On the poverty of deductivism

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Lars Pålsson Syll
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In mainstream macroeconomics, there has for long been an insistence on formalistic (mathematical) modelling, and to some economic methodologists (e.g. Lawson 2015, Syll 2016) this has forced economists to give up on realism and substitute axiomatics for real world relevance. According to the critique, the deductivist orientation has been the main reason behind the difficulty that mainstream economics has had in terms of understanding, explaining and predicting what takes place in modern economies. But it has also given mainstream economics much of its discursive power – at least as long as no one starts asking tough questions on the veracity of — and justification for — the assumptions on which the deductivist foundation is erected.

The kind of formal-analytical and axiomatic-deductive mathematical modelling that makes up the core of mainstream economics is hard to make compatible with a real-world ontology. It is also the reason why so many critics find mainstream economic analysis patently and utterly unrealistic and irrelevant.

Although there has been a clearly discernible increase and focus on ‘empirical’ economics in recent decades, the results in these research fields have not fundamentally challenged the main deductivist direction of mainstream economics. They are still mainly framed and interpreted within the core ‘axiomatic’ assumptions of individualism, instrumentalism and equilibrium that make up even the ‘new’ mainstream economics. Although, perhaps, a sign of an increasing – but highly path-dependent — theoretical pluralism, mainstream economics is still, from a methodological point of view, mainly a deductive project erected on a formalist foundation.

If macroeconomic theories and models are to confront reality there are obvious limits to what can be said ‘rigorously’ in economics.  For although it is generally a good aspiration to search for scientific claims that are both rigorous and precise, the chosen level of precision and rigour must be relative to the subject matter studied.  An economics that is relevant to the world in which we live can never achieve the same degree of rigour and precision as in logic, mathematics or the natural sciences.

An example of a logically valid deductive inference (whenever ‘logic’ is used here it refers to deductive/analytical logic) may look like this:

Premise 1: All Chicago economists believe in the rational expectations hypothesis (REH)
Premise 2: Bob is a Chicago economist
—————————————————————–
Conclusion: Bob believes in REH

In a hypothetico-deductive reasoning — hypothetico-deductive confirmation in this case — we would use the conclusion to test the law-like hypothesis in premise 1 (according to the hypothetico-deductive model, a hypothesis is confirmed by evidence if the evidence is deducible from the hypothesis). If Bob does not believe in REH we have gained some warranted reason for non-acceptance of the hypothesis (an obvious shortcoming here being that further information beyond that given in the explicit premises might have given another conclusion).

The hypothetico-deductive method (in case we treat the hypothesis as absolutely sure/true, we should rather talk of an axiomatic-deductive method) basically means that we

• Posit a hypothesis
  •Infer empirically testable propositions (consequences) from it
  •Test the propositions through observation or experiment
  •Depending on the testing results either find the hypothesis corroborated or falsified.

However, in science we regularly use a kind of ‘practical’ argumentation where there is little room for applying the restricted logical ‘formal transformations’ view of validity and inference. Most people would probably accept the following argument as a ‘valid’ reasoning even though from a strictly logical point of view it is non-valid:

Premise 1: Bob is a Chicago economist
Premise 2: The recorded proportion of Keynesian Chicago economists is zero
————————————————————————–
Conclusion: So, certainly, Bob is not a Keynesian economist

In science, contrary to what you find in most logic textbooks, only few argumentations are settled by showing that ‘All Xs are Ys.’ In scientific practice we instead present other-than-analytical explicit warrants and backings — data, experience, evidence, theories, models — for our inferences. As long as we can show that our ‘deductions’ or ‘inferences’ are justifiable and have well-backed warrants, other scientists will listen to us. That our scientific ‘deductions’ or ‘inferences’ are logical non-entailments simply is not a problem. To think otherwise is committing the fallacy of misapplying formal-analytical logic categories to areas where they are irrelevant or simply beside the point.

Scientific arguments are not analytical arguments, where validity is solely a question of formal properties. Scientific arguments are substantial arguments. Whether Bob is a Keynesian or not, is not something we can decide on formal properties of statements/propositions. We have to check out what he has actually been writing and saying to see if the hypothesis that he is a Keynesian is true or not.

In a deductive-nomological explanation — also known as a covering law explanation — we would try to explain why Bob believes in REH with the help of the two premises (in this case actually giving an explanation with only little explanatory value). These kinds of explanations — both in their deterministic and statistic/probabilistic versions — rely heavily on deductive entailment from premises that are assumed to be true. But they have precious little to say on where these assumed-to-be-true premises come from.

The deductive logic of confirmation and explanation may work well — given that they are used in deterministic closed models. 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 the science of economics. Applying the deductive-axiomatic method to real world systems immediately proves it to be excessively narrow and irrelevant. Both the confirmatory and explanatory ilk of hypothetico-deductive reasoning fail, since there is no way you can relevantly analyse 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, deduction is totally non-ampliative: the output of the analysis is nothing else than the input.

Just to give an economics example, consider the following rather typical, but also uninformative and tautological, deductive inference:

Premise 1: The firm seeks to maximise its profits
Premise 2: The firm maximises its profits when marginal cost equals marginal income
——————————————————
Conclusion: The firm will operate its business at the equilibrium where marginal cost equals marginal income

This is as empty as deductive-nomological explanations of singular facts building on simple generalizations:

Premise 1: All humans are less than 20 feet tall
Premise 2: Bob is a human
——————————————————–
Conclusion: Bob is less than 20 feet tall

Although a logically valid inference, this is not much of an explanation (since we would still probably want to know why all humans are less than 20 feet tall).

Deductive-nomological explanations also often suffer from a kind of emptiness that emanates from a lack of real (causal) connection between premises and conclusions:

Premise 1: All humans that take birth control pills do not get pregnant
Premise 2: Bob took birth control pills
——————————————————–
Conclusion: Bob did not get pregnant

Most people would probably not consider this much of a real explanation.

Learning new things about reality demands something else than a reasoning where the knowledge is already embedded in the premises. These other kinds of reasoning — induction and abduction — may give good, but not conclusive, reasons. That is the price we have to pay if we want to have something substantial and interesting to say about the real world.

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References

Lawson, Tony (2015): Essays on the nature and state of modern economics. Routledge.

Syll, Lars (2016): On the use and misuse of theories and models in mainstream economics. WEA Books.