Neither orthodox nor heterodox economists have a clear idea of the fundamental concepts income and profit. What is known with certainty from the elementary structural axiomatic analysis is that the conventional approaches are logically deficient.
If you apply a conception of total monetary profit that is, in the elementary case, different from Qm=C−Y+DN (legend see axioms) your theory is demonstrably false and therefore inappropriate for the solution of real-world problems. The definition of profit is not a matter of personal taste but of logical and material consistency. Ultimately, the selection of axioms determines analytical success or failure.
If you are a businessman you know the particular profit determinants of your firm but this does not give you the determinants of total profit for the business sector as a whole. The generalization of partial truths is prone to the fallacy of composition. From individual experience follows no correct profit theory. Because of this, business people do not know better than average citizens how the economy works.
If you are a consultant or advisor and your background knowledge contains assertions like: the value of the product equals the value of factor incomes, total income is the sum of wages and profits, distributed profit is equal to profit, or saving equals investment, your advice is not based on state-of-the-art analysis and is, at best, useless.
If you are a student you are expected to find out whether your teacher's theory is true or false or incomplete. Growth of knowledge is what science is all about. The acceptance of basic tenets of conventional economics is indicative of a lack of scientific acumen. From a student who has accepted supply-demand-equilibrium as an explanation not much is to be expected.
With regard to the formal foundations of a paradigm, it is not the case that anything goes. John Stuart Mill clearly stated the key question: “What are the propositions which may reasonably be received without proof? That there must be some such propositions all are agreed, since there cannot be an infinite series of proof, a chain suspended from nothing. But to determine what these propositions are, is the opus magnum of the more recondite mental philosophy.”
Neither Orthodoxy nor Heterodoxy has accomplished the opus magnum. Economics is still at the stage of a proto-science. A 'sequence of models' (Koopmans) is no substitute for a comprehensive theory that realizes both formal and material consistency.