There is a great deal of justified concern about continuity through scientific theory change. Our thesis is that, particularly in physics, such continuity can be appropriately captured at the level of conceptual frameworks using conceptual space models. Indeed, we contend that the conceptual spaces of three of our most important physical theories—Classical Mechanics, Special Relativity Theory, and Quantum Mechanics —have already been so modelled as phase-spaces. Working with their phase-space formulations, one can trace the conceptual changes and continuities in transitioning (...) from CM to QM, and from CM to SRT. By offering a revised severity-ordering of changes that conceptual frameworks can undergo, we provide reasons to doubt the commonly held view that CM is conceptually closer to SRT than QM. (shrink)

It is easy to show that in many natural axiomatic formulations of physical and even mathematical theories, there are many superfluous concepts usually assumed as primitive. This happens mainly when these theories are formulated in the language of standard set theories, such as Zermelo–Fraenkel’s. In 1925, John von Neumann created a set theory where sets are definable by means of functions. We provide a reformulation of von Neumann’s set theory and show that it can be used to formulate physical and (...) mathematical theories with a lower number of primitive concepts very naturally. Our basic proposal is to offer a new kind of set-theoretic language that offers advantages with respect to the standard approaches, since it doesn’t introduce dispensable primitive concepts. We show how the proposal works by considering significant physical theories, such as non-relativistic classical particle mechanics and classical field theories, as well as a well-known mathematical theory, namely, group theory. This is a first step of a research program we intend to pursue. (shrink)

Highly idealized models may serve various epistemic functions, notably explanation, in virtue of representing the world. Inferentialism provides a prima facie compelling characterization of what constitutes the representation relation. In this paper, I argue that what I call factive inferentialism does not provide a satisfactory solution to the puzzle of model-based—factive—explanation. In particular, I show that making explanatory counterfactual inferences is not a sufficient guide for accurate representation, factivity, or realism. I conclude by calling for a more explicit specification of (...) model-world mismatches and properties imputation. (shrink)

This article characterizes various species concepts in terms of set-theoretic models that license biological inferences and illustrates the logical connections among different species concepts. Species in this construal are abstract models, rather than biological or even tangible entities, and relate to individual organisms via representation, rather than the membership or mereological whole/part relationship. The proposal sheds new light on vexed issues of species and situates them within broader philosophical contexts of model selection, scientific representation, and scientific realism.

The paper conceptualizes economic models as metaphors. It presents two different approaches to economic modeling. In the first one, economic models are treated as isolations which aim at representing the real world. In the second, they are conceptualized according to various philosophical approaches that are close to fictionalism. The aim of such modeling is to persuade and not to represent. Next, the author tries to escape the dichotomy between models as isolations and models as purely rhetorical devices by referring to (...) N. Cartwright’s understanding of economic models. The issue of their realism is also considered. The final conclusion states that models are very similar to metaphors. (shrink)

First of all, I agree with much of what F.A. Muller says in his article ‘Reflections on the revolution in Stanford’. And where I differ, the difference is on the decision of what direction of further development represents the best choice for the philosophy of science. I list my remarks as a sequence of topics.

This article argues that the much-maligned ‘notational variants’ of a given formal linguistic theory play a role similar to alternative numerical measurement scales. Thus, they can be used to identify the invariant components of the grammar; i.e., those features that do not depend on the choice of empirically equivalent representation. Treating these elements as the ‘meaningful’ structure of language has numerous consequences for the philosophy of science and linguistics. I offer several such examples of how linguistic theorizing can profit from (...) adopting a measurement-theoretic viewpoint. The first concerns a measurement-theoretic response to a famous criticism of Quine's. Others follow from issues of simplicity in the current biolinguistics program. An unexpected similarity with behaviorist practices is also uncovered. I then argue that managable and useful steps can be taken in this area. (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.

Our main purpose here is to make some considerations about the definability of physical concepts like mass, force, time, space, spacetime, and so on. Our starting motivation is a collection of supposed definitions of closed system in the literature of physics and philosophy of physics. So, we discuss the problem of definitions in theoretical physics from the point of view of modern theories of definition. One of our main conclusions is that there are different kinds of definitions in physics that (...) demand different approaches. Within this context, we strongly advocate the use of the axiomatic method in order to discuss some issues concerning definitions. (shrink)

By understanding laws of nature as geometrical rather than linguistic entities, this paper addresses how to describe theory structures and how to evaluate their continuity. Relying on conceptual spaces as a modelling tool, we focus on the conceptual framework an empirical theory presupposes, thus obtain a geometrical representation of a theory’s structure. We stress the relevance of measurement procedures in separating conceptual from empirical structures. This lets our understanding of scientific laws come closer to scientific practice, and avoids a widely (...) recognised deficit in current philosophy of science accounts, namely to risk a collapse of the physical into the mathematical. (shrink)

