Using Self-Dual Lattices in Two-Dimensional k-Space for Self-Triality:
Fides in Anti-Realism

by
Dallas F. Bell, Jr.

(This paper was accepted for presentation at the conference "Perspectives on Political Science and Gender" organized by the International Political Science Association research committee 33, the study of political science as a discipline, during December 2013 in Helsinki, Finland.) 

Abstract:  Across the spectrum of political science there is a diversity of ideas.  Many of these ideas conflict and are not conducive to social and academic unity in an ever increasing global community.  The tool of self-dual lattices (Xiaoping Xu) is presented in two dimensions—eternal and temporal.  In physics, that space is mathematically identified as k-space.  This comparison of realities allows for a self-triality (R. Shankar) of ideas.  The fields of analytical and moral philosophy acknowledge the belief of anti-realism (M. Dummett).  Problematic anti-realists views of ethics (N. Chomsky and S. Žižek) are analyzed by the proposed visualization tools.  This process also aids in the development of a pragmatic philosophy model for meta-ethics (S. Blackburn) which can systematically unify aspects of truth in philosophy (Plato, Aristotle, R. Descartes, B. Spinoza, G. Hegel, and A. Rand) and political science.  As the concern of freewill (H. Ravven) and subjectivity by anti-realists is highlighted (D. Brink), fides is shown to be necessary for interpolating gaps in knowledge of finite abilities of humans.  This streamlines answers to the common questions of what are the standards for good and what is in the public's best interest.  In accordance with neuroscience, teaching methods and societal policies can be pursued with confidence and implemented.

Keywords:  self-dual lattices, k-space, self-triality, anti-realism, fides, systematic philosophy.

In group theory mathematics, a lattice is a discrete subgroup which spans the real vector space.  Physicists use the reciprocal lattice of a lattice where the Fourier transform of the spatial wave function[1] of the original lattice is represented.  This space is known as momentum space or k-space.  Two-dimensional lattices may be oblique, rectangular, rhombic, hexagonal, and square.  For our purposes we will focus on the square as seen in the figure presented later on which shows an eternal perspective and temporal perspective of the same entity for a self-dual contrast.[2]

A natural extension of self-duality is self-triality.[3]  If we map the eternal and temporal attribute of non-material concepts, such as love, mercy, justice, etc., we can test their reality by the observable consequences of compliance with them or non-compliance with them.  Finding real effects tells us that those attributes have undeniable finite standards based on infinite standards.  They are the substance that intellect must use for a chosen behavioral standard that provides purpose.  That choice is often referred to as morality which is not illusive, simply temporal, or ignorable without causing real consequences.

FIGURE.  This is a two-dimensional self-dual lattice (e.g. love, mercy, justice, etc.) in k-space.  The straight x and y axis lines represents eternal truth vectors of a specific concept (e.g. love, mercy, justice, etc.).  They are dotted to signify how each concept is infinitely interrelated, such as love, mercy, and justice, etc. require omniscience to understand the ellipsis and act with perfect wisdom—holiness.  The wave x and y axis lines represents finite, fuzzy, and temporal understanding vectors of the specific concept.  Dual comparisons can be made.  The connected wave boarder represents how anti-realists accept the position outside of a specific comparison.  The position is formed by necessity and pulled around the truth by the gravitational force of eternal absolutes.  It is circular reasoning[4] which is never able to reach a truth and can not result in advancement of knowledge.

Identified morality can not be replaced or substituted by any behavioral option other than its lowest standard, such as being unloving, unmerciful, unjust, etc.  That choice becomes the standard for immorality and evil when juxtaposed with the perfect eternal standard of good.  Of course, love, mercy, justice, etc. must be balanced with each other (e.g. to be perfectly merciful and perfectly just requires omniscience from omnipresence and wisdom from experience with a will to implement them).  Finite humans can't have completely perfect knowledge, wisdom, will, etc. and, thus, can not nor will not achieve the perfect eternal standard.

The eternal non-material aspects of intellect can only be accurately defined as absolutes.  Love, mercy, justice, etc. require faith by finite intellects to implement.  This is witnessed each day as numbers are used by people in mathematical operations even though all numbers are not comprehended by them.  Subsets of numbers from the infinite set of numbers are used to accomplish their purpose.  Just as basic numbers imply other things (i.e. adding, subtraction, etc.), non-material absolutes imply other things, such as forgiveness, redemption, grace, charity, loyalty, honesty, honor, patience, etc.[5]  Those items of morality are innately recognized as beautiful and craved for consoling human need.[6]

Real things have a nature whose characteristics show the essence of entity where knowledge is created and truth found.  Edmund G. A. Husserl's (1859-1938) eidetic intuition or essential intuition shows how we are able to grasp the possibility and impossibility, necessity, and contingency among formal categories and concepts. Categorial intuition, categorial abstraction, and essential intuition are considered the basis for logical and mathematical knowledge.

