II : Conceptualization in Western ontological thought.

06. Myth : simplifying "the beginning".

To situate, within the framework of Ancient Greek history, "the Greek miracle" in general and the advent of philosophy in particular, the following division is helpful :

• Neolithic Age (7000 - 2600 BCE) : settlements of farmers in Crete and mainland Greece ; 

• Bronze Age (2600 - 1100 BCE) : the Bronze Age, starting with the arrival of peaceful immigrants on Crete, can be divided in two periods :
  
  Minoan : This culture was palace-based. Between ca. 2600 and 1600 BCE, no Greek influence was present on the island. The Minoans reached their zenith between ca. 1730 and 1500 (the "Pax Minoica"). Two scripts are attested : hieroglyphic (not yet deciphered) & Linear A. The latter is nearly always used for administrative purposes (the count of peoples & objects). The last phase of the Minoan neopalatial civilization was characterized by Mycenæan influence (i.e. after ca.1600 BCE).
  Mycenæan : Initiated ca. 1600 BCE, the culture of these Greek speaking people spread over mainland Greece and reached Crete. It was strongly influenced by Minoan protopalatial (ending with the destruction of ca. 1730 BCE) & neopalatial culture, but remained loyal to its own Greek character. Eventually they conquered Crete (ca. 1450 BCE) and caused the elaboration of Greek Linear B based on Cretan Linear A, which is not a Greek language as evidenced by the few tablets found in Linear A (for example, the word for "total" -often used in administrative texts- cannot be understood as the archaic matrix of a Greek word).  
  
  So Minoan and Mycenæan cultures interpenetrated : before 1600 BCE, Crete had directly influenced the formation of Early Helladic Greece but was itself non-Greek (Linear A) - after 1450 BCE, Mycenæan Greece took over Minoan culture on Crete and Greek Linear B was used by the Minoan treasury of Crete in the postpalatial.
  

• Dark Age (1100 - 750 BCE) : "Dorian" Greece, pushing Greek culture a step back ;

• Archaic Age (750 - 478 BCE) : Greek culture reemerges ;

• Classical Age (478 - 323 BCE) : the "polis" and the emergence of classical, concept-rationalism.

Although the scattered Mycenæan refugees probably kept parts of their linguistic tradition alive, the cultural network which had existed beforehand had been destroyed by the Dorians and with it a unified cultural form in Greece based on a shared language. Moreover, Dorian culture was very likely oral.

During these obscure centuries, Greek culture, as a form shared by all the inhabitants of Greece, was nonexistent. The marauding barbarians, who had destroyed the fortified towns of the pre-Helladics, and had developed (thanks to Crete) into the grand Mycenæan culture, were themselves destroyed by horned plundering hordes from the North, identified by some as belonging to the Doric branch of the Greek family ... 

The second half of the tenth century BCE brought a distinct easing off in depopulation, isolation, metal-shortages, architectural and artistic impoverishment & regional disparities. Because important centers of Greek civilization were still wrapped in obscurity, one can however not claim the "Greek Renaissance" had already begun ... Moreover, these changes were confined to the Aegean and its coasts.

In the memory of these few scattered groups, settling in the South of Greece and able to safeguard the "original" Mycenæan form, Mycenæ became legendary & heroic. In a sense, the Mycenæans represented the "mythical" past of the Ancient Greeks ...

The length of the Dark Age (300 years) threw a devastating shadow on the survival of Mycenæan culture. Note the name of this period refers to how little is known about it and also points to the remarkable contrast between Doric Greece & Mycenæan culture. The Dorians had no written language of their own and did not use Linear B. Isolation and loss of skills characterized the period.

The archaic mentality emerging in Ionia around 750 BCE and prefigurated in the rigid Mycenæan "megaron" as well as in the complex geometrical design of Dorian pottery, was stern, courageous, young, linear and geometrizing. But just like the rigid Mycenæans had been fascinated by Minoan Crete and its "African" elliptic and chaotic natural scenery, these Archaic Greeks were awestricken by the formidable grandeur of (Afro-Egyptian culture. Their own insistence upon this should be taken serious. There was more than intellectual opportunism at work here. 

Of course, as Indo-Europeans, the Ionians had a couple of typical features of their own :

• individuality / authority : at the beginning of the Archaic Age, there was a "crisis of sovereignty" (Vernant, 1962). It implied a new political problem : Who should rule and by virtue of what authority ? The collapse of the Mycenæan palace civilization was followed by a return to the small tribal organization (cf. the "ethnos"). This tension between individuality and social unity is fundamental to understand Greek philosophy (culminating in the judgment of Socrates). The view an individual had the right to rule by virtue of divine lineage was undermined. Heroic individualism was slowly replaced by an egalitarian ideal, in which archaic aristocratic authority was challenged. The building of temples was an "argument" for the appropriation of civic authority and helpful to keep control of the foundation of the economic power of the landowners, the aristocrats (Hahn, 2001, p.237). They secured their claim by drawing a particular connection between themselves together with a given deity and so integrated the divergent fractions of the community through the regularity of worship ... This swing of the pendulum between the particularism of the aristocrats and the egalitarism of the democrats, remained a fundamental ingredient of Greek culture & animated the Classical Greek "polis" ;

• exploring mentality : at the beginning of the Archaic Age, the population quadrupled and citizenship was increasingly connected with land ownership, triggering a competition for land which motivated the colonization. But besides these external causes, the Greeks were a curious people, always eager to learn more by approving new ideas and linearizing them in accord with their own abstract (generalizing, universalizing) frame of mind. The dynamic nature of the Greek cultural form assisted a decontextualized approach (while in Egypt, a sedentary mentality reigned and the concrete concept never emerged without context) ;

• unique dynamical script : the importance of their new system of writing should not be underestimated : by fixating the vowels, the Greeks were able to describe an state of affairs with a precision no other script of antiquity possessed. This referential, objective linguistic capacity enabled them to communicate through writing with more ease, precision & objective validity. The Egyptian intellectual elite read and wrote hieroglyphs, also used a short-script (hieratic) and mastered a common script (Demotic, Coptic). The absence of vowels in hieroglyphic script eternalized it and made it ill-equipped to cover both the immediate situation as well as be precise. By adding vowels, the Greeks made writing referential, dynamical and objectifying ; 

• linearizing, geometrizing mentality : proportion, measurement, number, spatial organization, cyclical processes etc. "reveal" the structure, form, order, organization of the cosmos. Numbers are more than practical tools to categorize, for they reflect the genuine, authentic, essential features of any object. A number never stands alone, for it entertains numerous fixed mathematical relationships with other numbers and spatial characteristics. These are described in general, universal, abstract terms ("theoria"), to be distinguished from their particular, local, concrete applications in architecture, sculpture, poetry etc. ("techné") ;

• anthropomorphic theology :  deities had a human face and in the Mycenæan age, they were at times combined in one cult. At the beginning of the Archaic Age, the pantheon was systematized by Homer and Hesiod, and each deity received its task (as in human society). However, Greek religion was undogmatic, for no sacred text existed. Xenophanes was critical about Greek anthropo-morphic (and anthropocentric) polytheism, proposing One Supreme God who was unlike anything human. Typical for Greek soteriology (salvic theory), is insisting the human soul had to liberate itself from the physical body through purification (cf. "ascesis" in Orphism) or somehow trigger its release (cf. "katharsis" & "ekstasis" in the Dionysian cult). Most major Greek emancipatoric theories will return to this and understand the body as the prison of the soul (cf. Plato & Plotinus). This would become the cornerstone of the Greek idea of "mystery", as opposed to the Egyptian view on the mysteries, in which transformation and ascension are taught.

"Perhaps the greatest contribution of the Bronze Age to Classical Greece was something less tangible, but quite possibly inherited : an attitude of mind which could borrow the formal and hieratic arts of the East and transform them into something spontaneous and cheerful ; a divine discontent which led the Greek ever to develop and improve their inheritance."
Higgings, 1997, p.190 (my italics).

So from the middle and late eight century BCE, profuse changes came about in the outlook of Greek civilization. This "Greek Renaissance" was an Age of Revolution. Exploration and codification (through settlement) were its leitmotivs. This revival took place between ca. 750 and 650 BCE. 

The Corinthian expansion probably took place at the end of the ninth century BCE, while the establishment of a Greek settlement in the Levant is slightly earlier. These colonizations did not leave a strong impact, while the eighth century Greek colonies in southern Italy and Sicily shaped the history of these regions for the next centuries. The early colonizations consisted of forerunners of probably voluntary and spontaneous venturers, whereas those of the eight century were the work of organized bodies of Greeks, possibly led by an individual aristocrat and his retinue, stimulated by the growth of population in the Greek homeland.

Greeks may have been marauding the Egyptian Delta perhaps as early as ca. 800 BCE, if not earlier. Because Ionian mercenaries had successfully assisted Pharaoh Psammetichus I (664 - 610 BCE) in his battle against the Assyrians, the Greeks were welcomed in Egypt, enabling Miletus to found Neukratis and the Greeks to settle in the Delta of Lower Egypt. Pharaoh Amasis (570 - 526 BCE) allowed them to settle upstream (Heliopolis, Thebes). Of a direct influence of Ancient Egyptian thought on these early visitors is more than likely (cf. Hermes the Egyptian, part I, 2002).

Greek philosophy, the intellectual side of the "Greek miracle", was initiated in Asia Minor, starting in Ionia ca. 600 BCE. Initiated by Thales of Milete (ca. 652 - 545 BCE), it commenced with a pre-rational approach of nature (the material pole), and, thanks to Pythagoras of Samos (ca. 580 BCE - 500), who coined the term "philosophy", added a study of proportion and number (the mathematical pole). These early philosophers tried to do away with mythological explanations, whereas the symbolism of Pythagoras coupled their naturalism with a mysticism of numbers, allowing natural phenomena to be related to each other in abstract, theoretical terms.

Identifying the myths of Mycenæan heroism, the pantheon (Hesiod) and the works of Homer as representing the mythical and pre-rational phases of Greek cognition, we see the Ionians gather the central themes of Greek thought in proto-rational terms. A closure is realized by justifying the world by its origin & the role of man by symbolization. Each pre-Eleatic posits a pivot, an ontological foundation for what exists. The multiplicity of mythical views is challenged by the unification around a single principle. This proto-rationality exceeds itself, and paves the road for the conceptual rationality of the Eleatics, the sophists and Classical Philosophy.

With the introduction of conceptual rationality by Parmenides of Elea (ca. 515 - 440 BCE) & Democritus of Abdera (ca. 460 - 380/370 BCE), the stage is set for the ontological tradition of the West long before the Platonic and Peripatetic systems.

Thales of Miletus

There is a consensus, dating back at least to the 4th century BCE and continuing to our present academical history of Greek philosophy, of Thales of Miletus being the first Greek philosopher. According to the Greek thinker Apollodorus, he was born in 624 BCE. The Greek historian Diogenes Laërtius (ca. 3th century CE) placed his death in the 58th Olympiad (548 - 545 BCE), at the age of 78. He also affirms Thales traveled to Egypt, while Iamblichius explains how he advised other intellectual Greeks to go to Egypt in order to learn :

"Thales advised Pythagoras to go to Egypt and to entertain himself as much as possible with the priests of Memphis and Diospolis : it was from them that he had drawn all the knowledge which made him a sage and a scientist in the eyes of the masses."
Iamblichius : Life of Pythagoras, 12, my italics.

During his lifetime, the word "philosopher" (or "lover of wisdom") had not yet been coined. Thales was counted, however, among the so-called "Seven Wise Men" (the "sophoi"), whose name derives from a term designating inventiveness and practical wisdom rather than speculative insight (consistent with the Ancient Egyptians' notion of wisdom). In fact, today we reckon Thales to be the only "philosopher" on that list !

Thales tried to transmit to the Greeks the mathematical knowledge he had derived from the Babylonians (who, when conquering Egypt in the Third Intermediate Period, had influenced its astronomy profoundly). Thales sought to give it a more exact foundation and used it for the solution of practical problems, such as the determination of the distance of a ship as seen from the shore or of the height of the Gizza pyramids. Though he was also credited with predicting an eclipse of the Sun, it is likely he merely gave a natural explanation of one on the basis of Babylonian astronomical knowledge (cf. the Saros-period between eclipses). 

Thales' significance for Greek philosophy, lies less in his choice of water as the essential substance, than in his attempt to explain nature by the simplification of phenomena. Indeed, Thales searched for causes within nature itself rather than in the caprices of the anthropomorphic gods. He was deemed the first Greek to give a purely natural explanation of the origin of the world, free from all mythological ingredients and unnecessary complexities (linearization and homogeneity). The claim Thales was the founder of Greek philosophy rests primarily on Aristotle, who wrote he was the first (Greek) to suggest a single material substratum for the universe, namely, water, or moisture ...

Even though Thales renounced mythology, his choice of water as the fundamental building block of matter had its precedent in the Egyptian tradition (cf. "Nun", the undifferentiated primordial waters before time and space and its "Ba" or "soul", the autogenitor Atum). To Thales, the entire universe is a living organism, nourished by exhalations from water (cf. Egypt's organic, hylozoistic view on creation).

It is true Thales made a fresh start on the basis of what a person could observe and figure out by looking at the world as it presented itself. This procedure naturally resulted in a tendency to make sweeping generalizations on the basis of rather restricted but carefully checked observations. Milesian thought prompted philosophy to move beyond the localized, contextualized & traditional thought of the cultures surrounding it.

