Controversy about the infinite is more or less ubiquitous in philosophy. There are very few areas of philosophy where questions about the infinite do not arise; and there are very few areas of philosophy where questions about the infinite do arise, and where there is no serious dispute about how those questions should be answered. Furthermore, questions about the infinite are foundational in many areas of philosophy: There are many quite fundamental parts of philosophy in which the most basic questions that arise are concerned with the role of the infinite in those parts of philosophy.

Obviously enough, questions about the infinite arise in the most fundamental parts of logic and philosophy of mathematics. One of the most fundamental observations that one can make about the natural numbers — the numbers that are generated when one starts counting from one, adding one unit each time — is that there is no last or greatest natural number: for any number to which one counts, one can go further by adding more units. This observation is one of the fundamental sources of theorising about the infinite, and its consequences extend far beyond the domain of the philosophy of mathematics.

While there are serious questions about the development of concepts of the infinite in logic and mathematics, there are far more immediate problems about the development and application of concepts of the infinite in other realms.