Antirealist escape to the realm of possibilities

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Krzysztof Wójtowicz

Abstract

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.

Article Details

How to Cite
Wójtowicz, K. (2008). Antirealist escape to the realm of possibilities. Philosophical Problems in Science (Zagadnienia Filozoficzne W Nauce), (42), 15–27. Retrieved from https://zfn.edu.pl/index.php/zfn/article/view/244
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Articles

References

Balaguer M. [1998] Platonism and Anti-Platonism in Mathematics, New York, Oxford: Oxford University Press.

Chihara C. [1990] Constructibility and mathematical existence, Oxford: Clarendon Press.

Field H. [1980] Science Without Numbers, Oxford: Basil Blackwell.

Hellman G. [1989] Mathematics without Numbers, Oxford: Clarendon Press.

Putnam H. [1967] „Mathematics without foundations”, Journal of Philosophy 64, 5–22.

Wójtowicz K. [2003] Spór o istnienie w matematyce. Warszawa: Wydawnictwo Naukowe Semper.