Ultrafinitism

Ultrafinitism is the mathematical belief that the set of natural numbers is finite; at some point numbers become large enough that they simply cease to exist. The philosophy is an extreme form of finitism, which states that infinite objects (such as the transfinite ordinals) are nonexistent. Ultrafinitists state that the natural numbers have an ending, because they have no physical realization and/or cannot be computed.

The primary argument for ultrafinitism is that large natural numbers are circularly defined. A natural number is defined by applying the successor function to zero many times. And here we run into a bootstrapping issue: a googolplex is  where the number of copies of   is googolplex.

Googologists, for obvious reasons, will object to this philosophy.