"We're rethinking publishing and building a new platform from scratch," Williams said in a message on the site.
"Lots of services have successfully lowered the bar for sharing information, but there's been less progress toward raising the quality of what's produced."
"While it's great that you can be a one-person media company, it'd be even better if there were more ways you could work with others."
Stone and Williams are building the platform through their Obvious Corporation, an enterprise named for the notion that many great ideas seem "obvious" in retrospect.
"We believe publishing, and media much more broadly, is important... It's easy to forget this given how much pointless and destructive media is in the world," Williams said.
"But there's also more great stuff than ever before -- and we haven't even scratched the surface of what our smart devices and our networks that connect most of the planet might enable."
Reading Medium posts was open to anyone with a Twitter account, but posting was initially limited to an invitation-only group that Williams promised would expand rapidly to include those who register.