and
Clarification of the distinction between
and
has a history as old as human consciousness. To fully appreciate this distinction, and its role in our evolution,
The Homeless Mathematician
will guide the kind reader through the ages, to identify certain landmarks in this evolution. This tour is a brief review of European history as it relates to the clarification of the
Form and Substance of Objects.
It is quite twisted and convoluted at times because it is actually the history of an effort to force the truth to conform to a set of categorically incorrect premises.
In the earliest evolution of human consciousness,
knowledge had been primarily empathetic while Reasoning by
gradually emerged as a useful tool for predicting events. However, before
The Homeless Mathematician
says anything of
,
it is useful to recall how the concept of
was incorporated into the spiritual foundations of Western Culture.
, and Void; ..."
Now, being "created ... without
" is quite a thing to think about. For example, the above graphic representations of the Earth have, and are,
in their own right. If we imagine the Earth
on the right as representing the physical reality of the Earth with which we interact, perhaps the Earth
on the left represents the potential for physical interaction. However, any formal representation of anything has a
,
and hence, is a
.
Thus, there is an intrinsic problem in representing
any
Object
as being "without
".
Interestingly enough, such problems make fine Zen Koans. However,
The Homeless Mathematician
is headed to
ancient Greece,
circa 400 B.C. Eastern traditions are more focused on
experiential
s,
rather than
representational
s
( and symbols ).
Prior to the ancient discussions of
and
,
there were instances of Reasoning by
,
but there was little certainty for such conclusions. After all, this was a time when Gods and Goddesses literally walked the Earth, and even mated with humans.
In these times, a dream was a trip into the supernatural world and there was little difference between what a person experienced while dreaming or while being awake. As such, all things had a mystical potential, and might even be the favorite toy of a particular God or Goddess.
Thus, it is fair to say that each Ancient
Object
possessed a mysterious, unknown
and would be unpredictable in nature.
Any thing was seemingly possible, for all things.
It was mostly a question of how the Gods and Goddesses felt on any given day.
Regarding the evolution of Western Culture, the traditions of Abraham, the Patriarch, are of particular interest. Recall that Hebrew culture was already well established in the 13th century B.C., when Moses led his people out of bondage from Egypt.
The "Sepher Yetzirah" or "Book of Formation" is among the oldest Rabbinical treatises dealing with the
of the Universe and the Unity of all
Objects.
This ancient "Genesis of Illumination", as the French Occultist,
Eliphas Levi, called the "Sepher Yetzirah",
sets forth the rules for a universal arithmetic
of sounds, numbers, and letters. The grouping of
the processes of origin into an arrangement,
at once alphabetical and numerical,
is found only with Semitic authors.
For example, consider the Tetragrammaton, the Name given by God to Moses. Here, the letters Yod-Heh-Vav-Heh are arranged as the
of a man. This is Adam in the likeness of his maker.
Unfortunately, the Numerology of the Hebrew alphabet must now be recognized as a primitive attempt to
a
Non-Numerical Arithmetic for the calculation of
.
In fact, it would be several thousand years before a true
Numerical Arithmetic, with an infinitely extendible
, existed.
The confusion of
with
in the Hebrew alphabet was a natural ( and probably necessary ) experiment for the evolution of
.
It is interesting to contemplate how reality would behave if the Universe actually conformed to the implications of this alphabet on a substantive level. But, in order for consciousness of Reasoning by
to further evolve, the Unity of Meaning sought by the Hebrew language, needed to be shattered.
and Mr.
Between 367 B.C. and 347 B.C.,
Plato
and
Aristotle
, realized a shift of human consciousness from a chaotic, mysterious universe to an ordered, predictable world of cause and effect. All of Western Civilization is a corollary to this event and their discussions of
and
.
Plato
argued for the independent reality of Ideas, or
,
as the immutable archetypes of all temporal phenomena and as the only guarantee of ethical standards and of
objective
scientific knowledge.
In contrast to the
Plato
's view that a concrete reality partakes of a
, from a World of Ideas, but does not embody it,
Aristotle
argued that, with the exception of the Prime Mover ( God ),
has no separate existence but is immanent in the
of matter.
