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  1. Three Infinities in Early Modern Philosophy.Anat Schechtman - 2019 - Mind 128 (512):1117-1147.
    Many historical and philosophical studies treat infinity as an exclusively quantitative notion, whose proper domain of application is mathematics and physics. The main aim of this paper is to disentangle, by critically examining, three notions of infinity in the early modern period, and to argue that one—but only one—of them is quantitative. One of these non-quantitative notions concerns being or reality, while the other concerns a particular iterative property of an aggregate. These three notions will emerge through examination of three (...)
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  • ‘Chasing’ the diagram—the use of visualizations in algebraic reasoning.Silvia de Toffoli - 2017 - Review of Symbolic Logic 10 (1):158-186.
    The aim of this article is to investigate the roles of commutative diagrams (CDs) in a specific mathematical domain, and to unveil the reasons underlying their effectiveness as a mathematical notation; this will be done through a case study. It will be shown that CDs do not depict spatial relations, but represent mathematical structures. CDs will be interpreted as a hybrid notation that goes beyond the traditional bipartition of mathematical representations into diagrammatic and linguistic. It will be argued that one (...)
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  • Newton and Leibniz on Non-substantival Space.Alejandro Cassini - 2005 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 20 (1):25-43.
    The aim of this paper is to analyze Leibniz and Newton’s conception of space, and to point out where their agreements and disagreements lie with respect to its mode of existence. I shall offer a definite characterization of Leibniz and Newton’s conceptions of space. I will show that, according to their own concepts of substance, both Newtonian and Leibnizian spaces are not substantiva!. The reason of that consists in the fact that space is not capable of action. Moreover, there is (...)
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  • Inter-model connectives and substructural logics.Igor Sedlár - 2014 - In Roberto Ciuni, Heinrich Wansing & Caroline Willkommen (eds.), Recent Trends in Philosophical Logic (Proceedings of Trends in Logic XI). Cham, Switzerland: Springer. pp. 195-209.
    The paper provides an alternative interpretation of ‘pair points’, discussed in Beall et al., "On the ternary relation and conditionality", J. of Philosophical Logic 41(3), 595-612. Pair points are seen as points viewed from two different ‘perspectives’ and the latter are explicated in terms of two independent valuations. The interpretation is developed into a semantics using pairs of Kripke models (‘pair models’). It is demonstrated that, if certain conditions are fulfilled, pair models are validity-preserving copies of positive substructural models. This (...)
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  • The Bounds of Logic: A Generalized Viewpoint.Gila Sher - 1991 - MIT Press.
    The Bounds of Logic presents a new philosophical theory of the scope and nature of logic based on critical analysis of the principles underlying modern Tarskian logic and inspired by mathematical and linguistic development. Extracting central philosophical ideas from Tarski’s early work in semantics, Sher questions whether these are fully realized by the standard first-order system. The answer lays the foundation for a new, broader conception of logic. By generally characterizing logical terms, Sher establishes a fundamental result in semantics. Her (...)
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  • Do you have to be right to redescribe?Susan Goldin-Meadow & Martha Wagner Alibali - 1994 - Behavioral and Brain Sciences 17 (4):718-719.
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  • Representation: Ontogenesis and phylogenesis.Merlin Donald - 1994 - Behavioral and Brain Sciences 17 (4):714-715.
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  • Representational redescription: A question of sequence.Margaret A. Boden - 1994 - Behavioral and Brain Sciences 17 (4):708-708.
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  • Tools, Objects, and Chimeras: Connes on the Role of Hyperreals in Mathematics.Vladimir Kanovei, Mikhail G. Katz & Thomas Mormann - 2013 - Foundations of Science 18 (2):259-296.
    We examine some of Connes’ criticisms of Robinson’s infinitesimals starting in 1995. Connes sought to exploit the Solovay model S as ammunition against non-standard analysis, but the model tends to boomerang, undercutting Connes’ own earlier work in functional analysis. Connes described the hyperreals as both a “virtual theory” and a “chimera”, yet acknowledged that his argument relies on the transfer principle. We analyze Connes’ “dart-throwing” thought experiment, but reach an opposite conclusion. In S , all definable sets of reals are (...)
