Mark Colyvan

Reading [b:Stella Maris|60526802|Stella Maris (The Passenger, #2)|Cormac McCarthy|https://i.gr-assets.com/images/S/compressed.photo.goodreads.com/books/1658241766l/60526802._SX50_.jpg|95478000] spurred an interest in philosophy of mathematics, so I found a couple of recommendations for where to start and here I am. This book provides a somewhat brief overview of relevant topics mostly concentrating on current (as of 2012) issues of debate in the field, weighted towards those the author is particularly interested in and wants to push attention towards (paraconsistent logic, theories of mathematical explanation, mathematical notation). Thus it’s not a great source for getting up to speed on the central historical debates between realist (Platonist) and anti-realist (nominalist) interpretations of mathematics and mathematical entities, although it does go over those in a few earlier chapters. Those chapters were my favorite.

The discussion questions at the end of each chapter I found valuable for leading to more thought and development of the ideas presented, even though this necessarily took place just in my head and not in a classroom including other students, as the book was created for. A brief presentation and remarks about sources for further reading on those specific topics in the chapter is included at the end of each chapter as well, and these would seem to be valuable for the student.

Some understanding of formal logic and complex math would certainly be helpful, though I managed to muddle through ok, sometimes consulting other sources like the online Stanford Encyclopedia of Philosophy for assistance.

Includes some nice quotes:

“Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.” - Bertrand Russell, in “Recent Work on the Principles of Mathematics”

“In mathematics you don’t understand things. You just get used to them.” - John von Neumann

“Beauty is the first test: there is no permanent place in the world for ugly mathematics.” - G.H. Hardy in “A Mathematician’s Apology”

… (mehr)