不可或缺論證的合理性

In Defense of Indispensability Argument

柯建廷(Chien-Ting Ko)

指導教授 ： 楊金穆

國立臺灣大學/文學院/哲學研究所/碩士(2010年)

https://doi.org/10.6342/NTU.2010.00327

摘要

奎因(W. V. Quine)的不可或缺論證(indispensability argument)在數學實在論與唯名論的論爭裡，占有重要的地位。此論證被廣泛地視為是支持數學實在論最重要的論證之一，但也因此受到相當多不同的反對意見。
雖然奎因本人並未很清楚地以嚴格的論證形式表達此論證，但藉由他主要的哲學思想一般哲學界普遍認為，奎因的不可或缺論證(QIA)至少包含三個前提：(一)不可或缺論點─數學對於自然科學是不可或缺的、(二)自然主義─並沒有第一哲學，哲學是科學的延續、(三)確認的整體主義─在對於一個科學理論確認時，不僅確認著理論裡的物裡部分，也同時確認了理論裡的數學部分。
在第一章裡，根據奎因的哲學看法及當代哲學家普遍的意見，我嘗試對於不可或缺論證構作一完整的論證形式，並討論每個前提與奎因哲學看法間的關係。第二章則討論菲爾德(H. Field)對於不可或缺的挑戰，並結論出菲爾德的唯名論計劃很可能是失敗的，或至少只能獲致部分的成功。第三章討論梅蒂(P. Maddy)與索柏(E. Sober)各自針對自然主義與確認的整體主義的反對意見。並結論出在第一章裡所提出當代哲學家普遍認定的不可或缺論證形式過強，並提出一個無須基於確認整體主義的不可或缺論證(RQIA)。第四章裡則討論RQIA如何面對分離假說的相關問題。

關鍵字

不可或缺論證 ； 奎因 ； 數學實在論 ； 唯名論 ； 自然主義 ； 確認的整體主義

並列摘要

In the debate between mathematical realism and nominalism, Quine’s indispensability argument maintains an important status. It is widely regarded as the most potent argument supporting mathematical realism. However, it also faces various nominalists’ challenges.
Although it has never been explicitly formulated by Quine himself, Quine’s indispensability argument is often assumed to include three main premises: (1) indispensability thesis – mathematics is indispensable to natural science; (2) naturalism – there is no first philosophy and philosophy is continuous to science; (3) confirmational holism – the confirmation of scientific theories confirms not only its physical but also its mathematical components.
In chapter one, I try to give a preliminary form of QIA and discuss each premise in light of Quine’s general philosophical views. In chapter two, I consider Field’s challenge to the indispensability thesis and conclude that it is most likely Field’s nominalistic program is deemed to fail, or at least not completely successful. Chapter three discusses naturalism and confirmational holism theses in QIA, by reviewing Maddy’s view on naturalism and Sober’s objection to confirmational holism, I conclude that the preliminary version of QIA introduced in the beginning is too strong to be an ontological argument and an adequate version of QIA is put forward – RQIA (a version of QIA without confirmational holism). In chapter four, I try to give a way to deal with a variety of separation objections, which may be a challenge to RQIA.

並列關鍵字

indispensability argument ； Quine ； mathematical realism ； nominalism ； naturalism ； confirmational holism

參考文獻

Field, H. 1990. “Mathematics and Modality.” In Meaning and Method: Essays in Honour of Hilary Putnam: 213-33. (ed. Boolos, G.). Cambridge: Cambridge U.P.

Albert, D. 1994. “Bohm’s Alternative to Quantum Mechanics.” Scientific American. Vol.270, p.58-67.

Baker, A. 2003. “Quantitative Parsimony and Explanatory Power.” British Journal for the Philosophy of Science 54:245-59.

Balaguer, M. 1998. Platonism and Anti-Platonism in Mathematics. Oxford: Oxford University Press.

Balaguer, M. 2008. “Fictionalism in the Philosophy of Mathematics.” Stanford