Philosophy of Mathematics

(by Dlanorrenrag*)

Philosophy of Mathematics:

May some higher force, essence, or holism be expressing the bodies of each of us, with identifiable perspectives, as mere placeholders in some grand mathematical formula?

Perhaps, empirical investigations may lead us to derive some grand mathematical formula for unifying an understanding of all parameters that govern our physical degrees of freedom.

Perhaps, we may derive such formula even though Heisenberg’s uncertainty principle limits our investigations in physics and Godel’s incompleteness theorem limits our investigations in mathematics.

Even so, no mathematical formula that we can derive will predict or control all assignments under every degree of freedom.

If there is no model available to us for all that exists other than all that exists, then our mortal mathematics cannot model the completeness of all that exists. Perhaps, the only model for our universe is our universe. Mathematics cannot explicate a unifying formula or thing from which mathematics itself is derived. Mathematics in itself cannot account for itself.

For mortals, mathematics leverages our powers for relating among relatively measurable perspectives. That is, mathematics does not measure the whole of our universe or existence, except from such perspective as may be available to each locally sensate or sentient perspective or conversant.

The measurable potential for each perspective may continuously change, increase, or decrease in respect of whatever changes, increases, or decreases in limits may come to govern the horizon or frame of reference that is available to each perspective’s assigned position and duration in space-time.

We do not bootstrap any expression of an assumption into non-trivial “truth” merely by assigning an equality sign to both sides of a tautologically implied assumption that we have accounted for all significant factors.

Mathematical conceits especially lead us into “soft science” fallacies, such as about “rationality” of aspects of economics, politics, psychology, and morality.

We model mathematics for such “sciences,” even though, intuitively, morality and purposefulness may be beyond mathematics. After all, who can judge which among many possible events is truly most moral, best, or most conducive to overall long term pleasure, happiness, pragmatism, or civilizing purposefulness?

We experience pricing fluctuations in homage to “our marketplace of products and ideas.” Thus, we may “objectively deem” prices thereby expressed as being representative of our actual values. Yet, we also may subjectively intuit or come to appreciate that our actual values vary widely from whatever may be the prices assigned.

Often, we base or derive calculations and formulas upon assumptions that unspecified, unassigned, unconsidered, unanticipated, unknown, or unknowable factors or parameters are insignificant to our intuitions, purposes, or measurements.

We make our calculations as if apparent discretes (particles) must be manifestations of interactions among continuosities (waves). In searching for ultimate discretes, we tend to employ a calculus that assumes ultimate continuosities. We do this with no way of knowing, in respect of any ultimate truth, in what ultimate extent or quality we may be mixing apples with oranges.

Fundamental aspects about which we act as if we may measure and assign values seem to encompass inherent uncertainties, ambiguities, or paradoxes, making it difficult or impossible for different observers or conversants to communicate or consider precisely the “same thing.”

Even so, becoming conversant with mathematical conventions may help one presume to levitate upon airs of superiority.

Yet, being human always necessitates more than empirical rationalism. It also necessitates moral intuition.