In geometry, Thales has been credited with the discovery of five theorems :

(1) a circle is bisected by its diameter ;
(2) angles at the base of a triangle having two sides of equal length are equal ;
(3) opposite angles of intersecting straight lines are equal ;
(4) the angle inscribed in a semicircle is a right angle ;
(5) a triangle is determined if its base and the angles relative to the base are given.

The mathematical achievements of Thales are difficult to assess. The ancients credited particular discoveries to men with a general reputation for wisdom. However, their logic evidences the linear and geometric spirit of the Greeks. Surely, before Thales, Egyptians and Mesopotamians had arrived at the truths represented by these theorems. But the way the Greeks recorded and fixated knowledge in more abstract, discursive, denotative and context-independent terms, was highly original. It is these linearizing & symbolical activities which foremost characterize the "Greek miracle", not observation, recording and comparison. The latter can be done with proto-rational concepts too. But formal reason is precisely this : a reduction of a variety (a manifold) to a limited number of categories. This in order to seek a universal proposition (a conclusion) on the basis of a universal major and an empirical minor. The latter was provided by the storehouse of practical knowledge cherished in all important Egyptians temples (cf. Memphis, Heliopolis, Hermopolis, Abydos & Thebes).

Anaximander of Miletus

Thales' friend, disciple and successor, Anaximander of Miletus (ca. 611 - 547 BCE), is said to have given a more elaborate account of the origin and development of the ordered world (the cosmos). However, his writings are lost, and although still available to Apollodorus of Athens (cf. Chronica, ca. 140 BCE), they are not known to have been used by any other writer later than Aristotle and his successor Theophrastus of Eresus (ca. 370 - 285 BCE). The latter's Phusikos Doxai is also lost, but repeated by Simplicius (6th century CE). All ancient doxographers depend on the latter's Physics (Diels).

Doxography evidences Anaximander wrote treatises on geography, astronomy, and cosmology surviving for several centuries. He made a map of the known world, prized symmetry and introduced geometry and mathematical proportions into his efforts to map the heavens. Thus, his theories departed from earlier, more cosmogonic conceptions of the universe and prefigured the achievements of later astronomers.

Unfortunately, we only possess one sentence of Anaximander's writings. In this sentence, Anaximander explains a "need" or "necessity" (a moral imperative at work in creation) operating between the elements (as well as in human society) : 

"But where things have their origin, there too they must pass away, as it should ; for indeed, they give one another justice and penalty for their injustice, in accord with the ordinance of time."
Simplicius : Commentary on the Physics, 24.13v, my translation.

According to him, the cosmos developed out of the "apeiron", the boundless, infinite and indefinite (without distinguishable qualities). Aristotle would add : immortal, Divine and imperishable.

Within this "apeiron" something arose to produce the opposites of hot and cold. These at once began to struggle with each other and produced the cosmos. The cold (and wet) partly dried up (becoming solid Earth), partly remained (as water), and -by means of the hot- partly evaporated (becoming air and mist), its evaporating part (by expansion), splitting up the hot into fiery rings, which surround the whole cosmos. Because these rings are enveloped by mist, however, there remain only certain breathing holes visible to men, appearing to them as Sun, Moon, and stars. 

"The Greeks seem to have received from Egypt their old celestial architecture, as well as that of their temples. It is only when conceived in this way, as a roof, that the 'ouranos' can be described as 'brazen' or (in the Odyssey) as made of iron. The reference is no doubt to the great solidity of the edifice. Hesiod has much the same thing in mind when he calls it, 'a seat set firm'."
Kahn, 1994, p.139.

Anaximander realized upward and downward are not absolute. Downward means toward the middle of the Earth and upward away from it, so the Earth has no need to be supported by anything (as Thales had believed). Instead, he asserted the Earth remained in its unsupported position at the centre of the universe because it had no reason to move in any direction and therefore was at rest.

Starting from Thales' observations, Anaximander tried to reconstruct the development of life in more detail. Life, being closely bound up with moisture, originated in the sea. All land animals, he held, are descendants of sea animals. Gradually, however, the moisture will be partly evaporated, until in the end all things will have returned into the undifferentiated "apeiron", in order to pay the "penalty for their injustice", i.e. of having struggled against one another.

Anaximander subscribed to the philosophical view unity could definitely be found behind all multiplicity.

Anaximenes of Miletus

Anaximander's successor, Anaximenes of Miletus (ca. 585 - 525 BCE), taught Air was the origin of all things. Neither Thales nor Anaximander appear to have specified the way in which "the other things" arose out of the water or the "apeiron". Anaximenes, however, declared the other types of matter arose out of Air by condensation and rarefaction. In this way, what to Thales had been merely a beginning, became a fundamental principle remaining essentially the same through all of its transmutations.

Thus, the term "arche", which originally simply meant "beginning," acquired the new meaning of "principle," a term henceforth playing an enormous role in philosophy. This concept of a principle remaining the same through many transmutations is, furthermore, the presupposition of the idea nothing can come out of nothing. All of the comings to be and passing away we observe, are nothing but transmutations of something remaining essentially the same for ever (the law of conservation). 

Pythagoras of Samos

The Ionian naturalists (materialists) were individuals, and although Anaximander had Thales as a teacher, no "school" emerged after their death. With Pythagoras (ca. 580 BCE, island of Samos, Ionia  - ca. 500, Metapontum, Lucania), this son of an engraver of gems, we encounter the first Greek "school" of thought, a teaching in which religion, mysticism, mathematics and philosophy were allowed to interpenetrate each other and orchestrate a totally new symphonic whole, which will have a decisive influence on Greek thought as well as on Greek architecture. This was so unique, that Pythagorism may well be called the second major orientation in pre-Socratic philosophy next to Milesian materialism as a whole. 

According to tradition, the very word "philosophy" was coined by Pythagoras, who described himself as a "philo-sophos", a "lover" of wisdom. With his school, the scope of the Milesian "sophoi" was dramatically enlarged by the introduction of metaphysics, mystical experience and the philosophy of mathematics (including Pythagorean numerology). These speculative considerations took place "next to" physical inquires into the nature of all possible beings. With his emphasis on numbers and the theology of arithmetic (cf. Nicomachus of Gesara's The Theology of Arithmetic, ca. 100 CE), Pythagoras completed mathematics, for a complete study of geometry was taken for granted (for part of the "know-how" of the Milesian "sophoi").

The combination of geometry and arithmetic, was called the "tetraktys" (from "tetra", "four"), after the form of a four-tiered triangular patters of ten dots, the sacred symbol upon which Pythagorean Oats were sworn, and which probably had its origin in the arrangements of pebbles used to study mathematics. It is "holy", because of its summarizing manifestation of completion. It is "sacred", because it contains a secret which is kept out of sight of the inept ...

TETRAKTYS - ultimate sacred number
"delta" shaped form (cf. "deka", ten) in four ("tetra") rows
directly influenced Hebrew qabalah and its 10 "Sephiroth"
as well as the structure of the 4 qabalistic worlds

Unfortunately, none of the writings of Pythagoras have survived, and Pythagoreans invariably supported their doctrines by indiscriminately citing their master's authority. It is difficult to distinguish his teachings from those of his disciples, neither legends from historical fact. However, he is credited with the theory of the functional significance of sacred numbers in the objective world and in music (obtained by stopping a lyre string at various points along its length - the octave (2: 1), the fifth (3: 2) and the fourth (4: 3)). Other discoveries often attributed to him, like the incommensurability of the side and diagonal of a square, and the Pythagorean theorem stating the square of the hypotenuse of a right-angled triangle equals in area to the sum of the squares of the other two sides (well-known in Egypt and Mesopotamia), were probably developed only later by the Pythagorean school. 

Diogenius Laërtius also tells us Pythagoras entered the Egyptian temples and learned the secrets of their gods. This is a remarkable testimony. The Egyptian gods were hidden from sight. Nobody, except Pharaoh and his appointed priests, could enter the "holy of holies" and face the deity. There was no communication between the deities and humans, for gods communicate only with gods. In the Late New Kingdom, common people took Amun "in their heart" and the Hidden Supreme heard their prayers & supplications ... Does the fact Pythagoras entered parts of the inner spaces of the temple (decorated with the grand story of the pantheon), not make it likely he had learned how to read hieroglyphs and had satisfied the discipline of an Egyptian priesthood in decline ? Not to say he had become an Egyptian priest, but a wide variety of functions were in existence in Egyptian temples and some of them allowed access to areas which revealed much to those able to read the sacred writing, the "words of the gods" (cf. "lector" priest of the "House of Life" - in the Late Period Memphis, Sais and Bubastis had major libraries).

Iamblichus writes Pythagoras buried Thales and knew Anaximander before he stayed 22 years in Egypt and was initiated in the teachings of the priests of Thebes (plurality & unity of the Divine) and the doctrine of the resurrection of Osiris (the immortality of the soul). He would have received the sign of the winged disk in gold on his thigh, so that he was called "chrysomeros", or "he of the golden thigh". When the Persian Cambyses conquered Egypt in 525 BCE, he was made captive and brought to Chaldea. There he studied with the "magoi" for 12 years and learned about numbers and music. Other authors claimed he encountered Zarathoustra (being baptized in the Euphrate) and traveled to India were he met Gautama the Buddha (& was taught the doctrine of the "transmigration", i.e. rebirth ?). The teachings drew a large following in the Greek colony of Croton in southern Italy, were he went to live. A kind of Freemasonry "avant la lettre" rose among the aristocracy. It was a fraternity with Pythagoras as its "master". Its members had a lot of political power (based on "areté" and "ponós", excellence and effort), but were eventually massacred in a riot long after Pythagoras had died. The followers spread the principles and caused Pythagorism (or "Pythagoreanism") to become part of the Greek world. Iamblichus quotes his master, who had said : "number is the rule of forms and ideas, and the cause of gods and demons".

In all, the various accounts draw a cosmopolitan picture of Pythagoras. He was the first Greek philosopher in the universal sense of the word, for all beings were part of his reflection. His interests go further than the physical doctrines of the Milesians and for the first time in Greek history, philosophy, mathematics & religion were put in one system of thought.

The problem of describing Pythagorism is complicated by the fact the surviving picture is far from complete, being based chiefly on a small number of fragments from the time before Plato and on various discussions in authors who wrote much later - most of whom were either Aristotelians or Neo-Platonists. In spite of these historical uncertainties, the contribution of Pythagorism to Western culture has been significant and therefore justifies the effort, however inadequate, to depict what its teachings may have been.

Three levels may be discerned :

1. original teachings of Pythagoras ;

2. Pythagoras in Plato and Aristotle ;

3. teachings & influence of the Pythagorean school.

The character of original Pythagorism is controversial, and the conglomeration of disparate features it displayed is intrinsically confusing. Its fame rests, however, on some very influential ideas, and likely most of these prevailed in the school of Croton :

• the metaphysics of number and the conception reality, including music and astronomy, is, at its deepest level, mathematical in nature : Pythagoras' sufficient ground is not a cosmic substance but an inner organization or structure coupled with a liberating, salvic intentions, albeit ascetical & philosophical ;

• the use of philosophy as a means of spiritual purification : a lover of wisdom is more than an intelligent person aware of problems and their solutions, for his pursuit of wisdom must be a window to the immortal soul, the light of which draws him near to the original and fundamental level of reality : the mathematical order of being which whispers a hidden, mysterious language of silence, with a code available to the initiate only ; 

• the heavenly destiny of the soul and the possibility of its rising to union with the Divine : Pythagoras is not satisfied with the mundane, immanent perspective, for the Pythagorean philosopher is before all the rest a lover of unity and its experience, which implies transcendence, trance, osmosis etc. ; 

• the appeal to certain symbols, sometimes mystical, such as the "tetraktys", the golden section, and the harmony of the spheres : symbols are the residue of spiritual experiences and contain a code to trigger co-relative experiences later ; 

• the Pythagorean theorem : mathematics and the solution of particular problems are the "purest" way to encounter the immortal soul, for its language is that of sacred number ; 

• the demand members of the order shall observe a strict loyalty and secrecy : the order is a private affair and has no "outer order".

What could Pythagoras have learned from the priest of Memphis and Thebes ?

• the unity of the Divine : the absolute is One and Millions, invisible by nature and manifest in nature's forms ;

• the rule of truth and justice : all actions have to be weighed on the balance of truth to measure their order ;

• the order of creation : the cosmos unfolded as a series of numbers : 0 > 1 > 2 & 3 > 4 & 5 > 6, 7, 8, 9 ;

• the sacrality of "10" : Pharaoh, "son of Re", completes the Ennead + 1 = "10" order ;

• the creativity of thought and speech : the cosmos as conceived in the "mind" of the absolute ;

• geometrical solutions to practical problems : mathematical papyri testify Egypt's elementary abilities ;

• the magic of symbols : sacred script and ritual speech have powers beyond their physical form ;

• the rule of silence : the Egyptian gods and their priests were out of sight and hidden - silence was gold ;

• the harmony of opposites : all fundamental oppositions are bridged by a harmonic "third" ;

• the symbolism of numbers : each natural number (0 - 10) has "inner" meanings, purposes and relations.

There probably never existed a strictly uniform system of Pythagorean philosophy and religious beliefs, even if the school did have a certain internal organization. Pythagoras appears to have taught by pregnant, cryptic "akousmata" ("something heard") or "symbola". His pupils handed these on, formed them partly into Hieroi Logoi ("Sacred Discourses"), of which different versions were current from the 4th century BCE on, and they interpreted them according to their convictions.

