There are some terrific answers here (Hi William! :) so I'll aim to insert some things I haven't seen addressed.
Distraction for you:
Your most precious resource is your personal bandwidth and focus. This is a distraction that isn't helping build your business, and since this employee has "fired your company" (as some recruiters are wont to say) you will not see a return on further developmental time spent with them.
Risk for you, as an owner:
Today, would you hire an engineer to build your company (viz a viz your product) that wasn't taking the long view? Probably not, and by keeping them on staff, you're saying, "yes" to that, every day. What do you think the quality of the decision making will be when hands hit the keyboard?
Risk for you, as a leader:
By allowing them to stay, as a leader, you're telling your team that it's OK having people in some form or another "checked out." Unless this is a remote engineer or a team of one, their position (one foot out the door) will be socialized if it hasn't been already. That stalls any team storming/norming/performing in its tracks, because the team has some significant uncertainty associated with it.
Happy to discuss further!