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)

Many arguments found in the physics literature involve concepts that are not well-defined by the usual standards of mathematics. I argue that physicists are entitled to employ such concepts without rigorously defining them so long as they restrict the sorts of mathematical arguments in which these concepts are involved. Restrictions of this sort allow the physicist to ignore calculations involving these concepts that might lead to contradictory results. I argue that such restrictions need not be ad hoc, but can sometimes (...) be justified by considering some of the metaphysical issues surrounding the question of the applicability of mathematics to physical reality. 1 Introduction 2 Rejecting inferential permissiveness 3 The agreement problem 4 Independent objections to the liberal view. (shrink)

I show that the standard approach to modeling phenomena involving microscopic classical electrodynamics is mathematically inconsistent. I argue that there is no conceptually unproblematic and consistent theory covering the same phenomena to which this inconsistent theory can be thought of as an approximation; and I propose a set of conditions for the acceptability of inconsistent theories.

Throughout this paper, we are trying to show how and why our Mathematical frame-work seems inappropriate to solve problems in Theory of Computation. More exactly, the concept of turning back in time in paradoxes causes inconsistency in modeling of the concept of Time in some semantic situations. As we see in the first chapter, by introducing a version of “Unexpected Hanging Paradox”,first we attempt to open a new explanation for some paradoxes. In the second step, by applying this paradox, it (...) is demonstrated that any formalized system for the Theory of Computation based on Classical Logic and Turing Model of Computation leads us to a contradiction. We conclude that our mathematical frame work is inappropriate for Theory of Computation. Furthermore, the result provides us a reason that many problems in Complexity Theory resist to be solved.(This work is completed in 2017 -5- 2, it is in vixra in 2017-5-14, presented in Unilog 2018, Vichy). (shrink)

I erect a framework within the semantic view of theories for explaining the empirical success of internally inconsistent models and theories, with scientific realism in mind. The framework is an instance of the ‘content-driven’ approach to inconsistency, advocated by both Norton (Philos Sci 54:327–350, 1987) and Smith (Stud Hist Philos Sci 19:429–445, 1988a, In: Fine A, Leplin J (eds) PSA1988, 1988b), whose ideas my analysis aims to clarify and substantiate.

It is generally agreed upon today that scientific reasoning, like everyday reasoning, proceeds in a dynamic way: inferences derived at some stage in the reasoning process may at a later stage be rejected. This dynamics may be extrinsic or intrinsic. I shall call it extrinsic when previously derived conclusions are rejected on non-logical grounds, and intrinsic when their rejection is based on a purely logical analysis.

In this paper, I discuss the main difficulties one encounters whensolving problems with inconsistent constraints. I argue that in order to meetthese difficulties we need an inconsistency-adaptive logic that enables one toderive as many consequences as possible, but that at the sametime allows one to determine which consequences can be accepted. I showthat the inconsistency-adaptive logic ANA satisfies these requirements.

In this paper, I argue that logic hasan important role to play in the methodological studyof creativity. I also argue, however, that onlyspecial kinds of logic enable one to understand thereasoning involved in creative processes. I show thatdeductive and ampliative adaptive logics areappropriate tools in this respect.

Verisimilitude has the potential to deepen the understanding of mathematical progress, the principle of charity, and the psychology of regret. One obstacle is the widely held belief that two statements can vary in truthlikeness only if they vary in what they entail. This obstacle is removed with four types of counterexamples. The first concerns necessarily coextensive measurements that differ only with respect to their units. The second class of counterexamples is composed of mathematical falsehoods. The third class features inconsistent scientific (...) theories. The fourth class of cases features statements that are instructive but meaningless. (shrink)

Inconsistency-adaptive logics isolate the inconsistencies that are derivable from a premise set, and restrict the rules of Classical Logic only where inconsistencies are involved. From many inconsistent premise sets, disjunctions of contradictions are derivable no disjunct of which is itself derivable. Given such a disjunction, it is often justified to introduce new premises that state, with a certain degree of confidence, that some of the disjuncts are false. This is an important first step on the road to consistency: it narrows (...) down suspicion in inconsistent premise sets and hence locates the real problems among the possible ones. In this paper I present two approaches for handling such new premises in the context of the original premises. The first approach may apparently be combined with all paraconsistent logics. The second approach does not have the same generality, but is decidedly more elegant. (shrink)

. This paper proposes a generalization of the theory of the process of explanation to include consistent as well as inconsistent situations. The generalization is strong, for example in the sense that, if the background theory and the initial conditions are consistent, it leads to precisely the same results as the theory from the lead paper (Halonen and Hintikka 2004). The paper presupposes (and refers to arguments for the view that) inconsistencies constitute problems and that scientists try to resolve them.

