  The quantization of gravity offers a solution to the presence of
singularities in cosmology. Infinities are removed because of the existence of
finite quanta of spacetime. This is one of the most important prediction of
Loop Quantum Gravity. But treating gravity on the same footing as the other
quantum field theories introduces a different kind of infinities: the ones from
the renormalization procedure. In the covariant formulation of Loop Quantum
Gravity (Spinfoam) this kind of infinities are tamed by the presence of the
cosmological constant. These two results are guided by a specific perspective
on the appearance of infinity in physics: this is just interpreted as a
signpost that the theory should be improved. It arises from our limited
knowledge, and not as a fundamental fact of nature.
