Quantification of Theoretical Terms and the Falsifiability of Theories

Karl Popper introduced the notion that falsifiability rather than verifiability is the central desideratum of scientific theories. The debate of recent years among Popper, Kuhn, Lakatos and others has taught us how elusive is the criterion of falsifiability when it is applied to the actual enterprise of science in all of its rich historical detail. Not only is the line between observables and theoretical terms somewhat nebulous, but many alternative tests have been proposed for what should count as a 'decisive' falsification. In spite of these difficulties in applying the concept of falsifiability in a wholly clear-cut way to real historical cases, it is still a matter of considerable theoretical interest and importance to construct rigorous formal characterisations of falsifiability, and to see what kinds of formalised theories satisfy various falsifiability criteria. The lack of such formal characterisations will contribute an additional dimension of confusion and ambiguity in attempts to apply falsifiability notions to real scientific theories. Roughly speaking, a theory is falsifiable if there exist one or more sets of possible observations that could disconfirm the theory. We may well wish to impose an even stricter condition, strong falsifiability: if the theory is empirically false in any way, then there should exist possible sets of observations to disconfirm it. Thus (Rynasiewicz [1983]), VxFx is strongly falsifiable, while VxFx & 3xGx is only weakly falsifiable. For, in the former