THEORIA
Revista de Teoría, Historia y Fundamentos de la Ciencia
An International Journal for Theory, History and Foundations of Science

Coedición:
Euskal Herriko Unibertsitateko Argitalpen Zerbitzua / Servicio Editorial de la Universidad del País Vasco
Centro de Análisis, Lógica e Informática Jurídica (CALIJ)

Volume 30/3 - September 2015     pp. 311-483      ISSN 0495-4548 / ISSNe: 2171-679X

Editor: Andoni Ibarra                             Más información / Texto completo

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S . U . M . M . A . R . Y 

Monographic Section: 
History and Philosophy of Logic and Mathematics
Guest Editor: Gabriel Uzquiano

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Editors’ Introduction  .....  315-316
Gabriel Uzquiano

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UPV/EHU. Theoria, 2015, Vol. 30/3, pp. 317-329          ( www.a360grados.net )
DOI: 10.1387/theoria.14099 

On the Essence and Identity of Numbers
Mario Gómez-Torrente

Abstract: Taking as premises some intuitions about the essences of natural numbers, pluralities and sets, the paper offers an argument that the natural numbers could not be the “Zermelo numbers”, the “Von Neumann numbers”, the “Kripke numbers”, or the “positions in the ω-structure”, among other things. The argument’s conclusion is thus Benacerrafian in form, but it is emphasized that the argument is anti-Benacerrafian in substance, as it is perfectly compatible and in fact congenial with some views on which the numbers could be things of certain other kinds.

Keywords: Arithmetic, Ontology, Benacerraf

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UPV/EHU. Theoria, 2015, Vol. 30/3, pp. 331-348          ( www.a360grados.net ) 
DOI: 10.1387/theoria.14105

Non-Representational Mathematical Realism
Maria Jose Frapolli

Abstract: This paper is an attempt to convince anti-realists that their correct intuitions against the metaphysical inflationism derived from some versions of mathematical realism do not force them to embrace non-standard, epistemic approaches to truth and existence. It is also an attempt to convince mathematical realists that they do not need to implement their perfectly sound and judicious intuitions with the anti-intuitive developments that render full-blown mathematical realism into a view which even Gödel considered objectionable (Gödel 1995, p. 150).
I will argue for the following two theses: (i) that realism, in its standard characterization, is our default position, a position in agreement with our pre-theoretical intuitions and with the results of our best semantic theories, and (ii) that most of the metaphysical qualms usually related to it depends on a poor understanding of truth and existence as higher-order concepts.

Keywords: Realism, Representationalism, Existence, Truth

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UPV/EHU. Theoria, 2015, Vol. 30/3, pp. 349-363          ( www.a360grados.net )
DOI: 10.1387/theoria.14472

Essence Without Fundamentality
Agustin Rayo

Abstract: In Modality and Explanatory Reasoning, Boris Kment argues that a single notion of essence can be used to play two distinct theoretical roles. He thinks there is an important connec- tion between essence and metaphysical necessity, on the one hand, and between essence and metaphysical explanation, on the other. 
In this paper I will argue that it is not clear that a single notion of essence should be used to perform both these jobs. For whereas the project of giving metaphysical explanations requires a notion of essence that distinguishes between truths that are more or less “funda- mental” in a metaphysical sense, the project of shedding light on metaphysical necessity does not.

Keywords: essence, fundamentality

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UPV/EHU. Theoria, 2015, Vol. 30/3, pp. 365-392          ( www.a360grados.net )
DOI: 10.1387/theoria.14668

Truth, Demonstration and Knowledge. A Classical Solution to the Paradox of Knowability
Elia Zardini

Abstract: After introducing semantic anti-realism and the paradox of knowability, the paper offers a reconstruction of the anti-realist argument from the theory of understanding. The proposed reconstruction validates an unrestricted principle to the effect that truth requires the existence of a certain kind of “demonstration”. The paper shows that the principle fails to imply the problematic instances of the original unrestricted knowability principle but that the overall view still has unrestricted epistemic consequences. Appealing precisely to the paradox of knowability, the paper also argues, against BHK semantics, for the non-constructive character of the demonstrations envisaged by anti-realists, and contends that, in such a setting, one of the most natural arguments in favour of a revision of classical logic loses all its force.

