This paper discusses the logical possibility of testing inconsistent empirical theories. The main challenge for answering this affirmatively is to avoid that the inconsistent consequences of a theory both corroborate it and falsify it. I answer affirmatively by showing that we can define a class of empirical sentences whose truth would force us to abandon such inconsistent theory: the class of its potential rejecters. Despite this, I show that the observational contradictions implied by a theory could only be verified (provided (...) we make some assumptions), but not rejected. From this, it follows that, although inconsistent theories are rejectable, they cannot be rejected qua inconsistent. (shrink)

In this paper I formalise the falsificationist proposal omitting Popper’s requirement of consistency. This omission results in (i) trivial theories being falsifiable in an inappropriate sense of the term, but also in (ii) some inconsistent non-trivial theories being so in an appropriate one. This justifies a slight alteration of the definition of falsifiability that excludes (i) but allows (ii). Instead of requiring that a falsifiable theory be consistent, my proposal only requires that the intersection of its classes of potential corroborators (...) and falsifiers be empty. (shrink)

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)

A non-embracing consequence relation is one such that no set of wffs closed under it is equal to the set of all wffs. I prove that these relations have no deductive power if they are also extensive and monotonic.