Deduction, Induction, Abduction in Science and Economics

Deduction, Induction, Abduction in Science and Economics

10 Nov, 2025 at 13:37 | Posted in Theory of Science & Methodology | Leave a comment

In science — and economics — one could argue that there are basically three kinds of reasoning available:

(1) Deduction

• Premise 1: All Chicago economists believe in the Rational Expectations Hypothesis (REH).

• Premise 2: Robert Lucas is a Chicago economist.

• Conclusion: Robert Lucas believes in REH.

Here we have an example of a logically valid deductive inference (and, following Quine, whenever logic is used in this essay, ‘logic’ refers to deductive/analytical logic).

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 Robert Lucas 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 cases where we treat the hypothesis as absolutely certain/true, we 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 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 ‘valid’ reasoning even though, from a strictly logical point of view, it is nonvalid:

• Premise 1: Robert Lucas is a Chicago economist

• Premise 2: The recorded proportion of Keynesian Chicago economists is zero

• Conclusion: So, certainly, Robert Lucas is not a Keynesian economist

How come? Well, I suppose one reason is that in science, contrary to what you find in most logic textbooks, not many arguments 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, our colleagues listen to us. That our scientific ‘deductions’ are logical non-entailments simply is not a problem. To think otherwise is to commit the fallacy of misapplying formal-analytical logic categories to areas where they are pretty much 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 Robert Lucas is a Keynesian or not is not something we can decide based on the formal properties of statements. We have to check what the fellow has actually been writing and saying to see if the hypothesis that he is a Keynesian is true.

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

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 it to real-world systems, however, immediately proves it to be excessively narrow and hopelessly 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 — proportional 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 other 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 MC = MR

• Conclusion: The firm will operate its business at the equilibrium MC = MR

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

• Premise 1: All humans are less than 20 feet tall

• Premise 2: Robert Lucas is a human

• Conclusion: Robert Lucas 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 the birth control pill do not get pregnant

• Premise 2: Lars Syll took the birth control pill

• Conclusion: Lars Syll did not get pregnant

I imagine most people would agree that this is not much of a real explanation.

Learning new things about reality demands something other than a reasoning where the knowledge is already embedded in the premises. These other kinds of reasoning 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.

(2) Induction

• Premise 1: This is a randomly selected large set of economists from Chicago

• Premise 2: These randomly selected economists all believe in REH

• Conclusion: All Chicago economists believe in REH

In this inductive inference, we have an example of a logically non-valid inference that we would have to supplement with strong empirical evidence to really warrant. And that is no simple matter at all.

Justified inductions presuppose a resemblance of a sort between what we have experienced and know, and what we have not yet experienced and do not yet know. Just to exemplify this problem of induction, let me take two examples.

Let’s start with this one. Assume you’re a Bayesian turkey and hold a non-zero probability belief in the hypothesis H that “people are nice vegetarians that do not eat turkeys and that every day I see the sun rise confirms my belief.” For every day you survive, you update your belief according to Bayes’ Rule. Unfortunately — as Bertrand Russell famously noticed — for every day that goes by, the traditional Christmas dinner also gets closer and closer…

Or take the case of macroeconomic forecasting, which perhaps better than anything else illustrates the problem of induction. As a rule, macroeconomic forecasts tend to be little better than intelligent guesswork. Or in other words: macroeconomic mathematical-statistical forecasting models, and the inductive logic upon which they ultimately build, are as a rule far from successful. The empirical and theoretical evidence is clear. Predictions and forecasts are inherently difficult to make in a socio-economic domain where genuine uncertainty and unknown unknowns often rule the roost. The real processes that underlie the time series that economists use to make their predictions and forecasts do not conform with the inductive assumptions made in the applied statistical and econometric models. The forecasting models fail to a large extent because the kind of uncertainty that faces humans and societies actually makes the models, strictly seen, inapplicable. The future is inherently unknowable – and using statistics and econometrics does not in the least overcome this ontological fact. The economic future is not something that we can normally predict in advance. Better then to accept that as a rule “we simply do not know.”

Induction is sometimes a good guide for evaluating hypotheses. But for the creative generation of plausible and relevant hypotheses, it is conspicuously silent. For that, we need another – non-algorithmic and ampliative – kind of reasoning.

(3) Abduction

• Premise 1: All Chicago economists believe in REH

• Premise 2: These economists believe in REH

• Conclusion: These economists are from Chicago

In this case, again, we have an example of a logically non-valid inference – the fallacy of affirming the consequent. But it is nonetheless an inference that may be a strongly warranted and truth-producing – in contradistinction to truth-preserving deductions – reasoning, following the general pattern Evidence -> Explanation -> Inference.

