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Our best scientific theories explain a wide range of empirical phenomena, make accurate predictions, and are widely believed. Since many of these theories make ample use of mathematics, it is natural to see them as confirming its truth. Perhaps the use of mathematics in science even gives us reason to believe in the existence of abstract mathematical objects such as numbers and sets. These issues lie at the heart of the Indispensability Argument, to which this Element is devoted. The Element's first half traces the evolution of the Indispensability Argument from its origins in Quine and...

What is the nature of mathematical knowledge? Is it anything like scientific knowledge or is it sui generis? How do we acquire it? Should we believe what mathematicians themselves tell us about it? Are mathematical concepts innate or acquired? Eight new essays offer answers to these and many other questions. Written by some of the world's leading philosophers of mathematics, psychologists, and mathematicians, Mathematical Knowledge gives a lively sense of the current state of debate in this fascinating field.

One True Logic is a major contribution to the philosophy of logic. It is the first monograph explicitly to articulate a version of logical monism, the view that there is a single correct foundational logic. Logical monism is opposed to logical pluralism, according to which there are many correct logics. One True Logic provides a critical overview of the monism vs pluralism debate and argues for the former. It defends a particular monism, based on a highly infinitary logic. Breaking new ground on a number of fronts, it offers novel arguments for the genuine logicality of infinitary logic and...