unite without confusing ▪ discern without excluding
analytic logic. The science of the principles that govern the physical object experienced as a finite individual, having at one time a unique determination or contradictory determinations and at different times consecutive determinations. The farther of analytic logic is Aristotle.
Analytic principles are the principles of reflexive identity, contradiction, excluded third, and temporal (irreflexive) order. The cognitive faculty of analytic principles we call understanding. Are analytic principles real or apparent, natural or artificial principles of the physical object?
artificial. That which is unnatural or non spontaneous, and depends upon external cause and force for its existence and motion. The artificial is ephemeral and its fate is death. The end of the artificial is the natural. For instance, the end of artificial intelligence is natural intelligence, namely the power of self-ordering and self-originating independently of an external cause and force such as a transcendent God or an artificial machine.
continuous motion. Immanent or essential property of the real physical body thought of as an infinite whole and numbered by the real 1. Continuous motion is a) spontaneous; b) free of external cause and force; c) circular (reversible) receiving contrary (equal and opposite) forces; d) permanent; e) uniform; and f) has maximum speed equal to the speed of light, which we designate by the real 1. What is the founding principle of continuous motion? What form must the real, physical body have to receive continuous motion?
contradiction. The impossible unity and coexistence of opposite things. Contradiction is a quality of our incomplete observable world.
contrariety. The maximum unity of maximally different things. The necessary unity and coexistence of opposites. Contrariety is a quality of the complete physical world.
cosmic acceleration. The observable universe is in a phase of accelerating expansion. The fundamental quest in rational cosmology is to determine the origin, meaning and limit of this cosmic acceleration. We identify mankind’s accelerating growth with the universe’s accelerating expansion. Where is mankind and the universe going?
equivalence principle. An intellectual principle of our faculty of synthetic reason that stipulates the equality of unequal things; for instance the equality of matter and energy, of whole and part, of one and infinitely many. An alternative expression of the equivalence principle is the unity or coincidence of opposites (see Nicolas of Cusa), which we call contrariety. However, if by virtue of the analytic principle of contradiction no unequal things are equal, how then is it possible to equalize unequal things without absurdity, illusion or schizophrenia? Can this intellectual principle be at the same time an objective and constitutive principle of our real, physical world?
Euclidean geometry. The geometry of the time-conditioned, observable part of the real, physical universe. This observable part called observable or sensible universe is a finite variable increasing (or decreasing) indefinitely in time. In Euclidean space the extremities are determinate and unequal; Euclidean space is therefore discontinuous.
the founding principle of the physical universe. The universal principle or common point that unites our observable world’s infinite multiplicity of scattered parts, enables immediate communication across its distant regions, stabilizes its disruptive variation and assigns meaning and limit to its indefinite acceleration. What is the logical formulation and geometric expression of this founding principle?
globalization.The internally unbounded without internal distinctions and rigid boundaries is the infinite of Anaximander. It is also the infinite of globalization, which is a process of boundary breaking and community making, that is, a process aiming at discovering that which is common and universal among individual things and makes of them a permanent whole - a community whose members continuously communicate. Globalization can be equally thought of as an inductive process of moving from the individual to the universal, from the local to the global, of opening local boundaries and fixing universal boundaries. We distinguish different kinds of globalization, such as socio- economic-political, cultural, genetic, psychical and spatiotemporal.
▪ We have destructive globalization when we lose our individual identity without expanding it; (b) when we open our particular limits that separate us without fixing our universal limits that unites us; (c) when we increase society’s disruptive mobility without enhancing her cohesive stability; (d) when we develop artificial power at the expense of our natural power; (e) when we concentrate wealth without distributing it; (f) when we compress the entire world within our mind without comprehending it and unify things without discerning them. In this case human society will decompose itself into discontinuous, isolated individual parts increasingly diverging from each other similar to the receding galaxies of the observable universe and in war of all against all.
God. The idea of a constant and maximum limit to the infinite series of varying (increasing- decreasing) parts. What is the nature of this maximum limit? Is it accessible or inaccessible by the varying parts?
Hubble constant. The Hubble constant k denotes the rate of cosmic acceleration; it links v, the speed of a galaxy, with d, its distance from us on the surface of earth: v = kd.
