Computer Simulations, Idealizations and Approximations

It's uncontroversial that notions of idealization and approximation are central to understanding computer simulations and their rationale. What's not so clear is what exactly these notions come to. Two distinct forms of approximation will be distinguished and their features contrasted with those of idealizations. These distinctions will be refined and closely tied to computer simulations by means of Scott-Strachey denotational programming semantics. The use of this sort of semantics also provides a convenient format for argumentation in favor of several theses I shall propose concerning the role computer implemented approximations and idealizations play in fixing what the acceptance of an underlying scientific theory is or should be.