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An aid to this method, the scientific method, is Occam's Razor that demands the elimination of all unnecessary hypotheses. In other words, "keep it as simple possible" is the guiding principle.
From its beginning, empiricism was accompanied by the growth of materialism, the two together attaining their zenith of popularity towards the end of the 19th century. Although still dominant, these two philosophies commenced their inevitable slide as their foundations commenced to crumble.
Basic to scientific empiricism was a reliable mathematics. Things had looked good in the late 19th century with the publication of a brilliant work by maths genius, Gottleb Frege that had appeared to unite symbolic logic and mathematics. At last the dream of a certain method by which hypotheses could be accepted or rejected seemed to be in sight.
The first volume of Frege's two volume work, "Die Grundgesetze der Arithmetik" was based upon a system of pure logic and set theory. It was published in 1893, and received the accolades of his peer group.
The second volume was due to be published in about 1901, and was actually in press when Frege received a note from mathematician and logician, Bertrand Russell, pointing out a paradox affecting the fifth axiom of Frege's work that made the whole system inconsistent. Poor Frege immediately acknowledged the validity of Russell's point and added a note to his second volume stating the whole of his work was useless.
Apparently Russell thought there was a way around Frege's difficulty and, in collaboration with mathematician, Alfred North Whitehead, in 1911 produced "Principia Mathematica" which was then thought to have placed arithmetic on the same firm axiomatic foundation as Euclid's geometry. "Principia Mathematica" had a twenty year reign before being demolished in 1930 by Austrian logician, Kurt Godel.
Whitehead and Russell had hoped to establish a system of axioms and rules of deduction that were both consistent and complete. A system is consistent if contradictory statements cannot be derived within it; a complete one will generate all its true statements.
Godel proved that no finite consistent set of axioms can ever be complete. No matter how many more additional axioms are added to correct the deficiencies, there will always be at least one true theorem of the system that cannot be proved. Thus the consistency and completeness of arithmetic is forever unprovable. So if there are any proofs anywhere, they lie beyond logic, the axiomatic method, and arithmetic.
It transpired that, although today Godel's work was acknowledged as correct and a work of fantastic genius, it was also so difficult that initially few were aware of its existence. When it was shown to Bertrand Russell, he immediately recognized its correctness. However, it was not until considerably later that it became generally known and accepted.
In the meantime, mathematicians and logicians had agreed that Georg Cantor had been able to formulate a framework of set theory that appeared to serve as a foundation for mathematics. However this state of affairs came to an end in 1963, when Paul Cohen used Godelian methodology to do to set theory what Godel had previously done to axiomatic arithmetic. Since that time, it has been generally agreed that the illness is terminal. Full, formal, and certain logical proof is beyond the scope of us mere humans.
What then do the Urantia Papers tell us? "In the mortal state, nothing can be absolutely proved; both science and religion are predicated on assumptions. On the morontia level, the postulates of both science and religion are capable of partial proof by mota logic. On the spiritual level of maximum status, the need for finite proof gradually vanishes before the actual experience of and with reality; but even then there is much beyond the finite that remains unproved." (1139)
The first sentence of the Urantia Paper's statement has the stamp of having been written by someone familiar with, and competent in, formal logic. If made prior to 1935, the time of receipt of the Papers, the person making it surely would have also needed to be familiar with Godel's incompleteness theorem, hence must have been one of only a handful of experts, possibly none of them being then resident in the USA. By 1955, the time of first printing of The Urantia Book, the group of experts familiar with Godel's work had hardly expanded. Use logic to draw your own conclusions, realizing, of course, that a formal proof for your conclusions is impossible for us mere mortals.
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