In this paper, a new account of empirical claims in structuralism is developed. Its novelty derives from the use that is made of the linguistic approach to scientific theories despite the presumed incompatibility of structuralism with that approach. It is shown how the linguistic approach can be applied to the framework of structuralism if the semantic foundations of that approach are refined to do justice to the doctrine of indirect interpretation of theoretical terms. This doctrine goes back to Carnap but (...) has been advanced until the present day without a proper semantic explanation. (shrink)

Some scientific theories are inconsistent, yet non-trivial and meaningful. How is that possible? The present paper aims to show that we can analyse the inferential use of such theories in terms of consistent compositions of the applications of universal axioms. This technique will be represented by a preferred models semantics, which allows us to accept the instances of universal axioms selectively. For such a semantics to be developed, the framework of partial structures by da Costa and French will be extended (...) by a few elements of the Sneed formalism, also known as the structuralist approach to science. (shrink)

The distinction between the syntactic and the semantic approach to scientific theories emerged in formal philosophy of science. The semantic approach is commonly considered more advanced and more successful than the syntactic one, but the transition from the one approach to the other was not brought about without any loss. In essence, it is the formal analysis of atomic propositions and the analysis of deductive reasoning that dropped out of consideration in at least some of the elaborated versions of the (...) semantic approach. In structuralist theory of science, as founded by Sneed and Stegmüller, the focus is on global propositions concerning the question of whether or not certain empirical systems satisfy a set-theoretic predicate that encodes the axioms of a scientific theory. Hence, an analysis of deductive reasoning from atomic premisses with the help of a given theory is missing. The objective of the present paper is to develop a deductive system on the basis of the structuralist framework. This system comes with a novel formulation of empirical propositions in structuralism. (shrink)

This paper aims to set forth Carnapian structuralism, i.e., a syntactic view of the structuralist approach which is deeply inspired by Carnap’s dual level conception of scientific theories. At its core is the axiomatisation of a metatheoretical concept AE(T) which characterises those extensions of an intended application that are admissible in the sense of being models of the theory-element T and that satisfy all links, constraints and specialisations. The union of axiom systems of AE(T) (where T is an element of (...) the theory-net N) will allow us to present scientific theories in an axiomatic fashion so that deductive reasoning in science can be formalised. Thereupon defeasible and paraconsistent means of reasoning will be introduced. The logical study of scientific reasoning is the key motivation of Carnapian structuralism. A further motivation is to help overcome the syntactic-semantic split in the philosophy of science. (shrink)

Primarily addressed to readers unfamiliar with the structuralist approach in philosophy of science, we introduce the basic concepts that the contributions to this special issue presuppose. By means of examples, we briefly review set-theoretic structures and predicates, the potential and actual models of an empirical theory, intended applications, as well as links and specializations that are applied, among others, in reconstructing the empirical claim associated with a theory element.

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)

This article concerns the split between syntactic and semantic approaches to scientific theories. It aims at showing that an axiomatic representation of a scientific theory is a precondition of comprehending if the models of contain infinite entities. This result is established on the basis of the proposition that the human mind—which is finitely bounded for all we know—is not capable of directly grasping infinite entities. In view of this cognitive limitation, an indirect and finite representation of possibly infinite components of (...) the models of a scientific theory proves to be indispensable. Sets of axioms and sets of axiom schemes provide such a representation. These considerations will be cast into an argument for an axiomatic conception of scientific theories. The article concludes with a case study of the ideal gas model. (shrink)

A central topic in the logic of science concerns the proper semantic analysis of theoretical sentences, that is sentences containing theoretical terms. In this paper, we present a novel choice-semantical account of theoretical truth based on the epsilon-term definition of theoretical terms. Specifically, we develop two ways of specifying the truth conditions of theoretical statements in a choice functional semantics, each giving rise to a corresponding logic of such statements. In order to investigate the inferential strength of these logical systems, (...) we provide a translation of each truth definition into a modal definition of theoretical truth. Based on this, we show that the stronger notion of choice-semantical truth captures more adequately our informal semantic understanding of scientific statements. (shrink)

