Why does supply (and demand) shift left and right as opposed to up and down? I've wondered about this for a long time. In the past I rationalized it by saying that up and left were the same (or at least have the same overall effect), and that thinking in terms of left and right works for increase/decrease in both supply and demand curves. But things like taxes raise prices which is most intuitively viewed as an upward movement (although saying left and right are useful regardless). Then when I encountered Keynesian aggregate supply (which makes it obvious that left and up are not interchangable), I was astounded when I learned that decrease in supply, including supposedly taxes, actually moved the curve left, not up. Shouldn't taxes exist which increase price levels of all firms in order to pay for them, moving (Keynesian) aggregate supply up because whatever quantity of goods firms produce they have to set prices higher to pay for the cost of taxes?
Both ways of thinking are correct. They are two equivalent and complementary ways of thinking about the same thing:


Shift left (right): At each price, the quantity that producers are willing and able to supply has gone down (up).
Shift up (down): To get producers to supply each quantity, the required price has gone up (down).


Example where the supply curve shifts left or (equivalently) up: