If you're studying Szarkowski's The Photographer's Eye, you are already demonstrating more discernment than most.
The Nature of Photographs, by Stephen Shore, is almost a companion or sequel to Szarkowski. Two books by Robert Adams will inspire you: Beauty in Photography and Why People Photograph. Try Szarkowski's Looking at Photographs as well. Then, if you want to challenge yourself, pick up Susan Sontag's On Photography and Roland Barthe's Camera Lucida.
All of these books are short, but contain lifetimes of lessons. Each can be read over and over again and each time you will learn something new. And, not a single one talks about f-stops, ISO, noise, bokeh, crop factor, or any of the other drivel that bogs people down. They are all about vision and understanding this fascinating and addictive craft.