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.