# 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 | |||||||||

< | constructivism | < | real-, platon-, pragmat-, holism | - philosophical views | |||||||||

relative | undecidable | absolute/eternally | |||||||||||

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 | - Question about God | |||||||||||

formalism, deductivism, logicism | < | intuitionism | < | 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 | ||||||||

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.