Plato mentions Pythagoras only once (Republic, X.600). No details are given about the "Pythagorean way of life", which he compares with Homer. The Pythagorean teachings were obviously popular enough for Plato not to bother to discuss them. Not so for his pupil Aristotle, who wrote :

"Pythagoreans applied themselves to  mathematics, and were the first to develop this science ; and through studying it they came to believe that its principles are the principles of everything. And since numbers are by first nature among these principles, and they fancied that they could detect in number, to a greater extent than in fire and Earth and water, many analogues of what is and comes into being-such and such a property of number being justice,. and such and such soul or mind, another opportunity, and similarly, more or less, with all the rest - and since they saw further that the properties and ratios of the musical scales are based on numbers, and since it seemed clear that all other things have their whole nature modeled upon numbers, and that numbers are the ultimate things in the whole physical universe, they assumed the elements of numbers to be the elements of everything, and the whole universe to be a proportion or number."
Aristotle, Metaphysics, I, v. 1-3, 985b.

In  the 4th century BCE, Plato's inclination toward Pythagorism created a tendency -manifest already in the middle of the century in the works of his pupils- to interpret Platonic concepts as originally Pythagorean. Most of the literary sources ultimately hark back to the environment of Plato and Aristotle. Later, neo-Platonism, which developed in the third century CE, reworked Pythagorism. Although they claimed to reassert a true understanding of Plato, they took a syncretic approach and drew from other sources, such as Pythagorean number mysticism and the Hermetica.

By laying stress on certain inner experiences and intuitive truths revealed only to the initiated, Pythagorism seems to have represented a soul-directed, salvic idealism alien to the mainstream of pre-Socratic Greek thought, preoccupied with determining what the basic cosmic substance ("phusis") was. In contrast with Ionian naturalism, Pythagorism was akin to trends seen in mystery religions and mystical movements, such as Orphism, which often claimed to achieve a spiritual insight into the Divine origin and nature of the soul through intoxication. Yet, there are also aspects of it appearing to have owed much to the more sober, "Homeric" philosophy of the Ionians, especially regarding ascetics and the importance of mathematics. 

Indeed, the Pythagoreans displayed an interest in metaphysics (the nature of being), as did their naturalistic predecessors, though they claimed to find its key in mathematical form rather than in any cosmic substance. They accepted the essentially Ionian doctrines saying the world is composed of opposites and generated from something unlimited, but they added the idea of the imposition of limit (number) upon the unlimited and the sense of a musical harmony in the universe (a "music of the spheres", sounding to human ears as silence - cf. Aristotle, De Caelo, II.9). Again, like the Ionians, they devoted themselves to astronomical and geometrical speculations. Combining, as it does, a theory of number with a numerology and a speculative cosmology with a theory of the deeper, more spiritual reaches of the soul, Pythagorism interweaves religion and philosophy more inseparably than does any other movement in pre-Socratic thought. 

The occult blend of proportion & number with numerology, as well as speculative philosophy masked with the pursuits of religion, point to an emerging conceptual rationality still clinging to the proto-rational mode of thought, dependent of context & myth. Pythagorism achieves a grand synthesis, liberated from the necessities of local myth, multi-cultural and grasping an intrinsic "Homeric" tendency towards linearization. Pythagoras and his school were also the first to develop a system of thought influenced by many disparate sources (Ionian, Egyptian, Persian, Indian). These various elements were brought together, equilibrated and made to function as part of a larger whole. Just as the Ionian "sophoi" before him, this system of thought incorporated foreign sources, transcending them using a Greek mode of thought. But if we analyze the object - subject relationships at work, we cannot say of Pythagorism it has completely emancipated both sides. A symbolical adualism is still implied. Numbers are more than just mental conventions, but are an expression of the ontological structure of nature, and so refer to an extra-mental "ground", "foundation" or "hypokeimenon" (underlying thing, substratum). A "magical" sympathy exists between things. Wandering Pythagoras heralds urban Plato, who may be read as a direct student of the former.

Pythagorism differentiates between subject & object, and so is the earliest manifestation of conceptual rationality in Greece. Not yet a clear demarcation (as in Plato's "two worlds"), Pythagoras steps outside the continuum of ante-rationality.

Summary what ante-rationality accomplished.

Ante-rationality encompasses the three first, earliest layers of cognition, namely mythical, pre-rational and proto-rational thought, developing libidinal notions, tribal pre-concepts & imitative concrete concepts respectively. Concrete concepts are never decontextualized. These early Piagetian stages (cf. Stuurkunde, 1993, Cognition, 2003, Clearings, 2006) are characterized as follows :

Myth : the notion

First substage :

1. non-reflective adualism and only a virtual consciousness of identity ;

2. primitive action testifying a quasi complete indifferentiation between the subjective and the objective side of cognition ;

3. actions are quasi uncoordinated, i.e. random movements are frequent.

Second substage :

1. first decentration of actions with regard to their material origin (i.e. the physical body) ;

2. first objectification by a subject experiencing itself for the first time as the source of actions ;

3. objectification of actions and the experience of spatiality ;

4. objects are linked because of the growing coordination of actual actions ;

5. links between actions in means/goals schemes, allowing the subject to experience itself as the source of action (initiative), moving beyond the dependence between the external object and the acting body ;

6. spatial & temporal permanency and causal relationships are observed ;

7. differentiation (between object and subject) leads to logico-mathematical structures, whereas the distinction between actions related to the subject and those related to the external objects becomes the startingpoint of causal relationships ;

8. the putting together of schematics derived from external objects or from the forms of actions which have been applied to external objects.

Pre-rationality : the pre-concept

1. because of the introduction of semiotical factors (symbolical play, language, and the formation of mental images), the coordination of movements is no longer exclusively triggered by their practical and material actualizations without any knowledge of their existence as forms, i.e. the first layer of thought occurs : the difference between subject & object is a signal which gives rise to the symbol ;

2. upon the simple action, a new type of interiorized action is erected which is not conceptual because the interiorization itself is nothing more than a copy of the development of the actions using signs and imagination ;

3. no object of thought is realized but only an internal structure of the actions in a pre-concept formed by imagination & language ;

4. pre-verbal intelligence & interiorization of imitation in imaginal representations ;

5. psychomorph view on causality : no distinction between objects and the actions of the subjects ;

6. objects are living beings with qualities attributed to them as a result of interactions ;

7. at first, no logical distinction is made between "all" and "few" and comparisons are comprehended in an absolute way, i.e. A < B is possible, but A < B < C is not ; 

8. finally, the difference between class and individual is grasped, but transitivity and reversibility are not mastered ;

9. the pre-concepts & pre-relations are dependent on the variations existing between the relational characteristics of objects & can not be reversed, making them rather impermanent and difficult to maintain. They stand between action-schema and concept.

Proto-rationality : the concrete concept

1. for the first time stable concepts and relations emerge and the interiorized actions receive the status of "operations", allowing for transformations. The latter make it possible to change the variable factors while keeping others invariant ;

2. the increase of coordinations forms coordinating systems & structures which are capable of becoming closed systems by virtue of a play of anticipative and retrospective constructions of thought (imaginal thought-forms) ;

3. these mental operations, instead of introducing corrections when the actions are finished, exist by the pre-correction of errors and this thanks to the double play of anticipation and retroaction or "perfect regulation" ;

4. transitivity is mastered which causes the enclosedness of the formal system ;

5. necessity is grasped ;

6. constructive abstraction, new, unifying coordinations which allow for the emergence of a total system and auto-regulation (or the equilibration caused by perfect regulation) ;

7. transitivity, conservation and reversibility are given ;

8. the mental operations are "concrete", not "formal", implying that they (a) exclusively appear in immediate contexts and (b) deal with objects only (i.e. are not reflexive) ;

9. the concrete operatoric structures are not established through a system of combinations, but one step at a time ; 

10. this stage is paradoxal : a balanced development of logico-mathematical operations versus the limitations imposed upon the concrete operations. This conflict triggers the next, final stage, which covers the formal operations.

07. Conceptual rationality in Parmenides and Democritus.

The evolution from "mythos" to "logos", viewed as a reflective process of the understanding of thought by itself, went through stages characterized by a variety of object/subject-relationships.

In myth, non-reflective adualism pertains. This differentiates to bring about the pre-concept, allowing for a distinction between object and subject, but not without a psychomorph recuperation of the former by the latter. Pre-conceptual thinking seeks a hypostatic grounding of this subjective objectivity of pre-rationality. In Ancient Egypt, in particular in the Old Kingdom, this was realized by the introduction of the pre-concept of divine kingship, expressing a unique feature : the equilibrium of opposites. The dual nature of the monarchy was all-comprehensive and reflected in the regalia, in the royal titulary, in the royal rituals and festivals. Frankfort (1948) called the presence of the divine king and his institution of "transcendent significance". It was a unique phenomenon in the region, if not in the world. In the pre-Eleatics, the "arché" of nature ("physis") played the same cognitive role of "explaining" the constant intermixture of the objective & subjective poles of thought. It did so, by moving beyond the scarcely established demarcation, positing a "root-cause", borrowing its descriptive terms from the language of myth and the ongoing battle of the "enantia" or elements of nature (cf. water, air, fire and pre-existence).

The step from non-reflective adualism (myth) to pre-rationality is nothing less than a revolution. For the first time, the coordinations of a physical body are experienced by a subject as "its own", enabling this subject to distinguish between object and subject, albeit in psychomorph form. Cognition begins with notional myth, but the first pre-rational thought (or auto-reflection) is of pre-rationality. Likewise, the step from pre-rationality to proto-rationality, from pre-concept to concept, is crucial, for the ability to generate mental operations is added to the range of the cognitive differentiation between object and subject.

By integrating transitivity, proto-rationality offers a closure. Various classes of concrete concepts constitute practical "systems" operating logico-mathematical procedures within given contexts. Theoretical insights are absent, and no formal procedure is ever outlined. Practical inductivity (by entertaining the psychological connectedness between events), not formal causality, yields a vast storehouse of practical notions, pre-concepts and concrete concepts.

The formal operations of rational thought have no contextual entanglements, and give a universal, a-temporal embedding to the cognitive process through abstraction, categorization & linearization. Here the formal concept is introduced and theories see the light. Cognition is liberated from the immediate events and able to conceptualize logical & mathematical truths (deduction) as well as physical causalities in abstract terms, without any consideration for their actual occurrence, if any (cf. the inner thought-experiment). Thought is able to combine propositions into abstract systems and paradigms.

Parmenides of Elea

Parmenides of Elea (ca. 515 - 440 BCE), inspired by Pythagoras, who introduced the concept a priori, and pupil of Xenophanes (ca. 580/577 - 485/480 BCE), was the first Greek to develop, in poetical form, his philosophical insights about truth ("aletheia"). Thanks to the neo-Platonist Simplicius (490 - 560), 111 lines about the Way of Truth are extant. In it, the conviction dominates human beings can attain knowledge of reality or understanding ("noos"). But to know the truth, only two ways are open : the Way of Truth and the Way of Opinion. These are defined in terms of the expressions "is" and "is not".

The first is the authentic way, leading to the unity and uniqueness of "being". When using the copula "is", Parmenides points to the perfect identity of substantial "being", ascribed in a single sense. Hence, what is other than "being" itself has no being at all ... This is the second way, that of mere opinion ("doxa").

In his argument, Parmenides makes use of a three-tiered disjunction and a reductio ad absurdum. To answer the question : "Is a thing or is it not ?", three answers are deemed possible : (a) it is or (b) it is not or (c) it is and it is not.

By using the necessities of this logic, the formal conditions of knowledge become apparent. Two ways of inquiry are alone conceivable. The first, the journey of persuasion, attends on reality, on the fact a thing is, while the second, is without report and deals with that a thing is not and must not be. As one can neither know what is not (deemed absurd), nor tell of it, the second way is pointless. Only one way is thus left over : "being" is ungenerated, imperishable, entire, unique, unmoved and perfect. It never was nor will be, since it is now all together, one, indivisible. It has no parentage.

Let us consider the three answers. If a thing is and is not, then this either means that there is a difference due to circumstance or that "being" and "nonbeing" are different and identical at the same time. This answer is relative (circumstantial) or contradictory. If a thing is not, then it cannot be an object of a proposition. If this would not be the case, not-being would exists ! But this answer is pointless. As the last two answers are clearly false, and only three answers are possible, the first answer must, by this reductio ad absurdum, be true, namely : the object of thought "is" and equal to itself and being itself from every point of view.

Parmenides clearly accommodates formal rationality, the fourth stage in the self-reflective differentiation of cognition. Before the Eleatics, with Pythagoras as the exception to the rule, the difference between object and subject of thought remained psychomorph. The formal laws of logic were not yet brought forward in this way and used as tools to back an argument. The strong necessity implied by the laws of thought had not yet become clear. Ontologically, the proto-rational concept of change of Heraclitus (540 – 475 BCE) -with whom he is often paired- is indeed opposed to the static, single being of Parmenides, but epistemologically, the latter was the first to underline the importance of the formal characteristics a priori of all thought and the use of a chain of arguments. The mediating role of the metaphor is replaced by an emphasis on the distinction between the thinking subject (and its thoughts) and the reality of what is known. What is this "Being" ? What sense attaches to the verb "to be" in asserting and thinking ?

"... remaining the same and in the same state, it lies by itself and remains thus where it is perpetually, for strong necessity holds it in the bondage of a limit, which keeps it apart, because it is not lawful that Being should be incomplete, for it is not defective, whereas Not-being would lack everything. The same thing is for conceiving as is cause of the thought conceived ; for not without Being, when one thing has been said of another, will You find conceiving. And time is not nor will be another thing alongside Being, since this was bound fast by fate to be entire and changeless."
Parmenides, fragment 8, 29-35.I

Ironically (or by force of apory ?), the idealism of Parmenides, thinking the necessity of the object of thought, confuses between a substantialist and a predicative use of the verb "to be" or the copula "is". That something "is" (or "Dasein") is not identical with what something "is" (or "Sosein"). Properties (accidents) do exist apart from the "being" of the substances they describe. Absence of certain accidents can be expressed.

