The Foundations of Arithmetic: A Logico-Mathematical Enquiry into the Concept of Number


Gottlob Frege - 1884
    The book represents the first philosophically sound discussion of the concept of number in Western civilization. It profoundly influenced developments in the philosophy of mathematics and in general ontology.

Knowledge: A Very Short Introduction


Jennifer Nagel - 2014
    In this thought provoking Very Short Introduction, Jennifer Nagel considers the central problems and paradoxes in the theory of knowledge whilst drawing attention to the ways in which philosophers and theorists have responded to them. By exploring the relationship between knowledge and truth, and considering the problem of scepticism, Nagel introduces a series of influential historical and contemporary theories of knowledge, incorporating methods from logic, linguistics, and psychology, and using a number of everyday examples to demonstrate the key issues and debates.

Unknown Quantity: A Real and Imaginary History of Algebra


John Derbyshire - 2006
    As he did so masterfully in Prime Obsession, Derbyshire brings the evolution of mathematical thinking to dramatic life by focusing on the key historical players. Unknown Quantity begins in the time of Abraham and Isaac and moves from Abel's proof to the higher levels of abstraction developed by Galois through modern-day advances. Derbyshire explains how a simple turn of thought from this plus this equals this to this plus what equals this? gave birth to a whole new way of perceiving the world. With a historian's narrative authority and a beloved teacher's clarity and passion, Derbyshire leads readers on an intellectually satisfying and pleasantly challenging historical and mathematical journey.