Unsolvable Problems

The Unsolvable Problems, while bringing Hilbert, specially Functional Analysis, specially Spectral Theory have impact into Quantum Physic, Gödel Incompleteness Theorem, the fact is very complicated, began very early in the 18^th Century.

Russell and Whitehead in Principia of Mathematics wanted to bridge Mathematical Logic to Philosophical Logic, to achieve; they propose using axioms, inference rues and symbolic logic.

In the 19^th century the Italian Peano propose an Arithmetic (Dedekind–Peano axioms), to show natural numbers are consistence and completed, this assumption was fundamental for Russell and Whitehead,  Gödel dealt with the fundamental structure in mathematics deal with a stamen can be consistence, but more fundamental the method to show consistencies has been a disagreement between Cantor and Kronecker the later was a nomalist, meaning Mathematics needed to be deductive, where for Cantor (due to the Politics had a nervous breakdown—Cantor Continue Hypothesis Gödel in 1944 and Paul Cohen 1963 implied can´t be proof or disproof using Zerleno-Fraekel set theory ) inductions was the system to show consistence, this difference has not being resolved.

Russell project was never completed or recover from Gödel (an irony since Gödel was Platonist, since he believe the all truths of Mathematics existed in abstract).

 Baum and Wieck in their book on Logic, 1974 state the formal logic used in Philosophy is created in the context, Nietzsche reasoning was influenced by Afrikan Spir: Denken und Wirklichkeit and Afrikan show a logical dependent on context.

While Science used mathematics and indirectly used logical systems, as Wootton in the Invention of Science (2015), what we call the scientific method was driving by verification, Aristoteles in physics using logical reasoning propose the Democrious (Atom could not be Possible—against reason). The Greek Astronomer Aristarchus of Samos at 3Century BCE, propose Heliocentric model the only surviving Book, On sizes and distance between the Sun and Moon calculated the actual sizes of the Sun and earth, short time after Earatosthenes calculated the radii of the earth, but this model was not well receive due to Aristotle’s view of the Cosmos.

Spinoza Natura naturans (Ethics proposition 29) is passive, while we interpreted nature, beautiful models does not verified, the verification is only experiment can be verified.