Carnap's mature philosophy of science is an attempt to dissolve the scientific realism debate altogether as a philosophical pseudo-question. His argument depends upon a logico-semantic thesis regarding the structure of a scientific theory, and more importantly, a meta-ontological thesis regarding the explication of existence claims. The latter commits Carnap to a distinction between the analytic and the synthetic, which was allegedly refuted by Quine. The contemporary philosophy of science has therefore sought to distance itself from logico-semantic considerations, and has pursued (...) the scientific realism debate as an essentially epistemological thesis. I show however that one of the most prominent positions in this recent debate—van Fraassen's constructive empiricism—not only ends up in very close proximity to Carnap's attempted dissolution, but even provides the resources for extending and refining his programme. Rather than a historical footnote, Carnap's mature philosophy of science offers a live-option in the current debate. (shrink)

Rudolf Carnap delivered the hitherto unpublished lecture ‘Theoretical Concepts in Science’ at the meeting of the American Philosophical Association, Pacific Division, at Santa Barbara, California, on 29 December 1959. It was part of a symposium on ‘Carnap’s views on Theoretical Concepts in Science’. In the bibliography that appears in the end of the volume, ‘The Philosophy of Rudolf Carnap’, edited by Paul Arthur Schilpp, a revised version of this address appears to be among Carnap’s forthcoming papers. But although Carnap started (...) to revise it, he never finished the revision,1 and never published the unrevised transcript. Perhaps this is because variants of the approach to theoretical concepts presented for the first time in the Santa Barbara lecture have appeared in other papers of his (cf. the editorial footnotes in Carnap’s lecture). Still, I think, the Santa Barbara address is a little philosophical gem that needs to see the light of day. The document that follows is the unrevised transcript of Carnap’s lecture.2 Its style, then, is that of an oral presentation. I decided to leave it as it is, making only very minor stylistic changes—which, except those related to punctuation, are indicated by curly brackets.3 I think that reading this lecture is a rewarding experience, punctuated as the lecture is with odd remarks and autobiographical points. One can almost envisage.. (shrink)

Gerhard Schurz [2001, Journal for General Philosophy of Science, 32, 65-107] has proposed to reconstruct auxiliary hypothesis addition, e.g., postulation of Neptune to immunize Newtonian mechanics, with concepts from non-monotonous inference to avoid the retention of false predictions that are among the consequence-set of the deductive model. However, the non-monotonous reconstruction retains the observational premise that is indeed rejected in the deductive model. Hence, his proposal fails to do justice to Lakatos' core-belt model, therefore fails to meet what Schurz coined (...) "Lakatos' challenge". It is argued that Lakatos's distinction between core and belt of a research program is not mapable onto premise-set and consequence-set and that Schurz's understanding of a ceteris paribus clause as a transfinite list of interfering factors is problematic. I propose a simple reading of Lakatos's use of the term ceteris paribus clause and motivate why the term hypothesis addition, despite not being interpretable literally, came to be entrenched. (shrink)

I review the philosophical literature on the question of when two physical theories are equivalent. This includes a discussion of empirical equivalence, which is often taken to be necessary, and sometimes taken to be sufficient, for theoretical equivalence; and “interpretational” equivalence, which is the idea that two theories are equivalent just in case they have the same interpretation. It also includes a discussion of several formal notions of equivalence that have been considered in the recent philosophical literature, including (generalized) definitional (...) equivalence and categorical equivalence. The article concludes with a brief discussion of the relationship between equivalence and duality. The article is in two parts; this is Part 2, which addresses categorical equivalence, interpretational equivalence, and duality. (shrink)

I review the philosophical literature on the question of when two physical theories are equivalent. This includes a discussion of empirical equivalence, which is often taken to be necessary, and sometimes taken to be sufficient, for theoretical equivalence; and “interpretational” equivalence, which is the idea that two theories are equivalent just in case they have the same interpretation. It also includes a discussion of several formal notions of equivalence that have been considered in the recent philosophical literature, including (generalized) definitional (...) equivalence and categorical equivalence. The article concludes with a brief discussion of the relationship between equivalence and duality. The article is in two parts; this is Part 1, which addresses empirical equivalence and definitional equivalence. (shrink)

This paper seeks to evaluate the potential of the Newman objection to function as an immanent critique of Carnap's use of the Ramsey method of regimenting scientific theories. Stress is laid on the distinctive way in which ramseyfications are used by Carnap to formulate the analytic/synthetic distinction for the theoretical language and on the difference between the ontological and the epistemic readings of the Newman objection. While the former reading of the Newman objection is rejected as trading on an assumption (...) that Carnap did not share, the latter is accepted as critical. It is argued to turn on overlooking that the Ramsey sentence constitutes an idealization concerning which our normal expectations of what theories are like are bound to be frustrated. This idealisation need not reflect Carnap's considered view but can be regarded as adopted solely for the project of semantic explication. The distinctions drawn in the course of the argument also help to motivate Carnap's abstention from the discourse of realism and its denial. (shrink)

