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 ℤ +) for a given set, and two sets have the same cardinality if for a given machine their countable algorithms stop at the same time.

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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...

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Mythopoetics

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