Insufficiency of Popper’s Deductivism

Majid Hasan
Jul 23, 2017 · 6 min read

Popper (Logic of Scientific Discovery, 2002) uses falsification, in contrast to verification, as the criterion for demarcating science and metaphysics on the grounds that theories can be falsified through deductive reasoning, which yields logically certain and undeneiable truths, while verification relies on inductive reasoning, which only yields uncertain and probable truths. We argue that even falsification, in order to be complete and practically useful, must rely on inductive reasoning, as deductive reasoning cannot alone falsify the future predictions of any theory. To be perfectly clear, this criticism is not aimed at the idea of falsification itself, but on the argument that falsification can be done deductively, and that falsification is preferable to verification on the grounds that the former can be carried out solely through deductive reasoning.


Popper’s philosophy of science, as formulated in Logic of Scientific Discovery (2002), is centred around the question of demarcation of the realms of science and metaphysics. The key criterion that is used to demarcate science from metaphysics is empirical falsifiability. Science consists of empirically falsifiable claims/theories, while metaphysics does not. For example, the Newtonian theory of gravitation lies within the realm of science as it makes empirically falsifiable predictions, while Marx’s theory of social change falls within the domain of metaphysics as it does not make empirically falsifiable predictions.

The main reason for choosing falsifiability, in contrast to verifiability, as the demarcation criterion is that the falsifiability is within the domain of deductive reasoning, while verifiability does not. Theories/claims can be falsified through deductive logic, but verification requires inductive logic. And only deductive reasoning is acceptable, but inductive reasoning is not, because only deductive arguments can be certain, while inductive arguments are only probable. Consequently, only deductive arguments can be said to be objectively valid. Thus, Popper puts a great deal of emphasis on demarcating science from metaphysics on deductive grounds to retain the objective character of science. For example, in opposing the view that “the empirical sciences can be characterised by the fact that they use ‘inductive methods’, as they are called”, he argues: “Now it is far from obvious, from a logical point of view, that we are justified in inferring universal statements from singular ones, no matter how numerous; for any conclusion drawn in this way may always turn out to be false.” In opposition to these inductive views of science, Popper describes his aim as: “The theory to be developed in the following pages stands directly opposed to all attempts to operate with the ideas of inductive logic. It might be described as the theory of the deductive method of testing,” and describes his view as “‘deductivism’, in contrast to ‘inductivism’”.

The criticism put forward in this post is that deductive arguments are not sufficient to falsify a theory’s predictions, which is the most practically relevant aspect of falsification, and henceforth we refer to this criticism as the insufficiency problem. The main point of this criticism is that falsifying a universal claim is not sufficient to falsify its predictions, and while a basic statement (empirical observation) can deductively falsify a universal claim, it cannot deductively falsify the prediction of the universal claim, which can only be falsified inductively, if at all. For example, the observation that the Sun did not rise today, can deductively refute a universal statement, that the Sun will always rise, the relevance of such deductive falsifiability can be disputed. In this case, the absence of the Sun rising today only deductively falsifies the claim that the Sun did rise today, but it does not deductively falsify the claim that the Sun will rise tomorrow, or the day after tomorrow, or for that matter, on any specific day in the future or the past. However, what is most relevant from a practical perspective is whether the Sun will rise on days yet to come or not? And one cannot deductively derive anything about the rising of the Sun in the future from the rising of the Sun in the past.

More generally, deductively falsifying a universal claim, such as the claim that the Sun will always rise, does not deductively falsify any of its individual predictions, such as the prediction that the Sun will rise tomorrow. This is because a universal claim (the Sun will always rise) can be thought of as a conjunction of numerous particular claims (the Sun will rise today, and the Sun will rise tomorrow, and so on), and, as a result, falsifying the universal claim only implies that at least one of those particular claims is false. However, one cannot deduce which one, and how many, of the particular claims may be false. All one knows is that at least one of them is false. But it may be that the only particular claim that was false was the one that has already been observed to be false! In short, deductive falsification of a universal claim does not extend to its particular predictions.

In practice, it is often the future predictions of a universal theory that one is most interested in. For example, to plan for tomorrow, one is interested in knowing whether the Sun will rise tomorrow, and deductive reasoning does not help one determine it. One can only inductively draw inferences about the rising of the Sun tomorrow from the risings of the Sun in the past. If the Sun is frequently observed to not rise in the past few days, one may inductively infer that the chances of the Sun rising tomorrow are slim, and refute the prediction that the Sun will rise tomorrow — this refutation would however be based on an inductive argument, and not on a deductive argument.

If deductive reasoning cannot falsify specific predictions, and one is interested in the truth of these predictions, then there is no way to have a purely deductive theory of scientific method, and by extension, a purely deductive demarcation between scientific and non-scientific (metaphysical) theories. Since discarding a theory necessarily involves discarding its predictions, all falsification would involve some degree of inductive reasoning. The only way to deductively refute a theory would be to empirically refute every single prediction of the theory, which is humanly impossible, and, ironically, is also the Hume’s criticism of inductive reasoning, which argues that one can only be sure of the truth of an inductive claim by empirically verifying all its predictions. Thus, the same criticism that is used to discard inductive reasoning as a reliable ground for the scientific method, applies to Popper’s deductivism. To be complete in its aim of refutation, even deductivism would have to falsify every single prediction of the theory!

If inductivism is inevitable, then the Popper’s aim of obtaining a philosophy of scientific method that is untainted by inductive reasoning is untenable, and, hence, the reason to discard verifiability in favour of falsifiability is no longer valid. In general, a rejection of a more falsified theory is justified only because its future predictions are deemed less likely to be accurate, a conclusion drawn on inductive grounds. Hence, in practice, even falsifiability includes traces of inductive reasoning. If one allows for the possiblity a more falsified theory may make more accurate predictions in the future than a less falsified theory, which is logically possible, then it is desirable, even in a falsification paradigm, to use a formal inductive approach to infer the likelihood of falsification (falsifiability) of future predictions of various theories. And if even falsifiability cannot survive without inductive reasoning, it is unclear how one one can discard verifiability as an acceptable criterion for demarcating science from metaphysics on the grounds that verification involves inductive reasoning.

To conclude, the insufficiency criticism offered here can be summarised in these four observations: (1) the falsehood of a particular claim that logically follows from a universal claim does not logically follow from the falsehood of the universal claim (the Sun does not always rise does not imply that the Sun will not rise tomorrow); (2) any comprehensive and practically relevant refutation of a theory must entail a refutation of its future particular claims (predictions); (3) refutation of future predictions of theories is inductive in nature; (4) thus, any falsification of a theory, as it necessarily entails a falsification of the theory’s predictions, would involve some degree of inductive reasoning.

Majid Hasan

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