Simple assumptions represent a decisive reason to prefer one theory to another in everyday scientific praxis. But this praxis has little philosophical justification, since there exist many notions of simplicity, and those that can be defined precisely strongly depend on the language in which the theory is formulated. The language dependence is a natural feature—to some extent—but it is also believed to be a fatal problem, because, according to a common general argument, the simplicity of a theory is always trivial (...) in a suitably chosen language. But, this trivialization argument is typically either applied to toy-models of scientific theories or applied with little regard for the empirical content of the theory. This paper shows that the trivialization argument fails, when one considers realistic theories and requires their empirical content to be preserved . In fact, the concepts that enable a very simple formulation, are not necessarily measurable, in general. Moreover, the inspection of a theory describing a chaotic billiard shows that precisely those concepts that naturally make the theory extremely simple are provably not measurable. This suggests that—whenever a theory possesses sufficiently complex consequences—the constraint of measurability prevents too simple formulations in any language. This explains why the scientists often regard their assessments of simplicity as largely unambiguous. In order to reveal a cultural bias in the scientists’ assessment, one should explicitly identify different characterizations of simplicity of the assumptions that lead to different theory selections. General arguments are not sufficient. (shrink)

Rudolf Carnap’s mature work on the logical reconstruction of scientific theories consists of two components. The first is the elimination of the theoretical vocabulary of a theory in terms of its Ramsification. The second is the reintroduction of the theoretical terms through explicit definitions in a language containing an epsilon operator. This paper investigates Carnap’s epsilon-reconstruction of theories in the context of pure mathematics. The main objective here is twofold: first, to specify the epsilon logic underlying his suggested definition of (...) theoretical terms and a suitable choice semantics for it. Second, to analyze whether Carnap’s approach is compatible with a structuralist conception of mathematics. (shrink)

In this paper I reconstruct and compare criteria of theoreticity that have been developed by Carnap, Sneed and proponents of the Munich school of structuralist philosophy of science. For this purpose I develop a unified framework in which one can transform model-theoretic theory representations into linguistic ones, and vice versa. This bridges the gap between statement and non-statement view and allows a precise comparison of linguistic and model-theoretic criteria of theoreticity. In the final part I suggest a system of improved (...) definitions of theoreticity and pre-theoreticity. (shrink)

This paper presents in outline Luigi Ferrajoli’s axiomatic and general theory of law, as developed in his lifelong work Principia Iuris . The first section focuses on the three main aspects of the theory: the methodological, the theoretical and the pragmatic, which respectively represent the theory’s syntax, semantics and its pragmatics. Ferrajoli identifies three deontic gaps of norms: firstly, the one between their validity and efficacy ; secondly, the one between their justice and validity ; and finally, and most importantly, (...) the one between validity and existence (i.e. normative force). The presence of such gaps is, according to Ferrajoli, the extraordinary innovation that entrenched constitutions have brought into modern legal systems, by establishing norms that are superior to statutes and case law. In this sense, all normative phenomena (except for the constitution itself) can be conceived both as norms and as facts. In the second section the role of juridical science is briefly discussed. (shrink)

Patrick Suppes'' set-theoretical approach to the analysis of theories, and Joseph D. Sneed''s metatheory are briefly outlined. The notions of observation, illusion and hallucination are reconstructed according to these approaches. It is argued that the terms perception and truth are theoretical with respect to observation but nontheoretical with respect to illusion and hallucination. Hallucination is construed as a special kind of illusion.

Patrick Suppes' set-theoretical approach to the analysis of theories, and Joseph D. Sneed's metatheory are briefly outlined. The notions of observation, illusion and hallucination are reconstructed according to these approaches. It is argued that the terms ‘perception’ and ‘truth’ are theoretical with respect to observation but nontheoretical with respect to illusion and hallucination. Hallucination is construed as a special kind of illusion.

