The history of western thought can be traced following the different syntheses along its path because the progression of philosophical ideas works in a binary format: two contrasting ideas are discussed and sometimes a third idea arises uniting the two. Then an opposing idea leads to another synthesis, or not.

The first ideological opposition can be traced to the homeric poems, The Iliad and The Odyssey, dated before the VII century B.C. Both texts recount the relationships between the human and the divine represented by Achilles, Ulysses and the gods. The Illiad tells the tale of divine interventions and manipulation of human lives. The Odyssey, on the other hand, emphasises a hero who is able to look after himself without much divine intervention. As a sequel to The Iliad, The Odyssey evolves as a story moving from one of godly pupeteering to one of human freedom. This evolution is that of an epic hero who is capable of solving his own problems and it prefigures the later Greek tradition of investigating their world without reference to the divinities. It is a precursor of the polemic between a vertical and a horizontal worldview.

The Presocratics, living in small island states in the Aegean between the VII and V centuries B.C., inherited the mental categories of Greek mythological explanation mixed with the homeric outlook of self-made humanity. They proposed syntheses between logos and mitos through the concept of Kosmos(order), the idea that the universe could be analysed and explained through rational thought as well as mythology. 

They concentrated more on the rational aspect rather than the myths. Their aim was to explain the essence of nature(physis). The pythagorean sect proposed mathematics as the essential explanation; Thales contended it was water; Anaximander argued that it was air. These rational descriptions of the physical world led to a new proto-scientific explanation of the physical world which paralleled the traditional metaphysics of mythology. 

This horizontal worldview continued the homeric vision and was enriched through rationalisation of the physical; in the vertical view mythology still powered the metaphysical explanation of reality as in the Illiad or the Theogony of Hesiod. This flat versus upward vision would pervade western thought 

In the Socratic world of the next two centuries, V to IV B.C., the tensions were ethical, epistemological and physical. They were each formulated in pairs of vertical and horizontal patterns: Socrates focused his interest in the ethical question of social coexistence: how could people in the city state(polis) of Athens live together in harmony? The answer would influence the beginnings of political thought. Once again this reflexion on ethics was shaped by an up/down blueprint. Sparta resolved the conflict through top down military organisation, Corinth through oligarchy and the Athenians in the bottom up concept of democracy.

Plato, introduced a new problem: how do we know? For him the question of knowledge preceded the ethical problem of social cohesion. This new conflict is couched in terms of an opposition between a perfect mental representation in forms(morphe), ideas, and the sensory reality of physical matter(physis)He summarises his solution in The Allegory of the Cave where he values idealism over matter.

Aristotle, on the other hand, recognised the bias in Plato in favour of thought and against matter and he proposed an empirical investigation of nature through physical classification of the Kosmos. This was an open recognition of the opposition between physis and metaphysisAlthough he did not come up with a synthesis of idealism and empiricism he pointed the way towards future solutions through conversation (dialectics), a confrontation of opposing views with the goal of synthesising them.

In the Italian Renaissance painting 'The School of Athens' Raphael summarised the central binary views of western thought patterns by depicting Plato pointing vertically while Aristotle points horizontally.

The Hellenistic period began when Alexander the Great invaded Persia then expanded his empire to Egypt in 332 B.C. Ruling Egypt were the Ptolemies, a Macedonian family who had inherited the Greek tradition of investigation which inspired them to found the Library of Alexandria. It attracted scholars from all over the empire who took advantage of the hellenistic acceptance of syncretism. This mix of empirical and theoretical knowledge from the vast empire was the internet of its time producing an information synthesis between speculation and calculation in the form of mathematics.

When the Roman empire came to power it inherited Greek culture and continued its philosophies. The ethical and social question of coexistence posed by Socrates obtained differing philosophical solutions adopted by Roman intelectuals from the Greek tradition: Stoicism tended towards a synthesis of vertical and horizontal thinking the Kosmos, world order, is governed by a divine logos. Epicurianism concentrated more on the here and now thinking that the gods were distant and uninterested in humanity. Skepticism was a response to Plato's question on knowing. The skeptics represented doubt, even about sensory input, while still using logic to think about politics. 

