The book surveys how thinkers from Mill to Frege and Russell have understood number and class. It frames these notions through practical questions about how we experience quantity, and whether number can be explained by time, space, or pure logic. The discussion weighs empirical and Kantian views against analytic and formal theories, testing assumptions about why arithmetic should be thought of as a matter of observation, language, or abstract reasoning.

Readers will trace debates over extension versus intension, the role of abstraction, and the paradoxes that arise when counting infinite collections. The work also examines how ranges and functions contribute to defining numbers and classes, and it presents postulates proposed to ground the existence of these abstract entities. The tone is analytic but accessible, inviting verification by observable facts and careful argument.

Learn how different historical views connect number to time, space, or logic.
Explore the shift from purely extensional ideas of a class to more nuanced notions like ranges and abstraction.
See how famous paradoxes, such as Russell's, challenge simple definitions of classes and numbers.
Understand the motivations for introducing new logical postulates to ground these concepts.

Ideal for readers with an interest in the philosophy of mathematics, logic, and the foundations of arithmetic.

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