Epistemontological Paradox in Free Choices.
What exactly do we mean by the ‘existence’ of an object or event? Do we mean its physical identification and phenomenological description in real space time now and/or always? Or is it enough to rely on its probable metaphysical logic structure/function explanation when below the threshold of sensory resolution? Considering the relatively poor sensory resolution our human species brain is endowed with (as compared to other species), would you always rely on the truth value of the complex phenomenological description of any object/event? Or would you rather prefer the metaphysical logic explanation of the probable structure/function of any complex object/event as conditioned by the relevant circumstances surrounding the human observer and/or the observed/measured? If not yet satisfied, what if both approaches are hybridized as one epistemontological unit where the ontological moiety will only accept falsifiable observations or measurements by normal persons and the epistemological moiety is based on the appropriate mathematical logic deductive conclusions? Or would you rather settle for the inclusion of intuitionistic mathematics logic, possibilities and inductive logic approaches? This is the equivalent of asking if only the immanent quotidian experience is relevant in existential reality, or only the transcendental abstract speculations about a possible future is important or perhaps whether we should be existential realists and accept a compromise focused on the exigent circumstances and requirements of quotidian existential reality? To follow is a brief analysis of the seemingly paradoxical act of conscious free choices.
What level of cognitive awareness of reality is necessary and convenient to realize one’s role as a spouse, parent, neighbor, citizen, etc.? Charlie, my dog, does a wonderful job of our household security surveillance and has earned its living necessities of health, food, shelter, protection and conveniences of perks, toys, trips and love. How many of us would rather freely choose that seemingly ‘unchanging’ level of Sartrean existence because required adaptive changes are perceived as beyond our control? Nothing wrong if consciously and freely so willed. However, because of the self evident course of evolutionary changes, the Sartrean formula wouldn’t work beyond a few generations in obvious detriment to the species survival, unless we yield, like Charlie subconsciously did, and submit to the benevolent enslavement of your freedom. It became then the duty or choice for some historical few to prepare and plan for future changes sacrificing the ongoing ‘modern’ conveniences of having adopted a democratic, constitutional form of government with all the guarantees of freedom, healthy lives, psychic happiness and social cooperation (bps). This allows for the flourishing of all kinds of institutions and technologies whose aim is to maximize a bps equilibrium and keep all rules of law and analysis clearly spelled out inside a ‘safety box’ of standards that guide the ongoing generation. But generations evolve and the rules of law and the standards of social guidance need to keep pace with those changes. We need to, under the guidance of the immanent protocol inside the ‘safety box’, start thinking outside the box in the generation of transcendental rules of species survival today and the day after tomorrow.
The retired senior citizen may erroneously feel that, why change anything, ‘what has worked for my generation should be good enough for my grandchildren’. We have all witnessed the role information technology has played in fueling a psychosocial revolution in the non-western world. The new leaders have forged a new standard of biopsychosocial idealism based on metaphysical logic models a supercomputer can simulate. This conceptualization of the ideal leader of tomorrow is the brain child of the physical materialistic faith, mostly mathematicians and theoretical physicists. For them all of physical reality, the seen and the unseen, can be reduced to symbolic or sentential logic representations for computers to combine, permute, parse and bingo, there is the new probable survival map or kit for posterity to follow! Life under the new postmodern physical materialist cult will substitute the old dictatorial enslavement deeply rooted on inherited power and riches for the intellectual elites that fuels the monopolistic capitalism ambitions of exploitation of the underground few controlling all means of production. For the new intellectual underground combo -protected by the elected ‘politicians for sale’- adopting new and convoluted symbolic abstractions just adds new computer tools of analysis. Unfortunately, the premise of a robotic ‘living computer’ controlling the human decision making process is delusional if we bother to pay more attention to the real nature of the human species at random and not at the mostly self indulging prophets in the intelligentsia of think tanks of the few ‘Mega/Giga societies’. Actually, as it turns out, thinking outside the established physico-mathematical box standards and incorporating the real space time emotional human being existing in quotidian, ongoing reality as part of the standard model equation -as some try in developing and constructing an intuitionistivistic mathematical logic- requires abandoning the comfort of reviewing the familiar and adding another dimension of intellectual activity because it requires getting rid of the crutches supporting our standard views. The ‘bps’ approach demands practically modifying just about every aspect of our theoretical foundations, from methodology, theorems to technical vocabulary. Are the scholarly professional scientists, academicians and philosophers ready for the constructivism difficulties anticipated with its stricter notion of proof? One needs not deny the value and strength of the ‘standard proofs’, on the contrary you need to point them out and prove that you can provide a more credible functional solution by partially ignoring the standard proof as specifically relevant. One common point of disagreement is the mathematician’s insistence on not having to be concerned as to whether an ‘existing mathematical object/event’ has a physical reality or not, regardless of it being beyond instrumental sensory threshold to describe or not. I submit that it is possible to find algorithms compatible with both the alleged universal classical standards and the realistic intuitionistic approach suggested by our ‘bps’ brain dynamics model. It should not be surprising to witness the occasional low brow street brawl enacted by fundamentalist religionists of the theosophist and physical materialistic indoctrination/persuation when they ‘analyze’ the mathematics of the Axiom of Choice (AC) principle.
