Maddy’s Naturalistic Approach to Philosophy of Mathematics

Subject Areas : Philosophy

Omid Mohammad  Heydar ¹ (ندارد)

Received: 2013-03-08 Accepted : 2013-06-28 Published : 2013-08-23

Keywords: Naturalism, Philosophy of Mathematic, Willard van Orman&#x0D, &#x0D, Quine, Penelope Maddy, Second Philosophy,

Abstract :

Naturalism is an approach to the world phenomena from perspective ofnatural sciences. This approach avoids any kind of a priori philosophy and, ingeneral, any alleged knowledge of what is supernatural. In ontology,epistemology and methodology, naturalism by no means relies onmetaphysics or any kind of knowledge beyond the framework of empiricalsciences neither on any method and criterion except scientific methodologyand criteria. Naturalism, in one of its readings, considers philosophy as abranch of empirical science or a field of enquiry within the framework of sucha science. Penelope Maddy’s works on naturalism, especially in philosophy ofmathematics which this thesis intends to expound, are the continuation ofQuine’s works. Quine, as a prominent naturalist philosopher, is thepropounder of effective and thorough theories regarding naturalism, realismand other relevant areas. Unlike the past philosophers and epistemologists, hedoes not seek any basis, for empirical sciences, stronger than science, so thathe always relies on findings of empirical sciences. Penelope Maddy startsfrom Quine’s naturalism and, in response to the questions posed by othernaturalists in philosophy of mathematics, looks for a fundamental method,emphasizing on the set theory as a crucial basis in her arguments. Maddybelieves that if a conflict arises between philosophical explanation andsuccessful mathematical practices, it is philosophy that should retreat from itsposition. Neither philosophy nor science can annul or change methodologicalprinciples of mathematics, both science and philosophy being metamathematicaltrials for mathematics. Maddy’s important achievement innaturalistic philosophy of mathematics is heterogeneous naturalism to whichhe referred as the Second Philosophy. She recommends only mathematicalmethods and issues, and believes that other disciplines are not in the positionto be able to criticize mathematics.

References:

کواین، ویلارد ون اورمن، از محرک حسی تا دانش، ترجمه­ی مجید داوودی، انتشارات حکمت، چاپ اول، 1391ش.

2. مگی، براین، مردان اندیشه، ترجمه­ی عزت­الله فولادوند، انتشارات طرح نو، چاپ سوم، 1382ش.

3. میثمی، سایه، معنا و معرفت در فلسفه­ی کواین، انتشارات نگاه معاصر، چاپ اول، 1386ش.

 

4.  Maddy, P., Realism in Mathematics, Oxford University Press, 1990.

5. ـــــــ , Naturalism in Mathematics, Oxford University Press, 1997. (Reprinted 2002).

1. 6.  ـــــــ, “Naturalism-FriendsandFoes”, Philosophical Prespectives, 2001.

7. ــــــ , “Second philosophy”, Stanford Encyclopedia of Philosophy, 2003.

8. ـــــــ  , Second Philosophy; A naturalistic Method, Oxford University Press, 2007.

9. Paseau, A., “Naturalism in the philosophy of Mathematics”, Stanford Encyclopedia of Philosophy, 2008.