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21. Theoria. Revista de Teoría, Historia y Fundamentos de la Ciencia: Volume > 33 > Issue: 3
Summary
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22. Theoria. Revista de Teoría, Historia y Fundamentos de la Ciencia: Volume > 33 > Issue: 3
Contents of Volume 33
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monographic section i
23. Theoria. Revista de Teoría, Historia y Fundamentos de la Ciencia: Volume > 33 > Issue: 2
Mary Leng Guest Editor’s Introduction: Updating indispensabilities: Putnam in memoriam
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24. Theoria. Revista de Teoría, Historia y Fundamentos de la Ciencia: Volume > 33 > Issue: 2
Concha Martínez Vidal Putnam and contemporary fictionalism
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Putnam rejects having argued in the terms of the argument known in the literature as “the Quine-Putnam indispensability argument”. He considers that mathematics contribution to physics does not have to be interpreted in platonist terms but in his favorite modal variety (Putnam 1975; Putnam 2012). The purpose of this paper is to consider Putnam’s acknowledged argument and philosophical position against contemporary so called in the literature ‘fictionalist’ views about applied mathematics. The conclusion will be that the account of the applicability of mathematics that stems from Putnam‘s acknowledged argument can be assimilated to so-called ‘fictionalist’ views about applied mathematics.
25. Theoria. Revista de Teoría, Historia y Fundamentos de la Ciencia: Volume > 33 > Issue: 2
José Miguel Sagüillo Hilary Putnam on the philosophy of logic and mathematics
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This paper focuses on Putnam’s conception of logical truth as grounded in his picture of mathematical practice and ontology. Putnam’s 1971 book Philosophy of Logic came one year later than Quine’s homonymous volume. In the first section, I compare these two Philosophies of Logic which exemplify realist-nominalist viewpoints in a most conspicuous way. The next section examines Putnam’s views on modality, moving from the modal qualification of his intuitive conception to his official generalized non-modal second-order set-theoretic concept of logical truth. In the third section, I emphasize how Putnam´s “mathematics as modal logic” departs from Quine’s “reluctant Platonism”. I also suggest a complementary view of Platonism and modalism showing them perhaps interchangeable but underlying different stages of research processes that make up a rich and dynamic mathematical practice. The final, more speculative section, argues for the pervasive platonistic conception enhancing the aims of inquiry in the practice of the working mathematician.
26. Theoria. Revista de Teoría, Historia y Fundamentos de la Ciencia: Volume > 33 > Issue: 2
Otávio Bueno Putnam’s indispensability argument revisited, reassessed, revived
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Crucial to Hilary Putnam’s realism in the philosophy of mathematics is to maintain the objectivity of mathematics without the commitment to the existence of mathematical objects. Putnam’s indispensability argument was devised as part of this conception. In this paper, I reconstruct and reassess Putnam’s argument for the indispensability of mathematics, and distinguish it from the more familiar, Quinean version of the argument. Although I argue that Putnam’s approach ultimately fails, I develop an alternative way of implementing his form of realism about mathematics that, by using different resources than those Putnam invokes, avoids the difficulties faced by his view.
27. Theoria. Revista de Teoría, Historia y Fundamentos de la Ciencia: Volume > 33 > Issue: 2
Sorin Bangu Indispensability, causation and explanation
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When considering mathematical realism, some scientific realists reject it, and express sympathy for the opposite view, mathematical nominalism; moreover, many justify this option by invoking the causal inertness of mathematical objects. The main aim of this note is to show that the scientific realists’ endorsement of this causal mathematical nominalism is in tension with another position some (many?) of them also accept, the doctrine of methodological naturalism. By highlighting this conflict, I intend to tip the balance in favor of a rival of mathematical nominalism, the mathematical realist position supported by the ‘Indispensability Argument’ —but I do this indirectly, by showing that the road toward it is not blocked by considerations from causation.
28. Theoria. Revista de Teoría, Historia y Fundamentos de la Ciencia: Volume > 33 > Issue: 2
Susan Vineberg Mathematical explanation and indispensability
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This paper discusses Baker’s Enhanced Indispensability Argument (EIA) for mathematical realism on the basis of the indispensable role mathematics plays in scientific explanations of physical facts, along with various responses to it. I argue that there is an analogue of causal explanation for mathematics which, of several basic types of explanation, holds the most promise for use in the EIA. I consider a plausible case where mathematics plays an explanatory role in this sense, but argue that such use still does not support realism about mathematical objects.
