Inspired by the early Wittgenstein’s concept of nonsense (meaning that which lies beyond the limits of language), we define two different, yet complementary, types of nonsense: formal nonsense and pragmatic nonsense. The simpler notion of formal nonsense is initially defined within Tarski’s semantic theory of truth; the notion of pragmatic nonsense, by its turn, is formulated within the context of the theory of pragmatic truth, also known as quasi-truth, as formalized by da Costa and his collaborators. While an expression will (...) be considered formally nonsensical if the formal criteria required for the assignment of any truth-value (whether true, false, pragmatically true, or pragmatically false) to such sentence are not met, a (well-formed) formula will be considered pragmatically nonsensical if the pragmatic criteria (inscribed within the context of scientific practice) required for the assignment of any truth-value to such sentence are not met. Thus, in the context of the theory of pragmatic truth, any (well-formed) formula of a formal language interpreted on a simple pragmatic structure will be considered pragmatically nonsensical if the set of primary sentences of such structure is not well-built, that is, if it does not include the relevant observational data and/or theoretical results, or if it does include sentences that are inconsistent with such data. (shrink)

Pessimistic meta-induction is a powerful argument against scientific realism, so one of the major roles for advocates of scientific realism will be trying their best to give a sustained response to this argument. On the other hand, it is also alleged that structural realism is the most plausible form of scientific realism; therefore, the plausibility of scientific realism is threatened unless one is given the explicit form of a structural continuity and minimal structural preservation for all our current theories. This (...) essay aims to present what we call expansive structures, which are the structures that can be reconstructed from geometrized Newtonian gravitation and are capable of expanding into general relativity, explicitly. In this way, pessimistic meta-induction will be undermined. (shrink)

We present a sequent calculus of a paraconsistent logic QMPT0, which has the paraconsistent-type excluded middle law (PEML) as an initial sequent. Our system shows that the presence of PEML is essentially important for QMPT0. It also has special rules when the set of constant symbols is finite. We also discuss the cut-elimination property of our system.

Multialgebras have been much studied in mathematics and in computer science. In 2016 Carnielli and Coniglio introduced a class of multialgebras called swap structures, as a semantic framework for dealing with several Logics of Formal Inconsistency that cannot be semantically characterized by a single finite matrix. In particular, these LFIs are not algebraizable by the standard tools of abstract algebraic logic. In this paper, the first steps towards a theory of non-deterministic algebraization of logics by swap structures are given. Specifically, (...) a formal study of swap structures for LFIs is developed, by adapting concepts of universal algebra to multialgebras in a suitable way. A decomposition theorem similar to Birkhoff’s representation theorem is obtained for each class of swap structures. Moreover, when applied to the 3-valued algebraizable logics J3 and Ciore, their classes of algebraic models are retrieved, and the swap structures semantics become twist structures semantics. This fact, together with the existence of a functor from the category of Boolean algebras to the category of swap structures for each LFI, suggests that swap structures can be seen as non-deterministic twist structures. This opens new avenues for dealing with non-algebraizable logics by the more general methodology of multialgebraic semantics. (shrink)

In “The Toolbox of Science” (1995) together with Towfic Shomar we advocated a form of instrumentalism about scientific theories. We separately developed this view further in a number of subsequent works. Steven French, James Ladyman, Otavio Bueno and Newton Da Costa (FLBD) have since written at least eight papers and a book criticising our work. Here we defend ourselves. First we explain what we mean in denying that models derive from theory – and why their failure to do so should (...) be lamented. Second we defend our use of the London model of superconductivity as an example. Third we point out both advantages and weaknesses of FLBD’s techniques in comparison to traditional Anglophone versions of the semantic conception. Fourth we show that FLBD’s version of the semantic conception has not been applied to our case study. We conclude by raising doubts about FLBD’s overall project. (shrink)

One important role of belief systems is to allow us to represent information about a certain domain of inquiry. This paper presents a formal framework to accommodate such information representation. Three cognitive models to represent information are discussed: conceptual spaces, state-spaces, and the problem spaces familiar from artificial intelligence. After indicating their weakness to deal with partial information, it is argued that an alternative, formulated in terms of partial structures, can be provided which not only captures the positive features of (...) these models, but also accommodates the partiality of information ubiquitous in science and mathematics. (shrink)