Neoplatonism, however, which emerged in the middle of the 3rd century at the time of Roman imperial crisis, was the philosophy that offered a dominant synthesis of the Hellenistic tradition to the late Greco-Roman world. It overtook other philosophies offering a comprehensive theory of the universe and the place of the individual in it derived from hellenistic philosophy, religion and literature. Neoplatonism synthesised a thousand years of intellectual investigación systematically bringing together in dialogue(dialecticsempirical, moral and metaphysical theories from Plato, Aristotle and the Stoics. Neoplatonic thinking did not include epicurian notions perhaps because they did not coincide with traditional platonic emphasis on the metaphysical. 

Augustine of Hippo embraced neoplatonism in his Confessions (397-400 A.D.). Subsequently his life's work would be an effort to synthesise christianity and neoplatonism. In morality Augustine follows the neoplatonic ethics of the virtuous life which means to become like God. As a neoplatonist Augustine viewed the problem of evil in a binary fashion as a privation of good, not something substantial in itself. Mystical contemplation as a means of directly encountering God also came from his neoplatonic readings. His philosophical theology of original sin, free will, and the nature of man was influenced by Neoplatonism, too. His concept of God and the soul as immaterial, as opposed to the material body, is also neoplatonic. This body/soul opposition echoes Plato's matter/ideas binomial and the traditional vertical/horizontal opposition. However, in line with traditional platonic thinking the neoplatonic worldview emphasised the metaphysical rather than the physical.

Medieval western philosophy's main challenge was still to bring together the vertical and the horizontal visions, now called faith and reason. The dichotomy consisited of the conflict between biblical revelation from the theological tradition and sensory information from aristotelian empiricism. Averroës proposed the double truth theory arguing that the two types of knowledge were opposed. Thomas Aquinas rejected this approach, proposing that both types of knowledge were compatible: revelation guiding reason and reason clarifying and demystifying faith. In his Summa Theologica, composed between 1265 and 1274, Aquinas synthesises aristotelian natural philosophy and Christian theology. This conflict between aristotelian empiricism and revelation parallels the tension between the traditional horizontal/vertical interpretations of reality.

The Renaissance period started in 14th century Italy. It was less a synthesis and more a new beginning, a new vision based on studia humanitatis, research on traditional subjects but from Latin and Greek texts. In politics it included a gradual wresting of power from the religious authorities to promote a secularising vision of social organisation and a progressive use of the vernacular language to replace church latin. Italy had opted for a more horizontal vision in politics and historical interpretation.

In the rest of 15th and 16th century northern Europe christian sources were maintained as a driving force and the individual was promoted, but within religion. Humanism was a response to social change because the established religion couldn't cope. Erasmus directed criticism equally against the Popes' corruption, scholasticism, and Protestant dogma on predestination. 

The 16th century Reformation was a religious response to social literacy and Catholic abuses of power. The split took on the names of two horizontal approaches: empirical science and the aristotelian tradition. It was Bacon, Kepler and Copernicus who demonstrated that empiricism, not aristotelism, was the way forward. Northen Europe was gradually siding with the empirical against revelation in the humanist tradition of the Renaissance but also initiating political change fueled by religion. Transalpine Europe had opted for social and scientific horizontal change while retaining the vertical reference of reformed religion.

In southern Europe the Counter Reformation was a Catholic reaction to Protestant unorthodoxy. The dichotomy was between traditional and empirical knowledge. Scholasticism, Aristotle, and the Bible, were still held to be the sources of scientific knowledge. The Catholic south maintained a conservative epistemology based on a vertical vision and rejected the horizontal, empirical version. Scientists like Bruno had to accept this matrix or die at the stake. 

