It was not language that made man emerge from the animal kingdom, but mathematics.
Trialistic Cosmology
Syncretic Copernican (anthropodecentric) Three-world-doctrine
For all those, for whom the idea with the spaghetti monster is not completely satisfactory.
| Law of excluded middle | Law of noncontradiction | |||||||||
| Descartes world | < | Hume world | < | Plato world | ||||||
| conventional-, relativ-, reduktionism, functionalism, physicalism |
< | skepticism, constructivism |
< | platon-, pragmat-, holism, Idealism |
- philosophical views |
|||||
| relative | undecidable | absolute/eternally | ||||||||
| undirected | directed | does not exist | - Question about the time | |||||||
| nonfree | transactionalistic | free | - Question about the will | |||||||
| does not exist | mortal | immortal | - Question about the soul | |||||||
| type 2 / question of existence impossible | type 3 / necessary existence proven | - Question about God | ||||||||
| formalism, deductivism, logicism | < | intuitionism, constructivism | < | platonism | - mathematical views | |||||
| classical logic | paraconsistent logic, quantum logic, netzwork logic | |||||||||
| atoms, relations, sets | < | multisets, lists, trees, graphs | < | objekts, classes | - data structures | |||||
| unilateral signs (syntax) | < | bilateral signs (+semantics) | < | trilateral signs (+pragmatics) | - semiotics | |||||
As a good metaphor for the Three-world-doctrine works the Riemann sphere. The following equivalents apply to this:
Plato world = P(∞)
Descartes world = P(0)
Hume world = all P(x) for x ∈ ℂ \ {0}
The points x ∈ ℂ of the complex number plane are mapped to the intersection points P (x) of the lines through P (∞) with the number sphere on them.
Following this metaphor, one could say that the Descartes world P(0) as a kind of origin with the Plato world P(∞) as an Archimedean point together spans the Hume world. So the Hume world is the world we live in, but it would not exist without the other two. Compared to other Three-world-doctrines one could relate the Plato world to the world of the logos, but a separation between physical and mental worlds is not purposeful from a neutral monistic point of view. In a certain way, this three-world doctrine is probably a farewell to the hope to be able to find an intellectually honestly defensible world view with a compact and consistent basis. In this respect, it is also a synthesis of externalistic and internalistic theories or of Spinoza and Gödel, and as such, in a sense, a meta-religious system.
Mathematically, a Riemann sphere is a topological space and as such a compactification of the complex plane. By adding the ideal point P(∞), the infinite plane surface becomes a finite sphere. P(∞) represents in a certain way the infinity of the complex plane, and makes this by the compactification somewhat more controllable and more vivid.