Here we infer something based on what would be the best explanation given the law-like rule (premise 1) and an observation (premise 2). The truth of the conclusion (explanation) is nothing that is logically given, but something we have to justify, argue for, and test in different ways to possibly establish with any certainty or degree. And as always when we deal with explanations, what is considered best is relative to what we know of the world. In the real world, all evidence has an irreducible holistic aspect. We never conclude that evidence follows from hypothesis simpliciter, but always given some more or less explicitly stated contextual background assumptions. All non-deductive inferences and explanations are a fortiori context-dependent.

If we extend the abductive scheme to incorporate the demand that the explanation has to be the best among a set of plausible competing/rival/contrasting potential and satisfactory explanations, we have what is nowadays usually referred to as inference to the best explanation (IBE). In this way, IBE is a refinement of the original (Peircean) concept of abduction by making the background knowledge requirement more explicit.

In abduction, we start with a body of (purported) data/facts/evidence and search for explanations that can account for them. Having the best explanation means that you, given the context-dependent background assumptions, have a satisfactory explanation that can explain the fact/evidence better than any other competing explanation – and so it is reasonable to consider/believe the hypothesis to be true. Even if we do not (inevitably) have deductive certainty, our abductive reasoning gives us a licence to consider our belief in the hypothesis as reasonable.

Accepting a hypothesis means that you consider it to explain the available evidence better than any other competing hypothesis. The acceptability warrant comes from the explanatory power  of the hypothesis, and the conscious act of trying to rule out the possible competing potential explanations in itself  increases the plausibility of the preferred explanation. Knowing that we — after having earnestly considered and analysed the other available potential explanations — have been able to eliminate the competing potential explanations, warrants and enhances the confidence we have that our preferred explanation is the best — ‘loveliest’ — explanation, i. e., the explanation that provides us with the greatest understanding (given it is correct). As Sherlock Holmes had it (in ‘The Sign of Four’): ‘Eliminate the impossible, and whatever remains, however improbable, must be the truth.’ Subsequent confirmation of our hypothesis — by observations, experiments or other future evidence — makes it even more well-confirmed (and underlines that all explanations are incomplete, and that the models and theories that we as scientists use, cannot only be assessed by the extent of their fit with experimental or observational data, but also need to take into account their explanatory power).

This, of course, does not in any way mean that we cannot be wrong. Of course we can. Abductions are fallible inferences – since the premises do not logically entail the conclusion – so from a logical point of view, abduction is a weak mode of inference. But if the abductive arguments put forward are strong enough, they can be warranted and give us justified true belief, and hence, knowledge, even though they are fallible inferences. If you cannot live with that contingency and uncertainty, well, then you’re in the wrong business. If it is deductive certainty you are after, rather than the ampliative and defeasible reasoning in abduction – well, then get into maths or logic, not science.

What makes the works of people like Galileo, Newton, Marx, or Keynes, truly interesting is not that they described new empirical facts. No, the truly seminal and pioneering aspects of their works are that they managed to find out and analyse what makes empirical phenomena possible. Starting from well-known facts, these scientists discovered the mechanisms and structures that made these empirical facts possible.

Their works are good illustrations of the fact that in science we are usually not only interested in observable facts and phenomena. Since structures, powers, institutions, relations, etc., are not directly observable, we need to use theories and models to indirectly obtain knowledge of them. Deduction and induction do not give us access to these kinds of entities. They are things that to a large extent have to be discovered. Discovery processes presuppose creativity and imagination, virtues that are not very prominent in inductive analysis (statistics and econometrics) or deductive-logical reasoning. We need another mode of inference.

Inference to the best explanation is a (non-demonstrative) ampliative method of reasoning that makes it possible for us to gain new insights and come up with – and evaluate – theories and hypotheses that – in contradistinction to the entailments that deduction provides us with – transcend the epistemological content of the evidence that brought them about. And instead of only delivering inductive generalisations from the evidence at hand – as the inductive scheme – it typically opens up for conceptual novelties and retroduction, where we from analysis of empirical data and observation reconstruct the ontological conditions for their being what they are. As scientists, we do not only want to be able to deal with observables. We try to make the world more intelligible by finding ways to understand the fundamental processes and structures that rule the world we live in. The content-enhancing aspect of inference to the best explanation gives us the possibility of acquiring new and warranted knowledge and understanding of things beyond empirical sense data.

Outside mathematics and logic, scientific methods do not deliver absolute certainty or prove things. However, many economists are still in pursuit of the Holy Grail of absolute certainty. But there will always be a great number of theories and models that are compatible/consistent with facts, and no logic makes it possible to select one as the right one. The search for absolute certainty can never be anything other than disappointing since all scientific knowledge is more or less uncertain. That is a fact of the way the world is, and we just have to learn to live with that inescapable limitation of scientific knowledge.

The Mainstream Economic Fallacy

But most mainstream economists do not understand these basics!

Why?

