Carlo Cellucci
نویسندگان
چکیده
As a result of the failure of the foundational programs, in the past three decades there has been a revival in the empiricist philosophy of mathematics. In the latter several trends can be distinguished and among them an eminent position is occupied by a Millian one. A distinctive feature of the supporters of such trend is that, while considering the absolute certainty of mathematical propositions as an illusion, they do not intend to suggest skepticism as to the reliability of logical deduction. Like Mill they consider logical inference as absolutely infallible, only axioms are fallible. A significant representative of such trend is Penelope Maddy whose views, first proposed in a series of articles, are systematically presented in this book (RM for short). Classifying Maddy as a Millian may seem peculiar because her scanty remarks about Mill in RM are fairly critical. For example, in rejecting the view that our most basic general set theoretic beliefs are justified by simple enumerative induction, she claims that: " t h e i d e a t h a t ma t h e ma t i c s i s a s i mp l e i n d u c t i v e s c i e n c e g o e s b a c k t o Mi l l " (R M, p. 6 7 , footnote 77). However, including Maddy in the Millian camp seems justified in view of the following facts. 1) Like Mill, Maddy holds that it is impossible to ascribe any character of necessity to the truths of mathematics and to assume " t h a t t h e y a r e , T o d a y " n o o n e wo u l d e x p e c t e v e n t h e b e s t s c i e n t i f i c a r g u me n t s t o b e a b s o l u t e l y j u s t i f y i n g " and our ep i s t e mo l o g i c a l i n q u i r i e s i n ma t h e ma t i c s mi g h t e v e n …
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