Ever since Euclid came up with the idea of a set of axioms by which he could prove the truths of his geometry, early philosophers, followed by the rest of us, have been searching for a means of applying some form of axiomatic system by which, in combination with deductive logic,  hypotheses in other fields of knowledge could be absolutely proven. If this were possible, the hope was that, solely through our own reasoning power, we mere humans would be enabled to generate all possible truths.

Plato took up this challenge, concentrating his attention on what he considered to be the ultimate question--the very nature of reality itself. To bring attention to our faulty methods of thinking, he used the analogy of a cave where people were chained in such a way they could look only in a single direction to a wall upon which flickering shadows from the outside world supplied them with their sole source of knowledge other than what they might manage to generate in their own heads.

Plato's "prisoners in a cave" analogy was used by him to draw attention to the fact that we cannot guarantee that the concept of the reality of an object that we generate from our sensory perceptions is what that object really is. And, in fact, Plato thought that all the objects we perceive are actually imperfect and "less real" copies of master patterns which are unchanging and eternal.

Plato's "unchanging and eternal forms" are interesting to Urantia Book readers even in this hard-boiled age of a science founded almost entirely upon empirical observations. The Papers tell us that basically Plato was right, that all possibilities and potentials, both in transcendent and finite reality, are already in existence with the Absolutes of Infinity.

Apparently we deceive ourselves whenever we consider we have had an original concept. What we really have done in formulating our concept is to make a choice among the alternatives that come to us from the Absolute via the Supreme Being.

Presumably the pathway by which these alternatives are presented to us includes cosmic mind and the Adjutant Mind Spirits. This also means that Plato was not the originator of his proposal on "unchanging and eternal forms" but that it was his choice from the alternatives presented to his mind from an external source. Which may also be a contributing factor to why so many mathematicians believe that new theorems are not created by them, but are actually "pre-existent," and are discovered rather than created.

Plato and his pupil, Aristotle, had an enormous and long lasting effect on the thinking of the Western World. Aristotle was the originator of a system of logical thinking that became embedded in our culture. His three rules for logical thinking are given the names the laws of identity, contradiction, and the "excluded middle," symbolized as A = A; A and not-A; and either A or not-A.

All this seems rather simple, obvious, and logical, but quickly breaks down when we try to turn the laws into an exact means that will always generate the absolute truths of a system. For example, try writing down an infinite number and determining whether it is even, odd, or prime. Or decide whether the number "one" is a prime number, whether zero is a number, or to prove a number is equal to itself. And, getting away from mathematics, try to decide whether a photon of light is a particle or a wave or what are its speed and position. When we get down to the nitty-gritty, things are not so simple or so obvious.

For most of us, the primary and fundamental questions that stands out above all else are, "Does God exist and what is God like." Perhaps it is not surprising that philosophers and theologians have many times attempted to devise some means that would provide an answer.  In the West the best known of these goes by the name of the "Ontological Argument."

Ontology is a branch of metaphysics that studies being in general and the Ontological Argument is about the existence of God. The classical formulation is that of St Anselm in the 11th century and the classical refutation is that of philosopher, Immanuel Kant. Put crudely, Anselm argued that if the God who is the greatest does not exist, then a God who does really exist must be even greater and therefore must exist. Kant dismissed him on the basis of grammatical errors.

Anselm is also known as the father of  Scholasticism, a movement that utilized symbolic logic in a highly skilled manner over a number of centuries, and often for the justification of theological doctrines. Among the best known of the Scholastics are Thomas Aquinas, Duns Scotus, and William of Occam, the latter best known for the Occam's Razor principle.

Scholasticism eventually gave way to the empiricism advocated by Francis Bacon, Rene Descartes, David Hume, and others. Empiricism saw the demise of the dominance of "a priori" or deductive thinking and the rising dominance of the "a posteriori" or inductive method. The latter commences with an accumulation of empirical facts about a matter under investigation. From these, a theory is formulated but must be one which is open to further experimental testing. The whole process is then repeated until a satisfactory conclusion is obtained.

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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.