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The Structure of scientific theories

Urbana,: University of Illinois Press (1974)

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  1. A discussion on quantum non-individuality.Décio Krause & Jonas R. Becker Arenhart - 2012 - Journal of Applied Non-Classical Logics 22 (1-2):105-124.
    In this paper we consider the notions of structure and models within the semantic approach to theories. To highlight the role of the mathematics used to build the structures which will be taken as the models of theories, we review the notion of mathematical structure and of the models of scientific theories. Then, we analyse a case-study and argue that if a certain metaphysical view of quantum objects is adopted, one seeing them as non-individuals, then there would be strong reasons (...)
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  • Psychology as an Associational Science: A Methodological Viewpoint.Sam S. Rakover - 2012 - Open Journal of Philosophy 2 (2):143-152.
    Unlike the sciences (physics), psychology has not developed in any of its areas (such as perception, learning, cognition) a top-theory like Newtonian theory, the theory of relativity, or quantum theory in physics. This difference is explained by a methodological discrepancy between the sciences and psychology, which centers on the measurement procedure: in psychology, measurement units similar to those in physics have not been discovered. Based on the arguments supporting this claim, a methodological distinction is made between the sciences and psychology (...)
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  • (1 other version)Metaphysics for Positivists: Mach Versus the Vienna Circle.Erik C. Banks - 2013 - Discipline Filosophiche 23 (1):57-77.
    This article distinguishes between Machian empiricism and the logical positivism of the Vienna Circle and associated philosophers. Mach's natural philosophy was a first order attempt to reform and reorganize physics, not a second order reconstruction of the "language" of physics. Mach's elements were not sense data but realistic events in the natural world and in minds, and Mach admitted unobserved elements as part of his world view. Mach's critique of metaphysics was far more subtle and concerned the elimination of sensory (...)
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  • The Semantics of Scientific Theories.Sebastian Lutz - 2014 - In Anna Brożek & Jacek Jadacki (eds.), Księga pamiątkowa Marianowi Przełęckiemu w darze na 90-lecie urodzin. pp. 33-67.
    Marian Przełęcki’s semantics for the Received View is a good explication of Carnap’s position on the subject, anticipates many discussions and results from both proponents and opponents of the Received View, and can be the basis for a thriving research program.
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  • (1 other version)Models and Scientific Explanations.Robert C. Richardson - 1986 - Philosophica 37:59-72.
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  • Why It Is Time To Move Beyond Nagelian Reduction.Marie I. Kaiser - 2012 - In D. Dieks, S. Hartmann, T. Uebel & M. Weber (eds.), Probabilities, Laws and Structure. Springer. pp. 255-272.
    In this paper I argue that it is finally time to move beyond the Nagelian framework and to break new ground in thinking about epistemic reduction in biology. I will do so, not by simply repeating all the old objections that have been raised against Ernest Nagel’s classical model of theory reduction. Rather, I grant that a proponent of Nagel’s approach can handle several of these problems but that, nevertheless, Nagel’s general way of thinking about epistemic reduction in terms of (...)
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  • What Scientific Theories Could Not Be.Hans Halvorson - 2012 - Philosophy of Science 79 (2):183-206.
    According to the semantic view of scientific theories, theories are classes of models. I show that this view -- if taken seriously as a formal explication -- leads to absurdities. In particular, this view equates theories that are truly distinct, and it distinguishes theories that are truly equivalent. Furthermore, the semantic view lacks the resources to explicate interesting theoretical relations, such as embeddability of one theory into another. The untenability of the semantic view -- as currently formulated -- threatens to (...)
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  • Axiomatization and Models of Scientific Theories.Décio Krause, Jonas R. B. Arenhart & Fernando T. F. Moraes - 2011 - Foundations of Science 16 (4):363-382.
    In this paper we discuss two approaches to the axiomatization of scientific theories in the context of the so called semantic approach, according to which (roughly) a theory can be seen as a class of models. The two approaches are associated respectively to Suppes’ and to da Costa and Chuaqui’s works. We argue that theories can be developed both in a way more akin to the usual mathematical practice (Suppes), in an informal set theoretical environment, writing the set theoretical predicate (...)