From the substantialist point of view, not-being is pointless. Only an all-comprehensive "Being" can be posited. Parmenides asserted further predicates of the verb "to be", namely by introducing the noun-expression "Being", conceived as ungenerated, imperishable, complete, unique, unvarying and non-physical ...

He did not grasp the absence of certain properties as not-being, nor could he attribute different forms of "being" to objects. What Parmenides calls "Being", is an all-comprehensive being-there standing as being qua being, as "Dasein" in all the entities of the natural world (trapped in their "Sosein").

Democritus of Abdera

"All thinkers then agree in making the contraries principles, both those who describe the All as one and unmoved (for even Parmenides treats hot and cold as principles under the names of Fire and Earth) and those too who use the rare and the dense. The same is true of Democritus also, with his plenum and void, both of which exist, he says, the one as being, the other as not-being. Again he speaks of differences in position, shape, and order, and these are genera of which the species are contraries, namely, of position, above and below, before and behind ; of shape, angular and angleless, straight and round."
Aristotle : Physics, book 1, part 5.

Democritus of Abdera (ca. 460 - 380/370 BCE), geometer and known for his atomic theory, developed the first mechanistic model and introduced conceptual empiricism. His system represents, in a way more fitting than the aphorisms of Heraclitus, a current of thought radically opposing Eleatic thought, drawing its inspiration from the object of thought as posited by the senses.

The evidence of sensation cannot be denied. The Eleatics are obviously wrong. Instead of relying on the formal conditions of thought only, the origin of knowledge is given with the undeniable evidence put forward by the senses. Becoming, movement and change are fundamental. Hence, not-being exists. It is empty space, a void. If so, then being is occupied space, a plenum. The latter is not a closed unity or continuum, a Being, but an infinite variety of indivisible particles called "atoms".

The atoms are all composed of the same kind of matter and only differ from each other in terms of their quantitative properties, like extension, weight, form and order. They never change and cannot be divided. For all of eternity, they cross empty space in straight lines. Because these atoms collided by deviating ("clinamen") from their paths, the world of objects came into existence (why they moved away from their linear trajectories remains unexplained). Hence, the universe is composed of a multiplicity of atoms moving and colliding in empty space ... Each time this occurs, they form a vortex separated from the rest of the universe, thus forming a world on its own. Hence, an infinite number of simultaneous and successive worlds are in existence.

Objects emerge by the random aggregation of atoms. Things do not have an "inner" coherence or "substance" (essence). Everything is impermanent and will eventually fall apart under the pressure of new collisions. Atoms are characterized by quantitative features only. Thus, all spiritual, psychological and mental processes can be reduced to conglomerates of atoms moving without inner principle of unity. Thoughts, feelings, volitions and the like, are nothing more than mechanical activities between atoms. Qualities are subjective interpretations of quantities. Hence, the universe is material, quantitative, deterministic and without finality.

Regarding knowledge, Democritus conjectures that the senses are all derived from the sense of touch. The atoms bombard the senses and give a picture of the object emitting them. As a function of their speed, form etc. we can speak of sweet, blue etc. These names are only conventional and do not convey any real characteristic of the object in question.

This whole analysis does not lead to skepticism and pure relativism. Human beings are able to discover the true, real features of a thing behind the dark veil of the senses. This is rational knowledge. Indeed, without the latter, it would not be possible to develop the mechanistic model !

The logical difficulty is obvious : if all things are atoms, then how can rational knowledge be more reliable than sensation ? Moreover, how can atomism describe atoms without in some way transcending them ? In epistemological terms : how can the subject of knowledge be eclipsed hand in hand with a description of this "fact" ? There is a contradictio in actu exercito : although refusing the subject of knowledge any independence from the object of knowledge, the former is implied in the refusal. By the necessities of the architecture of conceptual thought, every observation implies a subject of observation.

The problems facing Democritus are those of realism (materialism) in general. They mirror those of Eleatic idealism (spiritualism). Both represent the two poles of the essential tension characterizing thought in pre-Socratic philosophy (cf. Clearings, 2006).

The pendulum-swing between realism and idealism, or, in other words, the exorcism of respectively either subject or object of knowledge, can be identified in pre-Socratic thought as the apory between Parmenides & Democritus. Both exemplify a movement of thought allowing it to exceed and thus reduce (repress) its natural anti-pode. Idealism rejects the object of sensation, realism the constructive activity of the subject of thought. Instead of harmonizing both, by introducing a principle of complementarity, thought is crippled by a contradiction. In each case, the necessities lay bare by this forced monism (either of mind or of matter), bring the structure of both poles to the fore : Parmenides thinks the logical conditions a priori, leading to oneness, universality and qualitative uniqueness, Democritus observes the empirical conditions a posteriori, bringing in an infinite series of singular atoms and quantitative multiplicity.

08. Conceptual rationality in the Sophists and Socrates.

"Nothing exists. If anything existed, it could not be known. If anything did exit, and could be known, it could not be communicated."
Gorgias of Leontini : On What is Not, or On Nature, 66 - 86.

With the start of the Vth century BCE, Greek philosophers showed less interest in cosmological issues, but instead turned to practical questions of education, economy & politics. On the one hand, international awareness made some question the natural foundation of morality and justice, which seemed more a matter of habit & convention ("nomos") than being the expression of the unchanging natural law ("physis"). On the other hand, the rise of powerful city-states ("polis") accommodated the study of good citizenship.

After the Persian Wars, the rich wanted "areté", virtue, merit and social esteem. And to be successful, especially in Athens, one had to be able to convince by using words. The sophists were wandering teachers paid to teach how to use words and arguments to win a cause. They were not concerned with the contents, nor with the truth-value of their mental strategies, but only with the result of convincing an audience hic et nunc.

Inventing rhetoric (cf. Gorgias), the sophists posited the relativity of thought, making the human the measure of all things in the process of escaping the wilderness (cf. Protagoras) or rejecting culture and embracing the right of the strong to express their natural instincts, i.e. enslaving the weak and glorifying egoism (cf. Callicles). Because of their blunt rejection of objective, extra-mental truth, both Socrates (470 - 399 BCE) & Plato tried hard to refute the relativism & skepticism of the Sophist they rejected.

By introducing the relativity of thought (skepticism and humanism), the sophists prompted a new quest for a comprehensive system. In it, the various facets developed since Thales would have to be brought together so true knowledge would remain certain and eternal (and not circumstantial and probable).

Socrates, as Plato, Xenophon & Aristophanes depict him, wanted to know the "eidos" or "essence" of words, not just their rhetoric, opportunistic applications. He was convinced there was an object, extra-mental reality which could be known by way of dialogue, conversation, induction and apory. View and method of Socrates influenced Plato.

09. Concept-realism : Plato and Aristotle.

The abstract concept is the core of formal rationality, maintaining a clear-cut demarcation between subject & object of experience. The object is felt to have substance & independence, while the subject is deemed active, interactive and symbolizing. Parmenides and Democritus were the first to explore the possibilities of the poles of conceptual thought, but a system of philosophy is absent. To combat the sophists thoroughly, Socrates & Plato launched a comprehensive philosophical inquiry, advancing Platonic concept-realism.

Greek concept-realism, gratifying the  tendency of conceptual thought to fossilize & substantialize its inherent duality, developed two radical answers and two major epistemologies. These were foremost intended to serve ontology, or the study of "real" beings, as does the logic underpinning them. Indeed, neither Plato or Aristotle developed the quantitative view of the world as proposed by Democritus. Their comprehensive systems contain no mathematical physics.

In concept-realism, concepts must refer to something "real", either in the mind or extra-mental. Our thoughts (even imaginations) are always about some thing. In concept-realism, this "real" is a sufficient ground guaranteeing the identity of every thing. For the Greeks, the "real" had to be universal ("ta katholou", or applicable everywhere and all the time). Given the duality of conceptual reason (formal rationality), two positions emerged : either these universals exist by themselves outside the sensoric world (the real is ideal - cf. Plato) or they only exist as the form of things in each individual thing (the ideal is real - cf. Aristotle). In the former, a cleavage occurs and dualism emerges (between being and becoming), in the latter, a quasi-Divine "intellectus agens" has to be posited. Again two reductions of the ongoing, crucial tension of thought, i.e. the continuous, shocking confrontations between object and subject of knowledge : the concordia discors characterizing formal, conceptual, discursive rationality.

Plato

For Plato (428 - 347 BCE), strongly influenced by Pythagoras and the Eleatics, there is a real, Divine world of ideas "out there" or, as in neo-Platonism, "in here", a transcendent realm of Being, in which the things of this fluctuating world participate. Ideas are those aspects of a thing which do not change.

Obviously then, truth is the remembrance ("anamnesis") of (or return to) this eternally good state of affairs, conceived as the limit of limits of Being or even beyond that. These Platonic ideas, like particularia of a higher order, are no longer the truth of this world of becoming but of another, better world of Being, leaving us with the cleaving impasse of idealism : Where is the object ?

The Platonic ideas exist objectively in a reality outside the thinker. Hence, the empirical has a derivative status. The world of forms is outside the permanent flux characteristic of the former, and also external to the thinking mind and its passing whims. A trans-empirical, Platonic idea is a paradigm for the singular things which participate in it ("methexis"). Becoming participates in Being, and only Being, as Parmenides taught, has reality. The physical world is not substantial (without sufficient ground) and posited as a mere reflection. If so, it has no true existence of its own (for its essence is trans-empirical). Plato projects the world of ideas outside the human mind and represents the transcendent pole of Greek concept-realism, for the "real" moves beyond our senses as well as our minds. To eternalize truth, nothing less will do.

Aristotle

Aristotle (384 - 322 BCE) rejects the separate, Platonic world of real proto-types, but not the "ta katholou", the generalities ("les généralités", "die Allgemeinen"), conceived, as conceptual realism demands, in terms of the "real", essential and sufficient ground of knowledge, the foundation of thought. So general, universal ideas do exist, but they are always immanent in the singular things of this world. There is no world of ideas "out there". There is no cleavage in what "is" and there is only one world, namely the actual world present here and now. The indwelling formal and final causes of things are known by abstracting what is gathered by the passive intellect, fed by the senses, witnessing material and efficient causes. The actual process of abstraction is performed by the intellectus agens, a kind of Peripatetic "Deus ex machina", reminding us of the impasse of realism : Where is the subject ?

"The faculty of thinking then thinks the forms in the images, and as what is to be pursued or avoided is already marked out for it in these forms, the faculty can, by being engaged upon the images, be moved, and this also in a way independent from sensation."
Aristotle : De Anima, III.7.

How is this first intellect able to derive by abstraction the universal on the basis of the particular ? How does it recognize the forms in the images without (Platonic) proto-types ? Even a very large number of particulars does not logically justify a universal proposition, as Aristotle knew. Induction has no final clause, for all past causes can never be known. How does this active intellect then recognize the similarities between properties offered by the passive intellect, if not by virtue of a measure which is independent from sensation (and so again introducing a world of ideas) ?

Aristotle posits the objective forms in the actual world. In the latter, both being and becoming operate. This was a major step forward, for ontological dualism is explicitly avoided, although implicitly reintroduced within psychology. The forms are realized in singulars, but known by accident of a universal intellect he does not study. For him, the "real" is known through the senses and the curious abstracting abilities of the mind. The workings of the intellectus agens remain dark. This concept-realism is immanent. All things are explained in terms of four causes : causa materialis, causa efficiens, causa formalis and causa finalis. Experience of the first two causes, triggers the process of cognition and knowledge of material bodies. Abstracting the last two causes, allows one to understand the "form" or essence of things.

In Platonic concept-realism, one cannot avoid asking the question : How can another world be the truth of this world ? The ontological cleavage seems totally unacceptable. Peripatetic thought summons a psychological critique, for how can the human soul possibly know anything if not by virtue of this remarkable active intellect ? Both reductions are problematic. Because they try to escape, in vain, the Factum Rationis, and so represent the two extreme poles of the concordia discors of thought, they form an apory. Plato, being an idealist, lost grip on reality. Aristotle, the realist, did not fully probe his own mind. Composite forms of both systems do not avoid the conflict, although they may conceal it better. The crucial tension of thought was not solved by Greek concept-realism. How to evolve formal rationality beyond this dilemma ?

The two major philosophical systems of Greek philosophy are examples of foundational thinking. Truth is eternalized and static. Concept-realism will always ground our concepts in a reality outside knowledge. Plato cuts reality in two qualitatively different worlds. True knowledge is remembering the world of ideas. Aristotle divides the mind in two functionally different intellects. To draw out and abstract the common element, an intellectus agens is needed. But, both positions reveal new insights : knowledge is impossible without innate forms (Plato) versus knowledge starts with sensation (Aristotle). Greek thought is unable to reconcile the extremes and so no armed truce ensued. One tried to avoid the concordia discors by eliminating the other side of the equation. These tensions, like open wires, short-circuited Medieval logic, preparing thought for its emancipation from fideism and fundamental theology.

10. Fideism or the onto-theological ground.

Although the Romans established a vast political unity (cf. the Pax Romana), focusing on monumental, lasting social, administrative and judicial order backed by a strong military, their intellectual influence on the Middle Ages was not as profound as the Greek legacy. The following components were decisive :

• the quality and variety of Greek philosophy : pre-Socratics, Plato-Aristotle, Hedonists, Epicurists, Cynics, neo-Platonists, Stoics, etc. ;

• Greek art and science : mathematics, geometry, cosmology, architecture, grammar, linguistics, drama, sculpture, etc. 

