On the Relationship Between Philosophy and Mathematics

In all my attempts to describe philosophical concepts, I have often resorted to using mathematical constructs, for example, I hold that the fundamental concept of God (the all-encompassing intelligence which transcends all existance) as a being that exists inside the Universe defies Logic. If God is Infinite Intelligence, and the Universe a creation of thought-power within that Infinite imagination, then to conceptualize God as creating the Universe around of instead of within Himself would a violation of Set Theory, since God himself/itself would be the Universal Set.
The fact that most philosophical theories can be mathematically conceptualized and demonstrated cannot be a mere coincidence. The Egyptian (and subsequently Pythagorean) definition of harmony as the union of opposites is manifest in both in Music (which is a form of applied mathematics) and the concept of odd/even numbers.
Perhaps the perfect backdrop for understannding the relationship between philosophy and math would be the 'Pythagorean' Cosmological Doctrine, i.e the idea that all things are numbers. Recall earlier the definition of harmony as the union of opposites. It applies to Music in that harmony is produced in any combination of notes (each of which can be assigned a mathematical value) whereby each note is a number of evenly spaced distances apart from the other notes in a finite set. From this we develop musical scales, then majors and minors, and finally chord progression.
The Union of Opposites is also found in masculine-feminine attraction. Men and women are attracted to each other specifically because of their diametrically opposed differences. The narrow-shouldered, wide-hipped, high-pitched woman is attracted to her 'numerical' opposite, the broad-shouldered, narrow- hipped, deep-voiced man. When men and women sing together, it is the differences in their pitch and tone that creates harmony. Men and women were meant to complement each other, not mirror.
It is no coincidence that in Plato's Republic, the speakers all agree that along with dialectic (logic) the guardians of the ideal city-state should study Music and Arithmetic. The three complement each other.
Philosophy is defined as a rational investigation into all reality in the light of first causes. Mathematics is the objective study of structure, change and space. It is a demonstration of causality, without the imposition of Time. The I-Ching, the ancient Chinese study of change, is perhaps the spirit of math in its purest form. It is a mathematical system whose thesis is that:

1) All things constantly change (similar to Heraclitus' Flux)
2) All things that change, change according to fixed, immutable laws.If philosophy is an attempt to discover the underlying nature of reality, and mathematics is composed of a set of symbols that, at their core, seek to quantify the Laws of the Universe, then mathematics represents nothing less than the 'proofs' of philosophy. It is the sentential logic which underpins ideas.It is the programming language of The Universe v.0, in much the same way that all software can eventually be reduced to binary code.