Inconsistencies between Theory and Observation and the Limits of Chunk and Permeate

During the last two decades, the emergence of paraconsistent logics as well as the study of some particular episodes from the history of science have motivated the development of formal reasoning strategies that aim at explaining how it is sometimes possible to reason sensibly from inconsistencies without necessarily arriving to arbitrary conclusions. One of such strategies is Chunk and Permeate (Brown and Priest 2004), in which information is broken up into consistent fragments and allowed to move restrictedly from one fragment to another. In what follows, I will introduce a case study from neutrino physics that, I believe, challenges the possibility of using Chunk and Permeate when dealing with some inconsistencies from the empirical sciences. 0. Introduction It is common to believe that if the basic principles of classical logic (or any other explosive logic) are assumed then, “an inconsistent theory implies any conceivable observational prediction as well as it is negation and thus tells us nothing about the world” (Hempel 2000: 79). So, if any case of inconsistent (non-trivial) science is provided 1 , it seems necessary to offer an explanation about how a scientific theory can be inconsistent and not become trivial at the same time; especially on the face of the classical assumption that an inconsistent set of premises leads us to assume any formula as its result. Some philosophers and logicians of science have addressed this problem by offering reasoning strategies that aim at explaining how it is sometimes possible to reason sensibly from inconsistencies without necessarily arriving to arbitrary conclusions. As a matter of fact, it has been suggested –at least, by the paraconsistent tradition– that some of such strategies could give a good explanation about how scientists could have reasoned from or with inconsistencies in both formal and empirical sciences. Some of the most popular examples of this are the early calculus (cf. Brown and Priest 2004), Bohr’s Hydrogen Atom (see Brown and Priest 2015), the Dirac Delta function (cf. Benham et al. 2014), Lobachevsky’s model of hyperbolic geometry for indefinite integrals (Friend 2013) or the inconsistencies related to Carnot’s theorem (cf. Meheus, 2002). However, while internal inconsistencies are well-documented in the literature and have been successfully explained by making use of some paraconsistent reasoning strategies, this does not happen with other types of inconsistencies in science, such as inconsistencies between theory and observation or inconsistencies between theories. And this is not a trivial issue. As a matter of fact, because we want our scientific theories to be able to give us information about the external world, no one can deny that empirical sciences legitimize, through their methodologies, the role of observation as fundamental for the construction, choice and application of scientific theories. Therefore, if one wants to analyze inconsistencies in empirical sciences, the aspects linked to observation should not, in any sense, be marginalized. Said otherwise, attention must be paid to inconsistencies between theory and observation while looking at inconsistent empirical theories (even from a formal point of view). In the philosophy of science, inconsistencies between theory and observation have been standardly tagged as “anomalies” (see for example Laudan 1977; Kuhn 1977; Priest 2002, 2005). 1 In what follows, I will assume that all the scientific theories that are interesting for my analysis are, “despite their inconsistencies, markedly better than their rivals on sufficiently many other criteria” (Priest 2002: 125), i.e., they are not-trivial and functional for particularly relevant scientific purposes (Martinez-Ordaz 2014).