This paper investigates the question of characterizing first-order LFIs (logics of formal inconsistency) by means of two-valued semantics. LFIs are powerful paraconsistent logics that encode classical logic and permit a finer distinction between contradictions and inconsistencies, with a deep involvement in philosophical and foundational questions. Although focused on just one particular case, namely, the quantified logic QmbC, the method proposed here is completely general for this kind of logics, and can be easily extended to a large family of quantified paraconsistent (...) logics, supplying a sound and complete semantical interpretation for such logics. However, certain subtleties involving term substitution and replacement, that are hidden in classical structures, have to be taken into account when one ventures into the realm of nonclassical reasoning. This paper shows how such difficulties can be overcome, and offers detailed proofs showing that a smooth treatment of semantical characterization can be given to all such logics. Although the paper is well-endowed in technical details and results, it has a significant philosophical aside: it shows how slight extensions of classical methods can be used to construct the basic model theory of logics that are weaker than traditional logic due to the absence of certain rules present in classical logic. Several such logics, however, as in the case of the LFIs treated here, are notorious for their wealth of models precisely because they do not make indiscriminate use of certain rules; these models thus require new methods. In the case of this paper, by just appealing to a refined version of the Principle of Explosion, or Pseudo-Scotus, some new constructions and crafty solutions to certain non-obvious subtleties are proposed. The result is that a richer extension of model theory can be inaugurated, with interest not only for paraconsistency, but hopefully to other enlargements of traditional logic. (shrink)

Schrödinger logics are logical systems in which the principle of identity is not true in general. The intuitive motivation for these logics is both Erwin Schrödinger's thesis that identity lacks sense for elementary particles of modern physics, and the way which physicists deal with this concept; normally, they understand identity as meaning indistinguishability . Observing that these concepts are equivalent in classical logic and mathematics, which underly the usual physical theories, we present a higher-order logical system in which these concepts (...) are systematically separated. A 'classical' semantics for the system is presented and some philosophical related questions are mentioned. One of the main characteristics of our system is that Leibniz' Principle of the Identity of Indiscernibles cannot be derived. This fact is in accordance with some authors who maintain that quantum mechanics violates this principle. Furthermore, our system may be viewed as a way of making sense some of Schrödinger's logical intuitions about the nature of elementary particles. (shrink)

In this paper we show that any reasoning process in which conclusions can be both fallible and corrigible can be formalized in terms of two approaches: (i) syntactically, with the use of defeasible reasoning, according to which reasoning consists in the construction and assessment of arguments for and against a given claim, and (ii) semantically, with the use of partial structures, which allow for the representation of less than conclusive information. We are particularly interested in the formalization of scientific reasoning, (...) along the lines traced by Lakatos’ methodology of scientific research programs. We show how current debates in cosmology could be put into this framework, shedding light on a very controversial topic. (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)

The semantic, or model-theoretic, approach to theories has recently come under criticism on two fronts: (i) it is claimed that it cannot account for the wide diversity of models employed in scientific practice—a claim which has led some to propose a “deflationary” account of models; (ii) it is further contended that the sense of “model” used by the approach differs from that given in model theory. Our aim in the present work is to articulate a possible response to these claims, (...) drawing on recent developments within the semantic approach itself. Thus, the first is answered by utilizing the notion of a “partial structure”, first introduced in this context by da Costa and French in 1990. The second claim is undermined by consideration of van Fraassen's understanding of “model” which corresponds well with that evinced by modem mathematicians. This latter discussion, in particular, has an impact on the continuing debate regarding the relative merits of the semantic and syntactic views and the developments presented here can be taken to provide further support to the former. (shrink)

A first step is taken towards articulating a constructive empiricist philosophy of mathematics, thus extending van Fraassen's account to this domain. In order to do so, I adapt Field's nominalization program, making it compatible with an empiricist stance. Two changes are introduced: (a) Instead of taking conservativeness as the norm of mathematics, the empiricist countenances the weaker notion of quasi-truth (as formulated by da Costa and French), from which the formal properties of conservativeness are derived; (b) Instead of quantifying over (...) spacetime regions, the empiricist only admits quantification over occupied regions, since this is enough for his or her needs. (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.

