数学真理困境的自然主义实在论求解

The Naturalistic Realist Solution to the Dilemma of Mathematical Truth

把数学对象看成是独立于人脑而存在的客观抽象物,同时要求为人们如何能够认识到这些对象提供直接的经验证据,这是贝纳塞拉夫数学真理困境对数学实在论提出的认识论难题。玛戴试图用折衷的柏拉图主义与一种双重认识论相结合的策略为这一难题提出了自然主义实在论的解答。然而,双重认识论必然导致两种本体论图景,其结果只能是玛戴一方面无法维护其所坚持的数学抽象本性,而另一方面又无法为人们认识数学对象的感知能力提供合理说明。

Taking mathematical object as objective abstract existing independent of human mind and in the meantime requiring to show the empirical evident of how we can get the knowledge of this kind of object is the epistemological problem of Benacerraf＇ s mathematical truth dilemma put forward for mathematical realists. By conjoining a compromised Platonism with a two - tiered epistemology naturalistic realist Penelope Maddy tries to reconcile the contradiction between the traditional Platonism and the empiricist epistemology, so as to get out of the dilemma. However, the two tiered epistemology has led to two kinds of pictures of ontology. As a result, naturalists could not insist on the abstractness of mathematics, nor could they provide a rational explanation for the sensation faculty of knowing the mathematical entity.