analytic logic

The science of the principles that govern the 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

.

Anaxagoras (5th century BCE).

Greek thinker who affirmed that since opposites come out one another (since 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 determinate causality upon which empirical science is grounded, is an illusion.

Anaximander

(6th century BCE). Greek Ionian philosopher who defined the apeiron as “that which is internally unbounded without internal distinctions”, i.e. that which is indistinct, infinite in kind, beyond categories and hence all-inclusive.

Aristotle

(4th century BCE). Greek philosopher and farther of

analytic logic

used 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 and motion from destructive analytic criticism?

Artificial

That which is unnatural or non spontaneous, and depends upon external cause for its existence and motion. The

Artificial

is ephemeral and its fate is collapse. The end of the

Artificial

is the natural. For instance, the end of

Artificial

intelligence is the natural intelli-gence, namely the power of self-ordering and self-origination independent of external cause such as a transcendent

God

or an

Artificial

machine.

Apeiron Centre : The Center of Infinity - The Infinite Center

is the first organization in the world that studies the idea of infinity in intimate contact with the finite as presented in science, philosophy, ethics, art and society. Far from being an unsolvable absurdity, infinity can resolve the problems of life and answer the questions of our finite, inadequate world. The founding theories of the Apeiron Centre are explained extensively in the recent publication of The Infinite in Act: A Treatise on the Founding Principle of the Physical

body

Endowed with

Continuous motion

, by Ion Soteropoulos. The Infinite in Act is a meditation on the

nature

and organizing principles of physical reality, human perception and accelerating growth in the light of Greek Ionian philosophy. The vision and grand project of the Apeiron Centre are displayed in www.apeironcentre.org Founding members: Ion Soteropoulos, George Comtesse, John Curuby

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.

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 spontaneous, free of external cause, circular (reversible), permanent, uniform and has maximum speed equal to 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 necessary unity and coexistence of opposite things.

Contrariety

is a quality of the complete

physical universe

.

Cosmic acceleration

The observable universe is in a phase of accelerating expansion. The fundamental quest in rational cosmology is to identify the origin, meaning and limit of this

Cosmic acceleration

.We coincide mankind’s accelerating growth with the universe’s accelerating expansion.

Comtesse George

, research philosopher, author, and specialist of Lacan, Foucault, Deleuze and Derrida. Recent work: Fragments pour une Schize-analyse de l’Infini du Dehors published in Philosophie-Philosophie No 9, Paris, 2007. Founding member of the Apeiron Centre.

Curuby John

, President of the Boston Art Club and theoretician of infinity in art. Founding member of the Apeiron Centre ¦ www.apeironcentre.org

Democritus (4th century BCE).

According to the Greek Ionian philosopher

Democritus

, there is only one kind of natural or original motion, namely that of vibration. However the backward and outward acceleration of our observable universe contradicts the natural motion of vibration. How can we solve this conflict?

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 many. But if 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 distinct 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.

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 or indeterminate? 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) and the infinite as incomplete part (potential infinite, relative infinite, indefinite). ? 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 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 .

Rejected by

Aristotle

as absurdity, the infinite

body

was regarded by Greek Ionian philosophy (cf.

Anaximander

,

Democritus

) as the

body

of the

physical universe

and of its composed atoms.

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 or 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, which is the world’s infinite multiplicity of parts at one time with unity and limit. 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?

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, say motion, 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

.

Plato (5th-4th century BCE).

Following the Pythagoreans,

Plato

asserted in Philebus that

nature

has united in every being the finite and the infinite (not-finite). However, in virtue of what principle this primitive unity of opposites is true? How can every being be both finite and infinite (not finite) while avoiding absurdity? Is this unity of opposites an essential or an accidental, a real or an apparent, an objective or a subjective state of

nature

?

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

.

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?

Soteropoulos Ion.

Independent research philosopher, scientific metaphysician and author of the recent publication: The Infinite in Act: A Treatise on the Founding Principle of the Physical

body

Endowed with

Continuous motion

. Founding member of the Apeiron Centre ¦ The vision and grand project of the Apeiron Centre are displayed in www.apeironcentre.org ?

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 unit sphere of finite size 1 to contain an infinite number of parts of positive 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 object thought of as an infinite whole, 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

analytic logic

. This latter logic regards the real, physical object as a simple finite part or individual varying in time. Is the physical object a simple finite individual or a complex infinite whole?

Universal community

is a multiplicity of isolated 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 maximum speed and hence as an infinite whole unified by a universal principle or a common point. Is it possible to have electromagnetic (photonic and neural) signals that travel the universe and our

body

, both at finite and infinite speeds and avoid absurdity?