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  • A Set of Axioms for Neoclassical Economics and the Methodological Status of the Equilibrium Concept.Arnis Vilks - 1992 - Economics and Philosophy 8 (1):51-82.
    It is widely agreed that the concept of general equilibrium and, in particular, general equilibrium existence proofs play a central role within the neoclassical approach to economic theory. There is much less agreement, however, on the concepts of general equilibrium and of neoclassical economic theory themselves.
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  • The classification of disciplines in biology: A plea for pluralism.W. J. van der Steen - 1980 - Acta Biotheoretica 29 (2):95-100.
    Pluralism is a sound strategy in classifying disciplines of biology. The relevance of a particular classification depends on various methodological issues, on the way in which the scientist's problems are specified, and on factual matters.
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  • Everything you always wanted to know about structural realism but were afraid to ask.Roman Frigg & Ioannis Votsis - 2011 - European Journal for Philosophy of Science 1 (2):227-276.
    Everything you always wanted to know about structural realism but were afraid to ask Content Type Journal Article Pages 227-276 DOI 10.1007/s13194-011-0025-7 Authors Roman Frigg, Department of Philosophy, Logic and Scientific Method, London School of Economics and Political Science, Houghton Street, London, WC2A 2AE UK Ioannis Votsis, Philosophisches Institut, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, Geb. 23.21/04.86, 40225 Düsseldorf, Germany Journal European Journal for Philosophy of Science Online ISSN 1879-4920 Print ISSN 1879-4912 Journal Volume Volume 1 Journal Issue Volume 1, Number 2.
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  • Truth and Physics Education.Robert Keith Shaw - 2010 - Dissertation, University of Auckland
    This thesis develops a hermeneutic philosophy of science to provide insights into physics education. -/- Modernity cloaks the authentic character of modern physics whenever discoveries entertain us or we judge theory by its use. Those who justify physics education through an appeal to its utility, or who reject truth as an aspect of physics, relativists and constructivists, misunderstand the nature of physics. Demonstrations, not experiments, reveal the essence of physics as two characteristic engagements with truth. First, truth in its guise (...)
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  • Generalised Quantum Theory—Basic Idea and General Intuition: A Background Story and Overview. [REVIEW]Harald Walach & Nikolaus von Stillfried - 2011 - Axiomathes 21 (2):185-209.
    Science is always presupposing some basic concepts that are held to be useful. These absolute presuppositions (Collingwood) are rarely debated and form the framework for what has been termed paradigm by Kuhn. Our currently accepted scientific model is predicated on a set of presuppositions that have difficulty accommodating holistic structures and relationships and are not geared towards incorporating non-local correlations. Since the theoretical models we hold also determine what we perceive and take as scientifically viable, it is important to look (...)
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  • A mid-level approach to modeling scientific communities.Audrey Harnagel - 2019 - Studies in History and Philosophy of Science Part A 76:49-59.
    This paper provides an account of mid-level models, which calibrate highly theoretical agent-based models of scientific communities by incorporating empirical information from real-world systems. As a result, these models more closely correspond with real-world communities, and are better suited for informing policy decisions than extant how-possibly models. I provide an exemplar of a mid-level model of science funding allocation that incorporates bibliometric data from scientific publications and data generated from empirical studies of peer review into an epistemic landscape model. The (...)
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  • L'explication en grammaire transformationnelle.Claude Panaccio - 1979 - Dialogue 18 (3):307-341.
    Malgré les critiques de toutes sortes dont elle fut et dont elle est encore l'objet, la grammaire transformationnelle est devenue en vingt ans, sous l'impulsion de Noam Chomsky, le paradigme dominant de la linguistique contemporaine. Et, bien sûr, l'incroyable rapidité de cette ascension s'est accompagnée de nombreuses crises de croissance. Linguistes, philosophes et psychologues, ainsi amenés à s'interroger sur les fondements épistémologiques de cette étrange discipline, se sont heurtés à de redoutables énigmes métathéoriques: de quel domaine factuel la linguistique est-elle (...)
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  • Unificationism: Philosophy for the modern disunified science of psychology.Arthur W. Staats - 1989 - Philosophical Psychology 2 (2):143-164.
