Search results for " philosophy of mathematics"
showing 5 items of 5 documents
Productive Ambiguity in Mathematics
2011
According to E. Grosholz, there is a phenomenon called `productive ambiguity' which plays a very important role in mathematics, and the sciences, because it is instrumental to the resolution of many open questions. The main task of this paper is that of assessing Grosholz's claim with regard to mathematics.
A route to agnosticism in mathematics
Bachelard, Enriques and Weyl: comparing some of their ideas
2012
Some aspects of Federigo Enriques mathematical philosophy thought are taken as central reference points for a critical historic-epistemological comparison between it and some of the main aspects of the thought of other his contemporary thinkers like Gaston Bachelard and Hermann Weyl. From what will be exposed, it will be also possible descry eventual educational implications of the historic-epistemological approach.
A Realist Philosophy of Mathematics
2007
The realism/anti-realism debate is one of the traditional central themes in the philosophy of mathematics. The controversies about the existence of the irrational numbers, the complex numbers, the infinitesimals, etc. will be familiar to all who are acquainted with the history of mathematics. This book aims mainly at presenting and defending a non-Platonist form of mathematical structural realism which, in the respect of the history of mathematics, harmonizes with a plausible epistemology that naturally arises from it.
MATHEMATICS AS A QUASI-EMPIRICAL SCIENCE
2006
The present paper aims at showing that there are times when set theoretical knowledge increases in a non-cumulative way. In other words, what we call ‘set theory’ is not one theory which grows by simple addition of a theorem after the other, but a finite sequence of theories T1, ..., T n in which Ti+1, for 1 ≤ i < n, supersedes T i . This thesis has a great philosophical significance because it implies that there is a sense in which mathematical theories, like the theories belonging to the empirical sciences, are fallible and that, consequently, mathematical knowledge has a quasi-empirical nature. The way I have chosen to provide evidence in favour of the correctness of the main thesis of t…