“Super-humans” is usually to be linked to Nietzsche or to Heidegger’s criticism to Nietzsche, or even to the ideology of Nazism. However, they can be properly underlain by philosophical and scientific anthropology as that biological species who will originate from humans eventually in the course of evolution. There is a series of more or less well-established facts in anthropogenesis, which would be relevant to the philosophical question about the “super-humans”: bipedalism, cooling by sweating, specific hair or its lack, omnivorous-ness, thumb opposition and apposition, vocal system of speech production, human brain, long childhood; our species is evolutionary young (about 200 000 years old), but it is the last survived descendant being genetically exceptionally homogenous (<00,01% genetic differences) of the genus “homo” (about 6 000 000 old). All this generates a few main features of our population: society, technics, language, and mind, which guarantee the contemporary absolute domination of mankind. The society has reached a natural limitation of earth. The technics depends on how much energy is produced. The mind is restricted by its carrier, i.e. by the brain. Thus only the language seems to be the frontier of any future development inducing a much better use of the former three. The recent informational technologies suggest the same. Language is defined as symbolic image of the world doubling it by an ideal or virtual world, which is fruitful for creativity and any modeling of the real world. Consequently, a gap between the material and the ideal world produces language. The language increases that gap in turn. Furthermore, the ideal world is secondary and derivative from the material world in origin and objectivity: Language serves for the world to be ordered. Thus language refers to the philosophical categories of ‘being’ and ‘time’. Any “super-language” should transcend some of those definitive borders of language and be a generalization. The involving of infinity can extend the language. Any human language is finite and addresses some finite reality. Thus the gap between reality and any model in language can be seen as that between infinity and its limitation to any finite representation: Finite representations dominate over society, technics, and the mind use. A “super-language” as an “infinite language” can be approached in a few reference frames: Husserl’s “Back to the things themselves!” if “phenomenon” in his philosophy is thought as the ‘word’ of the language of consciousness; the semantic and philosophical theory of symbol: from consciousness and language to reality; the concept of infinity in mathematics and its foundation: set or category theory; quantum mechanics and information: the coincidence of the quantum model and reality; quantum computer. Mankind is approached the problem of infinite language as the language of nature