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PL
The article is devoted to a popular presentation of two important styles of thinking concerning the problem of existence of mathematical objects: Chihara's linguistic constructivism, and Hellman's modal structuralism. According to Chihara, mathematical statements should be interpreted as referring to certain linguistic construction; according to Hellman, mathematics is the science of possible structures. The motivations and main ideas are examined (without going into technical details), and the similarities and differences between these two viewpoints are highlighted.
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EN
This paper focuses primarily on the realism-constructivism debate. Firstly, I clarify Goodman’s three main arguments for constructivism, and then I deal with the critical response to this doctrine by proponents of Devittian common-sense realism and scientific realism. In the next section, I discuss the main problems of Devittian realism as they are seen by critics. Finally, in line with Wittgenstein’s recommendation, I make “a linguistic turn” – by means of language analysis I try to shed new light on some of the old problems of the debate. It turns out that these old problems may disappear when we track the use of crucial terms within the relevant philosophical argumentation and when we are able to recognize conceptual statements. As a result, I claim that the philosophers interested in ontological issues should focus on particular problems of contemporary science (e.g., the interpretation of the double-slit experiment) rather than on the problem of the existence of things in general.
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