Skip to main content

Cardinal Numbers

Given a set S, a cardinal number M is the invariance of S after changes in the properties and relations of its objects. Two sets have the same cardinality if we can construct a one-to-one correspondence between its elements. These definitions are highly psychological. It implies a deeper identity of a set than the identity given by the extension of a property. Such identity would have to be a property since it can be predicated of more than one set. But how are we to know such substance in relation to which there occurs an invariance after changing properties and relations of objects? From a constructive point of view it would only make sense that such unmovable and unchangeable “Terminus” was to be introduced by definition (recursive). Then cardinal number would mean simply that we can construct a countable algorithm (in +) for a given set, and two sets have the same cardinality if for a given machine their countable algorithms stop at the same time.

Comments

Popular posts from this blog

Limen et Continuum

  Existence is Encounter. Meeting at the limen. In the limen, the masks disappear, that is, the basic intuitions of identities, such as the identity that I feel and think in relation to the tree that I see in front of me. The identity of the tree is a projection of mine: the unity of my process of perceiving the tree generates a mask in me, the ghost of a limited unity separated from everything else. The simplest form of intuitive understanding of masks and limen is given to us by numbers. Numbers intuitively express the liminal tension that is Existence. A little etymological note. Rythmos in Greek means flow. Arythmos (number) is what does not flow, what remains solidified. Numbers express the liminoid, and flow, rhythm, expresses the liminal. A rhythm becomes liminoid when we can trace patterns in it, that is, when we can construct masks of identities. Mathematics has spoken of flow using the Latin word “continuum”, the continuous. All modern science, since Leibni...

Ritual, Scientific Experiment and Truth

 Human rituals have their roots in animal behavior, and the animal pattern has its roots in the need for repetition of living organisms, in the cyclical structure of physiological actions. At the human level, ritual behavior involves a delimitation of space and time, as well as a different meaning of both with respect to the spaces and times of everyday experience. From the ritual ceremonies of cold societies, we observe the care and thoroughness of the shaman to determine with precision the spaces, times and elements that intervene in the rite. Sacred space delimits the world, not only as a place of action, but also the scope of meaning of the things contained in that space. It is a space loaded with meaning: there is an order in things. Time itself acquires its meaning in relation to this order of things, and cyclically closes the space in the “tempo” of the rite, a tempo that is a symbol of the tempo of the World. What is not in the rite or is not referable to the rite has no re...

What do we marry?

  The narrative tradition of India contains true gems of fantastic literature that give rise to the most entertaining ethical and metaphysical speculations. In the collection of stories from the 11th century Katha-Sarit-Sagara ( The Ocean that Contains Streams of Stories ), which collects traditional stories from India, the loquacious ghost of a corpse taken down from a gallows tells the king who took him off the macabre swing a very interesting tragicomic tale. Two friends undertook a pilgrimage to a sacred spa of the goddess Kali, and there they saw a beautiful girl. One of them fell ill with passion, stopped eating and sleeping, and was sure that he would die unless he could have that girl as his wife. His friend contacted her father and explained the situation. The father, hurriedly, went to the girl's parents in order to organize the wedding. Shortly after the hasty marriage, the young couple and her friend left for her parents' house. On the way, they ca...