29. Theoria. Revista de Teoría, Historia y Fundamentos de la Ciencia: Volume > 33 > Issue: 2
Matteo Plebani The indispensability argument and the nature of mathematical objects
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Two conceptions of the nature of mathematical objects are contrasted: the conception of mathematical objects as preconceived objects (Yablo 2010), and heavy duty platonism (Knowles 2015). It is argued that some theses defended by friends of the indispensability argument are in harmony with heavy duty platonism and in tension with the conception of mathematical objects as preconceived objects.
monographic section ii
30. Theoria. Revista de Teoría, Historia y Fundamentos de la Ciencia: Volume > 33 > Issue: 2
María de Paz, José Ferreirós Guest Editors’ Introduction: From basic cognition to mathematical practice
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31. Theoria. Revista de Teoría, Historia y Fundamentos de la Ciencia: Volume > 33 > Issue: 2
Rafael Núñez Praxis matemática: reflexiones sobre la cognición que la hace posible
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La matemática forma un cuerpo único de conocimiento. Entre otras cosas, es abstracta, exacta, eficaz, simbolizable y proporciona sorprendentes aplicaciones al mundo real. En el campo de la filosofía de la matemática el estudio de la práctica matemática ha devenido gradualmente una importante área de investigación. ¿Qué aspectos de la mente y el cuerpo humano hacen posible la particular práctica matemática? En este artículo, reviso brevemente algunas dimensiones cognitivas que juegan un papel crucial en la creación y consolidación de la matemática.
32. Theoria. Revista de Teoría, Historia y Fundamentos de la Ciencia: Volume > 33 > Issue: 2
Markus Pantsar Early numerical cognition and mathematical processes
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In this paper I study the development of arithmetical cognition with the focus on metaphorical thinking. In an approach developing on Lakoff and Núñez (2000), I propose one particular conceptual metaphor, the Process → Object Metaphor (POM), as a key element in understanding the development of mathematical thinking.
33. Theoria. Revista de Teoría, Historia y Fundamentos de la Ciencia: Volume > 33 > Issue: 2
Roy Wagner Cognitive stories and the image of mathematics
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This paper considers two models of embodied mathematical cognition (a modular model and a dynamic model), and analyses the image of mathematics that they support.
34. Theoria. Revista de Teoría, Historia y Fundamentos de la Ciencia: Volume > 33 > Issue: 2
José Ferreirós, Manuel J. García-Pérez ¿«Natural» y «euclidiana»?: Reflexiones sobre la geométrica práctica y sus raíces cognitivas
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Se discutirán críticamente algunas tesis recientes sobre cognición geométrica, específicamente la tesis de la universalidad planteada por Dehaene et al., y la idea de una “geometría natural” empleada por Spelke. Argumentaremos la necesidad de distinguir entre cognición visuo-espacial y conocimiento geométrico básico, y más aún, afirmaremos que este último no se puede identificar con la geometría euclidiana. El propósito principal del artículo es proponer una caracterización de la geometría básica, para lo cual se requiere una combinación de experimentos en cognición visuo-espacial con estudios en arqueología cognitiva e historia comparativa. Ofreceremos ejemplos de estos campos, con especial énfasis en la comparación de ideas y procedimientos geométricos de la antigua China y Grecia.
35. Theoria. Revista de Teoría, Historia y Fundamentos de la Ciencia: Volume > 33 > Issue: 2
Valeria Giardino Manipulative imagination: how to move things around in mathematics
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In the first part of the article, a semiotic reading of the embodied approach to mathematics will be presented. From this perspective, the role of the sensorimotor in mathematics will be considered, by looking at some work in experimental psychology on the segmentation of formulas and at an analysis of the practice of topology as involving manipulative imagination. According to the proposed view, representations in mathematics are cognitive tools whose functioning depends on pre-existing cognitive abilities and specific training. In the second part of the paper, the view of cognitive tools as props in games of “make-believe” will be discussed; to better specify this claim, the notion of affordance will be explored in its possible extension from concrete objects to representations.
36. Theoria. Revista de Teoría, Historia y Fundamentos de la Ciencia: Volume > 33 > Issue: 2
Sorin Costreie The geometrical basis of arithmetical knowledge: Frege and Dehaene
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Frege writes in Numbers and Arithmetic about kindergarten-numbers and “an a priori mode of cognition” that they may have “a geometrical source.” This resembles recent findings on arithmetical cognition. In my paper, I explore this resemblance between Gottlob Frege’s later position concerning the geometrical source of arithmetical knowledge, and some current positions in the literature dedicated to arithmetical cognition, especially that of Stanislas Dehaene. In my analysis, I shall try to mainly see to what extent (Frege’s) logicism is compatible with (Dehaene’s) intuitionism.
