The semantic approach to scientific representation is now long established as a favourite amongst philosophers of science. One of the foremost strains of this approach—the model-theoretic approach —is to represent scientific theories as families of models, all of which satisfy or ‘make true’ a given set of constraints. However some authors have criticised the approach on the grounds that certain scientific theories are logically inconsistent, and there can be no models of an inconsistent set of constraints. Thus it would seem (...) that the MTA fails to represent inconsistent scientific theories at all, and this raises concerns about the way it represents in general. In a series of papers and a recent book da Costa and French have developed a variant of the MTA approach which they call ‘partial structures’, and which they claim can accommodate inconsistent theories. I assess this claim, looking to two theories which have been called ‘inconsistent’: Bohr’s theory of the atom and classical electrodynamics. (shrink)

The paper examines philosophical issues that arise in contexts where one has many different models for treating the same system. I show why in some cases this appears relatively unproblematic (models of turbulence) while others represent genuine difficulties when attempting to interpret the information that models provide (nuclear models). What the examples show is that while complementary models needn’t be a hindrance to knowledge acquisition, the kind of inconsistency present in nuclear cases is, since it is indicative of a lack (...) of genuine theoretical understanding. It is important to note that the differences in modeling do not result directly from the status of our knowledge of turbulent flows as opposed to nuclear dynamics—both face fundamental theoretical problems in the construction and application of models. However, as we shall, the ‘problem context(s)’ in which the modeling takes plays a decisive role in evaluating the epistemic merit of the models themselves. Moreover, the theoretical difficulties that give rise to inconsistent as opposed to complementary models (in the cases I discuss) impose epistemic and methodological burdens that cannot be overcome by invoking philosophical strategies like perspectivism, paraconsistency or partial structures. (shrink)

The mathematical concept of pragmatic truth, first introduced in Mikenberg, da Costa and Chuaqui (1986), has received in the last few years several applications in logic and the philosophy of science. In this paper, we study the logic of pragmatic truth, and show that there are important connections between this logic, modal logic and, in particular, Jaskowski's discussive logic. In order to do so, two systems are put forward so that the notions of pragmatic validity and pragmatic truth can be (...) accommodated. One of the main results of this paper is that the logic of pragmatic truth is paraconsistent. The philosophical import of this result, which justifies the application of pragmatic truth to inconsistent settings, is also discussed. (shrink)

This paper is about the underlying logical principles of scientific theories. In particular, it concerns ex contradictione quodlibet (ECQ) the principle that anything follows from a contradiction. ECQ is valid according to classical logic, but invalid according to paraconsistent logics. Some advocates of paraconsistency claim that there are ‘real’ inconsistent theories that do not erupt with completely indiscriminate, absurd commitments. They take this as evidence in favor of paraconsistency. Michael (2016) calls this the non-triviality strategy (NTS). He argues that this (...) strategy fails in its purpose. I will show that Michael's criticism significantly over-reaches. The fundamental problem is that he places more of a burden on the advocate of paraconsistency than on the advocate of classical logic. The weaknesses in Michael's argument are symptomatic of this preferential treatment of one viewpoint in the debate over another. He does, however, make important observations that allow us to clarify some of the complexities involved in giving a logical reconstruction of a theory. I will argue that there are abductive arguments deserving of further consideration for the claim that paraconsistent logic offers the best explanation of the practice of inconsistent science. In this sense, the debate is still very much open. (shrink)

Niels Bohr’s model of the hydrogen atom is widely cited as an example of an inconsistent scientific theory because of its reliance on classical electrodynamics together with assumptions about interactions between matter and electromagnetic radiation that could not be reconciled with CED. This view of Bohr’s model is controversial, but we believe a recently proposed approach to reasoning with inconsistent commitments offers a promising formal reading of how Bohr’s model worked. In this paper we present this new way of reasoning (...) with inconsistent commitments and compare it with other approaches before applying it to Bohr’s model and offering some suggestions for how it might be extended to account for subsequent developments in old quantum theory. (shrink)

