Approaching Truth in Conceptual Spaces
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Approaching Truth in Conceptual Spaces Gustavo Cevolani1 Received: 23 May 2018 / Accepted: 19 November 2018 © Springer Nature B.V. 2018
Abstract Knowledge representation is a central issue in a number of areas, but few attempts are usually made to bridge different approaches accross different fields. As a contribution in this direction, in this paper I focus on one such approach, the theory of conceptual spaces developed within cognitive science, and explore its potential applications in the fields of philosophy of science and formal epistemology. My case-study is provided by the theory of truthlikeness (or verisimilitude), construed as closeness to “the whole truth” about a given domain, as described in the underlying language. I show how modeling propositions and their relations within a conceptual space has interesting implications for two issues in truthlikeness theory: the so called problem of language dependence, and that of measure sensitivity. I conclude by pointing at some open issues arising from the application of conceptual spaces to the analysis of philosophical problems. Keywords Truthlikeness · Verisimilitude · Truth approximation · Conceptual spaces · Geometry · Similarity · Language dependence · Measure sensitivity
1 Introduction Knowledge representation—how to formally represents beliefs, concepts, propositions, and information in general—is a central issue in a number of fields, including cognitive science, artificial intelligence, and the philosophical analysis of reasoning and cognition. Not surprisingly, however, scholars in different disciplines tend to privilege, for theoretical, practical and historical reasons, different formats of representation. Thus, in philosophy and (formal) epistemology, as well as in standard semantics and linguistics, information is often represented in terms of sentences, propositions, and possible worlds; whereas in many AI applications neural networks and other “connectionist” models are preferred. Usually,
* Gustavo Cevolani [email protected] 1
IMT School for Advanced Studies Lucca, Piazza San Francesco 19, 55100 Lucca, Italy
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not much effort is made to bridge the different approaches, and the corresponding models of representation are hardly inter-translatable. Recently, a great deal of attention has been devoted to so called conceptual spaces, which aim at providing a general framework of knowledge representation for the whole area of cognitive science (Gärdenfors 2000; Zenker and Gärdenfors 2015). The starting point of the conceptual spaces project is focusing on the underlying geometry of our “cognitive structures”, to borrow a term from Kuipers (2000, p. 10), and in particular on a geometric theory of properties and concept acquisition. Relying on an impressive array of theoretical and empirical work, Gärdenfors (2000) forcefully argues for what he calls the “conceptual” level of analysis, which is mid-way between the “symbolic” level of propositional representation and the “sub-conceptual” level exemplified
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