Penelope Maddy is a distinguished professor of logic and philosophy of science and mathematics, renowned for her influential work in the philosophy of mathematics. Her early research defended the view that mathematics describes a mind-independent reality accessible through intuition, proposing that some mathematical entities might be concrete rather than abstract. Later, she embraced a naturalist stance, advocating for the adoption of scientific methods in philosophy, particularly in discussions of science. She posits that mathematics operates distinctly from science, free from its constraints, and suggests that many traditional philosophical puzzles stem from misapplying language.
The book explores the foundational role of set theory axioms in mathematics, emphasizing the importance of evaluating these fundamental assumptions. It delves into the methods for assessing axioms and examines the philosophical context that supports these evaluations, providing insights into the interplay between mathematical proof and foundational assumptions.
Focusing on the justification of fundamental mathematical assumptions, the book critiques realism and advocates for naturalism, which emphasizes practical considerations within mathematics. Penelope Maddy defines naturalism and illustrates its application in set theory, providing a fresh perspective informed by contemporary philosophical and mathematical discourse. This accessible and insightful exploration appeals to readers from both fields, enriching their understanding of the philosophical underpinnings of mathematics.
What Do Philosophers Do? takes up the leading arguments for radical skepticism from an everyday point of view. A range of philosophical methods are examined and employed, for a revealing portrait of what philosophers do, and perhaps a quiet suggestion for what they should do, for what they do best.