Fides or faith becomes a real shield against the assault on absolute standards by untruth.[7]  Without patience faith can not grow.  Faith is not passive, but is rewarded by relieving unhealthy stress from cognitive dissonance.  Faith is an active pursuit of complete eternal truth.[8]  Truth must be defined as what is eternal reality.  Truth explains and so points to the Divine infinite intellect of truth.  What is real is also true.  Aleksandr Solzhenitsyn (1918-2008) observed that the more untrue beliefs are forced against true beliefs[9] the resulting extreme contrast of consequences[10] will produce a stronger faith in the true beliefs and a weaker faith in the untrue beliefs.

Western philosophers, since Plato (429-347 B.C.), have associated truth with stability and eternity as a guarantee of stability.  In Plato's Euthyphro, he said God either does good (is holy) because He does it or He corresponds to what is already good (and holy).  This is not "P" –or- "not P" logic and is a false dilemma.  It is more accurately argued that God is good (and holy) and so does good (is holy).  Baruch Spinoza's (1632-1677) absolute as God can be deconstructed into nihilism.  He implied God only exists through finite nodes and neither reality would appear real.  Usually the stability of truth is underpinned by an eternal infinite Creator.[11]  How then does rejection of this transcendent Being affect the view of truth?

William Shakespeare (1564-1616) wrote in Macbeth (Act 5, Scene 5) that "life is a tale told by an idiot, full of sound and fury, signifying nothing."  His moral philosophy describes moral anti-realism.  A realist holds that x (love, mercy, justice, etc.) exists independent of neurological existence in one's mind and anti-realists reject this thesis.  Their views include moral non-cognitivism, moral error, and subjectivism.  They believe that moral judgments do not aim at truth (moral non-cognitivism), even if they do aim at truth they fall short (moral error), and they believe moral facts only neurologically exist in the mind (subjectivity).

In analytic philosophy, anti-realism, a term attributed to Sir Michael Dummett, describes a position that denies objective reality or an entity as either true or false.  This implies that we should begin as tacit moral realists.  David O. Brink wrote (1989) that realism should be the meta-ethical starting point.  If anti-realism were defined as healthy normal skepticism of new knowledge or contradicting evidence of old knowledge, this would be realism.  Anti-realism must be more than mere skepticism.  It must be a position by faith that is anti-real which is epistemological nihilism.

The notion that anti-realism is expected to be accepted as real is self-defeating in that it is subjective by anti-realists' own definition.  Anti-realism can only exist if there is first realism.  The anti-thesis or counterfeit of anything only exist if there is first an original.  Again the anti-realists' position defeats its own assertions.

On the matter of anti-realism in linguistics, Noam Chomsky, linguistics professor at the Massachusetts Institute of Technology, doesn't know of much discussion. Working linguists, he supposes, tacitly assume, like physicists, that there are real entities in the world that correspond to theoretical posits like phonemes. There are debates on grammatical constructions. Some scholars think that they are real entities. Others, of whom Chomsky considers himself one, think that they are artefacts, and that the real entities are the underlying principles that interact to yield the superficial appearance of constructions.[12] 

Chomsky is opposed to scientific theories that are not empirical, such as those by Slavoj Žižek who is a senior researcher at the Institute for Sociology and Philosophy, University of Ljubljana, Slovenia.  Žižek is an atheist and communist that has said Hitler was not violent enough.[13]  Edmund Husserl did not limit understanding to empiricism.  He believed that experience is the source of all knowledge and worked on a method of phenomenological reduction which a subject may use to directly know an essence.  Existentialists believe that human experience is more important than abstract reasoning when searching for truth.  If one is an anti-realist then everything is existential.[14]

Temporal material aspects of reality are used to touch eternal non-material realities (love, mercy, justice, etc.).  This is much like a golden crown submerged in a container of water displaces a measurable volume of water that indicates the size of the crown.  Faith is the substance of things hoped for and the evidence of things not seen.[15]  To exchange information when communicating requires realism and ethics.  The idea of anti-realism is information, and if true is not to be accepted as true.  This means that every one's truth is equal and making up truth is a valid method of communicating and debating.  Lying would be legitimized. 