What is the magnitude and the nature of the Hubble constant? Is the Hubble constant determinate having one value or indeterminate having an infinity of values? Does the Hubble constant change with time or with space?
infinite (apeiron). Aristotle divided the infinite into the infinite as complete whole (infinite whole, actual infinite, absolute infinite, spherical infinite) and the infinite as incomplete part (potential infinite, relative infinite, indefinite, Euclidean infinite).
▪ The infinite whole or the infinite as maximum is the infinite, which has nothing external to itself and beyond itself. It is a proper infinite, free of time (of succession, comparison, computation) and the laws of arithmetic. We also have an infinite whole when we think of the whole’s infinite multiplicity of parts at once, as unity and one thing and with maximum speed. Does the infinite whole exist? Can we experience the infinite whole? What is the founding principle of the infinite whole?
▪ Potential infinite is the infinite, which always has something external to itself and beyond itself. It is an improper infinite, which in reality is a finite part indefinitely varying in time and obeying the laws of arithmetic. What are the organizing principles of the indefinitely varying finite part?
infinite body. A finite spherical body of radius 1 that has simultaneously an infinite magnitude (according to extension and division). Rejected by Aristotle as absurdity, the infinite body was regarded by Indian and Greek Ionian philosophy as the body of the physical universe and of its composed atoms (see Anaximander of Miletus and the atomists Leucippus and Democritus). Does the infinite body exist? If yes can we experience it?
infinite nature. By infinite nature we comprehend the infinite totality of things connected by the equivalence principle. Infinite nature is also existence of things according to the synthetic principle of equivalence.
infinite one is that which is neither finite nor infinite and therefore is indeterminate and impartial. The Infinite One is equally that which is both finite and infinite and therefore is complex. The Greek Ionian philosopher Anaximander (6th century BCE) regarded the impartial and synthetic Infinite One as the primitive substance, number and principle of the real physical body. By physical body we mean the physical universe and any member of the physical universe.
infinite sensibility. The faculty of perceiving the infinite whole, that is, the world’s infinite multiplicity of parts at once, with unity and limit and as one thing. If no finite sensibility is infinite, how then is it possible to have an infinite sensibility without absurdity? Is it possible to have a synthetic sensibility, which is both finite and infinite?
infinite whole. The infinitely many thought as one. Can we sense the infinitely many as one? Equivalent concepts are infinite one and infinite body.
the principle of least action. The perfection of the physical universe requires that the laws of motion and rest must be such as to obtain an effect with minimum motion and in minimum time. The principle of least action is derived from Aristotle’s original idea of immobile action where the ideal being (god or the physical universe), has the power to impart movement (to itself and to something other than itself) without being moved.
metaphysics. The science of the real, physical body (or physical being-thing-object) thought of as an infinite whole and defined as the sum total of an infinite number of parts. The physical body, which we number by the real whole 1, designates the physical universe and any member of the physical universe.
physical body. The real physical body thought of as an infinite whole is the sum total of an infinite number of parts. The physical body, which we number by the real whole 1, designates the physical universe and any member of the physical universe.
self-causality is according to the ancient Greek philosopher Anaxagoras a principle of the infinite universe and the infinite mind. Because everything is both cause and effect of itself, both before and after itself, that is, self-caused and self-ordered or self-ruled, we do not need an external cause, an artificial machine, a violent big bang, a transcendent God for originating, ordering and sustaining the universe and the mind.
singularity (cosmic). A region where the curvature of space-time is infinite and the size of space-time is zero. What are the fundamental properties of cosmic singularity? Is singularity destructive chaos or the source of continuous life and motion?
spherical geometry. The geometry of the real, physical universe numbered by the real whole 1 and defined as the sum total of an infinite number of parts. How is it possible for a sphere of finite size 1 to be actually infinitely divided into parts of positive size which added give a unit sphere of infinite size?
supreme good is the principle of equivalence, which is simultaneously a principle of justice, love and truth as well as the principle of continuous life and motion. Can we think of our cosmic acceleration as the realization of the supreme good? Where is the place of the supreme good relative to us here and now taken as the center of the universe?
synthetic logic. The science of the principles that govern the physical object thought of as an infinite whole or universe, having at one time contrary determinations. The cognitive faculty of synthetic logic is synthetic reason (logos –proportion – unity of opposites). Synthetic logic is the negation of the principles of analytic logic. This latter logic regards the real, physical object as a simple finite individual varying in time. Is the physical object a simple finite individual or a complex infinite whole? Is the finite individual conditioned by time a real or illusory property of the physical object?