Following ideas elaborated by Hering in his celebrated analysis of color, the psychologist and gestalt theorist Otto Selz developed in the 1930s a theory of “natural space”, i.e., space as it is conceived by us. Selz’s thesis is that the geometric laws of natural space describe how the points of this space are related to each other by directions which are ordered in the same way as the points on a sphere. At the end of one of his articles, Selz (...) tries to derive within his framework two of Hilbert’s axioms for Euclidean geometry. Such derivations would, according to Selz, disclose the psychological origin and meaning of the geometric axioms and would thus contribute to a clarification of their epistemological status. In the present article Selz’s theory is explained and analyzed, his basic principles are amended, and implicit assumptions are made explicit. It is shown that the resulting system is one of ordered affine geometry in which all of Hilbert’s axioms except the axioms of congruence and those of continuity are derivable. The primary aim of the present paper is to make explicit the basic principles behind Selz’s geometry of natural space. The question of the logical independence of these principle is not investigated. (shrink)

PORTUGUESE: Neste artigo, apresentaremos uma visão particular do desenvolvimento de teorias científicas que denominamos (inspirados em Ortega y Gasset) "perspectivismo". Discutiremos como, através desse enfoque, é possível compatibilizar diversas descrições aparentemente distintas e incompatíveis de uma suposta realidade que se investiga. Fazemos isso distinguindo entre a "realidade" (R) e a "descrição empírica da realidade" (Re). Aceitando que podemos ter diversas descrições empíricas de uma mesma realidade, discutimos o caso particular em que esse esquema é utilizado nos debates atuais acerca da (...) ontologia da física quântica, em especial da mecânica quântica não relativista. Como se sabe, essa teoria é compatível com distintas ontologias (ou metafísicas), em particular, pode ser vista como comprometida com uma ontologia de indivíduos, mas também com uma ontologia de não indivíduos. Ambas as alternativas são plausíveis e merecem ser desenvolvidas. Propomos que o perspectivismo aqui apresentado é neutro com relação à escolha de uma metafísica (ontologia), bem como aos debates entre realistas e antirrealistas em filosofia da ciência. Concluímos que passar do pluralismo aceito pelo perspectivista ao realismo ou antirrealismo envolve comprometimento com teses mais robustas acerca da relação entre realidade e descrição da realidade.ENGLISH: In this article we present a particular view of the development of scientific theories which (following Ortega y Gasset), we term "perspectivism". Making use of this view, we discuss how we can accommodate distinct and apparently incompatible descriptions of a supposed reality under investigation. We distinguish between a "reality" (R) and its "empirical description", (Re). Acknowledging that we can have diverse empirical descriptions of the same reality, we discuss the particular case in which the view is applied to current debates on the ontology of quantum physics, especially of non-relativistic quantum mechanics. As it is well known, this theory is compatible with treating quantum objects either as individuals or as non-individuals. Both ontologies are possible and deserve to be developed. We propose that the perspectivism developed here is neutral not only with respect to the choice of an ontology, but also concerning the debates among realists and anti-realists in the philosophy of science. We conclude that to go beyond the pluralism accepted by perspectivism, and to adopt realism or anti-realism, involves commitment to strong theses about the relation between reality and its descriptions. PORTUGUESE: Neste artigo, apresentaremos uma visão particular do desenvolvimento de teorias científicas que denominamos (inspirados em Ortega y Gasset) "perspectivismo". Discutiremos como, através desse enfoque, é possível compatibilizar diversas descrições aparentemente distintas e incompatíveis de uma suposta realidade que se investiga. Fazemos isso distinguindo entre a "realidade" (R) e a "descrição empírica da realidade" (Re). Aceitando que podemos ter diversas descrições empíricas de uma mesma realidade, discutimos o caso particular em que esse esquema é utilizado nos debates atuais acerca da ontologia da física quântica, em especial da mecânica quântica não relativista. Como se sabe, essa teoria é compatível com distintas ontologias (ou metafísicas), em particular, pode ser vista como comprometida com uma ontologia de indivíduos, mas também com uma ontologia de não indivíduos. Ambas as alternativas são plausíveis e merecem ser desenvolvidas. Propomos que o perspectivismo aqui apresentado é neutro com relação à escolha de uma metafísica (ontologia), bem como aos debates entre realistas e antirrealistas em filosofia da ciência. Concluímos que passar do pluralismo aceito pelo perspectivista ao realismo ou antirrealismo envolve comprometimento com teses mais robustas acerca da relação entre realidade e descrição da realidade. (shrink)

