Abstract
The present work is an attempt to bring attention to the application of several key ideas of Husserl ‘s Krisis in the construction of certain mathematical theories that claim to be altemative nonstandard versions of the standard Zermelo-Fraenkel set theory. In general, these theories refute, at least semantically, the platonistic context of the Cantorian system and to one or the other degree are motivated by the notions of the lifeworld as the pregiven holistic field of experience and that of horizon as the boundary of human perceptions and the de facto constraint in reaching limit-idealizations. Moreover, 1 try to give convincing reasons for the existence of an ultimate constitutional ‘vacuum’ of a subjective origin that is formally refiected in the application of a notion of actual infinity in dealing generally with the mathematical infinite.