articles
37. Theoria. Revista de Teoría, Historia y Fundamentos de la Ciencia: Volume > 33 > Issue: 1
Javier González de Prado Salas Still Unsuccessful: The Unsolved Problems of Success Semantics
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Success semantics is a theory of content that characterizes the truth-conditions of mental representations in terms of the success-conditions of the actions derived from them. Nanay (Philos Stud 165(1): 151-165, 2013) and Dokic and Engel (Frank Ramsey London: Routledge, 2003) have revised this theory in order to defend it from the objections that assailed its previous incarnations. I argue that both proposals have seemingly decisive flaws. More specifically, these revised versions of the theory fail to deal adequately with the open-ended possibility of unforeseen obstacles for the success of our actions. I suggest that the problem of ignored obstacles undermines success semantics quite generally, including alternative formulations such as Blackburn’s.La Semántica del Éxito es una teoría del contenido que caracteriza las condiciones de verdad de las representaciones mentales en términos de las condiciones de éxito de las acciones que se derivan de ellas. Nanay (Philos Stud 165(1): 151-165, 2013) y Dokic y Engel (Frank Ramsey London: Routledge, 2003) han revisado esta teoría para defenderla de objeciones que socavaban sus formulaciones previas. Aquí argumento que ambas propuestas se enfrentan a dificultades decisivas. Más específicamente, estas versiones revisadas de la teoría no responden satisfactoriamente al problema planteado por la posible existencia de un número indefinido de obstáculos imprevistos para el éxito de nuestras acciones. En el artículo sugiero que la posible presencia de obstáculos ignorados supone un problema general para la Semántica del Éxito, incluyendo formulaciones alternativas como la de Blackburn.
38. Theoria. Revista de Teoría, Historia y Fundamentos de la Ciencia: Volume > 33 > Issue: 1
Manuel Pérez Otero El dominio de lo mental en la filosofía de Williamson
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Según Williamson, saber y creer son estados mentales, pero creer algo verdadero y creer justificadamente algo verdadero no lo son. Ese tratamiento discriminatorio es relevante para la epistemología de Williamson. Su principal tesis epistemológica negativa (sobre la supuesta imposibilidad de definir el saber conforme a cierto formato tradicional) y su principal tesis epistemológica positiva (una definición, alternativa, del saber) están en peligro si su teoría metafísica sobre lo mental es incorrecta. Presento aquí un problema para dicha teoría: impone limitaciones implausibles a los posibles usos de conceptos y expresiones lingüísticas. Describiré algunas opciones que tendría Williamson para evitar el problema; pero sostendré que acarrean cierta dosis de arbitrariedad.For Williamson, knowing and believing are mental states, but believing truly and justifiedly-and-truly believing are non-mental states. This discriminatory approach is relevant to his epistemology: his main negative epistemological thesis (on the alleged impossibility of defining knowledge in accordance with a traditional scheme) and his main positive epistemological thesis (his own alternative definition of knowledge) depend on his metaphysical theory about the demarcation of the mental. I present here a problem for Williamson’s theory of the mental: it imposes implausible restrictions on possible uses of concepts and linguistic expressions. I will describe some options that Williamson would have at his disposal to evade the problem; but I maintain that these options carry some degree of arbitrariness.
39. Theoria. Revista de Teoría, Historia y Fundamentos de la Ciencia: Volume > 33 > Issue: 1
Josefa Toribio Implicit Bias: From Social Structure to Representational Format
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In this paper, I argue against the view that the representational structure of the implicit attitudes responsible for implicitly biased behaviour is propositional—as opposed to associationist. The proposal under criticism moves from the claim that implicit biased behaviour can occasionally be modulated by logical and evidential considerations to the view that the structure of the implicit attitudes responsible for such biased behaviour is propositional. I argue, in particular, against the truth of this conditional. Sensitivity to logical and evidential considerations, I contend, proves to be an inadequate criterion for establishing the true representational structure of implicit attitudes. Considerations of a different kind, which emphasize the challenges posed by the structural social injustice that implicit attitudes reflect, offer, I conclude, better support for deciding this issue in favour of an associationist view.En este artículo cuestiono la tesis de que la estructura representacional de las actitudes implícitas responsables del comportamiento implícitamente sesgado es proposicional—en lugar de asociacionista. De acuerdo con la propuesta criticada, si la conducta implícita sesgada puede ocasionalmente ser modulada por consideraciones lógicas y evidenciales, entonces la estructura de las actitudes implícitas responsables de esa conducta es proposicional. Cuestiono, en particular, la verdad de este condicional. Sostengo que la sensibilidad de las actitudes implícitas a consideraciones lógicas y evidenciales resulta ser un criterio inadecuado para establecer su verdadera estructura representacional. Consideraciones de otro tipo, que enfatizan los desafíos planteados por la injusticia social estructural que las actitudes implícitas reflejan, ofrecen, concluyo, un mejor apoyo para decidir esta cuestión a favor de una visión asociacionista.
40. Theoria. Revista de Teoría, Historia y Fundamentos de la Ciencia: Volume > 33 > Issue: 1
Mariela Destéfano, Fernanda Velázquez Coccia Teorías de doble proceso: ¿una arquitectura de procesos múltiples?
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Se ha distinguido entre arquitectura cognitiva unificada y arquitectura de procesos múltiples (Machery 2009). Basándonos en esta distinción, intentaremos mostrar que si se explicitan y analizan los criterios de coordinación entre procesos, las teorías de doble proceso para el razonamiento y la toma de decisiones tendrían dificultades para consolidarse como una arquitectura de procesos múltiples.It has been distinguished between unified cognitive architecture and multiple-process architecture (Machery 2009). Based on this distinction, we will try to show that if processes coordination criteria are explicated and analyzed, double-process theories for reasoning and decision making have difficulties to consolidate as multiple process architecture.