In this article I give an overview of some recent work in philosophy of science dedicated to analysing the scientific process in terms of (conceptual) mathematical models of theories and the various semantic relations between such models, scientific theories, and aspects of reality. In current philosophy of science, the most interesting questions centre around the ways in which writers distinguish between theories and the mathematical structures that interpret them and in which they are true, i.e. between scientific theories as linguistic (...) systems and their non-linguistic models. In philosophy of science literature there are two main approaches to the structure of scientific theories, the statement or syntactic approach -- advocated by Carnap, Hempel and Nagel -- and the non- statement or semantic approach --advocated, among others, by Suppes, the structuralists, Beth, Van Fraassen, Giere, Wojcicki. In conclusion, I briefly review some of the usual realist inspired questions about the possibility and character of relations between scientific theories and reality as implied by the various approaches I discuss in the course of the article. The models of a scientific theory should indeed be adequate to the phenomena, but if the theory is 'adequate' to (true in) its conceptual (mathematical) models as well, we have a model-theoretic realism that addresses the possible meaning and reference of 'theoretical entities' without relapsing into the metaphysics typical of the usual scientific realist approaches. (shrink)

AbstractBohmian mechanics grounds the predictions of quantum mechanics in precise dynamical laws for a primitive ontology of point particles. In an appraisal of the de-Broglie–Bohm theory, the paper discusses the crucial epistemological and conceptual role that a primitive ontology plays within a physical theory. It argues that quantum theories without primitive ontology fail to make contact with observable reality in a clear and consistent manner. Finally, it discusses Einstein’s epistemological model and why it supports the primitive ontology approach.

This Introduction has two foci: the first is a discussion of the motivation for and the aims of the 2014 conference on New Thinking about Scientific Realism in Cape Town South Africa, and the second is a brief contextualization of the contributed articles in this special issue of Synthese in the framework of the conference. Each focus is discussed in a separate section.

Frank Ramsey (1903-1930) is usually taken to be sympathetic to the Vienna Circle’s project. I will argue that this is not right. Ramsey was a pragmatist, and he put pragmatist objections to Wittgenstein’s Tractatus, objections which also had the Vienna Circle as their target. Ramsey thought the Circle’s position (like Wittgenstein’s) was mistaken in that, instead of starting with human inquiry, it tried to construct the world out of elementary particulars and logic, and resulted in an unacceptable solipsism. This paper (...) traces the trajectory of Ramsey’s pragmatist thought, and its relationship to the early Wittgenstein and the Vienna Circle. (shrink)

For decades Ryszard Wójcicki has been a highly influential scholar in the community of logicians and philosophers. Our aim is to outline and comment on some essential issues on logic, methodology of science and semantics as seen from the perspective of distinguished contributions of Wójcicki to these areas of philosophical investigations.

Abstract Artificial language philosophy (also called ‘ideal language philosophy’) is the position that philosophical problems are best solved or dissolved through a reform of language. Its underlying methodology—the development of languages for specific purposes—leads to a conventionalist view of language in general and of concepts in particular. I argue that many philosophical practices can be reinterpreted as applications of artificial language philosophy. In addition, many factually occurring interrelations between the sciences and philosophy of science are justified and clarified by the (...) assumption of an artificial language methodology. (shrink)

La parution de la monographic de Sneed,The Logical Structure of Mathematical Physics a suscité un renouveau d'intérêt en philosophie contemporaine des sciences. Cet ouvrage arrivait à un moment où l'épistémologie des sciences, telle que développée dans les milieux germaniques et anglo-saxons, accusait de graves insuffisances dans la reconstruction rationnelle du développement historique des théories physiques. Mis sur la défensive par les thèses et arguments historiques de Kuhn et de Feyerabend, ces milieux « orthodoxes » devaient reconnaitre l'état embryonnaire de ce (...) qui devait être uneépistémologie diachroniquedes sciences, une épistémologie du changement scientifique où les méthodes d'analyse formelle puissent être aussi mises á contribution. A cela s'ajoutait un certain malaise, une certaine stagnation de la problématique, plus synchronique, de l'approche traditionnelle issue du mouvement empiriste logique. Le probleme de la dichotomielangage théorique—langage observationnel, ainsi que son fidèle compagnon, le problème destermes théoriques, le statut épistémologique desrègies de correspondance, la dèfinition du concept d'analyticitéen science, autant de questions qui avaient été discutées et critiquées, à maintes reprises, pour aboutir à des résultats peu concluants aux yeux des philosophes, comme à ceux des physiciens préoccupés des fondements de leur discipline et à qui la teneur de cette discussion semblait souvent étrangère à la pratique scientifique. (shrink)

This paper aims to study the foundations of applied mathematics, using a formalized base theory for applied mathematics: ZFCAσ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathsf {ZFCA}_{\sigma }$$\end{document} with atoms, where the subscript used refers to a signature specific to the application. Examples are given, illustrating the following five features of applied mathematics: comprehension principles, application conditionals, representation hypotheses, transfer principles and abstract equivalents.

