The limits of mathematics

Eclectic Copernican Three-world-doctrine

For all those, for whom the idea with the spaghetti monster is somehow unsatisfactory.
 

      Law of excluded middle     Law of noncontradiction
Descartes world < Hume world < Plato world  
 
nominal-, logic-, conventional-, reduktionism  < constructivism < real-, platon-, pragmat-, holism - philosophical views
relative   undecidable   absolute/eternally - Question about the truth
nonfree   transactionalistic   free - Question about the will
does not exist   mortal   immortal - Question about the soul
type 2 / question of existence impossible   type 3 / existence proven   type 1 / question of existence paradox  - Question about God
 
formalism, deductivism, logicism < intuitionism < 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
 
absolute
computability
< computability < simulatability < formalizability < +unformalizability - mathematical principles
 
absolute
    measurability    
<     measurability     < orderability < nameability < +unnameability - statistically principles
  Einstein GR   Turing HP [Penrose OR]       Gödel IT


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 a Archimedean point spans the realm of the Hume world. So the Humeworld 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 effective from a neutral monistic point of view.

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