数学理论与虚构作品

Mathematical Theories and Fictions

虚构主义是当代数学哲学中的一种观点,在国际上得到一些学者的支持。通过在物理主义框架下理解虚构作品并比较数学理论与虚构作品,一方面可以更明确地回答有关虚构作品的本体论、认识论及语义学问题,另一方面可以更清晰地看出,数学理论与虚构作品在本体论、认识论及语义学方面有很大程度的相似性。这些结论支持一种彻底物理主义的数学哲学,同时也是对现有的虚构主义数学哲学的一种改进。

Fictionalism is a position in contemporary philosophy of mathematics,supported by some contemporary philosophers.By understanding fictions and comparing mathematical theories with fictions under physicalism,we can answer ontological,epistemological and semantic questions about fictions more clearly and can see more clearly the similarity between mathematical theories and fictions in terms of their ontological,epistemological and semantic aspects.These conclusions support a radically physicalistic philosophy of mathematics and they also constitute an improvement over the current fictionalism in philosophy of mathematics.