The ignorance behind inconsistency toleration
María del Rosario Martínez-Ordaz (UNAM)

part of: Inconsistency in Factual Science
December 10, 2019, 5:00am - 5:30am
Brazilian Academy of Philosophy

Institute of Philosophy of the Federal University of Rio de Janeiro
Rio de Janeiro

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Universidad Nacional Mayor de San Marcos

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Here I discuss the connections between inconsistency toleration and ignorance in the empirical sciences, and I explore the different kinds of ignorance that are present in cases of (alleged) inconsistent science.

In recent decades, philosophers of science have noticed that, at some point in their development, most scientific theories were thought to be inconsistent and scientists kept working with them, nonetheless. The tolerant attitude towards contradictions is often called inconsistency toleration, and it consists of the practice of knowingly reasoning with inconsistent information without threatening one’s rationality. Some philosophers have explained the possibility of rationally using inconsistent information in the sciences by referring to a sort of ignorance. These explanations usually include the following:

1. When having two scientific statements that contradict each other, scientists tend to assume that, at least, one of them is false [4, p.56].

2. If scientists are able to distinguish which of the conflicting propositions should be regarded as false (due to being an idealization, a fiction, among others), then they would be able to explain how they could satisfactorily work on seemingly false information [see 6].

3. However, most of the time, when confronted with an inconsistent set of information, scientists ignore, at least, which of the mutually contradictory statements should be regarded as false [cf. 2,3,1,5].

4. Once this ignorance is acknowledged, if scientists have no better alternative to the inconsistent set of propositions, the toleration of the contradiction becomes the only option at hand – however, such a tolerant attitude towards contradictions is often seen by scientists as a temporary resource.

Here I aim at identifying the type of ignorance that is at stake according to these explanations. In particular, I contend that, when scientists find a contradiction in their theories, if they ignore the truth values of the conflicting propositions (factual ignorance) or specific segments of their theory's theoretical structure, they can be rationally inclined to tolerate such a contradiction.

In order to do so, first, I explain the philosophical relevance of inconsistency toleration in the sciences. Later on, I deepen into the philosophical explanations that relate inconsistency toleration to ignorance. Furthermore, I present a case of inconsistency toleration in the empirical sciences and I explain it by appealing to both factual ignorance and ignorance of theoretical structure. Finally, I draw some conclusions regarding the role that ignorance could play when explaining under which circumstances it is rational to tolerate contradictions in the empirical sciences.


[1] B. Brown, “How to be realistic about inconsistency in science”, Studies in History and Philosophy of Science, 21(2) (1990), pp.281–294.

[2] O. Bueno,: “Empirical Adequacy: A Partial Structures Approach”, Studies in History and Philosophy of Science, 28 (1997), pp.585–610.

[3] O. Bueno,: “Why Inconsistency Is Not Hell: Making Room for Inconsistency in Science”, in Knowledge and Inquiry: Essays on the Pragmatism of Isaac Levi, Cambridge Studies in Probability, Induction and Decision Theory, Cambridge University Press, 2006, pp. 70–86.

[4] L. Laudan, Progress and its Problems: Towards a Theory of Scientific Growth, University of California Press, 1977.

[5] G. Priest,: “Inconsistency and the Empirical Sciences”, in Inconsistency in Science, edited by J. Meheus, Kluwer Academic Publishers, 2002, pp.119-128.

[6] D. Pritchard, “Epistemically useful false beliefs”, Philosophical Explorations, 20 (2017), pp.4–20.

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