I provide an interpretation of Wittgenstein's much criticized remarks on Gödel's First Incompleteness Theorem in the light of paraconsistent arithmetics: in taking Gödel's proof as a paradoxical derivation, Wittgenstein was right, given his deliberate rejection of the standard distinction between theory and metatheory. The reasoning behind the proof of the truth of the Gödel sentence is then performed within the formal system itself, which turns out to be inconsistent. I show that the models of paraconsistent arithmetics (obtained via the Meyer-Mortensen (...) collapsing filter on the standard model) match with many intuitions underlying Wittgensteins philosophy of mathematics, such as its strict finitism and the insistence on the decidability of any meaningful mathematical question. (shrink)

First, I discuss the older “theory-centered” and the more recent semantic conception of scientific theories. I argue that these two perspectives are nothing more than terminological variants of one another. I then offer a new theory-centered view of scientific theories. I argue that this new view captures the insights had by each of these earlier views, that it’s closer to how scientists think about their own theories, and that it better accommodates the phenomenon of inconsistent scientific theories.

A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. This book presents a comprehensive overview on paraconsistent logical systems to change (...) this situation. The book includes almost every major author currently working in the field. The papers are on the cutting edge of the literature some of which discuss current debates and others present important new ideas. The editors have avoided papers about technical details of paraconsistent logic, but instead concentrated upon works that discuss more 'big picture' ideas. Different treatments of paradoxes takes centre stage in many of the papers, but also there are several papers on how to interpret paraconistent logic and some on how it can be applied to philosophy of mathematics, the philosophy of language, and metaphysics. (shrink)

Advocates of certain paraconsistent logics claim that classical logic provides incorrect norms for reasoning about impossible situations. Some have taken this claim as a sufficient reason to modify classical accounts of consequence. In this paper, I explain and evaluate such an argument based on Graham Priest's fictional story, "Sylvan's Box." I will explain and evaluate an objection to this argument based on a consistent reading of Priest's story offered by Daniel Nolan. However, I will argue that the argument fails for (...) different reasons. It is not the case that classical logic provides incorrect norms for reasoning about impossible situations. I will discuss logical tools, offered by Daniel Nolan, compatible with classical accounts of consequence that allow for non-vacuous reasoning about impossibilities. Finally, I will offer an explanation for seeming tensions between certain classical logic principles and reasoning about impossibilities. (shrink)

World semantics for relevant logics include so-called non-normal or impossible worlds providing model-theoretic counterexamples to such irrelevant entailments as (A ∧ ¬A) → B, A → (B∨¬B), or A → (B → B). Some well-known views interpret non-normal worlds as information states. If so, they can plausibly model our ability of conceiving or representing logical impossibilities. The phenomenon is explored by combining a formal setting with philosophical discussion. I take Priest’s basic relevant logic N4 and extend it, on the syntactic (...) side, with a representation operator, (R), and on the semantic side, with particularly anarchic non-normal worlds. This combination easily invalidates unwelcome “logical omniscience” in- ferences of standard epistemic logic, such as belief-consistency and closure under entailment. Some open questions are then raised on the best strategies to regiment (R) in order to express more vertebrate kinds of conceivability. (shrink)

Disagreements about the definition, nature, structure, ontology, and content of scientific theories are at least partly responsible for disagreements in other debates in the philosophy of science. I argue that available theories of theories and conceptual analyses of *theory* are ineffectual options for overcoming this difficulty. Directing my attention to debates about the properties of particular, named theories, I introduce ‘theory eliminativism’ as a certain type of debate-reformulation. As a methodological tool it has the potential to be a highly effective (...) way to make real progress in the face of the noted problem. After the recommended reformulation questions of genuine importance to philosophy of science can still be asked and answered, but now without any possibility of disagreements about ‘theories’ compromising the debate. (shrink)

Please follow the link below for the most recent version of this paper: http://philsci-archive.pitt.edu/archive/00004005/.

The ubiquitous assertion that the early calculus of Newton and Leibniz was an inconsistent theory is examined. Two different objects of a possible inconsistency claim are distinguished: (i) the calculus as an algorithm; (ii) proposed explanations of the moves made within the algorithm. In the first case the calculus can be interpreted as a theory in something like the logician’s sense, whereas in the second case it acts more like a scientific theory. I find no inconsistency in the first case, (...) and an inconsistency in the second case which can only be imputed to a small minority of the relevant community. (shrink)