On the use of logic and mathematics in economics

27 Apr, 2019 at 12:44 | Posted in Economics | 2 Comments

1200-453314475-deductive-reasoning-example-4 Logic, n. The art of thinking and reasoning in strict accordance with the limitations and incapacities of the human misunderstanding. The basic of logic is the syllogism, consisting of a major and a minor premise and a conclusion – thus:

Major Premise: Sixty men can do a piece of work sixty times as quickly as one man.

Minor Premise: One man can dig a post-hole in sixty seconds; Therefore-
Conclusion: Sixty men can dig a post-hole in one second.

This may be called syllogism arithmetical, in which, by combining logic and mathematics, we obtain a double certainty and are twice blessed.

Ambrose Bierce The Unabridged Devil’s Dictionary

In mainstream economics, both logic and mathematics are used extensively. And most mainstream economists sure look upon themselves as “twice blessed.”

Is there any scientific ground for that blessedness? None whatsoever!

If scientific progress in economics lies in our ability to tell ‘better and better stories’ one would, of course, expect economics journals being filled with articles supporting the stories with empirical evidence confirming the predictions. However, the journals still show a striking and embarrassing paucity of empirical studies that (try to) substantiate these predictive claims. Equally amazing is how little one has to say about the relationship between the model and real-world target systems. It is as though explicit discussion, argumentation and justification on the subject aren’t considered to be required.

In mathematics, the deductive-axiomatic method has worked just fine. But science is not mathematics. Conflating those two domains of knowledge has been one of the most fundamental mistakes made in modern economics. Applying it to real-world open systems immediately proves it to be excessively narrow and hopelessly irrelevant. Both the confirmatory and explanatory ilk of hypothetico-deductive reasoning fails since there is no way you can relevantly analyze confirmation or explanation as a purely logical relation between hypothesis and evidence or between law-like rules and explananda. In science, we argue and try to substantiate our beliefs and hypotheses with reliable evidence. Propositional and predicate deductive logic, on the other hand, is not about reliability, but the validity of the conclusions given that the premises are true.

Deduction — and the inferences that go with it — is an example of ‘explicative reasoning,’ where the conclusions we make are already included in the premises. Deductive inferences are purely analytical and it is this truth-preserving nature of deduction that makes it different from all other kinds of reasoning. But it is also its limitation since truth in the deductive context does not refer to a real-world ontology (only relating propositions as true or false within a formal-logic system) and as an argument scheme is totally non-ampliative — the output of the analysis is nothing else than the input.

If the ultimate criterion of success of a model is to what extent it predicts and coheres with (parts of) reality, modern mainstream economics seems to be a hopeless misallocation of scientific resources. To focus scientific endeavours on proving things in mathematical models, is a gross misapprehension of what an economic theory ought to be about. Deductivist models and methods disconnected from reality are not relevant to predict, explain or understand real-world economies.


  1. Great post.

  2. as an argument scheme is totally non-ampliative — the output of the analysis is nothing else than the input
    To say that the output of a theoretical analysis by deductive reasoning is nothing other than the inputs is like claiming that a souffle is nothing more than eggs, flour, salt, milk and butter.
    It is certainly possible for an argument to fail and emerge as nothing more that a tautology, just as it is possible that a souffle improperly mixed fails to rise.
    The point of analysis is to identify the logic that underlies a system of functional relations, identifying the necessary and sufficient elements that control the “output” or results.
    Strictly speaking, analysis by itself is always a priori, making it idle and ill-conceived speculation when divorced entirely from observation, as some economists are wont to do. Moreover, for all the talk of rigor, I think economists very often fail to meet even minimum standards for doing analysis properly and with adequate critical attention. Conspicuously and with devastating results for doctrine, they fail to explore the implications of pervasive uncertainty for the social and political organization of the economy.
    That said, epistemologically, though analysis does not describe the world, theoretical analysis can help us to guess something about the world that we can not learn by direct observation alone, namely the cause-and-effect relationships. The world, we presume, is a logical place, and when we understand the logic of what we observe, we understand the world.
    We bring our theories to the world, not to test the theories but to test the world. A surveyor or a cartographer needs a geometry in order to measure and map the landscape. The map the cartographer makes is a model, but a model of a different character from a Euclidean theorem. Economists seem particularly prone to confusing their analytical models with maps, despite their own conspicuous failure to observe and measure systematically.

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