    Abstract Psychology's goal has been to become a science, taking the modern natural sciences as the model. It has not been understood that each science undergoes a transition from early disunification to later unification, that a fundmental dimension is involved that differentiates sciences. Psychology is a modern disunified science, distinguished by its chaotic knowledge and ways of operating. A philosophy of science based on modem unified science, as philosophies generally are, is inappropriate as a means of understanding psychology or of (...)
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  • The structure of evolutionary theory: A semantic approach.Not By Me - 1983 - Studies in History and Philosophy of Science Part A 14 (3):215-229.
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  • The structuralist view of economic theories: A review essay: The case of general equilibrium in particular.D. Wade Hands - 1985 - Economics and Philosophy 1 (2):303-.
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  • Causation, Coherence and Concepts : a Collection of Essays.Wolfgang Spohn - unknown
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  • What’s Right with a Syntactic Approach to Theories and Models?Sebastian Lutz - 2010 - Erkenntnis (S8):1-18.
    Syntactic approaches in the philosophy of science, which are based on formalizations in predicate logic, are often considered in principle inferior to semantic approaches, which are based on formalizations with the help of structures. To compare the two kinds of approach, I identify some ambiguities in common semantic accounts and explicate the concept of a structure in a way that avoids hidden references to a specific vocabulary. From there, I argue that contrary to common opinion (i) unintended models do not (...)
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  • How do models give us knowledge? The case of Carnot’s ideal heat engine.Tarja Knuuttila & Mieke Boon - 2011 - European Journal for Philosophy of Science 1 (3):309-334.
    Our concern is in explaining how and why models give us useful knowledge. We argue that if we are to understand how models function in the actual scientific practice the representational approach to models proves either misleading or too minimal. We propose turning from the representational approach to the artefactual, which implies also a new unit of analysis: the activity of modelling. Modelling, we suggest, could be approached as a specific practice in which concrete artefacts, i.e., models, are constructed with (...)
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  • Theory knitting: An integrative approach to theory development.David A. Kalmar & Robert J. Sternberg - 1988 - Philosophical Psychology 1 (2):153 – 170.
    A close scrutiny of the psychological literature reveals that many psychologists favor a 'segregative' approach to theory development. One theory is pitted against another, and the one that accounts for the data most successfully is deemed the theory of choice. However, an examination of the theoretical debates in which the segregative approach has been pursued reveals a variety of weaknesses to the approach, namely, masking an underlying theoretical indistinguishability of theoretical predictions, causing psychologists to focus unknowingly on different aspects of (...)
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  • Reinflating the semantic approach.Steven French & James Ladyman - 1999 - International Studies in the Philosophy of Science 13 (2):103 – 121.
    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, (...)
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  • (1 other version)To Save the Semantic View: An Argument for Returning to Suppes' Interpretation.Thomas Cunningham - 2008
    Recent work on the semantic view of scientific theories is highly critical of the position. This paper identifies two common criticisms of the view, describes two popular alternatives for responding to them, and argues those responses do not suffice. Subsequently, it argues that retuning to Patrick Suppes’ interpretation of the position provides the conceptual resources for rehabilitating the semantic view.
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  • Reduction in real life.Peter Godfrey-Smith - 2008 - In Jakob Hohwy & Jesper Kallestrup (eds.), Being Reduced: New Essays on Reduction, Explanation, and Causation. New York: Oxford University Press.
    The main message of the paper is that there is a disconnect between what many philosophers of mind think of as the scientific practice of reductive or reductionist explanation, and what the most relevant scientific work is actually like. I will sketch what I see as a better view, drawing on various ideas in recent philosophy of science. I then import these ideas into the philosophy of mind, to see what difference they make.1 At the end of the paper I (...)
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  • Review symposium : Laurens Laudan. Progress and its problems: Toward a theory of scientific growth. Berkeley and Los Angeles: The University of California Press, 1977. Pp. X + 257.Laudan's progress and its problems. [REVIEW]David L. Hull, Andrew Lugg, Robert E. Butts & I. C. Jarvie - 1979 - Philosophy of the Social Sciences 9 (4):457-465.