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  • Leibniz’s Infinitesimals: Their Fictionality, Their Modern Implementations, and Their Foes from Berkeley to Russell and Beyond. [REVIEW]Mikhail G. Katz & David Sherry - 2013 - Erkenntnis 78 (3):571-625.
    Many historians of the calculus deny significant continuity between infinitesimal calculus of the seventeenth century and twentieth century developments such as Robinson’s theory. Robinson’s hyperreals, while providing a consistent theory of infinitesimals, require the resources of modern logic; thus many commentators are comfortable denying a historical continuity. A notable exception is Robinson himself, whose identification with the Leibnizian tradition inspired Lakatos, Laugwitz, and others to consider the history of the infinitesimal in a more favorable light. Inspite of his Leibnizian sympathies, (...)
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  • Modality and Anti-Metaphysics.Stephen K. McLeod - 2001 - Aldershot: Ashgate.
    Modality and Anti-Metaphysics critically examines the most prominent approaches to modality among analytic philosophers in the twentieth century, including essentialism. Defending both the project of metaphysics and the essentialist position that metaphysical modality is conceptually and ontologically primitive, Stephen McLeod argues that the logical positivists did not succeed in banishing metaphysical modality from their own theoretical apparatus and he offers an original defence of metaphysics against their advocacy of its elimination. -/- Seeking to assuage the sceptical worries which underlie modal (...)
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  • Physics and Leibniz's principles.Simon Saunders - 2002 - In Katherine Brading & Elena Castellani (eds.), Symmetries in Physics: Philosophical Reflections. New York: Cambridge University Press. pp. 289--307.
    It is shown that the Hilbert-Bernays-Quine principle of identity of indiscernibles applies uniformly to all the contentious cases of symmetries in physics, including permutation symmetry in classical and quantum mechanics. It follows that there is no special problem with the notion of objecthood in physics. Leibniz's principle of sufficient reason is considered as well; this too applies uniformly. But given the new principle of identity, it no longer implies that space, or atoms, are unreal.
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  • (1 other version)Representational redescription and cognitive architectures.Antonella Carassa & Maurizio Tirassa - 1994 - Carassa, Antonella and Tirassa, Maurizio (1994) Representational Redescription and Cognitive Architectures. [Journal (Paginated)] 17 (4):711-712.
    We focus on Karmiloff-Smith's Representational redescription model, arguing that it poses some problems concerning the architecture of a redescribing system. To discuss the topic, we consider the implicit/explicit dichotomy and the relations between natur al language and the language of thought. We argue that the model regards how knowledge is employed rather than how it is represented in the system.
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  • Leibnizian soft reduction of extrinsic denominations and relations.Ari Maunu - 2004 - Synthese 139 (1):143-164.
    Leibniz, it seems, wishes to reduce statements involving relations or extrinsic denominations to ones solely in terms of individual accidents or, respectively, intrinsic denominations. His reasons for this appear to be that relations are merely mental things (since they cannot be individual accidents) and that extrinsic denominations do not represent substances as they are on their own. Three interpretations of Leibniz''s reductionism may be distinguished: First, he allowed only monadic predicates in reducing statements (hard reductionism); second, he allowed also `implicitly (...)
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  • Marks and traces: Leibnizian scholarship past, present, and future.Brandon Look - 2002 - Perspectives on Science 10 (1):123-146.
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  • A (leibnizian) theory of concepts.Edward N. Zalta - 2000 - History of Philosophy & Logical Analysis 3 (1):137-183.
    In this paper, the author develops a theory of concepts and shows that it captures many of the ideas about concepts that Leibniz expressed in his work. Concepts are first analyzed in terms of a precise background theory of abstract objects, and once concept summation and concept containment are defined, the axioms and theorems of Leibniz's calculus of concepts (in his logical papers) are derived. This analysis of concepts is then seamlessly connected with Leibniz's modal metaphysics of complete individual concepts. (...)
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  • Making Sense of Sense Containment.Antonio Negro - 2017 - History and Philosophy of Logic 38 (4):364-385.
    Proposition 5.122 of Wittgenstein’s Tractatus has been the source of much puzzlement among interpreters, so much so that no fully satisfactory account is yet available. This is unfortunate, if only because the containment account of logical consequence has a venerable tradition behind it. Pasquale Frascolla’s interpretation of proposition 5.122 is based on a valid argument and one true premise. However, the argument explains sense containment only in an indirect way, leaving some crucial questions unanswered. Besides, Frascolla does not address the (...)
