Former Mayor Rudy Giuliani started off an appearance on CBS’ “Face The Nation” by expressing “deep sympathy” for the black men killed by police in Louisiana and Minnesota, and the five police officers killed in Dallas. He should have stopped there.

Instead, he said on Sunday that black children are less endangered by police than by “other black kids.” He admonished black children to be “respectful” to police, despite recent examples of police shootings in which respectful behavior didn’t appear to help. And he called Black Lives Matter, a movement calling attention to structural racism in 2016, “inherently racist.” Giuliani doubled down Monday, saying on Fox News Channel that he has “saved a lot more black lives than Black Lives Matter.”

The comments were widely criticized. But they also represent an out-of-date point of view. Giuliani rightly decries gun violence and violence against police, but doesn’t seem to understand the equally obvious truth that police reforms are necessary and the police killings of minorities are part of a systemic issue that must be addressed. In a live-streaming age, this truth is impossible to ignore.

But Giuliani is a remnant of a different world, the former mayor of a city once polarized by cases like the brutalizing of Abner Louima and police shooting of Amadou Diallo — a city riven by racial disparities that the mayor did little to ease. It is a mindset shared by presumptive Republican nominee Donald Trump, whom Giuliani supports and who gave a dog-whistling speech Monday, saying “make America safe again.” A mindset formed when the city regularly endured more than 1,000 yearly homicides, which contributed to the election of a law-and-order mayor.

Those numbers have plummeted — beginning before and throughout Giuliani’s tenure, but also after. On Monday, the city announced half-year crime numbers for 2016. Though crime has ticked up in the Bronx and other sections, serious crimes citywide are at historic lows despite the end of stop-and-frisk, a tactic favored by Giuliani.

We live in a safer city than the one Giuliani presided over, and we have the opportunity to make it a fairer one. That means abandoning Giuliani’s backward thinking.