The Apostle Paul, a doctor of law and rhetoric, warned that it is not generally profitable to engage anti-realists and relativists in debate.[16]  Contrary to absolutists, anti-realists or relativists[17] rationalize formal debate as separate from public speech, which is opinion in their opinion.  They believe gamesmanship is applied to argumentation as a game that has special rules that require the debater to develop the best possible case for their side regardless of their personal opinion.[18]

A discussion can not be agreed on if there is no real agreement on real truth for an answer.[19]  The answers to the questions on college entrance exams and exams themselves would be equal for anti-realists.  If all views are equal, they are ultimately both true and untrue at the same time ("x" and "not x").  Love and unloving, mercy and unmerciful, just and unjust would be the same rendering the antecedent words redundant.  This is why anti-realists, historically referred to as fools,[20] must be physically corrected for their behavior that violates material and non-material natural laws.[21]

Recent World Universities Debating Champion, Yoni Cohen-Idov has observed that it is difficult to divide debaters into the two groups of either relativists or realists.  He assumes on most issues that debaters are generally somewhere in the middle.  Debating requires prominent participants to have a wide range of perceptions that they may be arbitrarily obliged to genuinely defend.  That being the case, he says relativists, who do not subscribe to one paradigm, would likely have an advantage over a realist that may be required to defend a position they know to be untrue.[22]

It is reasonable argued that natural law must be inerrant,[23] which is consistent with being the laws of God.  Materially, we know that weeds grow in a garden without being planted there but contribute to a healthy environment.  Non-materially, we know that young children do not have to be taught to lie or steal but need to be taught to use freewill to choose attributes of repentance and forgiveness.[24]  Those examples show how natural laws are understood as inerrant when an understanding of them is more complete.  They are a compelling force seen in the material orbits of electrons and non-material moral restraint in love, mercy, justice, etc.  They are definable and real emanating from an inerrant Compeller Creator.[25]    

The tetralemma is a reference to the idea that there are four logical possibilities to a proposition x: true, not true, both true and not true, and neither.  The possibility of being both true and not true is from the Dignāga-Dharmakīrti Buddhist school.[26]  This teaching is from the tradition of Nāgārjuna (c. 150-250 A.D.), a Buddhist philosopher.[27]  His "either-or" or "both-and" beliefs are reducible to "either-or" nullifying the "both-and" option.

Moral objectivism is no less real than the physical world in existence and consequence.  This explains why Eastern Buddhists' ethics is turning toward Western Judeo-Christian meta-ethical realism, such as with the Yogācāra school,[28] just as Western philosophers are turning toward the anti-realism of the east--Anathema.[29]  As was noted earlier, the anti-realists' position is a necessity for people that have a blind faith that is anti-Creator and anti-transcendent.

Common features of philosophical method include: methodic doubt of the truth of one's beliefs, argument supporting a solution to the doubt, and dialectic presentation of the solution by argument before critical philosophers that assist in judging the merits.  This whole process is technically useless for anti-realists.  Their views prevent development of systematic sciences and philosophy.  Widely known systematic philosophers are Plato, Aristotle (382-322 B.C.), René Descartes (1596–1650), Spinoza, Georg Wilhelm Friedrich Hegel (1770-1831), Ayn Rand (1905-1982), etc.  John McCumber, a distinguished professor of Germanic Languages at the University of California at Los Angeles, recommends the introduction to Hegel's Phenomenology of Spirit as a classic example of systematic philosophy.[30]

Nicholas of Cusa's (1401-1464) On Learned Ignorance is recommended by Clyde Lee Miller, professor of philosophy at Stony Brook University.[31]  Cusanus wrote that knowing God was not possible by mere human means.  He and George Washington Carver (1864-1943) believed that knowing the Creator and His creation required asking the Creator and then waiting on His subsequent revelation.

The ancient Hebrew King, Solomon, wrote that mercy and truth purge failing the eternal standards and by fear of the Creator men depart from those evil failings.[32]  The Creator has imputed eternal truth into our temporal reality and we view it with fuzzy human standards.  Solomon also said those people that keep understanding will find good.[33]  Understanding is a prerequisite to knowing good and evil and how to process experience and knowledge.  Defining good and evil first requires defining purpose which first requires defining the ultimate authority.

There is an old fable that demonstrates the human inadequately of understanding.  A variation of the tale begins with a boy getting a horse for his birthday.  The villagers agreed that this was good.  The theologian said, "We shall see."  The horse threw the boy and broke his back.  The villagers agreed that this was bad.  The theologian said, "We shall see."  Military officers came to the village and took all the boys to war except the boy with the broken back.  The villagers agreed that this was good.  The theologian said, "We shall see."

