Literary Discussions

Isaac Newton's physics could account for the motion of cannon balls but was inadequate for intergalactic and sub-atomic phenomena.

One NOVA special points out that the sub-atomic quantum world is so chaotic that even existence/non-existence is vague and yet the quantum world composes the planetary systems and galaxies which move with clockwork precision and predictable regularity.

"Model Theory" is the study of the extent to which some mathematical axiomatic system ACTUALLY resembles physical reality. Descartes coined the term "imaginary number" for the square root of -1 as a form of mockery because he did not believe that such a number could exist. But Maxwell's wave equations require the existence of the imaginary "i" square root of negative 1.  Around 1900 a convention of all the world's mathematicians convened to decide upon the great unsolved problems for the 20th century to tackle. One problem was "Fermat's Last Theorem" which was solved around the 1980s or early 90s by Andrew Wiles.  The four-color map maker problem (to prove that any map may created with only four colors) was solved around 1980s using a computer to prove many thousands of cases and from that generalized to all cases. 

But at that convention a great dispute arose between David Hilbert, who believed that any mathematical truth should be provable, and Kurt Godel, who believed that of necessity there must be some truths which are not provable in the context of a finite axiomatic system. David Hilbert's tombstone reads "We must know. We shall know."  Godel proved that Hilbert was wrong with the "Indefiniteness Theorem."

One problem is the self-referential aspect of any language, even mathematical language, which can suggest to us that something exists when in fact it may not.  It is meaningful to speak of a red flower or red lips or a red sunset but we come to the problem of qualia when we try to speak of "redness" as a thing-in-itself apart from physical reality. Plato had the same problem when he spoke of ideal, mathematical FORMS (Eidei) of things like Justice and Beauty which somehow cause pale shadows in our world of particular instances of justice or beauty.