Modal logic has been applied in many different areas, as reasoning about time, knowledge and belief, necessity and possibility, to mention only some examples. In the present paper, an attempt is made to use modal logic to account for the semantics of theoretical sentences in scientific language. Theoretical sentences have been studied extensively since the work of Ramsey and Carnap. The present attempt at a modal analysis is motivated by there being several intended interpretations of the theoretical terms once these (...) terms are introduced through the axioms of a theory. (shrink)

The aim of this paper is to provide a unified account of scientific and mathematical change in a thoroughly empiricist setting. After providing a formal modelling in terms of embedding, and criticising it for being too restrictive, a second modelling is advanced. It generalises the first, providing a more open-ended pattern of theory development, and is articulated in terms of da Costa and French's partial structures approach. The crucial component of scientific and mathematical change is spelled out in terms of (...) partial embeddings. Finally, an application of this second pattern is made, with the examination of the early formulation of set theory. (shrink)

In order to develop an account of scientific rationality, two problems need to be addressed: (i) how to make sense of episodes of theory change in science where the lack of a cumulative development is found, and (ii) how to accommodate cases of scientific change where lack of consistency is involved. In this paper, we sketch a model of scientific rationality that accommodates both problems. We first provide a framework within which it is possible to make sense of scientific revolutions, (...) but which still preserves some (partial) relations between old and new theories. The existence of these relations help to explain why the break between different theories is never too radical as to make it impossible for one to interpret the process in perfectly rational terms. We then defend the view that if scientific theories are taken to be quasi-true, and if the underlying logic is paraconsistent, it's perfectly rational for scientists and mathematicians to entertain inconsistent theories without triviality. As a result, as opposed to what is demanded by traditional approaches to rationality, it's not irrational to entertain inconsistent theories. Finally, we conclude the paper by arguing that the view advanced here provides a new way of thinking about the foundations of science. In particular, it extends in important respects both coherentist and foundationalist approaches to knowledge, without the troubles that plague traditional views of scientific rationality. (shrink)

The partial structures approach has two major components: a broad notion of structure (partial structure) and a weak notion of truth (quasi-truth). In this paper, we discuss the relationship between this approach and free logic. We also compare the model-theoretic analysis supplied by partial structures with the method of supervaluations, which was initially introduced as a technique to provide a semantic analysis of free logic. We then combine the three formal frameworks (partial structures, free logic and supervaluations), and apply the (...) resulting approach to accommodate semantic paradoxes. (shrink)

Abstract: According to Luciano Floridi (2008) , informational structural realism provides a framework to reconcile the two main versions of realism about structure: the epistemic formulation (according to which all we can know is structure) and the ontic version (according to which structure is all there is). The reconciliation is achieved by introducing suitable levels of abstraction and by articulating a conception of structural objects in information-theoretic terms. In this essay, I argue that the proposed reconciliation works at the expense (...) of realism. I then propose an alternative framework, in terms of partial structures, that offers a way of combining information and structure in a realist setting while still preserving the distinctive features of the two formulations of structural realism. Suitably interpreted, the proposed framework also makes room for an empiricist form of informational structuralism (structural empiricism). Pluralism then emerges. (shrink)

Strong negation is a well-known alternative to the standard negation in intuitionistic logic. It is defined virtually by giving falsity conditions to each of the connectives. Among these, the falsity condition for implication appears to unnecessarily deviate from the standard negation. In this paper, we introduce a slight modification to strong negation, and observe its comparative advantages over the original notion. In addition, we consider the paraconsistent variants of our modification, and study their relationship with non-constructive principles and connexivity.

Cartwright and her collaborators have elaborated a provocative view of science which emphasises the independence from theory &unknown;in methods and aims&unknown; of phenomenological model building. This thesis has been supported in a recent paper by an analysis of the London and London model of superconductivity. In the present work we begin with a critique of Cartwright's account of the relationship between theoretical and phenomenological models before elaborating an alternative picture within the framework of the partial structures version of the semantic (...) approach to theories. Drawing on the recent histories of superconductivity by Dahl and Gavroglu, together with the original works by London and London and by F. London separately, and taking due consideration of the heuristic aspects, we argue that the historical details fail to support Cartwright et al.'s claims but that they fit comfortably within the partial structures framework. (shrink)

We expose the main ideas, concepts and results about Jaśkowski's discussive logic, and apply that logic to the concept of pragmatic truth and to the Dalla Chiara-di Francia view of the foundations of physics.

An introduction to the model-theoretic approach in the philosophy of science is given and it is argued that this program is further enhanced by the introduction of partial structures. It is then shown that this leads to a natural and intuitive account of both "iconic" and mathematical models and of the role of the former in science itself.