Simon Blackburn, retired professor of philosophy Cambridge University, says it is generally agreed among philosophers of science that there is no model or algorithm or recipe for finding a new theory.  It takes imagination.[34]  Meta-ethics[35]  explores the connection between values, reasons for action and motivation by asking what moral standards provide the reason to do or not do something as well as the nature of freewill and moral responsibility.

Doron Shultziner, member of the faculty of medicine at Tel Aviv University, wrote in his 2013 paper Genes and Politics: A New Explanation and Evaluation of Twin Study Results and Association Studies in Political Science[36] on how premature the attempts are to associate political tendencies with specific genes.  He recommended the 1997 twin studies by N. Martin et al. in Nature Genetics and the 1986 writings of the Proceedings of the National Academy of Sciences of the United States of America.[37]

Conversely, Heidi Ravven, professor of religious studies at Hamilton College, wrote in her recent book titled The Self Beyond Itself: An Alternative History of Ethics, the New Brain Sciences, and the Myth of Free Will that Spinoza and neuroscience argue against free will.[38]  Spinoza's view was that things seen as good and evil were simply good or bad for humans in this deterministic universe.  With self-dual lattices in k-space it can be seen that it takes finite minds with freewill to value something more than something else.  However, in eternity one thing is infinitely better than something else as valued by omniscient intellect.

Humans have emotional feelings of guilt from breaking moral absolutes or law (to love, to be merciful, to be just, etc.) which is doing wrong and not good.  Shame is not just a result of breaking absolutes and should not be confused with guilt.  Today, shame is largely defined as the result of an accepted failure of not living up to one's own standard (i.e. not feeling smart due to receiving a perceived low test score, etc.) or another person's standard(s) (i.e. not feeling pretty after a parent or teacher says we are ugly, etc.) which may be independent of absolutes.  These negative experiences produce the false feeling of not being worthy of love, mercy, justice, etc.  A person with guilt recognizes their freewill in having done something contrary to eternal absolutes, which is acknowledged as bad.  Whereas, someone with shame may be exhibiting that they themselves are bad independent of absolutes.

In looking at the (material) human mechanism as opposed to the (non-material) freewill agency of humans, there are three neurotransmitters that are prominent in adolescent (student) development: dopamine (controls movement, emotional regulation and ability to experience pain and pleasure which are low in adolescents resulting in mood swings and emotional control problems), serotonin (regulates mood, anxiety, and impulse control which are low in adolescents resulting in a decrease in impulse control), and melatonin (regulates the circadian rhythm and sleep cycles which are also low in adolescents resulting in a need for more sleep).

Longitudinal MRI studies of the human mechanism show a second surge of neuron growth in the brain just before puberty.  This surge reflects the one seen in infants and results in a thickening of gray thinking matter.  Rewiring of the brain continues into the 20's, especially in the prefrontal cortex responsible for executive decision making.  The two mechanisms for rewiring are pruning (cleaning out unused synapses) and myelination (covering neural connections with a fatty coating of myelin to speed up conduction of nerve impulses).[39]

The adolescent (student) brain is plastic and adaptable to experience.  In The Republic, Plato said the highest goal of education is to teach the knowledge of good.  Hitler is quoted as saying that he wanted to raise a generation of young people devoid of conscience, imperious, relentless, and cruel.[40]  The Earth First founder defined good as behavior that he perceives benefits the Earth, meaning anything he does not perceive as benefiting the Earth he deems as evil to be stopped.

Neopythagoreansim, parallels Neoplatonism (Plato doctrine) and is named for Pythagorean doctrine, promoted the non-material elements of numbers.  The reality of the non-material is evidenced by their being modeled with material examples, such as lattices presented heretofore.  The material model(s) can be seen as having come from the preexistent non-material entity.

Christian realism is a philosophy promoted by theologian Reinhold Niebuhr (1892-1971).  He argued that horrific/sinful events, such as the Holocaust, prevent a Kingdom of God being possible on Earth.[41]  Ideas to the contrary are merely a Promethean illusion.  Charles Jones, teacher of international relations theory and Latin American International Politics at the University of Cambridge, has suggested that International Law and normative theory presuppose Christian ethics despite the edifice of secularism that seems to pervade International Relations Theory.[42]

Aristotle wrote in his Ethics that government should act in the public's best interest or good which is related to justice.  We can find what is universally good by testing options with self-dual lattices.[43]  Either by accepting the truth of eternal realities as standards for temporal realism or rejecting them for a disproven anti-realist and anti-truth position,[44] each choice[45] acknowledges their reality and points to their faith of acceptance.  Teaching methods and societal policies based on absolutes can be prioritized and pursued with confidence as they are implemented to trusting students.