How is "correct" tire pressure related to tire volume?
If you ignore the strength in the tire walls (pretty much zero for bike tires) then the pressure (which = force / area ) multiplied by the contact area of the tire on the road must be the force you are putting on the road (ie. the weight of you and the bike).

So for a large tire contact patch you need a lower pressure to support your weight, for a small area narrow tire you need a much higher pressure