The Holy Grail of Science
30 Dec, 2025 at 10:42 | Posted in Theory of Science & Methodology | Leave a comment
Traditionally, philosophers have focused mostly on the logical template of inference. The paradigm-case has been deductive inference, which is topic-neutral and context-insensitive. The study of deductive rules has engendered the search for the Holy Grail: syntactic and topic-neutral accounts of all prima facie reasonable inferential rules. The search has hoped to find rules that are transparent and algorithmic, and whose following will just be a matter of grasping their logical form. Part of the search for the Holy Grail has been to show that the so-called scientific method can be formalised in a topic-neutral way. We are all familiar with Carnap’s inductive logic, or Popper’s deductivism or the Bayesian account of scientific method.
There is no Holy Grail to be found. There are many reasons for this pessimistic conclusion. First, it is questionable that deductive rules are rules of inference. Second, deductive logic is about updating one’s belief corpus in a consistent manner and not about what one has reasons to believe simpliciter. Third, as Duhem was the first to note, the so-called scientific method is far from algorithmic and logically transparent. Fourth, all attempts to advance coherent and counterexample-free abstract accounts of scientific method have failed. All competing accounts seem to capture some facets of scientific method, but none can tell the full story. Fifth, though the new Dogma, Bayesianism, aims to offer a logical template (Bayes’s theorem plus conditionalisation on the evidence) that captures the essential features of non-deductive inference, it is betrayed by its topic-neutrality. It supplements deductive coherence with the logical demand for probabilistic coherence among one’s degrees of belief. But this extended sense of coherence is (almost) silent on what an agent must infer or believe.
In mainstream economics, there has long been an insistence on formalistic (mathematical) modelling, and to some economic methodologists this has forced economists to abandon realism and substitute axiomatics for real-world relevance. According to this critique, the deductivist orientation has been the principal reason behind the difficulty mainstream economics has had in understanding, explaining and predicting what occurs in modern economies. Yet it has also granted mainstream economics much of its discursive power—at least so long as no one begins asking difficult questions about the veracity of, and justification for, the assumptions upon which the deductivist foundation is erected.
The sort of formal-analytical and axiomatic-deductive mathematical modelling that constitutes the core of mainstream economics is difficult to reconcile with a real-world ontology. It is also why so many critics find mainstream economic analysis palpably and utterly unrealistic and irrelevant.
Although there has been a clearly discernible increase in, and focus upon, ‘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 largely framed and interpreted within the core ‘axiomatic’ assumptions of individualism, instrumentalism and equilibrium that underpin even the ‘new’ mainstream economics. Although perhaps a sign of an increasing—yet highly path-dependent—theoretical pluralism, mainstream economics remains, from a methodological point of view, principally a deductive project built upon 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 sound aspiration to seek 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 logic, mathematics or the natural sciences.
An example of a logically valid deductive inference (wherever ‘logic’ is used here it refers to deductive/analytical logic) may appear as follows:
Premise 1: All Chicago economists believe in the rational expectations hypothesis (REH)
Premise 2: Bob is a Chicago economist
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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 yielded a different conclusion).
The hypothetico-deductive method (if we treat the hypothesis as absolutely certain/true, we ought rather to speak of an axiomatic-deductive method) essentially means that we:
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Posit a hypothesis
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Infer empirically testable propositions (consequences) from it
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Test the propositions through observation or experiment
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Depending on the testing results, either find the hypothesis corroborated or falsified.
However, in science we regularly employ 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 non-valid:
Premise 1: Bob is a Chicago economist
Premise 2: The recorded proportion of Keynesian Chicago economists is zero
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Conclusion: So, certainly, Bob is not a Keynesian economist
In science, contrary to what one finds in most logic textbooks, 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. So long as we can show that our ‘deductions’ or ‘inferences’ are justifiable and have well-backed warrants, other scientists will attend to us. That our scientific ‘deductions’ or ‘inferences’ 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 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 based on the formal properties of statements/propositions. We must examine what he has actually written and said 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 very 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 originate.
The deductive logic of confirmation and explanation may work well—provided they are used in deterministic closed models. In mathematics, the deductive-axiomatic method has worked perfectly well. But science is not mathematics. Conflating these two domains of knowledge has been one of the most fundamental errors 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 variants of hypothetico-deductive reasoning fail, since there is no way one 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 accompany it—is an example of ‘explicative reasoning,’ where the conclusions we draw are already contained within the premises. Deductive inferences are purely analytical and it is this truth-preserving nature of deduction that distinguishes it from all other kinds of reasoning. But this is also its limitation, since truth in the deductive context does not refer to a real-world ontology (relating propositions only as true or false within a formal-logic system) and, as an argument scheme, deduction is entirely non-ampliative: the output of the analysis is nothing other than the input.
To give an economics example, consider the following rather typical, yet 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 revenue
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Conclusion: The firm will operate its business at the equilibrium where marginal cost equals marginal revenue
This is as empty as deductive-nomological explanations of singular facts built upon simple generalisations:
Premise 1: All humans are less than 20 feet tall
Premise 2: Bob is a human
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Conclusion: Bob is less than 20 feet tall
Although a logically valid inference, this is scarcely an explanation (since we would still probably wish to know why all humans are less than 20 feet tall).
Deductive-nomological explanations also often suffer from a sort of emptiness stemming from a lack of real (causal) connection between premises and conclusions:
Premise 1: All humans who take birth control pills do not become pregnant
Premise 2: Bob took birth control pills
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Conclusion: Bob did not become pregnant
Most people would probably not consider this 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—induction and abduction—may provide good, but not conclusive, reasons. That is the price we must pay if we wish to have something substantial and interesting to say about the real world.
