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 18th 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 19th 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.