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  • Kripke on Naming and Necessity.R. B. De Sousa - 1974 - Canadian Journal of Philosophy 3 (3):447-464.
    Some wag reported the following story: Scholars have recently established that the Iliad and the Odyssey were not, after all, written by Homer. They were actually written by another author, of the same name.The majority of current theories of naming and reference, including ones as divergent in other respects as those of Russell and Searle, would rule this story impossible. They would do so on roughly these grounds: the sense and reference of the name ‘Homer’ is determined, given the absence (...)
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  • Representational redescription, memory, and connectionism.P. J. Hampson - 1994 - Behavioral and Brain Sciences 17 (4):721-721.
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  • The risks of rationalising cognitive development.Beatrice de Gelder - 1994 - Behavioral and Brain Sciences 17 (4):713-714.
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  • The Epistemological Functions of Symbolization in Leibniz’s Universal Characteristic.Christian Leduc - 2014 - Foundations of Science 19 (1):53-68.
    Leibniz’s universal characteristic is a fundamental aspect of his theory of cognition. Without symbols or characters it would be difficult for the human mind to define several concepts and to achieve many demonstrations. In most disciplines, and particularly in mathematics, the mind must then focus on symbols and their combinatorial rules rather than on mental contents. For Leibniz, mental perception is most of the time too confused for attaining distinct notions and valid deductions. In this paper, I argue that the (...)
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  • Précis of Beyond modularity: A developmental perspective on cognitive science.Annette Karmiloff-Smith - 1994 - Behavioral and Brain Sciences 17 (4):693-707.
    Beyond modularityattempts a synthesis of Fodor's anticonstructivist nativism and Piaget's antinativist constructivism. Contra Fodor, I argue that: (1) the study of cognitive development is essential to cognitive science, (2) the module/central processing dichotomy is too rigid, and (3) the mind does not begin with prespecified modules; rather, development involves a gradual process of “modularization.” Contra Piaget, I argue that: (1) development rarely involves stagelike domain-general change and (2) domainspecific predispositions give development a small but significant kickstart by focusing the infant's (...)
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  • The Failure of Leibniz's Infinite Analysis view of Contingency.Joel Velasco - manuscript
    Abstract : In this paper, it is argued that Leibniz’s view that necessity is grounded in the availability of a demonstration is incorrect and furthermore, can be shown to be so by using Leibniz’s own examples of infinite analyses. First, I show that modern mathematical logic makes clear that Leibniz’s "infinite analysis" view of contingency is incorrect. It is then argued that Leibniz's own examples of incommensurable lines and convergent series undermine, rather than bolster his view by providing examples of (...)
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  • Dissociation, self-attribution, and redescription.George Graham - 1994 - Behavioral and Brain Sciences 17 (4):719-719.
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  • The challenge of representational redescription.Thomas R. Shultz - 1994 - Behavioral and Brain Sciences 17 (4):728-729.
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  • Representational change, generality versus specificity, and nature versus nurture: Perennial issues in cognitive research.Stellan Ohlsson - 1994 - Behavioral and Brain Sciences 17 (4):724-725.
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  • A Tale of Two Thinkers, One Meeting, and Three Degrees of Infinity: Leibniz and Spinoza (1675–8).Ohad Nachtomy - 2011 - British Journal for the History of Philosophy 19 (5):935-961.
    The article presents Leibniz's preoccupation (in 1675?6) with the difference between the notion of infinite number, which he regards as impossible, and that of the infinite being, which he regards as possible. I call this issue ?Leibniz's Problem? and examine Spinoza's solution to a similar problem that arises in the context of his philosophy. ?Spinoza's solution? is expounded in his letter on the infinite (Ep.12), which Leibniz read and annotated in April 1676. The gist of Spinoza's solution is to distinguish (...)
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  • The logic of leibniz’s generales inquisitiones de analysi notionum et veritatum.Marko Malink & Anubav Vasudevan - 2016 - Review of Symbolic Logic 9 (4):686-751.