The Age of Reason in the 17th century saw a continuation of the vertical/horizontal division. 

In northern Europe, already in favour of an empirical approach, this split concerned politics, not religion which had been settled during the Reformation. In England the opposition played out in a Civil war: Hobbes favoured the vertical vision seen in his support of absolutism and the divine rights of the king; Locke represented a horizontal outlook proposing the social contract and the separation of powers among the executive, Parliament and the judicial system.

In southern Europe verticality and horizontality went under the names of revelation and reason. Descartes believed in God but his division was within the human individual: thought/existence, another expression of the opposing metaphysical or physical definitions. Pascal opposed both empiricism and reason with revelation. Malebranche aimed to synthesise rational cartesian thought with Augustin's religious neoplatonism. He linked divine ideas to sensory perception in a synthesis of platonic idealism and physical experience called occasionalism.

During the Enlightenment in 18th century northern Europe scientific empiricism won the battle of the traditional opposition beween the physical and the metaphysical. Physics proposed a deterministic reality as the approach to understanding nature, replacing revelation. However that left philosophers without a goal since they did not employ the scientific method. This led to a return to Plato's epistemological question: how do we know? The answers were premised purely from a horizontal worldview:

In an extreme form of empiricism Berkeley argued that we cannot directly know anything outside our minds. Hume also adopted a more limited empirical approach saying that the brain constructs sense from an otherwise chaotic reality. Adam Smith's economic theory proposed a free market, which although it appeared chaotic was guided by an invisible hand. Kant proposed a vision (in the homeric tradition of immanence) arguing that knowledge resulted from a synthesis of experience and concepts. He also placed limitations on human knowability stating that we could know appearances(phenomenon) but not the thing in itself(noumenon).

In southern Europe the Enlightenment synthesis between religious transcendence and rational materialism took the intermediary form of metaphysical materialismThis relates to the presocratic tradition of searching for the essence of Nature in fire, water, air, numbers... Using skepticism to question authority Voltaire argued for free will against determinism, yet recognised that humans are governed by natural laws. In ethics he sustained that correct action was guided by reason. Skepticism also motivated Diderot in his writings for l'Encyclopédie. He combined rationalism with faith in the human mind, although recognising its limitations. His goal was to radicalise empiricism towards a materialistic metaphysics through eclecticism but avoiding dogma.

The 19th and 20th centuries in the USA created three syntheses

The Romantic tradition retained a synthesis between the vertical and the horizontalNature and God. Thoreau saw the physical domain as an integral part of the spiritual. William James reconciled science and religion in theism

However other syntheses dispensed with the vertical and concentrated on the horizontal oppositions and emphasised their limitations. Yet this led to an uneasy certainty: there are limits to our understanding. Pragamatism synthesised reasoning and empiricism in Pierce's thought. He claimed that neither the empirical method nor the rational could achieve certainty, that reality is in flux and cannot be precisely determined. James argued that our perception of the physical world is unclear. Darwinism influenced the theory of knowledge since if reality was changing we could only know it at the point of observation, not in its entirety.

In the 19th & 20th centuries in northern Europe the opposition was between philosophy and scienceUnder the growing influence of scientific certainty philosophers began to seek a solid basis for their thinking. In ethics Bentham's utilitarianism argued that the happiness of the greatest number was a solid basis for legality, society and morality. Fichte and Hegel proposed a model for human thought reminiscent of Aristotle's dialecticsthesis, antithesis then synthesis. Husserl's proposed phenomenology as a philosophical base arguing for a study of consciousness within the flow of experience. Charles Darwin based his theory of evolution, darwinism, on the science of biology disregarding theological explanations but the theory was then applied as a philosophical explanation for social phenomena, psychology and the concept of change. Nietzsche argued for perspectivism: knowledge and understanding are conditioned by how we are seeing objects but from our perspective which is from one place at a time and from a specific angle and we don't see the whole thing. He argued that knowledge of the totality is illusory. Russell agrees with perspectivism and thinks that our senses tell us lies because they perceive snapshots, not change so he promoted a 'skepticism of the senses'. Wittgenstein cautions that philosophical skepticism itself has its limits: excessive doubt undermines rationality and so the basis for doubting. Heidegger introduced a holistic vision of cartesianism explaining existence and thought as two sides of one coin. Humans relate to the external reality by constructing theories about it. The philosophers of this era searched for a solid basis for their philosophy and ended up questioning the limits of their own knowledge.

