Philosophy of Mathematics: Selected Readings by Paul BenacerrafThis is something of an introduction to the philosophy of math for me. I have read some papers and one book on the subject, but nothing covering this broad of an area. The collection is packed full of the papers that other papers cite. I do like going to the sources and this is a extremely illuminating anthology of primary sources. You not only get the feel of the early to mid 20th century philosophy of math, which always interested me, but you get a whole lot of paradigmatic arguments of major schools of thought in the field.
The only criticism would be a mild one. Given the size of the book, it seems impossible, but it would be exceedingly helpful as a textbook if the editors (as esteemed as they seem to be) were to give small introductions or contextualization to each paper.
As is, though, it provides a great breadth of helpful papers and arguments in the field. It also sharply points out some major distinctions in philosophy, let alone phil of math (e.g. realism/anti-realism, epistemology stances, etc). I found some papers to be difficult but clear enough in context. The order of the papers (within the larger sections) were helpful in suggesting a dialogue between the authors.
Overall, wonderful and I will keep this book on hand for rereading. It isnt exactly a book you can read once.
The Complicated Relationship Between Philosophy, Mathematics, and Science
The philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics. It aims to understand the nature and methods of mathematics, and finding out the place of mathematics in people's lives. The logical and structural nature of mathematics itself makes this study both broad and unique among its philosophical counterparts. The origin of mathematics is subject to arguments and disagreements. Whether the birth of mathematics was a random happening or induced by necessity duly contingent upon other subjects, say for example physics, is still a matter of prolific debates.
This course brings together two of the most fundamental and widely-applicable intellectual skills. Mathematical knowledge and the ability to use it is the most important means of tackling quantifiable problems, while philosophical training enhances the ability to analyse issues, question received assumptions and clearly articulate understanding. The combination provides a powerful background from which to proceed to graduate study in either mathematics or philosophy or to pursue a diverse range of careers. Historically, there have been strong links between mathematics and philosophy; logic, an important branch of both subjects, provides a natural bridge between the two, as does the philosophy of mathematics. The degree is founded on the belief that the parallel study of these related disciplines can significantly enhance your understanding of each. The Philosophy Faculty is the largest in the UK, and one of the largest in the world, with more than 70 full-time members and admitting around undergraduates annually to read the various degrees involving Philosophy.