paralyzed: Frozen in place and unable to move or act, such as by
the hold person spell. A paralyzed character has effective Dexterity
and Strength scores of 0 and is helpless, but can take purely mental
actions. A winged creature flying in the air at the time that it
becomes paralyzed cannot flap its wings and falls. A paralyzed
swimmer can’t swim and may drown. A creature can move through a
space occupied by a paralyzed creature—ally or not. Each square
occupied by a paralyzed creature, however, counts as 2 squares.
The above is the only exception to the rule because only casters have mental actions. But if you look at the description of Paralysis it actually contradicts itself.
Anyway, we aren't talking about casters here, we are talking about the Fighter.