Several philosophers of science construe models of scientific theories as set-theoretic structures. Some of them moreover claim that models should not be construed as structures in the sense of model theory because the latter are language-dependent. I argue that if we are ready to construe models as set-theoretic structures (strict semantic view), we could equally well construe them as model-theoretic structures of higher-order logic (liberal semantic view). I show that every family of set-theoretic structures has an associated language of higher-order (...) logic and an up to signature isomorphism unique model-theoretic counterpart, which is able to serve the same purposes. This allows to carry over every syntactic criterion of equivalence for theories in the sense of the liberal semantic view to theories in the sense of the strict semantic view. Taken together, these results suggest that the recent dispute about the semantic view and its relation to the syntactic view can be resolved. (shrink)

Both realists and instrumentalists have found it difficult to understand (much less accept) Carnap's developed view on theoretical terms, which attempts to stake out a neutral position between realism and instrumentalism. I argue that Carnap's mature conception of a scientific theory as the conjunction of its Ramsey sentence and Carnap sentence can indeed achieve this neutral position. To see this, however, we need to see why the Newman problem raised in the context of recent work on structural realism is no (...) problem for Carnap's conception; and we also need to locate Carnap's work on theoretical terms within his wider program of Wissenschaftslogik or the logic of science. (shrink)

La rinascita negli ultimi decenni di un nutrito dibattito intorno alla nozione di analiticità dopo le critiche a suo tempo mosse da Quine alla batteria di nozioni utilizzate da Rudolf Carnap (ad esempio, postulati di significato, regole semantiche, definizioni implicite, convenzioni e stipulazioni esplicite) prende le mosse da una riflessione critica sulle argomentazioni di Quine e tenta, da un lato, di approfondire meglio il legame fra analiticità e conoscenza a priori, e, dall’altro, di capire meglio il ruolo che la definizione (...) può svolgere nella costituzione del significato e nella formulazione di verità concettuali. Questa nuova concezione è detta “epistemica” ed ha fra i suoi più autorevoli fautori Crispin Wright, Bob Hale e Paul Boghossian. Boghossian, al pari di molti filosofi critici della nuova concezione epistemica, come Timothy Williamson, conviene però con Quine nel sostenere che gli enunciati analitici hanno portata fattuale e vertono anch’essi sul mondo, oltre che sul linguaggio. Anche per questa ragione essi possono rendere possibile una genuina estensione delle nostre conoscenze. Tuttavia una seconda linea di obiezioni facenti capo dapprima a Paul Horwich, e in seguito agli stessi Wright e Hale, mette in evidenza rispettivamente due difficoltà corrispondenti alle questioni dell’arroganza e dell’accettazione. In questa discussione una parte importante è svolta dalla ripresa e della discussione del condizionale di Carnap, impiegato per rendere conto del ruolo che i termini teorici svolgono nel quadro dell’intera teoria cui appartengono, senza con ciò sposare le conseguenze dell’olismo quineano. La tesi centrale che questo lavoro cerca di rendere plausibile è che una lettura attenta degli ultimi scritti di Carnap mostri come il carattere aperto che egli attribuisce ai termini teorici in ragione, sia dello loro intrinseca indeterminatezza, sia delle revisioni imposte dalle scoperte scientifiche, è perfettamente compatibile con la fattorizzazione del contenuto di una teoria scientifica data in una parte linguistica, il condizionale di Carnap, riguardante la costituzione del significato di un certo termine teorico, e nella sua controparte empirica, che consente di registrare l’impatto dell’esperienza sulla teoria in questione. Se praticabile, questa concezione può a buon diritto entrare nel novero delle teorie epistemiche dell’analiticità, senza accampare alcuna pretesa di far rivivere i fasti della conoscenza a priori classica. (shrink)

I review the philosophical literature on the question of when two physical theories are equivalent. This includes a discussion of empirical equivalence, which is often taken to be necessary, and sometimes taken to be sufficient, for theoretical equivalence; and "interpretational" equivalence, which is the idea that two theories are equivalent just in case they have the same interpretation. It also includes a discussion of several formal notions of equivalence that have been considered in the recent philosophical literature, including definitional equivalence (...) and categorical equivalence. The article concludes with a brief discussion of the relationship between equivalence and duality. (shrink)