• anthropocentrism : the human and his emancipation were of central concern ;

• ideal of the abstract : study devoid of practical consequences, aiming at absolute knowledge coupled with tolerance, dialogue, contradiction and argumentation ;

• impact of reason on action : the search for harmony, measure and balance.

The Christian Empire of Constantine the Great (ca.274/288 - 337) heralded the beginning of the end of "Pagan" philosophy and the indoctrination "de manu militari" of Catholic dogma (cf. Council of Nicea of 325 CE). Both in Rome, Alexandria and Constantinople, revealed knowledge was deemed superior than independent, rational thinking and philosophy was made to serve fundamental theology. The latter was based on an exegesis of the canon of the New Testament (a name invented ca. 190 CE). These 27 books  were accepted by the majority of the Roman Church as late as 382 CE (Concilium Romanum).

In 415 CE, the Hellenized Egyptian scientist & Platonic philosopher Hypathia of Alexandria (ca. 370 - 415), the inventor of the astrolabe and the hydrometer, was brutally murdered by a raging Christian mob tolerated by the Patriarch Cyril of Alexandria (ca. 375 - 444). They tore off her clothing and dragged her through the streets of the city till she died ! In 529 CE, under the Christian emperor Justinianus, who commissioned the Hagia Sophia, the Platonic Academy at Athens was closed. To fight those who made a different choice (or "heretics"), institutionalized Christianity was all but loving & kind. In those days, and for many more centuries to come, violence, repression, blacklisting, the suppression & burning of manuscripts, the rewriting of history etc. would remain common practices in both Western Catholicism and Eastern Orthodoxy alike.

Revealed knowledge was eternal and absolute, for unveiling the "Creator-God" of all possible things, i.e. God as the ground of grounds and focal point of a theology rooted in the axiom of the existence of this transcendent God (onto-theology). Educated by Late Hellenism, early Christian thinkers allowed Greek concepts to infiltrate the emerging Christian theology and its apology, in particular those of Plato and neo-Platonism, as evidenced by the first "sum" of Christian philosophy (or philosophy of the revealed texts), the work of Augustine of Hippo (354 - 430). For him, three "imperial" principles of faith stood firm : the Incarnation of the Son of God, the God-Man Jesus Christ and the Representative of Christ on Earth (the Pope of Rome).

The major difference between ancient philosophy (rooted in the maxim "know thyself") and the end of Late Hellenism, is the beginning of a purely theoretical and abstract pursuit, divorced from the oral tradition of the art of living. If ancient philosophy had been a way of life (in the "polis"), implying the total person (including affects and volition besides cognition), the Middle Ages would develop a purely intellectual, exegetic scholastic approach, still with us in philosophy today. Spiritual exercises were no longer deemed part of philosophy, but were integrated in Christian spirituality. Religion realized the transformation of one's personality and oriented one's whole way of being, not philosophy. Of course, the conceptions of Christocentric & Trinitarian monotheism, as well as the sense of hierarchy and liturgy, serving Roman & Byzantine Christianity, sum up, albeit "Christianized", the essence of Paganism.

Fideism holds faith above reason, or worse, denies reason its place. However, as soon as faith needs to be explained to convert the infidel or to refute the arguments of critical non-believers, reason is needed (cf. the Apologetics). Then, as the servants of dogma, logic and philosophy accommodate theology, and adapt to the necessities of sacred, miraculous texts ...

When Imperial Rome's upper classes turned Christian, they were driven by Late Hellenistic fears (the collapse of a weakened empire) and spiritual pessimism (cf. the astral fatalism of Pagan religions). The intellectual elite sought refuge in the salvic simplicity advocated by the Roman centrist, based on an act of will, a leap of faith, but not in the elaborate trappings of the mysteries, nor in the Gnostics. Thus, Christian intellectuals (starting with Augustine and ending with Thomas Aquinas) slowly "Christianized" Pagan philosophy, "explaining" the religion of Jesus Christ in a logic borrowed from Late Hellenism. Even Trinitarian theology could benefit from the elaborated triadic speculations of neo-Platonism.

In the 9th century, thanks to the Carolingian Renaissance, and the organization of the Palatine School, a remote ancestor of the Renaissance "university" ("turned towards unity") was created. Europe, under the political will of Charlemagne, was awakened to its "rational" inheritance and embraced the importance of education and learning (for the upper classes). Although short-lived, its influence would not completely vanish.

Usually depicted as a transitional figure between fideist & scholastic theology, the Benedictine Anselm of Canterbury (1033 - 1109) was a protagonist of the Augustinian tradition. Philosophy is only dialectica (logic, rhetoric, linguistic) and part of theology. Nevertheless, his position within this fideist movement is rationalistic, for he seeks the "rationes necessariae" (necessary reasons) for the existence of God, but also for revelations as the Holy Trinity and the Incarnation of Christ. However, his rationalism is provisional, for Anselm believes so he may understand ("credo ut intelligam"), but does not seek to understand in order to believe.

The context in which he operated, the vows he took, deny Anselm to openly profess the distinction between philosophy and theology, and so, even if he had not been able to find the necessary reasons for Divine existence, he would not, therefore, have rejected the existence of God. Perhaps is it fair to say Anselm is the most dialectical pole within the Augustinian movement and its blatant fideism, overturned by Thomas Aquinas (1225 - 1274).

11. Real and rational science in scholasticism.

In his Isagoge, a work translated by Boethius, Porphyry (232/3 - ca. 305) had written :

"I shall not say anything about whether genera and species exist as substances, or are confined to mere conceptions ; and if they are substances, whether they are material or immaterial ; and whether they exist separately from sensible objects, or in them immanently."
Porphyry : Isagoge, 1, introduction.

For Boethius, considering these matters to be "very deep", the answer is Aristotelian : the universals have an objective existence in particular physical things only, but the mind is able to conceive genera and species independent of these bodies.

For Isidore of Sevilla, who died in 636 CE, etymology was the crucial science, for to know the name ("nomen") of an object gave insight into its essential nature. Hence, he posits an implicate adualism between the name (or word) and its reality or "res". This symbolic adualism or natural sympathy (correspondence) differentiates not between an "inner" subjective state of consciousness and an "outer" objective reality (cf. ante-rationality and its psychomorphism). This view was a blunt return to Plato and the Eleatic cleavage between "is" & "is not". Indeed, the core of the Augustinian interpretation of Christianity is neo-Platonic. Here, symbolical adualism (between "nomen" and "res") walks hand in hand with ontological dualism, for the true name of a thing reveals its unchanging, transcendent essence or substance by way of a direct, transcendent intuition, precisely because there is a radical division between the perfect, true world of Being and the incomplete, false world of becoming, only bridged by the Holy Spirit and His intuitive gifts. So, true knowledge, necessary and eternal, is not derived from the senses, nor from the workings of the human mind, but is placed in the soul by God, who sheds light upon our mind (illuminism).

Clearly the problem of universals touched the foundation of fideist thinking, which tried to identify general names (like "God") in the mind with universal objects in extra-mental reality.

On the one hand, there was the ultra-realistic position, or "exaggerated realism", found in the De Divisione Naturae of John Scotus Eriugena (ca. 810 - 877) and the work of Remigius of Auxerre (ca. 841 - 908), who taught that the species is a "partitio substantialis" of the genus. The species is also the substantial unity of many individuals. Thus, individuals only differ accidentally from one another. All beings are thus modifications of one Being. A new child is not a new substance, not a new "soul", but a new property of the already existing substance called "humanity" (a kind of monopsychism avant la lettre may be noted).

On the other hand, very soon heretics in dialectic rose. For Eric (Heiricus) of Auxerre (841 - 876), general names had no universal objects corresponding to them. Universals concepts arise because the mind gathers together ("coarctatio") the multitude of individuals and forms the idea of species. This variety is again gathered together to form the genus. Only individuals exist. By the process of "coarctatio", many genera form the extensive concept of "ousia" ("substantia"). In the same line, Roscelin (ca. 1050 - 1120) held that a universal is only a word ("flatus vocis") and so "nihil esse praeter individua" ...

Peter Abelard

In the Middle Ages, this apory between exaggerated realists ("reales") and nominalists ("nominales"), itself a logico-linguistic transposition of the ontological apory between Plato and Aristotle (cf. concept-realism), is best illustrated by the clash between William of Champeaux (1070 - 1120), and Abelard (1079 - 1142). The latter was a rigorist dialectic arguing against the "antiqua doctrina", and, according to the famous Bernard of Clairvaux (1090 - 1153), an agent of Satan !

Abelard argued, that according to William of Champeaux, only ten different substances or "essences" exist (namely the 10 categories of Aristotle). Hence, all living beings, subsumed under "substance", are substantially identical, and so Socrates and the donkey Brunellus are the same. In his early days, William of Champeaux taught, against his teacher Roscelin, that the individual members of a species only differ accidentally from one another. But this identity-theory came under severe attack and so he changed it. Some say as a subterfuge, William later replied to Abelard with his indifference thesis, according to which two members of the same species are the same thing, not "essentialiter" but "indifferenter". Peter and Paul are "indifferently" men (they thus possess humanity "secundum indifferentiam"), because as Peter is rational, so is Paul, whereas their humanity is not the same, i.e. their nature is not numerically the same, but like ("similis"). In fact, agreeing with one of Abelard's polemical interpretations, he is saying the universal substances of both are alike, applying indifferently to both or any other man.

Abelard's "nominalism" is a denial of ultra-realism in epistemology, i.e. against the adualism between "vox" and "res". He does not refute Platonic "ideae" preexisting in the mind of God, but understands these as the metaphysical foundation of the real similarities in status between objects of the same species, and not of the particular objects (as Platonism insists). So the ideas explain how two things may be alike, but objects do not participate in ideas, nor are these ideas the "ousia" or "substantia" of objects.

Abelard's analysis states the distinction between the logical and the real orders, but without the denial of the objective foundation of the universals. This early nominalism is a moderate realism. He demonstrated how one could deny exaggerated realism without being obliged to reject the objectivity of genera and species.

For Abelard, universals were by nature inclined to be ascribed to several objects. They are only words, not things (against the "reales"). When identified with words, universals are not reduced to mere "sound" (which is also a "res"), but to the signifying power of words (against the "nominales"). This "significatio" of words is not a concept accompanying the word (a mere contents of mind, i.e. exclusively subjective), but gives expression or meaning to the objective status of the word (semantics). This status is a human convention based on real similarities between the particulars, but these real "convenientia" are not a "res", not "nihil" but a "quasi res", for example, it is not the substance "homo" that makes human beings similar, but the "esse hominem".

For Abelard, objectivity, found in universal propositions, is a human convention based on real similarities between particulars. The latter exist on their own. Ideas are the metaphysical foundation of the similarities between objects. They are not the "ousia", "eidos", essence or substance of things. These conventions have a special status, for they stand between being and nothing.

The extraordinary contribution of Abelard to scholastic epistemology is that he was able to avoid the apory of the concordia discors by introducing a third option :

1. universale ante rem : the universals exist before the realities they subsume : Platonism ;

2. universale in re : the universals only exist in the realities ("quidditas rei") of which they are abstractions : Aristotelism ;

3. universale post rem : universals are words, abstact universal concepts with a meaning, given to them by human convention, in which real similarities between particulars are expressed. These are not "essentia" and not "nihil", but "quasi res".

This juggling may conceal the larger issue at hand : if extra-mental objects are particulars and mental concepts universals, then how to think their relationship ? Does an extra-mental foundation of universals exist ? The Greeks as well as the Scholastics answered affirmatively. The idea of a foundation of knowledge was still present.

For the Scholastics, given their preoccupation with God, the problem was to know whether an objective, extra-mental reality corresponded to the universals in the mind ? If so, then the mere concept of "God" might entail Divine existence, as the a priori proof tries to argue. If not, rational knowledge resulted in skepticism and Divine existence might be argued a posteriori only. Greek rationalism was concept-realism & ontological, whereas Medieval dialectics was foundational and logico-linguistic (psychological).

Abelard's solution involves a crucial distinction : universals are not real, but they are words (real sounds) with a significance referring to real similarities between real particulars. Because of their meaning, they are more than "nothing". The foundation of his nominalism is "the real" as evidenced by similarities between objects, whereas the "reales" supposed an ante-rational symbiosis between "verbum" and "res", between Platonic ideas and material objects ("methexis").

William of Ockham

"Although it is clear to many that a universal is not a substance existing outside the mind in individuals and really distinct from them, still some are of the opinion that a universal does in some manner exist outside the mind in individuals, although not really but only formally distinct from them. (...) However, this opinion appears to me wholly untenable."
Ockham : Summa totius logicae, I, c.xvi.

With the Franciscan monk William of Ockham (1290 - 1350), theologian & philosopher, the "via moderna" received its most logical of defenders. Thomists, Scotists and Augustinians formed the "via antiqua". It is their realism, Platonic (the essence is transcendent) as well as Aristotelic (the essence is immanent), which was firmly rejected. Instead, nominalism was promoted, but one without objective universals. It was hence more radical than Abelard's. No reality ("quid rei") is ever attained, but only a nominal representation ("quid nominis").

For Ockham, the metaphysics of essences was introduced into Christian theology and philosophy from Greek sources. So, contrary to Abelard's moderate nominalism, his strict nominalism did not incorporate them. There are no universal subsistent forms, for otherwise God would be limited in His creative act by these eternal ideas. Indeed, every idea is limited by its own individuality. This non-Christian invention has no place in Christian thought. Universals are only "termini concepti", final terms signifying individual things which stand for them in propositions.

