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,
Phenomenalism, Idealism
- philosophical views
 
relative   undecidable   absolute/eternally - Question about the truth
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   type 1 / question of existence paradox - Question about God
 
formalism, deductivism, logicism < intuitionism, constructivism < platonism - mathematical views
classical logic    intuitionistic logic, modal 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.

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