Think of supply and demand in terms of labor and wages. As the demand for labor increases, the price of that same labor increases (inflation). As the supply of labor increases (unemployment), the price of labor decreases. The Phillips Curve is but one generalization of the principles of Supply & Demand, as applied to unemployment (excessive supply) and inflation (excessive demand).

The break down of Economics is more along the lines of Monetarists and Keynesians. The Laffer Curve crowd has never really gotten a foothold in the academic world of Economics.