What work (or works) are best for beginning an independent study of the philosophy of mathematics?
Some historical :
Morris Kline, Mathematics: The Loss of Certainty, 1980
Marcus Giaquinto, The Search for Certainty : A Philosophical Account of Foundations of Mathematics, 2002.
Some anthologies, like :
- Stewart Shapiro (editor), The Oxford Handbook of Philosophy of Mathematics and Logic, 2005.
Very useful also the articles in Stanford Encyclopedia of Philosophy (with bibliography) starting with Philosophy of Mathematics.