    TheGenerales Inquisitiones de Analysi Notionum et Veritatumis Leibniz’s most substantive work in the area of logic. Leibniz’s central aim in this treatise is to develop a symbolic calculus of terms that is capable of underwriting all valid modes of syllogistic and propositional reasoning. The present paper provides a systematic reconstruction of the calculus developed by Leibniz in theGenerales Inquisitiones. We investigate the most significant logical features of this calculus and prove that it is both sound and complete with respect to (...)
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  • Redescribing redescription.Terry Dartnall - 1994 - Behavioral and Brain Sciences 17 (4):712-713.
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  • Leibniz and Sensible Qualities.Christian Leduc - 2010 - British Journal for the History of Philosophy 18 (5):797-819.
    This paper discusses the problem of sensible qualities, an important, but underestimated topic in Leibniz's epistemology. In the first section, the confused character of sensible ideas is considered. Produced by the sensation alone, ideas of sensible qualities cannot be part of distinct descriptions of bodies. This is why Leibniz proposes to resolve sensible qualities by means of primary or mechanical qualities, a thesis which is analysed in the second section. Here, I discuss his conception of nominal definitions as distinct empirical (...)
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  • (1 other version)Abstract objects.Gideon Rosen - 2008 - Stanford Encyclopedia of Philosophy.
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  • Leibniz's Argument for the Identity of Indiscernibles in his Correspondence with Clarke.Gonzalo Rodriguez-Pereyra - 1999 - Australasian Journal of Philosophy 77 (4):429 – 438.
    In Section 21 of his fifth letter to Clarke Leibniz attempts to derive the Identity of Indiscernibles from an application of the Principle of Sufficient Reason to God´s act of creation, namely that God has a reason to create the world he creates. In this paper I argue that this argument fails, not just because the Identity of Indiscernibles is false, but because there is a counterexample to one of the premises that Leibniz cannot satisfactorily rule out.
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  • Toward a History of Mathematics Focused on Procedures.Piotr Błaszczyk, Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz, Semen S. Kutateladze & David Sherry - 2017 - Foundations of Science 22 (4):763-783.
    Abraham Robinson’s framework for modern infinitesimals was developed half a century ago. It enables a re-evaluation of the procedures of the pioneers of mathematical analysis. Their procedures have been often viewed through the lens of the success of the Weierstrassian foundations. We propose a view without passing through the lens, by means of proxies for such procedures in the modern theory of infinitesimals. The real accomplishments of calculus and analysis had been based primarily on the elaboration of novel techniques for (...)
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  • Transforming a partially structured brain into a creative mind.Annette Karmiloff-Smith - 1994 - Behavioral and Brain Sciences 17 (4):732-745.
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  • From the decline of development to the ascent of consciousness.Philip David Zelazo - 1994 - Behavioral and Brain Sciences 17 (4):731-732.
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  • Urbild und Abbild. Leibniz, Kant und Hausdorff über das Raumproblem.Marco Giovanelli - 2010 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 41 (2):283-313.
    The article attempts to reconsider the relationship between Leibniz’s and Kant’s philosophy of geometry on the one hand and the nineteenth century debate on the foundation of geometry on the other. The author argues that the examples used by Leibniz and Kant to explain the peculiarity of the geometrical way of thinking are actually special cases of what the Jewish-German mathematician Felix Hausdorff called “transformation principle”, the very same principle that thinkers such as Helmholtz or Poincaré applied in a more (...)
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  • What Does God Know but can’t Say? Leibniz on Infinity, Fictitious Infinitesimals and a Possible Solution of the Labyrinth of Freedom.Elad Lison - 2020 - Philosophia 48 (1):261-288.
    Despite his commitment to freedom, Leibniz’ philosophy is also founded on pre-established harmony. Understanding the life of the individual as a spiritual automaton led Leibniz to refer to the puzzle of the way out of determinism as the Labyrinth of Freedom. Leibniz claimed that infinite complexity is the reason why it is impossible to prove a contingent truth. But by means of Leibniz’ calculus, it actually can be shown in a finite number of steps how to calculate a summation of (...)
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  • Cauchy’s Infinitesimals, His Sum Theorem, and Foundational Paradigms.Tiziana Bascelli, Piotr Błaszczyk, Alexandre Borovik, Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz, Semen S. Kutateladze, Thomas McGaffey, David M. Schaps & David Sherry - 2018 - Foundations of Science 23 (2):267-296.
    Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy’s proof, and discuss the related epistemological questions involved in comparing distinct interpretive paradigms. Cauchy’s proof is often interpreted in the modern framework of a Weierstrassian paradigm. We analyze Cauchy’s proof closely and show that it finds closer proxies in a different modern framework.
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  • Interpreting the Infinitesimal Mathematics of Leibniz and Euler.Jacques Bair, Piotr Błaszczyk, Robert Ely, Valérie Henry, Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz, Semen S. Kutateladze, Thomas McGaffey, Patrick Reeder, David M. Schaps, David Sherry & Steven Shnider - 2017 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 48 (2):195-238.
    We apply Benacerraf’s distinction between mathematical ontology and mathematical practice to examine contrasting interpretations of infinitesimal mathematics of the seventeenth and eighteenth century, in the work of Bos, Ferraro, Laugwitz, and others. We detect Weierstrass’s ghost behind some of the received historiography on Euler’s infinitesimal mathematics, as when Ferraro proposes to understand Euler in terms of a Weierstrassian notion of limit and Fraser declares classical analysis to be a “primary point of reference for understanding the eighteenth-century theories.” Meanwhile, scholars like (...)
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  • The real problem with constructivism.Paul Bloom & Karen Wynn - 1994 - Behavioral and Brain Sciences 17 (4):707-708.
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  • On the Origin of Symbolic Mathematics and Its Significance for Wittgenstein’s Thought.Sören Stenlund - 2015 - Nordic Wittgenstein Review 4 (1):7-92.
    The main topic of this essay is symbolic mathematics or the method of symbolic construction, which I trace to the end of the sixteenth century when Franciscus Vieta invented the algebraic symbolism and started to use the word ‘symbolic’ in the relevant, non-ontological sense. This approach has played an important role for many of the great inventions in modern mathematics such as the introduction of the decimal place-value system of numeration, Descartes’ analytic geometry, and Leibniz’s infinitesimal calculus. It was also (...)
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  • Beyond modularity: Neural evidence for constructivist principles in development.Steven R. Quartz & Terrence J. Sejnowski - 1994 - Behavioral and Brain Sciences 17 (4):725-726.
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  • Situating representational redescriptionin infants' pragmatic knowledge.Julie C. Rutkowska - 1994 - Behavioral and Brain Sciences 17 (4):726-727.
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  • Restricciones de la aplicación del principio de sustituibilidad de los idénticos salva veritate en Leibniz.Oscar Esquisabel - 2014 - Dois Pontos 11 (2).
    O princípio de intersubstituição dos idênticos salva veritate, que constitui uma peça de importância central para a teoria leibniziana da demostração, para não falar de suas implicações ontológicas, recebeu a crítica de que encerra uma confusão entre uso e menção. Em contraste com essa crítica, o presente trabalho defende a tese de que o princípio não está suscetível a essa pretensa confusão, utilizando, para tanto, a distinção leibniziana entre “a consideração do modo de conceber” e a “consideração da coisa mesma”. (...)
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  • Beyond connectionist versus classical Al: A control theoretic perspective on development and cognitive science.Rick Grush - 1994 - Behavioral and Brain Sciences 17 (4):720-720.
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  • Redescription of intentionality.Norman H. Freeman - 1994 - Behavioral and Brain Sciences 17 (4):717-718.
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  • Arguments against linguistic “modularization”.Susan H. Foster-Cohen - 1994 - Behavioral and Brain Sciences 17 (4):716-717.
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  • What's getting redescribed?Robert L. Campbell - 1994 - Behavioral and Brain Sciences 17 (4):710-711.
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  • (1 other version)Representational redescription and cognitive architectures.Antonella Carassa & Maurizio Tirassa - 1994 - Behavioral and Brain Sciences 17 (4):711-712.
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  • “Free rides” in Mathematics.Jessica Carter - 2021 - Synthese 199 (3-4):10475-10498.
    Representations, in particular diagrammatic representations, allegedly contribute to new insights in mathematics. Here I explore the phenomenon of a “free ride” and to what extent it occurs in mathematics. A free ride, according to Shimojima, is the property of some representations that whenever certain pieces of information have been represented then a new piece of consequential information can be read off for free. I will take Shimojima’s framework as a tool to analyse the occurrence and properties of them. I consider (...)
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