  Hilbert’s program rested on the insight that, au fond, the  only part of mathematics whose reliability is entirely beyond  question is the finitistic, or concrete part: in  particular, finite manipulation of surveyable domains of distinct  objects including mathematical symbols presented as marks on paper.  Mathematical propositions referring only to concrete objects in this  sense Hilbert called real, concrete, or  contentual propositions, and all other mathematical  propositions he distinguished as possessing an ideal, or  abstract character. (Thus, for example, \(2 + 2 = 4\) would  count as a real proposition, while there exists an odd perfect  number would count as an ideal one.) Hilbert viewed ideal  propositions as akin to the ideal lines and points “at  infinity” of projective geometry. Just as the use of these does not violate any truths of the “concrete” geometry of the  usual Cartesian plane, so he hoped to show that the use of ideal  propositions—even those of Cantorian set theory—would  never lead to falsehoods among the real propositions, that, in other  words, such use would never contradict any self-evident fact  about concrete objects. Establishing this by strictly concrete,  and so unimpeachable means was thus the central aim of Hilbert’s  program. Hilbert may be seen to have followed Kant in attempting to  ground mathematics on the apprehension of spatiotemporal  configurations; but Hilbert restricted these configurations to  concrete signs (such as inscriptions on paper). Hilbert regarded  consistency as the touchstone of existence, and so for him the  important thing was the fact that no inconsistencies can arise within the realm of concrete signs, since correct descriptions of concrete  objects are always mutually compatible. In particular, within the  realm of concrete signs, actual infinity cannot generate  inconsistencies since, again along with Kant, he held that this  concept cannot correspond to any concrete object. Hilbert’s view  seems accordingly to have been that the formal soundness of  mathematics issues ultimately, not from a logical source,  but from a concrete   one[27],  in much the same way as the consistency of truly reported empirical  statements is guaranteed by the concreteness of the external   world[28].  