Three Papers on and around the Access Problem

The three papers which make up this dissertation form part of a larger project, which aims to solve the 'access problem' for realism about mathematics by providing a clear and plausible example of what a satisfying explanation of human accuracy about objective mathematical facts could look like. They fit into this project as follows.;The first paper argues that one cannot explain our use of good mathematical axioms and inference rules merely by saying that any syntactically consistent (mathematical) proof procedures we had accepted would have given meaning to our mathematical vocabulary in such a way as to ensure their own correctness.;The second paper outlines my core two-part strategy for solving the access problem: 1) reduce the problem of accounting for human access to mathematical facts to the problem of accounting for access to combinatorial possibility 2) use the fact that human beings face pressure to correctly predict and explain the behaviour of concrete objects to explain our possession of good methods of reasoning about combinatorial possibility. It largely focuses on part 2) of this story.;The third paper develops part 1) of the two-part story above. It motivates and helps defend a (loosely) neo-carnapian explanation for mathematicians' freedom to introduce new kinds of objects, like the complex numbers and the sets. If this neo-carnapian explanation is correct, then there's an easy route from the kind of accuracy about combinatorial possibility discussed in the second paper to accuracy about more familiar mathematical topics.