Needless to remind the readers that in a cosmology controlled and ruled by a mathematical logic, there is no reality or ‘intelligent design’ other than that phenomenologically measured or the result of a metaphysical logic parsing among symbolic/sentential logic representations. This leaves no room to accommodate relevant, falsifiable and complex subjective experiences that resist being symbolically framed for deductive mathematical analysis, i.e., anything beyond this ‘objective’ threshold is a ‘mathematical object’ with no conceivable physical reality where its phenomenological subjective manifestations just ‘emerge’. This is the equivalent of the radical theosophy and their subjective convictions by faith alone that violate all of natural laws, e.g., particulate matter can emerge into ‘existence’ from a ‘vacuum’ or we can gain information from an ever-receding linear infinity. Nature abhors both the vacuum and infinities just like it does when conveniently ignoring the physical presence and relevance of the complex human brain in the decision making process. This does not mean that the ‘standard’ positions are as probably good as they will ever get to be even when we make allowances for our intrinsic brain dynamics sensory and cognitive limitations. But, there is no good reason to stop searching for answers to refine on either of these extremes cosmologies or propose a new one. Is it not obvious that the truth worth of a mathematical statement can only be conceived via a physical brain constructive effort that proves it to be true or not? What else, besides the phenomenologically experienced seems to say my dog Charlie Boy with his own psychosis of curiosity as he inquisitively stares deep into our also curious eyes.
To elaborate further on the example, consider the standard abstract contrivance/notion of an absolute non-empty set containing a collection of all non-empty sets which ‘logically’ cannot contain itself. Since our human species cannot yet prove or disprove the existence of open ended infinities or absolute vacuums, we can consciously and intuitively choose to ignore the classical proof and invoke the convenient abstract concept of a transfinity (a perfectly logical probability space time coordinates between infinity and finiteness in spite of the lack of verifiable space time coordinates), so long as it is consistent with mathematical logic and allows for phenomenological predictions of corroborated behavioral experiences or measurements. Iff necessary or convenient one may even choose to assume that there ‘exists’ a common denominator to all sets to suit my intended other conclusions, crazy things like, if nothing better, all subset members of the set have minimum and maximum dimensional values! Comparing any two invisible physical particles r, s either:
Likewise for any three particles r, u, v either:
if u u or r < v
After all, in our human 4-d mesoscopic real space time world any application ultimately must rely on only finitely many measurements or falsifiable experiences. This is what always happens in applied real time mathematics. What must be remembered is that there is a commitment of the intuitionist mathematician to construct not for self indulgence but should always imply a search for the honest probability to find the physical reality embedding the abstract intuition.