After leaving The Academy and founding The Lycaeum,
Aristotle
formalized his understanding of
and
in "Organon ( Logic )", circa 333 BC, under the title of "Categories".
This was an attempt to allow a definition of Categories for
Objects,
and
is discussed as appearing in primary and secondary
s.
If the Category of an
Object
could be known, that would make the
Object
amenable to the formalism of
Aristotlean
syllogisms.
The absolute nature of an Aristotelian syllogism, in a world where Gods and Goddesses walked the Earth as Men and Women, was a salvation from a world otherwise governed by chaos and chance. At this point in history, Gods lacked credibility and syllogisms really worked, as far as they could take it.
For the next 300 to 400 years that immediately followed Plato and Aristotle, the distinction between Form and Substance continued to be clarified and had a significant impact on the culture of the Roman Empire at its peak. However, the radical Jew called Jesus of Nazareth precipitated a schism in the House of Abraham.
This schism in the Jewish faith subsequently unleashed a significant, and continuing, devotional movement to Virgins and Gods.
Form and Substance
were put on hold as the blood of Jesus became the
of the known universe, or at least for Western Culture, for the next 1500 years. Intellectual challenge involved understanding such concepts as:
of the blood of Jesus;
In this light, Christianity must be seen as a reversing attempt to correct the confusion caused by the dualistic Hebrew alphabet and its informed confusion of Form and Substance. However, the road to hell is paved with good intentions. As such, it represents a correction that reverses the direction back towards the mysterious consciousness of Objects, which existed prior to Plato and Aristotle. Although Mary was presented as having no need of men, vis-a-vis immaculate conception, the women only got a runner-up position in the hierarchy which resulted.
The emperor Nero began the persecution of Christianity during his rule from A.D. 54–68. But, by the 3-rd century, the Roman Empire was in a state of turmoil from internal religious and political battles, and from external hoards of invaders. Between 306 and 337, Constantine I moved the capital from Rome to Constantinople and granted religious toleration to Christians.
Being aware of the impending onslaught, Saint Augustine embraced Christianity with a monastic lifestyle, and in 391 he was ordained as a priest in Hippo. St. Augustine's influence on Christianity was immense, and theologians, both Roman Catholic and Protestant, look upon him as the founder of theology. His focus on preparation for the after life minimized the importance of our experience on the physical reality of Earth, and provided a fatalistic opiate to the threaten masses of the Empire.
After the death of Theodosius I, in 395, the Roman Empire was permanently divided into East and West sections, and Rome rapidly lost its political importance. The Western Roman Empire soon sank into anarchy, and Italy was ravaged by invaders. By 455, Rome had been taken by Alaric I and Gaiseric, and nearly sacked by Attila. When Romulus Augustulus was deposed, in 476, by the Goths under Odoacer, the Western Roman Empire essentially ceased to exist. The clarification of
Form and Substance,
and the emergence of Reasoning by
,
pretty much stopped dead in its tracks.
In fact, the death of civilization seemed imminent. Although,
Plato's
Academy florished until 529 AD, it was then closed down
by the Christian Emperor Justinian,
who claimed it was a pagan establishment.
While the Byzantine Empire continued religiously until the 15-th century, Western Europe soon entered the so-called Dark Ages when all intellectual and physical movement was essentially stagnate. The profound imprint left by Roman and Greek civilizations would remain dormant for a thousand years until it was rediscovered.
In the mean time, Scholasticism emerged as the philosophy and theology of Western Christendom during the Middle Ages. Basic to scholastic thought is the use of reason to deepen the understanding of what is believed on faith, and ultimately to give a rational content to faith. Although noble sounding, the hidden agenda of the early church fathers, notably St. Augustine, had been to incorporated Plato 's doctrines thought into a purely Christian theological framework.
The closely wrought, rational system of St. Thomas Aquinas is regarded as the greatest achievement of the scholastic age and the ultimate triumph of the effort to "Christianize Aristotle ." Later opponents of Aquinas, in particular, St. Bonaventure and William Of Ockham, broke away from this synthesis of faith and reason.