It was Peter of Spain (thirteenth century), who's exact identity is unknown, who had distinguished between probable reasoning (dialectic), demonstrative science & sophistical reasoning. Ockham was influenced by this emphasis placed on syllogistic reasoning leading to probable conclusions. Hence, arguments in philosophy (as distinct from logic) are probable (terministic) rather than demonstrative. Formal logic is demonstrative, whereas terministic logic is probable.

For Ockham, who took the equipment to develop this terminist logic from his predecessors, empirical data were primordial and exclusive to establish the existence of a thing. The validity of inferring from the existence of one thing to the existence of another things was questioned. He distinguished between the spoken word ("terminus prolatus"), the written word ("terminus scriptus") and the concept ("terminus conceptus" or "intentio animæ"). The latter is a natural sign, the natural reaction to the stimuli of a direct empirical apprehension. Only individual things exist. By the fact a thing exists, it is individual. There cannot be existent universals, for if a universal exists, it must be an individual, which is a contradictio in terminis (for universals are supposed to subsume individuals).

This focus on the objects which are immediately known, goes hand in hand with the principle of economy to get rid of the abstracting "species intelligibiles". What is known as "Ockham's Razor" was a common principle in Medieval philosophy. Because of his frequent usage of the principle (cf. the Franciscan vow of poverty), his name has become indelibly attached to it. In Ockham's version it reads : "Pluralitas non est ponenda sine neccesitate." (plurality should not be posited without necessity). In general terms, this principle of simplicity or parsimony is to always prefer the least complicated explanation for an observation.

Radical nominalists, like Nicolas of Autrecourt (ca. 1300 - ca. 1350), who belonged to the Faculty of Arts, would say no inference from the existence of one thing to the existence of another thing could be demonstrative or cogent, but only probable. Hence, necessity and certainty, idolized by the foregoing metaphysical systems, were gone. No demonstration of God's existence was possible. Such matters have to be relegated to the order of adherence to revealed knowledge or faith. At this point, theology and philosophy separate and the latter becomes a "lay" activity. This is not yet apparent in Ockham, who remains a theologian seeking to find a way to rethink the "proof" of God's existence in merely a posteriori terms.

Against his predecessors, Ockham accepts "being" as one concept common to creatures and God, meaning "being" is predicable in a univocal sense of all existent things. Without such a concept of being, the existence of God could not be conceived. But, this does not mean that this concept acts as a bridge between empirical observation of creatures and the existence of God. The concept of being is univocal in the sense that this concept is common to a plurality of things, neither accidentally or substantially alike (thus avoiding pantheism).

These thought bring the distinction between "scientia realis" and "scientia rationalis" to the fore. The former is concerned with real, individual things. He agrees with Aristotle that only individuals exist, but rejects the doctrine that science is of the universal. The latter are not forms realized in individuals (realities existing extramentally). Real science is only concerned with universal propositions, i.e. with their truth or falsity (for example : "Man is capable of laughter."). To say a universal proposition in science is "true", is to say that it is verified in all individual things of which the "terms" of the proposition are the natural signs. The terms known by real science stand for individual things, whereas the terms of the propositions of rational science (like logic) stand for other terms.

With Ockham, concept-realism is finally relinquished. The universals are limit-concepts. The foundational approach is also left behind. The nominal representations arrived at in real science are terministic, i.e. probable, not certain. They concern individuals, never extra-mental "universals". Real science deals with true or false propositions referring to individual things. These empirical data are primordial and exclusive to establish the existence of a thing. The concept ("terminus conceptus" or "intentio animæ") is a natural sign, the natural reaction to the stimuli of a direct empirical apprehension. Rational science is possible, but it does not concern natural signs but other terms.

For Ockham, the long scholastic dealings with concept-realism were futile. Universals are not before, not in and not after particulars. They are simply abrogated. Given the religious context at hand, only faith remains. Science is given a limited extension only. Nevertheless, by positing empirical data as primordial, Ockham comes close to realism, grounding knowledge (subreptively ?) in direct empirical apprehension, as would Thomas Aquinas before him. The latter had returned to concept-realism and backed Aristotle. Intellectual knowledge (science) derived from the senses and from abstraction (cf. the intellectus agens). The influence of Thomism was so vast that Ockham's message passed unnoticed.

12. Rationalism and empirism of nature.

"The scholastic university, dominated by theology, would continue to function up to the end of the eighteenth century, but from the sixteenth to the eighteenth centuries, genuinely creative philosophical activity would develop outside the university, in the persons of Descartes, Spinoza, Malebranche and Leibniz."
Hadot, 1995, p.270.

Between the 16th and 18th centuries, Europe developed a new vision of the human. Differing radically from anything before, it became an example for non-Europeans to follow. Eventually, this new ideal conquered the civilized world. Its essential components were :

• focus on the empirical : the transcendent realities of myth and religion are replaced by what the senses bring ;

• humanism : the human is put in the center and given an ultimate value to which everything else had to be subdued. Egocentrism & the subjugation of nature to the will of the human prevailed ; 

• openness : commerce brings the unknown into focus and exploration is of the order of the day, everything is possible & there are no sacred grounds ;

• pluralism & tolerance : slowly the realization dawned that other people, groups, nations etc. have the right to take their own development at heart ;

• rationalism & utility : science & technology are deemed crucial to eliminate the difficulties encountered : anticipation, prediction, self-control, efficiency, argumentation etc. become more important ;

• pretence : the rational, calculating, planning and self-controlling Westerner becomes highly optimistic and develops pride in his enormous achievements, anticipating to become God himself, i.e. achieve immortality on Earth ;

• democracy : with the French Revolution (1789), a new political consciousness dawned. Divine kingship could no longer be accepted and with its demise the world was again transformed.

René Descartes

"Il y a déjà quelque temps que je me suis aperçu que, dès mes premières années, j'ai reçu quantité de fausses opinions pour véritables, et que ce que j'ai depuis fondé sur des principes si mal assurés ne saurait être que fort douteux et incertain ; et dès lors j'ai bien jugé qu'il me fallait entreprendre sérieusement une fois dans ma vie de me défaire de toutes les opinions que j'avais reçues auparavant en ma créance, et commencer tout de nouveau dès les fondements, si je voulais établir quelque chose de ferme et de constant dans les sciences."
Descartes, R. : Meditations, 1, § 1a.

To seek indubitable truth, René Descartes (1596 - 1650) turned to methodological doubt. He left the Jesuit college of La Flèche and was ashamed of the amalgam of doubts and errors he had learned there. Traditional philosophy consisted of various contradicting opinions, grosso modo Platonic or Peripatetic. History was a series of moral lessons (cf. Livius) and philosophy was still restricted to logic. The experimental method was absent, and various authorities ("auctoritates") were studied (Galenus, Aristotle, Avicenna, etc.). Aim was to harmonize the magisterial contradictions (cf. the "sic et non" method). In the interpretation of these sources, a certain creativity was at work. However, in the mind of Cartesius, the only constructive point of his education, so the Discourse on Method (1637) tells us, was the discovery of his own ignorance.

This discovery prompted Descartes to reject all prejudices and seek out certain knowledge. Nine years he raises doubts about various conjectures and opinions covering the whole range of human activities. Eventually, doubt is raised regarding three sources of knowledge :

1. authority : as contradictions always arise between authorities a higher criterion is needed ;

2. senses : maybe waking experience is just a "dream" or a "hallucination" ? Can this be or not ? Also : the senses give confused information, so a still higher criterion is needed ;

3. reason : how can we be certain some "malin génie" has not created us such, that we accept self-evident reasoning although we are in reality mislead and in fatal error ?

However far doubt is systematically applied, it does not extend to my own existence. Doubt reveals my existence. If, as maintained in the Principles of Philosophy, the word "thought" is defined as all which we are conscious of as operating in us, then understanding, willing, imagining and feeling are included. I can doubt all objects of these activities of consciousness, but that such an activity of consciousness exists, is beyond doubt.

Thus, the "res cogitans", "ego cogitans" or "l'être conscient" is the crucial factor in Cartesian philosophy. Its indubitable, intuitively grasped truth ? Cogito ergo sum : I think, therefore I am. That I doubt certain things may be the case, but the fact that I doubt them, i.e. am engaged in a certain conscious activity, is certain. To say : "I doubt whether I exist." is a contradictio in actu exercito, or a statement refuted by the mere act of stating it.

The certainty of Cogito ergo sum is not inferred but immediate and intuitive. It is not a conclusion, but a certain premiss, an axiom. It is not first & most certain in the "ordo essendi", but as far as regards the "ordo cognoscendi". It is true each time I think, and when I stop thinking there is no reason for me to think that I ever existed. I intuit in a concrete case the impossibility of thinking without existing. In the second Meditation, Cogito ergo sum is true each time I pronounce or mentally conceive it ...

Having intuited a true and certain proposition, Descartes seeks the general criterion of certainty implied. Cogito ergo sum is true and certain, because he clearly and distinctly sees what is affirmed. As a general rule, all things which I conceive clearly and distinctly are true. In the Principles of Philosophy, we are told "clear" means that which is present and apparent to an attentive mind and "distinct" that which contains within itself nothing but what is clear.

Although he has arrived at a certain and clear proposition, he does not start to work with it without more ado. Indeed, suppose God gave me a nature which causes me to err even in matters which seem self-evident ? To eliminate this "very slight" doubt, Descartes needs to prove the existence of a God who is not a deceiver. Without this proof, it might be so that what I conceive as clear and distinct, is in reality not so (cf. Does the Divine exist ?, 2005).

Both in the Meditations and the Principles of Philosophy, substance is demonstrated after proving the existence of God. However, the "I" in Cogito ergo sum, is not a transcendental ego (a mere formal condition of knowledge), but "me thinking". Despite various contents of thought, the thing that cannot be doubted is not "a thinking" or "a thought", but a thinking ego conceived as a substance. This ego is not formal, nor the "I" of ordinary discourse, but a concrete existing "I". Descartes uncritically assumes the Scholastic notion of substance, while this doctrine is open to doubt, as Kant will show. Thinking does not necessarily require a thinker, and the ego cogitans must not be a thing which thinks, but a mere transcendental ego accompanying every cogitation (cf. Kant).

At this point, the apory resulting from a mismanagement of the concordia discors or armed truce between object and subject of thought, animating all possible thought, reappeared and entered modernism.

Transcendental logic makes both terms of the formal equation offered by the Factum Rationis necessary and not reducible. In terms of acquiring knowledge, this implies object and subject of knowledge have to be used simultaneously. But like Plato and the "reales" after him, Descartes eclipses the object of knowledge by inflating an ego cogitans in terms of a substantial ego, solely reflecting on itself, and as Leibnizean monad, without windows on the world and the alter ego. The Spinozist definition of God and freedom being the mature example of the substantializing (ontologizing) effect of this idealistic reduction of the discordant concord or armed truce of thought.

"By God, I mean the absolutely infinite Being - that is, a substance consisting in infinite attributes, of which each expresses for itself an eternal and infinite essentiality."
Spinoza : Ethics, Part I, definition VI.

"That thing is called 'free', which exists solely by the necessity of its own nature, and of which the action is determined by itself alone. That thing is inevitable, compelled, necessary, or rather constrained, which is determined by something external to itself to a fixed and definite method of existence or action."
Spinoza : Ethics, Part I, definition VII.

Because he did not rely on the object of knowledge (deemed doubtful), Descartes rooted his whole enterprise in an ideal ego constituting the possibility and expansion of knowledge. All idealists after him would do the same. The end result of this reduction is a Platonizing theory of knowledge grounded by ontological idealism.

David Hume

In his Treatise of Human Nature (1739) and Enquiry concerning human Understanding (1748), David Hume (1711 - 1776) seeks to develop a science of man. As Locke (1632 - 1704), he envisages a critical and experimental foundation.

"Nature is always too strong for principle."
Hume, D. : Enquiry concerning the Principles of Morals, 12, 2, 128.

"Perceptions" represent the general contents of mind, and are divided in impressions and ideas. The former strike the mind with vividness, force and liveliness, whereas the latter are faint images of these in thinking. Impressions are either of sensation or of reflection. The latter are in great measure derived from ideas.

Like Ockham, Hume is a nominalist. Real or ideal universals are not the foundation to erect the science of man. Unlike Descartes, he is an empirist : the senses are the foundation of knowledge, not the intuition of the existence of the cogito. Two kinds of propositions are possible :

1. analytic : the predicate is part of the subject - these tautologies are universal and necessary, but restricted to geometry and arithmetic. All a priori propositions are analytic and have nothing to say about the world of fact, but only add structural meaning by connecting identical propositions ;

2. synthetic : the predicate is not part of the subject and an extramental reality is implied. All synthetic propositions are a posteriori and have always something to say about the world.

The extra-mental reality sought can be no other than the one offered by direct or indirect empirical experience.

1. direct synthetic propositions : the predicate is attached to the subject because of what is immediately empirically perceived here and now ;

2. indirect synthetic propositions : the predicate is attached to the subject because we move from what be know to be a direct, given fact to a state of affairs which is not (yet) empirically given. These propositions are problematic because a necessary and objective connection between our idea of causality and real events cannot be demonstrated. Moreover, logically the move from a finite series of particular observations to an infinite, necessary law can never be warranted (cf. the problem of induction in naive realism).

