A new conceptual framework for understanding multiscaling in classical field theories in general, and in turbulence in particular, is proposed. Multiscaling refers to the phenomenon that structure functions of different order are characterized by independent scaling exponents. In our approach the time dependence of the fields is taken explicitly into account. The fields are assumed to be Hölder continuous in space with a range of Hölder exponents, with the worst singularities having a shorter lifetime. As a result, the time averaged structure functions exhibit a spectrum of scaling exponents as is seen in experiments on turbulence. By taking higher order structure functions one exposes again the more singular spatial contributions. We expect that this framework reflects the equations of motion better than the currently popular fractal and multifractal models.