The ignorance behind inconsistency toleration
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The ignorance behind inconsistency toleration María del Rosario Martínez-Ordaz1 Received: 24 March 2019 / Accepted: 18 February 2020 © Springer Nature B.V. 2020
Abstract Inconsistency toleration is the phenomenon of working with inconsistent information without threatening one’s rationality. Here I address the role that ignorance plays for the tolerance of contradictions in the empirical sciences. In particular, I contend that there are two types of ignorance that, when present, can make epistemic agents to be rationally inclined to tolerate a contradiction. The first is factual ignorance, understood as temporary undecidability of the truth values of the conflicting propositions. The second is what I call “ignorance of theoretical structure”, which is lack of knowledge of relevant inference patterns within a specific theory. I argue that these two types of ignorance can be explanatory of the scientists’ rational disposition to be tolerant towards contradictions, and I illustrate this with a case study from neutrino physics. Keywords Inconsistency toleration · Factual ignorance · Ignorance of theoretical structure · Measurement of solar neutrinos’ flux
1 Introduction A contradiction is a pair of propositions where one is a negation of the other. A set of propositions is trivial if every proposition is derivable from it. According to the Principle of Explosion, any set of propositions, if closed under classical logic or any other explosive logic, is trivial if containing a contradiction. Given the role that classical logic has played in the development and conceptual foundations of science and philosophy through time, it is not surprising that scientists and philosophers have regarded contradictions as extremely malignant. There is a recurring view in the traditional literature of logic and philosophy of science which holds that the use of inconsistent information in the sciences entails the irrationality of the scientists. If assuming the basic principles of classical logic (or any other explosive logic), “an inconsistent theory implies any conceivable observational
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María del Rosario Martínez-Ordaz [email protected] Program of Postgraduate Studies in Philosophy, Federal University of Rio de Janeiro, Lago Sao Francisco de Paula 1, Rio de Janeiro, RJ 20051-070, Brasil
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prediction as well as its negation and thus tells us nothing about the world” (Hempel 2000: p. 79). Therefore, any scientist who consciously trusts such a theory must be irrational. Pace these traditional intuitions, in recent decades, philosophers and historians of science have noticed that, at some point in their development, most scientific theories were thought to be inconsistent or falsified or incompatible with the best theories from other domains. Scientists kept working with such theories nonetheless. Some of the most famous examples of this are: Aristotle’s theory of motion, the early calculus, Bohr’s theory of the atom and Classical Electrodynamics, among others. This has given the impression that contradictions
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