Suppose the observed psychological connection between fact A and fact B is continuous. Is it necessary ? My (or our) witnessing the connection more than once, does not imply that it will work tomorrow. As we do not know whether this psychological continuity is valid and based on the reality of causality, i.e. a law working independently from the mind, skepticism results. The universal value of scientific laws cannot be demonstrated, neither can the reality of the world (within and without). Science is restricted to statements of probability.

The Achilles Heel of this position is the status of the sense-data and the formation of concepts. It is unclear how sense-data can be identified without conceptual connotation, which is not a sense datum. Moreover, sensation is introduced as a sufficient ground. "Adequatio intellectus ad rem" is presupposed (as in all forms of empirical realism). Finally, how can similarities between sense-data be observed ? Empiricism identifies truth with the naive correspondence between concept and fact.

The ontologisms a priori & a posteriori (of Greek concept-realism and the Medieval scholastics of universals) gave way to the crucial distinction between analytic and synthetic propositions. On the one hand, Descartes, by introducing a substantial ego cogitans and its intuitive cogito ergo sum, reintroduced a kind of Platonism by (a) positing innate ideas and (b) backing his criterion of truth with a proof of God (making use of the criterion). On the other hand, Hume, by rejecting all but direct synthetic propositions, was unable to explain how we could draw out the common element without innate cognitive structures. Remember how Aristotle was forced to call in his intellectus agens to make abstractions possible ! Is rationalism not a return to the symbolical adualism (inneism) and its "leges cogitandi sunt leges essendi" (the laws of thinking are the laws of reality) ? Is empirism not the modern equivalent of the system of Democritus and the subsequent "veritas est adequatio rei et intellectus" ("truth is the correspondence between the intellect and reality) ? These constant pendulum-movements between subject and object of knowledge were identified by Kant and deemed a "scandal" ... How, in the light of these major apories, is knowledge possible ?

13. Kant, the shipwreck of foundationalism & criticism.

Immanuel Kant

"We thus see that all the wrangling about the nature of a thinking being, and its association with the material world, arises simply from our filling the gap, due to our ignorance, with paralogisms of reason, and by changing thoughts into things and hypostatizing them."
Kant, I. : Critique of Pure Reason, A394-398.

With his "Copernican Revolution", Kant (1724 - 1804) completes the self-reflective movement initiated by Descartes, focusing on the subject of experience. The scholastic substantialism of Descartes, identifying thought itself with his own existence as a substantial ego cogitans, is no longer presupposed. Kant probes into the pre-conditions of thought insofar as the human thinks. The idealist move from the empirical fact of thought to a thinking substance is not made. Incorporating rationalism and empirism, he avoids the battle-field of the endless (metaphysical and ontological) controversies by (a) finding and (b) applying the conditions of possible knowledge. The latter are discovered in the cognitive act and the cognitive system of which it is an application. An armed truce between object and subject had to be realized. Inspired by Newton (1642 - 1727) and turning against Hume, Kant deems synthetic propositions a priori possible (Hume only accepted direct synthetic propositions a posteriori). Why ? Because the system of categories produces scientific statements of fact which, contrary to Hume's skepticism, are always valid and necessary. This system stipulates the conditions of valid knowledge a priori and is therefore intended as the transcendental foundation of all possible knowledge, found rooted in the transcendental subject of cognition, not as an empirical ego, but as a universal condition of application in all possible thinking.

So Kant's aim was to find the conditions enabling statements of fact to be universal & necessary, i.e. as binding as the analytics of mathematics. Then, and only then, a universal and necessary science is possible. Without apory, philosophy explains how the universal physical laws of Newton are what they are. The scandal is over ... ?

With Kant, rational thought matured. Unlike concept-realism (Plato or Aristotle) and nominalism (Ockham or Hume), critical thought, inspired by Descartes, is rooted in the "I think", the transcendental condition of empirical (ego) self-consciousness without which nothing can be properly called "experience". This "I", the apex of the system of transcendental concepts, is "of all times" and represents the idea of the connected of experiences a priori. This is not a Cartesian substantial ego cogitans, nor an empirical datum, but the formal condition accompanying every experience of the empirical ego. It is the transcendental (conditional) unity of all possible experience (or apperception) a priori. Like the transcendental system of which it is the formal head, it is, by necessity, shared by all those who know.

"What can I know ?" is the first question asked by Kant. Which conditions make knowledge possible ? This special reflective activity was given a new word, namely "transcendental", not to be confused with "transcendent". This meta-knowledge is not occupied with outer objects, but with our manner of knowing these objects, so far as this is meant to be possible a priori (A11), i.e. always, everywhere and necessarily so. Kant's aim is to prepare for a true, immanent metaphysics, different from the transcendent, dogmatic ontologisms of the past, turning thoughts into things.

Modern, self-reflective thought, initiated by Descartes, implies the meditative capacity of mentally reflecting thoughts, as if the mind where a reflective surface. Cleaning it by eliminating the stains of authority, ideas and sense-input, Descartes continued to witness his own image and to identify it with his actual, physical, empirical ego-experience. Cogito ergo sum is not a conclusion, nor an inference. It seems a direct experience (intuition) of reality through ideality, in the case of Cartesius : irrespective of contents -what I think-, but only of form -that I think-. The free thinking initiated by Descartes and his self-reflective move away from scholastic substantialism is depersonalized & formalized by Kant. Transcendental inquiries involve a special meta-knowledge, produced by a particular reflective activity aiming at referring thought back to itself. In other words, critical thought introduces reflexivity or a relation holding between an element and itself (like in the case of co-referentially).

The transcendental system of the conditions of possible knowledge (or transcendental logic) is a hierarchy of concepts defining the objective ground of all possible knowledge, both in terms of the synthetic propositions a priori of object-knowledge (transcendental analytic covering understanding), as well as regarding the greatest possible expansion under the unity of understanding. These transcendental concepts are not empirical, but surface thanks to the reflexive transcendental method, bringing to consciousness principles which cannot be denied because they are part of every denial. They are "pure" because they are empty of empirical data and stand on their own, while rooted in (or suspended on) the transcendental "I think" and its Factum Rationis, the fact of reason. For Kant, reason, the higher faculty of knowledge, is only occupied with understanding, while the latter is only processing the input from the senses. Reason has no intellect to inform it. There is no faculty higher than reason.

"All our knowledge begins with the senses, proceeds thence to the understanding, and ends with reason. There is nothing higher than reason for working up the material of intuition & comprehending it under the highest unity of thought."
Kant, I. : Critique of Pure Reason, B355.

For Kant, the process of acquiring knowledge runs as follows :

1. transcendental aesthetic : empirical knowledge : a variety of direct, multiple, unordered, nameless impressions (Hume), called "Empfindungen" (or sensations) are synthesized by the forms of representation "space" (related to geometry) and "time" (related to arithmetics) and turned into "Erscheinungen" (or phenomena). These representations reflect the structure of our receptive apparatus. They are meant to structure sensations into phenomena ;

2. transcendental analytic : scientific knowledge : phenomena are only objectified by thought, but do not constitute an object of knowledge, for this is realized in propositions. The phenomena need to be structured by the 12 categories of understanding, corresponding to 12 different types of propositions (quantity, quality, relation and modality, each viewed from three angels). This categorization of phenomena leads to object-knowledge (synthetic propositions a priori). The categories are meant to structure phenomena into object-knowledge ;

3. transcendental dialectic : metaphysical knowledge : the variety of objects known is brought to a higher unity. A last, sufficient ground is sought and found in the ideas of reason : "ego", "world" and "God" (derived from the category of relation). These ideas are not things and only serve understanding, nothing more. While stimulating the mind's continuous expansion, they regulate understanding and bring it to a more comprehensive, reasonable unity. They are meant to structure understanding into an immanent metaphysics.

The 2 forms of representation, 12 categories (brought to unity by 3 ideas) make the object possible, rather than vice versa. The human mind is the active originator of experience, rather than just a passive recipient of perception, as Hume thought. The mind can not be a tabula rasa, a "blank tablet", so Descartes is right. The whole transcendental system is innate. Even on the level of the transcendental aesthetics, sensations, the only source of knowledge acknowledged, as Locke claimed, must always be processed to be recognized, or they would just be "less even than a dream" or "nothing to us". Both sensations, representation and categorization are necessary to constitute an object of knowledge.

Kant aimed to do for philosophy what Newton had done for physics : a universal system allowing one to explain the movements of planets as well as that of falling apples. He could not accept skepticism and the relativism it engenders. Not finding this firm ground in the objective, outward reality (as a transcendent world of Platonic ideas or universal forms immanent in matter), his transcendental method cleared the foundations of the subjective apparatus of thought, deemed universal. By thus making the subject of experience active after the reception of the sensation (analytic object-knowledge after the aesthetic synthesis of phenomena), all possible knowledge was about the "thing-for-us" and never about the absolute "thing-as-such".

Where did Kant miss out on his own Copernican revolution ?

The first to point to the major flaw was F.H.Jacobi (1743 - 1819), who -in 1787- asked : Were does the "matter" of the sensation ("Empfindung") turned into phenomena ("Erscheinung") come from ? Kant supposed our sensations were somehow caused by reality-as-such, the famous "Ding-an-sich". But how can this be ? Causality cannot be invoked, for the nameless sensations are pre-categorial. Neither can the world-as-such be thought as temporally first and the sensations last, for the former is outside time. Hence, the way our senses receive information is obscured, compromising Kant's epistemology. If Kant needs the "noumenon" to start up the engine of the categories, then he clearly does not use the "thing-as-such" as a negative, formal and empty limit-concept, and the Copernican Revolution is incomplete. And if this is the case, and it is, then his attempt at justifying knowledge a priori fails. So far the idealists were correct : knowledge cannot find a sufficient ground in the transcendental apparatus, for the latter depends on the very thing it tries to avoid : a direct, unmediated contact with reality !

Kant's system, although transcendental, and thus devoid of any attempt to explain the possibility of knowledge by ontology, retains the postulate of foundation, by which true knowledge is certain, universal and necessary. Hence, he still needed an Archimedic point outside knowledge. Scientific knowledge is considered to be a system of synthetic propositions a priori, and so indirect synthetic statements may pass the critical test (while for Hume only direct propositions were certain). Kant's philosophy is Newtonian, and so absolute principles are acknowledged both in sensation (time, space), understanding (forms, categories) as well as in reason (the ideas). At the same time, clear demarcations avoid their abuse and potential corruptive effect on thought.

14. Criticism and the Münchhausen-trilemma.

For good reasons, the history of philosophy is divided in pre- and post-Kantian. For with the crucial Copernican Revolution, the activity of the subject of knowledge was finally fully acknowledged. The categorial scheme is deemed to yield object-knowledge in the form of synthetical propositions a priori. So a Newtonian science of absolute certainties is possible. The skepticism of Hume (also at work in Ockham) is overturned. Causality can be thought and so the connectivity of our knowledge guaranteed. The catch ? By pursuing his foundational course, Kant had to introduce a pseudo-causality before causality in order to explain (describe) how the motor of the categories is fuelled. Moreover, the cleavage between becoming and being was reintroduced as the abyss between "noumena" and "phenomena". To avoid these problems, parts of the transcendental exercise of Die Kritik der Reinen Vernunft had to be redone.

With Kant, a totally new perspective unfolds : criticism highlights the limitations, demarcations, frontiers and borders of thought. It is not possible to step outside ourselves and witness the world from some real external or ideal internal vantage point. The subjective structure cannot be removed and so what we call "objective" cannot be identified as observation without interpretation. Conceptually, the latter is impossible. There is no point of intersection between the lines created by our thoughts and reality-as-such, i.e. absolute, noumenal reality. The lines bounce on the mirror-surface of phenomena and do not allow concepts to probe into noumenal reality itself.

Contrary to ante-rationality, formal rationality is able to operate without immediate context. Abstract concepts in various systems of signs emerge. The technological advances this type of thinking initiates, in particular by identifying an imperative chain of abstract commands to solve problems, were already obvious in Alexandria, but more so in modern times. In philosophy, formal rationality has not objectified the conditions of its own operation. It lacks reflexivity. In most systems of thought, ontology is placed before epistemology. This means a certain state of affairs is implicitly or explicitly presupposed before explaining the possibility of knowledge. Either the kickable qualities (cf. Popper) of reality are idolized, and turned into an underlying thing, a solid brickwork of stubbornly unyielding particles and forces, or the laws of thought are deemed sufficient to say what "is" and what "is not", and so constitute a "hypokeimenon" (cf. the tradition from Parmenides to Habermas).

To begin with ontology, is like starting with the fruit of philosophy. It also betrays the need to secure knowledge in an absolute sense. The foundation is a given (not a fruit) and is called in to subreptively ground knowledge by "explaining" it. Empiricism appeals to the senses. Rationality calls in the universality of signs.

Platonic and Peripatetic concept-realism was replaced by Medieval scholasticism. Modern empirism & rationalism reframed the theories of the reales & nominales, backing their position with realism or idealism respectively. Reflective, discursive, formal reasoning lacks reflexivity, and presupposes a sufficient ground before knowledge in which the latter is made to root. Either a real world "out there" is considered to be given, or an ideal subject and its truth-bearing structures pre-determine the act of knowledge. Thought has to make its surface reflective (capable of reflecting light) and investigate itself. With this realization, the critical layer of cognition becomes operational. Formal thought has to be integrated in the critical operation.

Critical thought uncovers the limits of conceptual thinking. Empirico-formal systems only know reality as it appears to them, not as it is by itself, as such (cf. the Copernican Revolution in epistemology). Hence, the world is epistemologically divided between "phenomena" and "noumena", between what is processed by our understanding (by virtue of the categorial schemes of out thinking capacity) and the intellectual intuition of things as they are as such.

