The Friedman controversy originates from
Friedman, M. (1953) "The Methodology of Positive Economics"", in: Essays in Positive Economics, Chicago and London, University of Chicago Press"
Friedman distinguishes assumptions of a theory (like utility and profit maximization) from implications of a theory, like equilibrium prices going up or down as a result of certain variables of the theory going up or down. Friedman opposes the idea of evaluating a theory by testing the realism of its assumptions. He opposes the idea of abandoning assumptions when they are discovered to be not realistic.
A first group erring in this respect, according to Friedman, are those abandoning the assumptions of "perfectness" of competition an of monopoly in analysis market price formation. In the time Friedman wrote, E.H. Chamberlin (The Theory of Monopolistic Competition, Cambridge Mass.: Harvard Un. Press, 1933) and Joan Robinson (Economics of Imperfect Competition, London: Macmillan 1933)had started a new line of research, attraction considerable attention from theoretical economists, with the "theory of monopolistic competition" or "theory of imperfect competition" as its core. It modelled market imperfections and studied the properties of these models: how prices and quantities of consumption goods and factors of production are determined.
A second and recurrent example he uses (although he claims somewhere it is unimportant!) in his article is the following publication:
Lester R.A., "Shortcomings of Marginal Analysis for Wage-Employment Problems", American Economic Review XXXIV, March 1946.
Lester had succeeded in prompting a debate on empirical research he had done on profit maximization by talking to managers and owners of firms. His observations made clear that entrepreneurs do not decide by reference to something like marginal cost and marginal revenue. Lester had concluded that theories based on the assumption of profit maximization in the marginalist sense are not realistic. This had triggered a debate with marginalist theory defended and under attack.
Friedman's position is that the realism of assumptions is irrelevant if you want to know whether a theory is "good". It is only the approximate conformity of its implications with observation that counts. Moreover, Friedman claims, if you want such conformity, quite often you will be successful using unrealistic assumptions. Assumptions should be abstract, that is, only depict the main features of the process modelled, ignoring less relevant details. Implications are all statements derivable from the theory that concern the class of phenomena the theory is designed to explain. Assumptions do not concern that class. So, their realism does not matter. They should be simple. They should enable us to explain "much by little".
Friedman's article raised a controversy that got strangled in a great amount of different and ill defined notions of the terms "theory", "assumption", and "implication", in which he received support and criticism from many of the greatest economists of his time. the early literature has been listed for those interested. The most notable critic was P.A. Samuelson, who claimed no meaningful distinction between "theory", "assumptions", and "implications" can be made, and these terms al refer to exactly the same thing, the model used.