Cover of Theoria: An International Journal for Theory, History and Foundations of Science
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Displaying: 141-160 of 1749 documents


monographic section
141. Theoria: An International Journal for Theory, History and Foundations of Science: Volume > 33 > Issue: 3
Robin Jeshion Katherine and the Katherine: On the syntactic distribution of names and count nouns
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Names are referring expressions and interact with the determiner system only exceptionally, in stark contrast with count nouns. The-predicativists like Sloat, Matushansky, and Fara claim otherwise, maintaining that syntactic data indicates that names belong to a special syntactic category which differs from common count nouns only in how they interact with ‘the’. I argue that the-predicativists have incorrectly discerned the syntactic facts. They have bypassed a large range of important syntactic data and misconstrued a critical data point on which they ground the-predicativism. The right data offers new compelling syntactic grounds for referentialism.
142. Theoria: An International Journal for Theory, History and Foundations of Science: Volume > 33 > Issue: 3
Robert Stalnaker Diagnosing sorites arguments
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This is a discussion of Delia Fara’s theory of vagueness, and of its solution to the sorites paradox, criticizing some of the details of the account, but agreeing that its central insight will be a part of any solution to the problem. I also consider a wider range of philosophical puzzles that involve arguments that are structurally similar to the argument of the sorites paradox, and argue that the main ideas of her account of vagueness helps to respond to some of those puzzles.
143. Theoria: An International Journal for Theory, History and Foundations of Science: Volume > 33 > Issue: 3
Timothy Williamson Supervaluationism and good reasoning
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This paper is a tribute to Delia Graff Fara. It extends her work on failures of meta-rules (conditional proof, RAA, contraposition, disjunction elimination) for validity as truth-preservation under a supervaluationist identification of truth with supertruth. She showed that such failures occur even in languages without special vagueness-related operators, for standards of deductive reasoning as materially rather than purely logically good, depending on a context-dependent background. This paper extends her argument to: quantifier meta-rules like existential elimination; ambiguity; deliberately vague standard mathematical notation. Supervaluationist attempts to qualify the meta-rules impose unreasonable cognitive demands on reasoning and underestimate her challenge.
book reviews
144. Theoria: An International Journal for Theory, History and Foundations of Science: Volume > 33 > Issue: 3
Fernando Rudy Hiller Building better beings: A theory of moral responsibility
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145. Theoria: An International Journal for Theory, History and Foundations of Science: Volume > 33 > Issue: 3
Summary
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146. Theoria: An International Journal for Theory, History and Foundations of Science: Volume > 33 > Issue: 3
Contents of Volume 33
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monographic section i
147. Theoria: An International Journal for Theory, History and Foundations of Science: Volume > 33 > Issue: 2
Mary Leng Guest Editor’s Introduction: Updating indispensabilities: Putnam in memoriam
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148. Theoria: An International Journal for Theory, History and Foundations of Science: 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.
149. Theoria: An International Journal for Theory, History and Foundations of Science: 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.
150. Theoria: An International Journal for Theory, History and Foundations of Science: 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.
151. Theoria: An International Journal for Theory, History and Foundations of Science: 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.
152. Theoria: An International Journal for Theory, History and Foundations of Science: 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.
153. Theoria: An International Journal for Theory, History and Foundations of Science: 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
154. Theoria: An International Journal for Theory, History and Foundations of Science: Volume > 33 > Issue: 2
María de Paz, José Ferreirós Guest Editors’ Introduction: From basic cognition to mathematical practice
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155. Theoria: An International Journal for Theory, History and Foundations of Science: 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.
156. Theoria: An International Journal for Theory, History and Foundations of Science: 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.
157. Theoria: An International Journal for Theory, History and Foundations of Science: 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.
158. Theoria: An International Journal for Theory, History and Foundations of Science: 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.
159. Theoria: An International Journal for Theory, History and Foundations of Science: 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.
160. Theoria: An International Journal for Theory, History and Foundations of Science: 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.