As a closing argument in this brief non-technical exposition we’d like to dwell on the mathematic purist’s classic insistence on the absolute truth value of their proof of the Law of the Excluded Middle (LEM), which quite convincingly states that P ‘things’ cannot simultaneously physically exist and not exist ("P or not-P" for every logical proposition P, A∨ ¬A ). Who would dare challenge that tautology of classical logic based on a metaphysical abstraction divorced completely from the self evident facts about the brain dynamics of human beings spelling out its cognitive limitations in the ontological perceptual and epistemological conceptual domains of discourse? What is the rationale behind exclusively investing on the absolute truth of mathematical logic abstractions premised on often convenient, and admittedly convincing axioms like LEM? The problem arises from the average observer ignoring the physical reality of a human brain as the main player in co-generating an introspective self search for his identity made possible with the evolution of a language faculty as amply discussed and analyzed elsewhere.* There is a fundamental difference between the role practitioners of professional areas play, e.g., lawyers, clinicians, engineers, etc. in providing real time functional answers to immanent problems challenging the very biopsychosocial equilibrium of real time humans as opposed to the universal goals armed chair academicians, researchers, philosophers have their sights on. Are there two different logics the Sartrean relativism or the radical physic materialistic abstractions? The paradox consists in having both logical approaches simultaneously coexisting in the same individual able to engage in deep self introspective but conscious dissociation of immanent emotional self and a transcendental rational self! To harmonize these conflicting strategies we prefer the hybridization strategy of bridging both into an epistemontological existential unit incorporating the best parts of both. We all work best within the set of axiomatic tools we have consciously chosen. Thus the mathematical purists depend more on the symbolic representation of language statements whose truth is validated by a set of standard axiomatic logical rules as opposed to procedural constructions functionally validated within specific different logic rules for combining the statements, some of which may not even be computable.
The best example of an attempted reconciliation of an informed but ineffable intuition and the tempting truthfulness of LEM was the attempt by L.E.J Brouwer to incorporate the existential experience of physical ‘change’ as monitored by a physical human brain into the metaphysical logic symbolism of mathematical abstractions. He concluded in mid 20th. century that mathematical symbolic representations are convenient creations of the mind (we call it the brain) structured for marketing communication purposes among colleagues.
A nutshell, one has the conscious choice of adopting one of two conflicting intuitions about ongoing real time change, either particulate matter is changing, e.g., integrating discontinuous invisible physical particles into visible sensory realities as falsifiably experienced when a cell (a) divides and forms a visible organ (b) or is continuous as our brain also experiences it? Which intuition is correct? The cell (a) is very different form same cell (a’) ready to divide by mitosis. Ergo, if (a) then (not a) = (b). Likewise, the human brain, unable to phenomenologically distinguish (a) from (b) retains in living memory the (a) he experienced even when it can be proven otherwise it’s no longer there! The invisible change produces the living experience of continuity. Until we reach the potential of a physical description or falsifiable observation experience of change, there is no choice but to affirm the truth of the existential realism, however wrong it may all turn out to be in the future generations, if ever. Which of the two paradoxical intuitions would the reader adopt? Is particulate discontinuous quantum particles more credible than a continuous reality? Could there be a receding physical boundary we can feel comfortable when adopting the abstraction of a set of all sets in existence or do we prefer to adopt a boundless infinite reality poem? What about the equivalent probability of a reciprocal information transfer between transfinite coordinates in n-1 d space time and premotor neocortex phase space mediated by dark baryonic DNA/RNA receptor as posited in our bps model. We even suggested a submodel of a cooperative transfer involving EM and gravitational procession that remains unchallenged? An expansion on the limitation and possibilities of this approach we invite read: http://plato.stanford.edu/entries/intuitionism/#TheCon
SUMMARY AND CONCLUSIONS.
For the benefit of more specialized readers we quote from Stanford Encyclopedia of Philosophy.”
“The existence of the natural numbers is given by the first act of intuitionism, that is by the perception of a move of time and the falling apart of a life moment into two distinct things: what was, 1, and what is together with what was, 2, and from there to 3, to 4, … In contrast to classical mathematics, in intuitionism all infinity is considered to be potential infinity. In particular this is the case for the infinity of the natural numbers. Therefore statements that quantify over this set, such as (∃n A(n) ∨ ¬∃nA(n)), have to be treated with caution. On the other hand, the principle of induction is fully acceptable from an intuitionistic point of view………Thus in the context of the natural numbers, intuitionism and classical mathematics have a lot in common. It is only when other infinite sets such as the real numbers are considered that intuitionism starts to differ more dramatically from classical mathematics, and from most other forms of constructivism as well..”
Dr. Angell O. de la Sierra, Esq. In Deltona, Florida Early Winter 2013
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