Because in mainstream economics, it is not inference to the best explanation that rules the methodological roost, but deductive reasoning based on logical inference from a set of axioms. Although — under specific and restrictive assumptions — deductive methods may be usable tools, insisting that economic theories and models ultimately have to be built on a deductive-axiomatic foundation to count as being economic theories and models, will only make economics irrelevant for solving real-world economic problems. Modern deductive-axiomatic mainstream economics is sure very rigorous – but if it’s rigorously wrong, who cares?

Instead of making formal logical argumentation based on deductive-axiomatic models the message, I think we are better served by economists who more than anything else try to contribute to solving real problems — and in that endeavour, inference to the best explanation is much more relevant than formal logic.

Most mainstream economic models are abstract, unrealistic, and present mostly non-testable hypotheses. One important rationale behind this kind of model-building is the quest for rigour, and more precisely, logical rigour. Formalisation of economics has been going on for more than a century and with time it has become obvious that the preferred kind of formalisation is the one that rigorously follows the rules of formal logic. As in mathematics, this has gone hand in hand with a growing emphasis on axiomatics. Instead of basically trying to establish a connection between empirical data and assumptions, ‘truth’ has come to be reduced to a question of fulfilling internal consistency demands between conclusion and premises, instead of showing a ‘congruence’ between model assumptions and reality. This has, of course, severely restricted the applicability of economic theory and models.

In their search for the Holy Grail of deductivism, mainstream economists are forced to make assumptions with standardly precious little resemblance to reality. When applying this deductivist thinking to economics, mainstream economists usually set up “as if” models based on a set of tight axiomatic assumptions from which consistent and precise inferences are made. The beauty of this procedure is of course that if the axiomatic premises are true, the conclusions necessarily follow. The snag is that if the models are to be relevant, we also have to argue that their precision and rigour still hold when they are applied to real-world situations. They (almost) never do.

The one-eyed focus on validity and consistency makes much of mainstream economics irrelevant, since its insistence on deductive-axiomatic foundations does not earnestly consider the fact that its formal logical reasoning, inferences, and arguments show an amazingly weak relationship to their everyday real-world equivalents. Searching in vain for absolute and deductive knowledge and ‘truth,’ these economists forgo the opportunity of getting more relevant and better (defeasible) knowledge. For although the formal logic focus may deepen our insights into the notion of validity, the rigour and precision has a devastatingly important trade-off: the higher the level of rigour and precision, the smaller is the range of real-world applications. Consistency does not take us very far. As scientists, we cannot only be concerned with the consistency of our universe of discourse. We also have to investigate how consistent our models and theories are with the universe in which we happen to live.

Mainstream economic theory today is in the story-telling business whereby economic theorists create make-believe analogue models of the targeted real economic system. This modelling activity is considered useful and essential. To understand and explain relations between different entities in the real economy, the predominant strategy is to build models and make things happen in these “analogue-economy models” rather than engineering things happening in real economies. This formalistic-deductive modelling strategy certainly impresses some people, but the one-sided, almost religious, insistence on axiomatic-deductivist modelling as the only scientific activity worthy of pursuing in economics, forgets that in the realm of science it ought to be considered of little or no value to simply make claims about the model and lose sight of reality.

Theories and models being ‘coherent’ or ‘consistent’ with data do not make the theories and models success stories. To have valid evidence is not enough. What economics needs is sound evidence. The premises of a valid argument do not have to be true, but a sound argument, on the other hand, is not only valid but builds on premises that are true. Aiming only for validity, without soundness, is setting the economics aspirations level too low for developing a realist and relevant science.

In science, nothing of substance has ever been decided by just putting things in the right logical form. Those scientific matters that can be dealt with in a purely formal-analytical matter are only of second-order interest. The absurdity of trying to analyse and explain real-world systems equipped with analytical rather than substantial scientific arguments becomes clear as soon as we become aware that this is fundamentally a denial of the field-dependent character of all science. What counts as a justified inference in economics is not necessarily equivalent to what counts in sociology, physics, or biology. They address different problems and questions, and – a fortiori – what is considered absolutely necessary in one field, may be considered totally irrelevant in another.

Abduction and inference to the best explanation show the inherent limits of formal logical reasoning in science. No new ideas or hypotheses in science originate by deduction or induction. In order to come up with new ideas or hypotheses and explain what happens in our world, scientists have to use inference to the best explanation. All scientific explanations inescapably rely on a reasoning that is, from a logical point of view, fallacious. Thus – in order to explain what happens in our world, we have to use a reasoning that logically is a fallacy. There is no way around this – unless you want to follow the barren way that mainstream economics has been following for more than half a century now – retreating into the world of thought experimental ‘as if’ axiomatic-deductive-mathematical models.

The more mainstream economists insist on formal logic validity, the less they have to say about the real world. And real progress in economics, as in all sciences, presupposes real-world involvement, not only self-referential deductive reasoning within formal-analytical mathematical models.