Quasi-truth (a.k.a. pragmatic truth or partial truth) is typically advanced as a framework accounting for incompleteness and uncertainty in the actual practices of science. Also, it is said to be useful for accommodating cases of inconsistency in science without leading to triviality. In this paper, we argue that the formalism available does not deliver all that is promised. We examine the standard account of quasi-truth in the literature, advanced by da Costa and collaborators in many places, and argue that it (...) cannot legitimately account for incompleteness in science. We shall claim that it conflates paraconsistency and paracompleteness. It also cannot properly account for inconsistencies, because no direct contradiction of the form S ∧ ¬S can be quasi-true according to the framework; contradictions simply have no place in the formalism. Finally, we advance an alternative interpretation of the formalism in terms of dealing with distinct contexts where incompatible information is dealt with. This does not save the original program, but seems to make better sense of the apparatus. (shrink)

We consider the problem of therelationship between the quantum and theclassical domains from the point of view that itis possible to speak of a direct physicaldescription of quantum systems havingphysical properties. We put emphasis, inevidencing it, on the specific quantum conceptof indistinguishability of identical in aconceptual way (and not in a logical way in thevein of ``da Costa's school''). In essence, thesubsequent argumentation deals with therelationship between the classical and thequantum, with the problem of the quantum theoryof measurement. Even in (...) the absence of adefinitive response to this problem, the bestattitude for the time being, as we cannot reducethe classical and the quantum one to the other,seems to be to accept their pacific coexistence,and this is possible with the toleranceprinciple of the ``pragmatic truth'' developedfrom a logical point of view by Newton daCosta.RESUMO. As áreas quântica eclássica enquanto provisórioscoexistentes parallelos. Abordamos oproblema da relação entre as áreasdo quântico e do clássico considerandoque é possível falar de umadescrição física direta de sistemas quânticos tendo propriedades.Insistimos, para isto, sobre o conceitoespecificamente quântico daindicernabilidade dos idênticos de um ponto devista conceptual (não de um ponto de vistalógico à maneira da ``escola da Costa'')como evidenciando isto. O essencial daargumentação a seguir tem como enfoquea relação clássico-quântico, como problema da teoria quântica damedição. Mesmo não tendo umaresposta definitiva para este, a melhor atitudepor enquanto, já que não se podemreduzir um ao outro o clássico e oquântico, nos parece ser esta de aceitar suacoexistência pacífica, o que épossível com o princípio detolerância da ``verdade pragmática''desenvolvida logicamente por Newton da Costa. (shrink)

In this work, the first of a series, we study the nature of informal inconsistency in physics, focusing mainly on the foundations of quantum theory, and appealing to the concept of quasi-truth. We defend a pluralistic view of the philosophy of science, grounded on the existence of inconsistencies and on quasi-truth. Here, we treat only the ‘classical aspects’ of the subject, leaving for a forthcoming paper the ‘non-classical’ part.

We apply the recently elaborated notions of 'pragmatic truth' and 'pragmatic probability' to the problem of the construction of a logic of inductive inference. It is argued that the system outlined here is able to overcome many of the objections usually levelled against such attempts. We claim, furthermore, that our view captures the essentially cumulative nature of science and allows us to explain why it is indeed reasonable to accept and believe in the conclusions reached by inductive inference.

Scientific change has two important dimensions: conceptual change and structural change. In this paper, I argue that the existence of conceptual change brings serious difficulties for scientific realism, and the existence of structural change makes structural realism look quite implausible. I then sketch an alternative account of scientific change, in terms of partial structures, that accommodates both conceptual and structural changes. The proposal, however, is not realist, and supports a structuralist version of van Fraassen’s constructive empiricism (structural empiricism).

Based on da Costa's and French's notions of partial structures and pragmatic truth, this paper examines two possible characterizations of the concept of empirical adequacy, one depending on the notion of partial isomorphism, the other on the hierarchy of partial models of phenomena, and both compatible with an empiricist view. These formulations can then be employed to illuminate certain aspects of scientific practice.An empirical theory must single out a specific part of the world, establish reference to that part, and say—by (...) way of contingent, substantial claim about the world—that its models fit that. Now, how exactly can this be done? Bas C. van Fraassen. (shrink)

The notion of empirical adequacy has received recent philosophical attention, especially within the framework of the semantic approach. Empirical adequacy, as explicated in the semantic approach, concerns the relationship between empirical substructures and some phenomena. The aim here is to differentiate this notion of empirical adequacy from one concerning the relationship between data and phenomena. Distinguishing each notion of empirical adequacy emphasizes different aspects of scientific practice—one concerning theory-development from the basis of an established theory, the other concerning theory-development from (...) the basis of data-fitting, where established theory may not foster further development. To illustrate this contrast, an example from financial economics is considered. (shrink)

Abstract A general framework is proposed for accommodating the recent results of studies into ?natural? decision making. A crucial element of this framework is the notion of a ?partial structure?, recently introduced into the semantic approach to scientific theories. It is through the introduction of this element that connections can be made with certain problems regarding inconsistency and rationality in general.