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  • Blaug's economic methodology.Douglas W. Hands - 1984 - Philosophy of the Social Sciences 14 (1):115-125.
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  • Naturalisms in philosophy of mind.Steven Horst - 2008 - Philosophy Compass 4 (1):219-254.
    Most contemporary philosophers of mind claim to be in search of a 'naturalistic' theory. However, when we look more closely, we find that there are a number of different and even conflicting ideas of what would count as a 'naturalization' of the mind. This article attempts to show what various naturalistic philosophies of mind have in common, and also how they differ from one another. Additionally, it explores the differences between naturalistic philosophies of mind and naturalisms found in ethics, epistemology, (...)
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  • Models and fictions in science.Peter Godfrey-Smith - 2009 - Philosophical Studies 143 (1):101 - 116.
    Non-actual model systems discussed in scientific theories are compared to fictions in literature. This comparison may help with the understanding of similarity relations between models and real-world target systems. The ontological problems surrounding fictions in science may be particularly difficult, however. A comparison is also made to ontological problems that arise in the philosophy of mathematics.
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  • (1 other version)Simulations, models, and theories: Complex physical systems and their representations.Eric Winsberg - 2001 - Proceedings of the Philosophy of Science Association 2001 (3):S442-.
    Using an example of a computer simulation of the convective structure of a red giant star, this paper argues that simulation is a rich inferential process, and not simply a "number crunching" technique. The scientific practice of simulation, moreover, poses some interesting and challenging epistemological and methodological issues for the philosophy of science. I will also argue that these challenges would be best addressed by a philosophy of science that places less emphasis on the representational capacity of theories (and ascribes (...)
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  • Simulations are not models.John Simpson - unknown
    The aim of this paper is to argue that simulation is the activity of inferring future states. I argue that simulations instantiate models and that models are complexes of representations, so the inference in question makes use of the relations between the representations in a simulation's associated model. It follows that simulations should not be properly considered to be models in general, despite it being the case that they are commonly treated, or referred to, as being models, or even models (...)
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  • Causes, proximate and ultimate.Richard C. Francis - 1990 - Biology and Philosophy 5 (4):401-415.
    Within evolutionary biology a distinction is frequently made between proximate and ultimate causes. One apparently plausible interpretation of this dichotomy is that proximate causes concern processes occurring during the life of an organism while ultimate causes refer to those processes (particularly natural selection) that shaped its genome. But ultimate causes are not sought through historical investigations of an organisms lineage. Rather, explanations referring to ultimate causes typically emerge from functional analyses. But these functional analyses do not identify causes of any (...)
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  • Forty years of 'the strategy': Levins on model building and idealization.Michael Weisberg - 2006 - Biology and Philosophy 21 (5):623-645.
    This paper is an interpretation and defense of Richard Levins’ “The Strategy of Model Building in Population Biology,” which has been extremely influential among biologists since its publication 40 years ago. In this article, Levins confronted some of the deepest philosophical issues surrounding modeling and theory construction. By way of interpretation, I discuss each of Levins’ major philosophical themes: the problem of complexity, the brute-force approach, the existence and consequence of tradeoffs, and robustness analysis. I argue that Levins’ article is (...)
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  • Can a reductionist be a pluralist?Daniel Steel - 2004 - Biology and Philosophy 19 (1):55-73.
    Pluralism is often put forth as a counter-position to reductionism. In this essay, I argue that reductionism and pluralism are in fact consistent. I propose that there are several potential goals for reductions and that the proper form of a reduction should be considered in tandem with the goal that it aims to achieve. This insight provides a basis for clarifying what version of reductionism are currently defended, for explicating the notion of a fundamental level of explanation, and for showing (...)
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  • Kuhn's changing concept of incommensurability.Howard Sankey - 1993 - British Journal for the Philosophy of Science 44 (4):759-774.
    Since 1962 Kuhn's concept of incommensurability has undergone a process of transformation. His current account of incommensurability has little in common with his original account of it. Originally, incommensurability was a relation of methodological, observational and conceptual disparity between paradigms. Later Kuhn restricted the notion to the semantical sphere and assimilated it to the indeterminacy of translation. Recently he has developed an account of it as localized translation failure between subsets of terms employed by theories.
