Robert M. Gary writes:

I was wondering about that because Anthony's assertion that there is a
specical medical for deaf pilots that only allows them to fly with
another pilot makes no sense.

A deaf pilot can get just about any certificate except certain types of
commercial certificate; essentially she can obtain anything that doesn't
require radio communication. During the medical, she must take a Special
Medical Flight Test to verify that she can recognize an engine failure,
recognize an approaching stall, and recognize retractable gear emergencies.
If she passes that, eventually she'll get a SODA and her medical.

First, what would be the purpose of such
a medical since you don't need a medical to fly with another pilot?

The medical allows a deaf pilot to fly alone.

Second, how could you get a private without meeting the solo
requirements?

Deaf pilots can solo by avoiding airspaces that require radio.

They can fly into controlled airspace requiring radio if they have a copilot
who can handle the radio. It's not clear whether this copilot must also be a
licensed pilot, but he probably does, since the deaf pilot's license
specifically says that it is valid only for flight without radio, so the
copilot would technically be the PIC and would therefore require a license of
his own, even if he were not flying the plane.