In southern Europe the emphasis was on relegating metaphysics in favour of the empirical. Comte's theory of positivism rejected metaphysics and theology as epistemologies and proposed scientific empiricism, not for absolute truth but for credible knowledge. Sartre's existentialism followed Heidegger to argue that ideas come from experience thus synthesising the cartesian dichotomy of existence and thoughtThe structuralist model by Levi-Strauss synthesises different kinds of knowledge like myths, rituals and data in anthropological studies. Merleau-Ponty synthesises structuralism and phenomenology. He makes the transition from analysing perception to the study of existence itself using the tools of structuralism and language. In post-structuralism Foucault followed Kant arguing that in contrast to the classical vision initiated by Descartes language is not an instrument of thought but independent from thought. In the cartesian model thinking and being are linked, but Kant states that thinking is not representing since ontology and mental perception are unrelated because reality is always more than its representation. Yet Foucault criticises Kant contending that the 'I' cannot be simultaneously the object and source of transcendental representations. He adds that modern philosophers haven't demonstrated Kant's hypothesis. Derrida's deconstruction sets out to subvert the binary thinking behind western philosophy but proposes no synthesis in its place.

In contemporary western thought classical physics is opposed to the quantum mechanics model. The first is deterministic according to Einstein but the Copenhagen interpretation presents quantum physics as random. Bohm suggested a holistic theory of non-locality: that the universe is physically interconnected at the quantum level which no human will be able to access. This is in line with the skeptical tradition which the Enlightenment deepened that as humans we cannot know reality. It is also not unlike the mystical traditions which encourage humility faced with the wholeness of the universe. Chinese Dao in Taoism refers to the non-subject non-object holistic unity yet this can’t be measured. It appears that the horizontal cannot be understood without a reference to the vertical.

In 1930 Paul Dirac published the book “Principles of Quantum Mechanics” in which he synthesised Heisenberg’s work on matrix mechanics and Erwin Schrödinger’s work on wave mechanics into a single mathematical formalism called the Dirac equation. This brought together two of the most important ideas in science: quantum mechanics, which describes the behaviour of tiny objects; and Einstein's special theory of relativity, which describes the behaviour of fast-moving objects. Dirac's equation describes how particles like electrons behave when they travel close to the speed of light. The Dirac equation also predicted the existence of antimatter – the mirror image of all known particles. Antimatter was later found to exist in the real world. (Is all matter fundamentally binary?)

Rovelli has put forward the Loop Quantum Gravity theory to integrate time and space from classic into quantum physics. Space is chain mail and time its movements.

String theory is another attempt to combine the General theory of relativity and Quantum mechanics. Veneziano observed that the force uniting protons and neutrons could be explained using the Euler beta function. Veneziano's mathematics describe the vibration of energy filaments like strands of string. This theory aims to synthesise macro and micro physics through gravity.

ConclusionRovelli insists that progress in scientific thought has worked through synthesising contradictions. He gives these examples: "Newton discovered universal gravity by combining Galileo’s parabolas with the ellipses of Kepler. Maxwell found the equations of electromagnetism by combining the theories of electricity and magnetism. Einstein discovered relativity by way of resolving an apparent conflict between electromagnetism and mechanics.Seven Brief Lessons on Physics (2014). It appears that philosophical thought works in the same way. Perhaps humans simply think in a binary fashion whether of science or of philosophy.

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