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monographic section i
1. 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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2. 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.
3. 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.
4. 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.
5. 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.
6. 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.
7. 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
8. 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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9. 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.
10. 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.