The Peano axioms are finite. The numbers they describe are unbounded. Finite human brains understand this.

My 1,300 cm3 is capable of understanding the function f(x) = 3x, which is unbounded, therefore finite physical size does not prevent the brain from dealing with unbounded functions.

In general, a finite machine can easily deal with unbounded numbers simply by taking unbounded amounts of time to do so. This is not as much of a problem as it may sound, since there will intevitably be an upper bound to the utilities involved in all dilemma's I actually encounter (unless my lifespan is infinite) but not the utilities I could, in theory, compute.