universal community is a multiplicity of parts unified into a whole by a universal principle and a common point. The unified whole is endowed with permanent life and is composed of parts in continuous communication. A universal community has a universal reason, a universal sense, a universal will.
universe. Analogical to Plato’s intelligible/sensible division of the world, the universe is divided into real, physical universe defined as the sum total of its infinite number of parts, and sensible or observable universe defined as the finite, observable and variable part of the physical universe. This variable part indefinitely accelerates in time. What are the fundamental properties and organizing principles of these two universes?
universal sensibility (see also infinite sensibility) is the synthetic faculty of sensing the universe’s infinite multiplicity of scattered parts as one thing, immediately with infinite speed and hence as an infinite whole unified by a universal principle or a common point. Is it possible to have electromagnetic (photonic) and electrochemical (neural) signals that travel the universe and our body with infinite speed and infinite temperature without burning the whole?
Anaxagoras (fifth century BCE). Greek Ionian thinker who asserted that since opposites come out of one another (for instance, something comes out of nothing and vice versa), they must have been present in one another always. It follows that everything is present in everything and that external or determinate causality upon which empirical science is grounded is an illusion.
Anaximander (sixth century BCE). Greek Ionian philosopher who defined the infinite (to apeiron)as “that which is internally unbounded without internal distinctions”, that is, that which is indeterminate, infinite in quality, beyond categories and hence all-inclusive. The infinite is neither finite nor infinite and therefore is indeterminate and impartial. The infinite is both finite and infinite and therefore complex. Because the infinite is the common substance and principle from which all things originate and to which all things return, its form is spherical.
Aristotle (fourth century BCE). Greek philosopher and farther of analytic logic. He employed analytic principles of thought to show the absurdities of infinity and motion. If infinity and motion are real properties of the physical world, how can we save infinity, motion and the physical world from destructive analytic criticism?
Chinese thinkers of the school of Tao (sixth to fifth century BCE). Tao, the way and principle of heavens, is the unity and interpenetration of opposites called contraries. Every being in the infinite universe is a complex indeterminate whole, which is both female (yin) and male (yang) and neither female (yin) nor male (yang).
Democritus (fourth century BCE). Greek Ionian philosopher who asserted that atoms are finite bodies that move with infinite speed in the infinite void.Moreover he asserted thatthere is only one kind of natural or original motion, namely that of vibration. However the one-way backward and outward acceleration of our observable universe contradicts the natural and symmetric motion of vibration. How can we solve this conflict?
Heraclitus (sixth century BCE). Greek Ionian philosopher who lived in Ephesus. He identified God with Logos (proportion), which similar to fire unites opposite things and ensures that change between opposites will be proportional balanced and continuous. According to Heraclitus the unity of things escapes our particular perception; it lies beneath the visible surface and depends upon a balanced action-reaction between opposites.
Plato (fifth-fourth century BCE). Following the Pythagoreans, Plato asserted in his Philibus that nature has united in every being the finite and the infinite (not-finite). However, in virtue of what principle is this primitive unity of opposites true? How can every being be both finite and infinite while avoiding absurdity? Is this unity of opposites a principle of the mind (faculty of synthetic reason) or a principle of the physical world? Is it an essential or an accidental, a real or an apparent principle of nature?
Pythagoras (sixth century BCE). Greek philosopher from the island of Samos who asserted that two principles, the limited and the unlimited, govern all bodies, that everything numbered by the whole 1 is a complex unity of opposites, of the limited and the unlimited. In the Pythagorean system, the unlimited is an even, female number and the limited is an odd, male number.
Indian thinkers of the Upanishads. Indic sacred scriptures principally written between ninth and fifth century BCE. Their exposed doctrine asserts the unity of the inner self or soul (atman) with the outer ultimate reality (Brahman) through contemplation and meditation.
If the outer ultimate reality (defined as the sum total of an infinite number of outer realities) has an infinite extension and the inner self or soul (defined as the sum total of an infinite number of inner realities) has a zero extension, then from their unity emerges the real magnitude 1 of the physical whole 1, which is the ratio between its greatest outer part and its smallest inner part.
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