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Foundations without Foundationalism media planner can be such a criticalStewart Shapiro presents a distinctive and persuasive view of the foundations of mathematics, arguing controversially that second order logic has a central role to play in laying these foundations. To support this contention, he first gives a detailed development of second order and higher order logic, in a way that will be accessible to graduate students. He then demonstrates that second order notions are prevalent in mathematics as practised, and