On Monday, Sen. Rand Paul said that he'd heard of "many tragic cases of walking, talking normal children who wound up with profound mental disorders after vaccines" — a concern that has not been substantiated despite years and years of scientific research into the topic.

Throughout his comments during an interview on CNBC, Paul maintained, "I'm not arguing vaccines are a bad idea. I think they're a good thing." He called them "one of the biggest medical breakthroughs we've had," and added, "I think public awareness of how good vaccines are for kids and how they are good for public health is a great idea."

Yet his nod to the all-too-common — and unsubstantiated — belief that vaccines can cause mental problems in children seems to undercut that certainty.

This belief doesn't divide neatly along political lines, as I wrote earlier today. Indeed, on Twitter, several conservatives strongly disagreed with Paul's remarks — as many did with Gov. Chris Christie for vaccine-related comments earlier Monday.

Rand Paul saying he "heard" of vaccinated kids suffering "profound mental disorders" spoken like a true doctor. So scientifically rigorous! — Philip Klein (@philipaklein) February 2, 2015

The Stupid Party: typical anti-vaxxer a Bay Area-hippie or Manhattan liberal, but it's Republicans who are pandering to them. Why? — Mike Warren (@MichaelRWarren) February 2, 2015

SHUT UP RAND — PEG ن (@pegobry) February 2, 2015

Many beliefs that vaccines cause autism are based on one fraudulent and debunked study, as Julia Belluz explained today.

Here's the context of Paul's remarks. (His office released a follow-up statement reiterating that Paul believes vaccines "should be administered to children," but remaining silent on the issue of mental health.)