In the 20th century, neo-Kantianism reconstructed parts of Kant's system. What can I know ? is answered without presupposing synthetic proposition a priori are possible. The science of certainties is replaced by the science of probabilities and approximations. Demonstrative intentions are replaced by a terminist logic. This means modernism, as the via moderna had before, took the next step by abolishing foundational thinking. To show this radical move does not automatically lead to relativism or skepticism, is one of the underlying motifs of the present exercise in critical thought.

According to Sextus Empiricus, it was the skeptic Pyrrho of Elis (ca. 365 - 275 BCE) who taught conflicts between two (or more) criteria of truth automatically lead to an apory or an antinomy, i.e. a contradiction posed by a group of individually plausible but collectively inconsistent propositions. The truth of a given criterion can only be argued using true propositions. But, whenever a given criterion is justified, a petitio principii or circular argument is involved. Discussions about the criterion of truth are therefore unending and without solution.

Much later, the problems of foundational thinking were summarized by the Münchhausen-trilemma (Albert, 1976). Its logic proves how every possible kind of foundational strategy is necessarily flawed. The trilemma was named after the Baron von Münchhausen, who tried to pull himself out of a swamp by his own hair !

Every time a theory of knowledge accommodates the postulate of foundation, three equally unacceptable situations occur. A justification of proposition P implies a deductive chain A of arguments A', A", etc. with P as conclusion. How extended must A be in order to justify P ?

1. regressus ad infinitum :
   there is no end to the justification, and so no foundation is found (A', A", etc. does not lead to P) ;

2. petitio principii :
   the end P is implied by the beginning, for P is part of the deductive chain A. Circularity is a valid deduction but no justification of P, hence no foundation is found ;

3. abrogation ad hoc :
   justification is ended ad hoc, the postulate of justification is abrogated, and the unjustified sufficient ground (A' or A" or ...) is accepted as certain because, seeming certain, it needs no more justification.

The Münchhausen-trilemma is avoided by stopping to seek an absolute, sufficient ground for science. This happens when one accepts genuine science is terministic. In mathematics and physics, major changes have happened since Newton, and who is able to disprove the revolutions of tomorrow ? Hence, the categorial system cannot be absolute, although some of its general features are necessary in a normative way (for we use them when we think).

On the level of transcendental logic and the theory of knowledge, object and subject of thought are fundamental critical concepts. On the level of the practice of knowledge, experiment & argumentation are crucial. Realism and idealism are the proposed transcendental ideas of reason (instead of ego, world & God, crucial for psychology, cosmology & religious philosophy).

The end result of the proper regulative use of the ideas of the Real and the Ideal (leading to experimentation and argumentation respectively), is not a synthetic proposition a priori, but object-knowledge which is considered, for the time being, as very likely true by the community of sign-interpreters. These empirico-formal propositions are always a posteriori, and may be direct (reality-for-me) or indirect (reality-for-us). Critical epistemology is there to remind us of the natural tendency of reason to hypostatize its ideas.

If the idea of the real is turned into an object (like extra-mental, kickable and kicking things out there), then true knowledge is "adequatio intellectus ad rem". But, we do not know whether knowledge is made possible by a real world. Suppose the latter is the case, then how to reconcile this with the facts that (a) observation co-depends on theoretical connotation and (b) observation unfolds in a conceptual pattern which develops in the act of observing ?

If the idea of the ideal is turned into an object, then true knowledge is given by the "consensus omnium" and "leges cogitandi sunt leges essendi" persists. But, knowledge is not made possible by an ideal theory or ideology. For if so, then we blind ourselves from the fact that synthetic propositions are also statements about some thing extra-mental, escaping (inter) subjectivities. These two criteria of truth, although discordant, operate simultaneously, and regulate the development of thought. Correspondence and consensus are integrated in a coherence theory of truth.

In accord with Ockham's terministic probabilism and the view of all knowledge as "approximative", contemporary criticism finds comfort that only probable, not certain empirico-formal knowledge is possible, and that no sufficient ground for the possibility of knowledge needs to be found. This position is open and so free to investigate all possible expansions of knowledge. Dogmatic and ontological fossilizations are excluded from this secure but narrow point of view.

Facts are not monolithical, but hybrids.

On the one hand, they are theory-dependent and as such determined by intersubjective languages, theories and their arguments. Of this a descriptive analysis is possible, for we can test ourselves to realize how extended the influence of subjective connotations is on direct and indirect observation. In quantum mechanics, the total experimental set-up, observer included, co-determines the outcome of the experiment.

On the other hand, so must we think, facts are theory-independent. If not, then there is no genuine object of knowledge, whereas the proposition in which this is affirmed ("There is no object of knowledge.") has as object the absence of the object of knowledge. Universal illusion would pertain. The conviction (or belief) in the theory-independent face of facts is not descriptive for it cannot be observed (every observer has a unique set of space-time coordinates and cannot step out him or herself to observe). Ergo, the theory-independence of facts is normative and belongs to what we must think in order to think properly. And this is precisely what thinkers thinking properly have been doing all the time. Suppose we accept all conceptual thinkers have been deluded, then the argument of illusion holds, and skepticism is irreversible.

Also in science, the problems posed by skepticism had to be addressed. Especially since Kant, the question "What can I know ?" has been crucial. The apory between "realism" and "idealism" is also without final result. The foundational approach favored since Plato and Aristotle has caused a pendulum movement between two criteria of truth (consensus versus correspondence). To move beyond this, the antinomic problems of justificationism (i.e. the foundational, fundamentalist thinking within science) must be clear : if, on the one hand, real "sense data" are the only building-blocks of "true" knowing, as realism maintains, then why is the definition of the word "sense datum" not a sense datum ? Also : how can a "naked" or "raw" sense datum be observed if our mental framework co-constitutes our observation ? If, on the other hand, ideal linguistic symbols and speech-situations are the exclusive arena of truth, as idealism maintains, then how can knowledge be knowledge if it is in no way knowledge of something (i.e. a "res" and not only "flatus voci") ?

A focus of truth "behind the mirror" (as Kant put it) comes within reach if and only if both perspectives, experiment (correspondence, objectivity) and argumentation (consensus, intersubjectivity) are used together, and this in a regulative, non-constitutive (unfoundational) way. The criterion of truth is not justified by a sufficient ground outside knowledge, but by discovering the normative principles governing all possible knowledge. The latter are bi-polar but interactive and never exclusive, as 19th century, Newtonian scientific thinking claimed. Insofar as either realism or idealism are accepted, the logical merits of the truth claim of science do not exceed the religious criterion of truth. It cannot escape the apory as long as it identifies with objectivity at the expense of subjectivity and intersubjective symbolization (as in logical positivism, materialism, scientism, instrumentalism, reductionism and epiphenomenalism) or with subjectivity and intersubjective symbolic activities with disregard for entities independent of the human sphere (as in spiritualism, idealism and humanism).

Facts are not only experimental and not only theoretical. They are hybrids, composed of what we know (our theories) and, so must be think, the realities outside our minds. The latter cannot be isolated from the former, for the subjective conditions of knowledge cannot be removed without causing the perversity of reason. Empirico-formal object-knowledge is always the product of two vectors at work simultaneously. Not because of some ulterior reason, but because it must be so and has always been so. Epistemology is hence not descriptive, but normative.

Although the Copernican Revolution posits the subject and its constructivist activities, Kant's epistemology is a attempt to still adhere to the postulate of foundation, for synthetic judgments a priori are rooted in the cognitive, categorial apparatus of the subject of experience, without which no thinking is possible. In other worlds, the constructions of my mind are per definition those of other minds. These categories hold true for the object of experience insofar as this object is constituted in observation by our capacity of observation and knowledge. For Kant, scientific knowledge (empirico-formal propositions) does not deal with reality-as-such, but with reality-for-us. However, as contemporary mathematics, relativity & quantum mechanics disagree with the principles of Newtonian physics Kant thought to be anchored in our minds for ever, it becomes clear that these categories are not absolutely certain and not a priori. Kant's attempt to anchor science failed, although his unearthing the active subject became a fundamental and irreversible asset of modern epistemology.

Science has no anchor and is for ever set adrift on the limitless ocean. We may throw out our nets, but will only catch those fish unable to slip through the mazes, and there are only a few nets on board. Scientists erect buildings on the edge of or in the swamp. Such flooded bottomland, saturated with water, is constantly shifting. Yet, despite its instability, science tries to build a platform above it that will hold out for a while. How long nobody knows. But not forever, that much we do know ... Then we need another net, another set of poles driven into the swamp. In view of the vastness of the material universe, this procedure is practically unending. Likewise for the expansion of knowledge. Scientists cannot play for God. They are sailors on a leaking ship lost in the vastness, finding no harbor to accost. To them to repair their vessel while aboard ...

It took more than two centuries before the antinomy between realism and idealism was critically superseded by a normative theory on the possibility and the production of knowledge (cf. Clearings, 2006). In contemporary scientific practice, scientific facts are the outcome of two simultaneous vectors : on the one hand, objective experiments and their repetition, and, on the other hand, intersubjective communication between the community of sign-interpreters. Logic provides a few a priori conditions, related to the form, clarity and elegance of the symbols of a theory. Epistemology adds a few objective and intersubjective criteria and the local research-unit will foster a series of a posteriori rules of thumb. Nevertheless, despite all possible care, scientific knowledge cannot be absolutist or radical, but instead delicate, prudent & provisional. Indeed, divorced from the metaphysical aim to anchor knowledge, genuine science cannot be a new dogmatic religion, but a method to acquire fallible knowledge.

Indeed, empirico-formal knowledge, or knowledge of facts, is conditional, relative, hypothetical and historical, although a clear theory explaining a lot of phenomena will (provisionally) always be called "true", meaning "very probable", not "certain". A set of such theories will constitute a tenacious scientific paradigm, covering entities which "kick" and "kick back". But things may change, and usually they do ...

"It is an hypothesis that the sun will rise tomorrow : and this means that we do not know whether it will rise."
Wittgenstein, L. : Tractatus Logico-Philosophicus, 6.36311.

Regarding the justification of its truth claim, formal and critical rationality developed their argument in three stages :

1. uncritical & foundational : true knowledge corresponds with real, repeatably observable objects (naive realism under the guise of materialism) or true knowledge is the object of an ideal theory (naive idealism under the guise of spiritualism or ideology). Greek conceptual realism developed both variants. In both strategies, the error consists in the implicate use of the contra-thesis. Real objects are also co-determined by the theoretical connotations of their observers. Ideal objects are always also referring to a "something" outside the grasp of a theoretical discourse. The foundation of science is objectified : the "real" world "out there" or the "ideal" theory of reason. For Kant, the apory empiricism versus rationalism was a scandal ;

2. critical & foundational : asking for the limitations of human knowledge, Kant rooted cognition in the cognitive apparatus (cf. the Copernican Revolution). In this way, the foundation sought was interiorized and its a priori categorized. By making the ego cogito (the "I Think" of the Factum Rationis) the foundation of knowledge, Kant succeeded in making reality-as-such fall outside science ! Likewise, for Kant, meta-rational knowledge (intellectual perception) was denied to man, who's capacity to know, divorced from any direct contact with "das Ding an sich", seems trivial. The foundation of science is subjectified (not in an idealism but in a transcendentalism) ;

3. critical & normative : in the previous century, the foundational approach was relinquished and in this way, the aporia threatening justification was avoided. Science produces terministic empirico-formal propositions. These are treated "as if" they represent a high probability, but never a certain truth. This likelihood is posited by repeatable tests and the intersubjective dialogues and argumentations of all involved sign-interpreters. The end result is fallible knowledge, although, for the time being, highly probable.

With the end of foundational thinking, the confrontation between incompatible foundations is over. Scientific knowledge is probable, historical and relative. Facts may change over time, and nobody is able to predict for certain what the future holds. The future is open. Moreover, scientific investigations are always conducted against the background of untestable information. Insofar as the latter is arguable, metaphysics is possible. But the latter is never testable, only arguable. Finally, who decides who the "involved sign-interpreters" are and/or when a certain threshold is "critical" ? In order to define these and other matters, science evokes a series of a posteriori conditions representing the idiosyncrasies of the local research-unity, the "opportunistic logic" of their fact-factory and the style of their pursuit of scientific, factual knowledge. These conditions determine the practice of knowledge.

Philosophy and science should remain open and postpone their final judgments. Both must be totally recuperated from the hang-over of their shameful foundational history over the last two millennia. The only role of science is to confirm or deny probable fact. The task of philosophy is to uncover the laws ruling epistemology, esthetics & ethics as well as develop a theoretical picture of the whole (speculation or metaphysics).

Ontology no longer roots object and subject in a self-sufficient ground or eternal, certain foundation. The possibility of knowledge is grounded in knowledge itself. Critical thought raises the reflective to the reflexive. Epistemology is a normative discipline, bringing out the principles, norms and maxims of true knowledge. These must be used in every correct cogitation producing valid knowledge.

The principles of thought are given by transcendental logic, the norms by the theory of knowledge (and truth) and the maxims by the knowledge-factory or applied epistemology. Science deals with propositions arrived at by the joint efforts of experimentation and argumentation. The discordant concord of both object and subject is necessary and their defenses should never be put down, nor should their truce, which is essential to produce knowledge that works, be broken. Both object and subject constitute knowledge, and each aim differently. Testing requires the monologue of nature, whereas argumentation is dialogal. Scientific knowledge is in the form of empirico-formal propositions which are terministic (probable) and fallible. They are formulated against the implicit or explicit background of untestable metaphysical speculations and always imply a "ceteris paribus" clause.