Keywords: paradox of knowability; semantic anti-realism, truth

Articles             --------------------------------------------

UPV/EHU. Theoria, 2015, Vol. 30/3, pp. 395-414          ( www.a360grados.net )
DOI: 10.1387/theoria.13150

La argumentación abstracta en Inteligencia Artificial: problemas de interpretación y adecuación de las semánticas para la toma de decisiones
Gustavo Adrián Bodanza

Abstract: El modelo de marcos argumentativos abstractos es actualmente la herramienta más utilizada para caracterizar la justificación de argumentos derrotables en Inteligencia Artificial. Las justificciones se determinan en base a los ataques entre argumentos y se formalizan a través de semánticas de extensiones. Aquí sostenemos que, o bien algunos marcos argumentativos carecen de sentido bajo ciertas concepciones de ataque específicas, o bien las semánticas más usadas en la literatura, basadas en el concepto de defensa conocido como admisibilidad, no resultan adecuadas para justificar, en particular, argumentos para la toma de decisiones.

Keywords:  argumentación abstracta, relaciones de ataque, semánticas de extensiones, toma de decisiones

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UPV/EHU. Theoria, 2015, Vol. 30/3, pp. 415-429          ( www.a360grados.net )
DOI: 10.1387/theoria.12009

The Eleatic and the Indispensabilist
Russell Marcus

Abstract: The debate over whether we should believe that mathematical objects exist quickly leads to the question of how to determine what we should believe. Indispensabilists claim that we should believe in the existence of mathematical objects because of their ineliminable roles in scientific theory. Eleatics argue that only objects with causal properties exist. Mark Colyvan’s recent defenses of Quine’s indispensability argument against some contemporary eleatics attempt to provide reasons to favor the indispensabilist’s criterion. I show that Colyvan’s argument is not decisive against the eleatic and sketch a way to capture the important intuitions behind both views.

Keywords: Indispensability Argument; Eleatic Principle; Platonism; Mark Colyvan

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UPV/EHU. Theoria, 2015, Vol. 30/3, pp. 431-447          ( www.a360grados.net )
DOI: 10.1387/theoria.12647

Why Pursue Unification? A Social-Epistemological Puzzle
Randall Harp, Kareem Khalifa

Abstract: Many have argued that unified theories ought to be pursued wherever possible. We deny this on the basis of social-epistemological and game-theoretic considerations. Consequently, those seeking a more ubiquitous role for unification must either attend to the scientific community’s social structure in greater detail than has been the case, and/or radically revise their conception of unification.

Keywords: unification, social epistemology, game theory, science; theory pursuit

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UPV/EHU. Theoria, 2015, Vol. 30/3, pp. 449-463          ( www.a360grados.net ) 
DOI: 10.1387/theoria.13208

On the Social Nature of Objectivity: Helen Longino and Justin Biddle
Jaana Eigi

Abstract: According to Helen Longino, objectivity is necessarily social as it depends on critical interactions in community. Justin Biddle argues that Longino’s account presupposes individuals that are completely open to any criticism; as such individuals are in principle able to criticise their beliefs on their own, Longino's account is not really social. In the first part of my paper I argue that even for completely open individuals, criticism for maintaining objectivity is only possible in community. In the second part I challenge Biddle’s interpretation of Longino’s conception of the individual. I conclude that Longino’s account is necessarily social.

Keywords: Biddle; Collins; criticism; epistemic subject; Kusch; Longino; objectivity; social epistemology; rule-following; tacit knowledge

Book Reviews  …..  467-470

Wenceslao J. González (ed.) 2014:  Bas van Fraassen’s Approach to Representation and Models in Science
Xavier de Donato