Some philosophers have recently argued that contrary to the traditional view, good scientific theories can in fact be logically inconsistent. The literature is now full of case-studies that are taken to support this claim. I will argue however that as of yet no-one has managed to articulate a philosophically interesting view about the role of logically inconsistent theories in science that genuinely goes against tradition, is plausibly true, and is supported by any of the case studies usually given.

This paper deals with a relatively recent trend in the history of analytic philosophy, philosophical logic, and theory of science: the philosophical study of the role of inconsistency in empirical science. This paper is divided in three sections that correspond to the three types of inconsistencies identified: (i) factual, occurring between theory and observations, (ii) external, occurring between two mutually contradictory theories, and (iii) internal, characterising theories that entail mutually contradictory statements.

This paper deals with a relatively recent trend in the history of analytic philosophy, philosophical logic, and theory of science: the philosophical study of the role of inconsistency in empirical science. This paper is divided in three sections that correspond to the three types of inconsistencies identified: (i) factual, occurring between theory and observations, (ii) external, occurring between two mutually contradictory theories, and (iii) internal, characterising theories that entail mutually contradictory statements.

This dissertation offers a proof of the logical possibility of testing empirical/factual theories that are inconsistent, but non-trivial. In particular, I discuss whether or not such theories can satisfy Popper's principle of falsifiablility. An inconsistent theory Ƭ closed under a classical consequence relation implies every statement of its language because in classical logic the inconsistency and triviality are coextensive. A theory Ƭ is consistent iff there is not a α such that Ƭ ⊢ α ∧ ¬α, otherwise it is inconsistent. (...) We say, instead, that Ƭ is non-trivial iff there is at least one α such that Ƭ ⊢ α, otherwise we say that it trivial. This happens because classical logic satisfies the principle of explosion, according ex contradictione sequitur quodlibet (from a contradiction anything follows). Under these conditions inconsistent classical theories would be compatible with any well-formed formula, which makes them useless for science. There are, however, so-called paraconsistent logics in which the principle of explosion does not generally hold and in which a theory can be (simply) inconsistent, but also absolutely consistent. It is in this logical framework that we can prove that some inconsistent theories can be falsifiable. (shrink)