by From Lars Syll Mathematics, especially through the work of David Hilbert, became increasingly viewed as a discipline properly concerned with providing a pool of frameworks for possible realities. No longer was mathematics seen as the language of (non-social) nature, abstracted from the study of the latter. Rather, it was conceived as a practice concerned with formulating systems comprising sets of axioms and their deductive consequences, with these systems in effect taking on a life of their own. The task of finding applications was henceforth regarded as being of secondary importance at best, and not of immediate concern. This emergence of the axiomatic method removed at a stroke various hitherto insurmountable constraints facing those who would mathematise the discipline of
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from Lars Syll
Mathematics, especially through the work of David Hilbert, became increasingly viewed as a discipline properly concerned with providing a pool of frameworks for possible realities. No longer was mathematics seen as the language of (non-social) nature, abstracted from the study of the latter. Rather, it was conceived as a practice concerned with formulating systems comprising sets of axioms and their deductive consequences, with these systems in effect taking on a life of their own. The task of finding applications was henceforth regarded as being of secondary importance at best, and not of immediate concern.
This emergence of the axiomatic method removed at a stroke various hitherto insurmountable constraints facing those who would mathematise the discipline of economics. Researchers involved with mathematical projects in economics could, for the time being at least, postpone the day of interpreting their preferred axioms and assumptions. There was no longer any need to seek the blessing of mathematicians and physicists or of other economists who might insist that the relevance of metaphors and analogies be established at the outset. In particular it was no longer regarded as necessary, or even relevant, to economic model construction to consider the nature of social reality, at least for the time being …
The result was that in due course deductivism in economics, through morphing into mathematical deductivism on the back of developments within the discipline of mathematics, came to acquire a new lease of life, with practitioners (once more) potentially oblivious to any inconsistency between the ontological presuppositions of adopting a mathematical modelling emphasis and the nature of social reality. The consequent rise of mathematical deductivism has culminated in the situation we find today.
I think the ‘confidence’ mainstream economists have in their own theories and models, basically is a question of methodology. When applying deductivist thinking to economics, economists usually set up “as if” models based on a set of tight axiomatic assumptions from which consistent and precise inferences are made. The snag is that if the models are to be relevant, we also have to argue that their precision and rigour still holds when they are applied to real-world situations. They often don’t. When addressing real economies, the idealizations necessary for the deductivist machinery to work, simply don’t hold.
The world as we know it has limited scope for certainty and perfect knowledge. Its intrinsic and almost unlimited complexity and the interrelatedness of its organic parts prevent the possibility of treating it as constituted by ‘atoms’ with discretely distinct and stable causal relations. Our knowledge accordingly has to be of a rather fallible kind.
To search for precision and rigour in such a world is self-defeating, at least if precision and rigour are supposed to assure external validity. The only way to defend such an endeavour is to take a blind eye to ontology and restrict oneself to prove things in closed model-worlds. Why we should care about these and not ask questions of relevance is hard to see. We have to at least justify our disregard for the gap between the nature of the real world and our theories and models of it.
Deductivist closed-system theories, as all the varieties of the Walrasian general equilibrium kind, could perhaps adequately represent an economy showing closed-system characteristics. But since the economy clearly has more in common with an open-system ontology we ought to look out for other theories — theories who are rigorous and precise in the meaning that they can be deployed for enabling us to detect important causal mechanisms, capacities and tendencies pertaining to deep layers of the real world.
Rigour, coherence and consistency have to be defined relative to the entities for which they are supposed to apply. Too often they have been restricted to questions internal to the theory or model. But clearly, the nodal point has to concern external questions, such as how our theories and models relate to real-world structures and relations. Applicability rather than internal validity ought to be the arbiter of taste.