The present paper examines the role of exact results in the theory of many‐body physics, and specifically the example of the Mermin‐Wagner theorem, a rigorous result concerning the absence of phase transitions in low‐dimensional systems. While the theorem has been shown to hold for a wide range of many‐body models, it is frequently ‘violated’ by results derived from the same models using numerical techniques. This raises the question of how scientists regulate their theoretical commitments in such cases, given that the (...) models, too, are often described as approximations to the underlying ‘full’ many‐body problem. (shrink)

The paper highlights the import of the paraconsistent movement, list some motivations for its origin, and distinguishes some stands with respect to para-consistency. It then discusses some sources of inconsistency that are specific for worldviews, and the import of the paraconsistent turn for the worldviews enterprise.

Renormalization in Quantum Field Theory (QFT) has frequently been regarded, by philosophers as well as by scientists, as an exemplary case of bad methodological behavior. The feeling that renormalization was somehow an illegitimate way to extract results, an ad hoc maneuver without an independent rationale, was (and is) common among physicists and philosophers, who wonder, at the same time, about the unprecedented accuracy of the empirical results achieved by the illegitimate method. Teller (1989) has recently tried to dispel the air (...) of illegitimacy around this technique. His lucid presentation, however, leaves one wondering why any sufficiently well-informed person could ever have thought of renormalization as an ad hoc move.Part of the reason, I think, is that renormalization — or so the common view goes — came to the rescue of a sadly lingering theory, the pre-1947 Quantum Electrodynamics (QED). A theory with such a bad record of solved empirical and conceptual problems could simply not be correct. (shrink)

Inconsistencies between scientific theories have been studied, by and large, from the perspective of paraconsistent logic. This approach considered the formal properties of theories and the structure of inferences one can legitimately draw from theories. However, inconsistencies can be also analysed from the perspective of modelling practices, in particular how modelling practices may lead scientists to form opinions and attitudes that are different, but not necessarily inconsistent. In such cases, it is preferable to talk about disagreement, rather than inconsistency. Disagreement (...) may originate in, or concern, a number of epistemic, socio-political or psychological factors. In this paper, we offer an account of the ‘loci and reasons’ for disagreement at different stages of the scientific process. We then present a controversial episode in the health sciences: the studies on hypercholesterolemia. The causes and effects of high levels of cholesterol in blood have been long and hotly debated, to the point of deserving the name of ‘cholesterol wars’; the debate, to be sure, isn’t settled yet. In this contribution, we focus on some selected loci and reasons for disagreement that occurred between 1920 and 1994 in the studies on hypercholesterolemia. We hope that our analysis of ‘loci and reasons’ for disagreement may shed light on the cholesterol wars, and possibly on other episodes of scientific disagreement. (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)

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.

Scientific explanations arc subject to the occurrence of inconsistencies. To rule them out in many cases demands the construction of new theories. As the examples of complementary explanations show, that may take a while. Furthermore, even if possible in principle, it is not always reasonable to eliminate inconsistencies immediately, e.g., by bringing in a more sophisticated formal language. After all, under some circumstances a provisional, not fully coherent explanation may be better than none. In any case, we need a logically (...) controlled approach to such inconsistencies. Modern logic provides the tools which are necessary to solve this task. We will mention two alternative approaches. (shrink)

It has recently been argued by Davey (2014) that inconsistency is never tolerated in science, but only discretely isolated. But when talking about inconsistencies in science, not much attention has been paid to the inconsistencies between theory and observation. Here I will argue that inconsistency toleration actually takes place in science, and that when we examine actual inconsistent theories, inconsistencies between theory and observation look anything but homogeneous. I will argue, appealing to certain properties of empirical theories, especially holism, that (...) at least two sub-types of inconsistencies regarding theory and observation can be distinguished: those that satisfy a criterion of observational independence and those that do not. (shrink)

Logical analyses of scientific representations of the world have usually focused on axiomatized or axiomatizable theories. As practiced, science seldom employs such theories. Rather, we find aggregations of claims, the logical relations of which are not as neat as philosophers of science might like them to be. Indeed, a common feature of such aggregations is the presence of certain “theoretical anomalies,” statements that are in some way incompatible with the remainder of the corpus. Huygens’ description of light as exhibiting an (...) asymmetry with respect to its direction of propagation in polarization phenomena was such an anomaly because of its inconsistency with his account of light as longitudinal waves in a medium. (See Sabra 1981, pp. 226-227.) Although the occurrence of these anomalies is indicative of a problem that must be dealt with, inconsistent representations of the world are not without significant heuristic value. (shrink)