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  • Models and the Semantic View.Martin Thomson-Jones - 2006 - Philosophy of Science 73 (5):524-535.
    I begin by distinguishing two notions of model, the notion of a truth-making structure and the notion of a mathematical model (in one specific sense). I then argue that although the models of the semantic view have often been taken to be both truth-making structures and mathematical models, this is in part due to a failure to distinguish between two ways of truth-making; in fact, the talk of truth-making is best excised from the view altogether. The result is a version (...)
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  • Shared structure need not be shared set-structure.Elaine Landry - 2007 - Synthese 158 (1):1 - 17.
    Recent semantic approaches to scientific structuralism, aiming to make precise the concept of shared structure between models, formally frame a model as a type of set-structure. This framework is then used to provide a semantic account of (a) the structure of a scientific theory, (b) the applicability of a mathematical theory to a physical theory, and (c) the structural realist’s appeal to the structural continuity between successive physical theories. In this paper, I challenge the idea that, to be so used, (...)
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  • Kuhn, Lakatos, and the image of mathematics.Eduard Glas - 1995 - Philosophia Mathematica 3 (3):225-247.
    In this paper I explore possibilities of bringing post-positivist philosophies of empirical science to bear on the dynamics of mathematical development. This is done by way of a convergent accommodation of a mathematical version of Lakatos's methodology of research programmes, and a version of Kuhn's account of scientific change that is made applicable to mathematics by cleansing it of all references to the psychology of perception. The resulting view is argued in the light of two case histories of radical conceptual (...)
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  • Science and Core Knowledge.Susan Carey & Elizabeth Spelke - 1996 - Philosophy of Science 63 (4):515 - 533.
    While endorsing Gopnik's proposal that studies of the emergence and modification of scientific theories and studies of cognitive development in children are mutually illuminating, we offer a different picture of the beginning points of cognitive development from Gopnik's picture of "theories all the way down." Human infants are endowed with several distinct core systems of knowledge which are theory-like in some, but not all, important ways. The existence of these core systems of knowledge has implications for the joint research program (...)
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  • (1 other version)Can quantum analogies help us to understand the process of thought? [2nd ed.].Paavo Pylkkanen - 2014 - Mind and Matter 12 (1):61-91.
    A number of researchers today make an appeal to quantum physics when trying to develop a satisfactory account of the mind, an appeal still felt to be controversial by many. Often these "quantum approaches" try to explain some well-known features of conscious experience (or mental processes more generally), thus using quantum physics to enrich the explanatory framework or explanans used in consciousness studies and cognitive science. This paper considers the less studied question of whether quantum physical intuitions could help us (...)
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  • The Semantic Approach, After 50 Years.Bas C. Van Fraassen - 2024 - In Claus Beisbart & Michael Frauchiger (eds.), Scientific Theories and Philosophical Stances: Themes from van Fraassen. De Gruyter. pp. 23-86.
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  • The scientific demarcation problem: a formal and model-based approach to falsificationism.Attard Jeremy - manuscript
    The problem of demarcating between what is scientific and what is pseudoscientific or merely unscientific - in other words, the problem of defining scientificity - remains open. The modern debate was firstly structured around Karl Popper's falsificationist epistemology from the 1930's, before diversifying a few decades later. His central idea is that what makes something scientific is not so much how adequate it is with data, but rather to what extent it might not have been so. Since the second half (...)
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  • Neo-Nagelian reduction: a statement, defence, and application.Foad Dizadji-Bahmani - 2011 - Dissertation, London School of Economics
    The thesis proposes, defends, and applies a new model of inter-theoretic reduction, called "Neo-Nagelian" reduction. There are numerous accounts of inter-theoretic reduction in the philosophy of science literature but the most well-known and widely-discussed is the Nagelian one. In the thesis I identify various kinds of problems which the Nagelian model faces. Whilst some of these can be resolved, pressing ones remain. In lieu of the Nagelian model, other models of inter-theoretic reduction have been proposed, chief amongst which are so-called (...)