The use of models of scientific theories should not be done without qualifications about the mathematics being used to build the models. This looks obvious, at least for logicians, but generally, it is not to the philosopher of science. Thus, some details about this point seem useful for both. Since any quick revision in the literature shows that in most cases, mainly after the raising of the semantic approach, the models are taken to be set-theoretical structures, in discussing the issue (...) we shall be concerned more with set theories, the locus where the play is usually developed. (shrink)

On the received view, the Representational Theory of Measurement reduces measurement to the numerical representation of empirical relations. This account of measurement has been widely criticized. In this article, I provide a new interpretation of the Representational Theory of Measurement that sidesteps these debates. I propose to view the Representational Theory of Measurement as a library of theorems that investigate the numerical representability of qualitative relations. Such theorems are useful tools for concept formation that, in turn, is one crucial aspect (...) of measurement for a broad range of cases in linguistics, rational choice, metaphysics, and the social sciences. (shrink)

This essay will be divided into three parts. In the first part, we discuss the case of infintesimals seen as a bridge between the discrete and the continuous. This leads in the second part to a discussion of the nature of numbers. In the last part, we follow up with some observations on the obvious applicability of mathematics.

The first invariance principle, called “meaningfulness,” is germane to the common practice requiring that the form of a scientific law must not be altered by a change of the units of the measurement scales. By itself, meaningfulness does not put any constraint on the possible data. The second principle requires that the output variable is “order-invariant” with respect to any transformation (of one of the input variables) belonging to a particular family or class of such transformations which are characteristic of (...) the law. These principles are formulated as axioms of a theory. Taken together, meaningfulness and order-invariance axioms have strong consequences on the feasible theories. Three applications of our results are discussed in details, involving the Lorentz–FitzGerald contraction, Beer's law, and the Monomial laws, each of which is derived from three axioms implementing meaningfulness and order-invariance concepts. (An “initial condition” axiom is also used.) Not all scientific laws are order-invariant in the sense of this paper. An example is van der Waals' equation. (shrink)

Some of the forerunners of quantum theory regarded the basic entities of such theories as 'non-individuals'. One of the problems is to treat collections of such 'things', for they do not obey the axioms of standard set theories like Zermelo- Fraenkel. In this paper, collections of objects to which the standard concept of identity does not apply are termed 'quasi-sets'. The motivation for such a theory, linked to what we call 'the Manin problem', is presented, so as its specific axioms. (...) At the end, it is shown how quantum statistics can be obtained within quasi-set thbeory. (shrink)

I briefly discuss the epistemological role of quasi-set theory in mathematics and theoretical physics. Quasi-set theory is a first order theory, based on Zermelo-Fraenkel set theory with Urelemente. Nevertheless, quasi-set theory allows us to cope with certain collections of objects where the usual notion of identity is not applicable, in the sense that $x = x$ is not a formula, if $x$ is an arbitrary term. Basically, quasi-set theory offers us some sort of logical apparatus for questioning the need for (...) identity in some branches of mathematics and theoretical physics. I also use this opportunity to discuss a misunderstanding about quasi-sets due mainly to Nicholas J. J. Smith, who argues, in a general way, that sense cannot be made of vague identity. (shrink)

The structure of natural languages is usually studied from three major different but interconnected points of view: syntax, semantics, and pragmatics. If we consider that the main purpose of natural languages is communication, we should consider another dimension for languages, which deals with the influence of internal states of communicating individuals on meanings. Such a dimension we refer to as internalism. Within this context, internalism cannot be confused with psycholinguistics, in the same way pragmatics cannot be confused with sociolinguistics. In (...) particular, we argue, language is tied to its systematic use. This view leads us to a non-realist perspective on linguistics. We analyze the role of natural languages into dialogues, by comparing our proposal to the dialogical approach to logic, which considers a dialogue as a game. Within our approach, there is no way to guarantee that two parties involved in a dialogue are playing the same game, due to unavoidable differences in their respective internal states. Another contribution of this paper is to argue that semantics plays a more fundamental role than syntax in the cognitive acquisition of languages. (shrink)

Chalmers’ zombie argument against physicalism about consciousness supposes that every property of a composed physical system supervenes on the system’s fundamental constituents. In this paper, I discuss the significance of this supposition and I show that the philosophy of physics provides good grounds to resist it. As a result, I conclude that the zombie argument does not rule out a physicalist view of consciousness that conceives it as emergent in the sense of S-emergence. I finish by discussing some objections.