Imagine a federal government that works to defend the sanctity of human life and to uphold the sacrament of marriage,” he said. But Mr. Cruz says he is a champion of personal liberty, too, and gay people who love each other are demanding their liberty to marry, just not in a way he finds acceptable. No data support Mr. Cruz’s claim that insurance premiums are “skyrocketing” under Obamacare. Immigrants, legal and otherwise, are building this country, and efforts to vacuum-seal the border would continue to fail, and the country would suffer from its hostility to its immigrants no matter what Mr. Cruz says. The rest of the world, of course, is indifferent to one Republican’s oratorical dog whistles. The global climate will keep changing, and causing calamities, with or without the acknowledgment of Mr. Cruz and his fellow climate know-nothings.

Mr. Cruz’s speech was an exercise in crowd-pleasing dissonance; the contradictions slip by if you’re not paying attention. America is great but needs to be made great again. Privacy is sacrosanct, and government should not get between you and your doctor, unless you’re a woman who wants to avoid or end a pregnancy. Mr. Cruz wants to repeal programs that protect some immigrants from deportation, but he has also said in the past that Republicans need to do better with Hispanic voters or risk extinction as a national party. His federalist views are incoherent: he wants states to be free to experiment with marijuana legalization, but attacked Mr. Obama for not cracking down on states that do so.

Mr. Cruz wants voters who sent him to Washington to keep him in Washington, with a promotion, though he says, “The answer will not come from Washington.”

A heated, crowded presidential primary can be wearying, but useful for sorting out differences and contradictions and determining where a party stands on things. Mr. Cruz, whose oratory captures so many Republican paradoxes and idiocies, especially on immigration and health care, has set a solid baseline for the messy job ahead.