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  • Philosophical foundations of neuroeconomics: economics and the revolutionary challenge from neuroscience.Roberto Fumagalli - 2011 - Dissertation, London School of Economics
    This PhD thesis focuses on the philosophical foundations of Neuroeconomics, an innovative research program which combines findings and modelling tools from economics, psychology and neuroscience to account for human choice behaviour. The proponents of Neuroeconomics often manifest the ambition to foster radical modifications in the accounts of choice behaviour developed by its parent disciplines. This enquiry provides a philosophically informed appraisal of the potential for success and the relevance of neuroeconomic research for economics. My central claim is that neuroeconomists can (...)
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  • Against ‘Interpretation’: Quantum Mechanics Beyond Syntax and Semantics.Raoni Wohnrath Arroyo & Gilson Olegario da Silva - 2022 - Axiomathes 32 (6):1243-1279.
    The question “what is an interpretation?” is often intertwined with the perhaps even harder question “what is a scientific theory?”. Given this proximity, we try to clarify the first question to acquire some ground for the latter. The quarrel between the syntactic and semantic conceptions of scientific theories occupied a large part of the scenario of the philosophy of science in the 20th century. For many authors, one of the two currents needed to be victorious. We endorse that such debate, (...)
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  • Naturalización de la Metafísica Modal.Carlos Romero - 2021 - Dissertation, National Autonomous University of Mexico
    ⦿ In my dissertation I introduce, motivate and take the first steps in the implementation of, the project of naturalising modal metaphysics: the transformation of the field into a chapter of the philosophy of science rather than speculative, autonomous metaphysics. -/- ⦿ In the introduction, I explain the concept of naturalisation that I apply throughout the dissertation, which I argue to be an improvement on Ladyman and Ross' proposal for naturalised metaphysics. I also object to Williamson's proposal that modal metaphysics (...)
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  • Extending Similarity-based Epistemology of Modality with Models.Ylwa Sjölin Wirling - 2022 - Ergo: An Open Access Journal of Philosophy 8 (45).
    Empiricist modal epistemologies can be attractive, but are often limited in the range of modal knowledge they manage to secure. In this paper, I argue that one such account – similarity-based modal empiricism – can be extended to also cover justification of many scientifically interesting possibility claims. Drawing on recent work on modelling in the philosophy of science, I suggest that scientific modelling is usefully seen as the creation and investigation of relevantly similar epistemic counterparts of real target systems. On (...)
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  • MODIFIED STRUCTURE-NOMINATIVE RECONSTRUCTION OF PRACTICAL PHYSICAL THEORIES AS A FRAME FOR THE PHILOSOPHY OF PHYSICS.Vladimir Kuznetsov - forthcoming2021 - Epistemological studies in Philosophy, Social and Political Sciences 4 (1):20-28.
    Physical theories are complex and necessary tools for gaining new knowledge about their areas of application. A distinction is made between abstract and practical theories. The last are constantly being improved in the cognitive activity of professional physicists and studied by future physicists. A variant of the philosophy of physics based on a modified structural-nominative reconstruction of practical theories is proposed. Readers should decide whether this option is useful for their understanding of the philosophy of physics, as well as other (...)
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  • Aspectos metafísicos na física de Newton: Deus.Bruno Camilo de Oliveira - 2011 - In Luiz Henrique de Araújo Dutra & Alexandre Meyer Luz (eds.), Coleção rumos da epistemologia. pp. 186-201.
    CAMILO, Bruno. Aspectos metafísicos na física de Newton: Deus. In: DUTRA, Luiz Henrique de Araújo; LUZ, Alexandre Meyer (org.). Temas de filosofia do conhecimento. Florianópolis: NEL/UFSC, 2011. p. 186-201. (Coleção rumos da epistemologia; 11). Através da análise do pensamento de Isaac Newton (1642-1727) encontramos os postulados metafísicos que fundamentam a sua mecânica natural. Ao deduzir causa de efeito, ele acreditava chegar a uma causa primeira de todas as coisas. A essa primeira causa de tudo, onde toda a ordem e leis (...)
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  • Foundations of applied mathematics I.Jeffrey Ketland - 2021 - Synthese 199 (1-2):4151-4193.
    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.
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