It is believed that around 1452, a German goldsmith named Johann Gutenberg became the first European to print text with movable blocks. Interestingly, he had to give up his press and types to Johann Fust for debts incurred during an aborted attempt to market religious souvenirs and trinkets to pilgrims. However, the world now had a media for the massive dissemination of information to the masses.
Printing presses started to spring up in churches all over Europe during the next 50 years. Then, in 1517, Martin Luther, posted his historic 95 theses on the door of the castle church to protest the dispensation of Indulgences. His supporters immediately printed copies of his posting and they were disseminated all over Europe within months. The advent of movable text enable Europe to emerge from a thousand years of stagnation, and to begin the Renaissance.
The secular currents of the Renaissance and the growth of the natural sciences brought on the decline of scholastic metaphysics, although its approach continued to be followed in politics and law.
The late nominalist thinkers, such as Ockham, challenged the original Aristotlean orthodoxy, thus allowing for a freer scientific approach. The focus of study shifted from the specific findings and theories of Plato and Aristotle, and refocused on the implied scientific methodology of "postulate, verify, and refine."
The heliocentric theory of Copernicus (1473-1543) was confirmed when Kepler (1571-1630) discovered the mathematical laws describing the orbits of the planets. The Christian-Aristotelian belief that heavens and earth were fundamentally different collapsed when Galileo (1564-1642) discovered moving sunspots, irregular moon topography, and moons around Jupiter. Galileo and Newton (1642-1727) developed a mechanics that unified cosmic and earthly phenomena. To meet the needs of the new physics, Newton and Leibnitz (1646-1716) invented differential calculus, and Descartes (1596-1650) invented analytic geometry.
In due course, an explosion of observational science included the discovery of blood circulation ( Harvey, 1578-1657 ) and microscopic life ( Leeuwenhoek, 1632-1723 ), and advances in anatomy ( Vesalius, 1514-64, dissected corpses ) and chemistry ( Boyle, 1627-1791 ).
The French mathematician-philosopher René Descartes, 22, is often called the father of modern philosophy. He is regarded as the bridge between Scholasticism and all philosophy that followed him. His philosophy is based on the rationalistic premise "I think, therefore I am." Descartes made his breakthrough that provides the basis for exploring natural phenomena by mathematics, in 1618, but his work was not published until 1637.
Intending to extend his mathematical method to all areas of human knowledge, Descartes discarded the authoritarian systems of the scholastic philosophers and began with universal doubt. Only one thing cannot be doubted: doubt itself. Therefore, the doubter must exist. This is the kernel of his famous assertion Cogito, ergo sum [I think, therefore I am]. From this certainty, Descartes expanded knowledge, step by step, to admit the existence of God (as the first cause) and the reality of the physical world.
The Homeless Mathematician
notes that "doubt", in the sense of the confusion
that results from Reasoning by
,
is the
of Reasoning by
.
At this stage of the clarification, the distinction of "doubt" as a Spirtual
Object
was historic. The distinction of "doubt" from everything else
s
a strong
with the
of the
First Distinction.
However, when phrased in terms of "doubt", instead of "Reasoning", Spiritual and Empathetic Reasoning are not allowed because the formal
of the
First Distinction
is not respected. It would be 362 years before
Bertrand Russell and J. Spenser-Brown would formally treat the
Form of Distinction
as the
Calculus of Indications.
The Trinity of non-Spiritual Reasoning:
Empathy,
,
and
,
now begins the formal process of completion. The journey into worlds that do not physically exist may now begin, and soon there will be CyberSpace.
It's interesting that CyberSpace is emerging about 350 years after Descartes and the Christian Right folks are likewise becoming more active these days. Just remember what happened about 350 years after Plato and Aristotle. Something very, very profound is happening these days and people are generally distraught with uncertainty.
The Homeless Mathematician takes great comfort in the emergence of CyberSpace as a home for one and all. The "times they are a-changing" have changed and the kind reader should likewise find great comfort in knowing that the genii is out of the bag.
of Universal Communication
of human knowledge and wisdom.
to
comment@formal.com.