The Pre-Socratic Philosophers were all those Greek thinkers before Socrates, who can be usefully divided into Naturalistic Philosophers and political Sophists. The former will be dealt with here the latter in their own section.
Milesians (Early Ionic)
Natural Philosophy began around 600 BC with Thales who developed the idea of an Arche, an originating state or being, that could be described, and from which everything emerged and developed according to it's natural laws. For most Greeks the Arche was essentially understood as a primal Substance, in the form of Matter (Hyle), whose state was at first chaotic but which became ordered, or took Form (Eidos), when some kind of Transcendental Mind willed it or entered it. It then became the Arche (First Ruling Principle), producing everything under the organising principle which emerged within it. This organising principle existed potentially within the original Substance, but manifest as it became ordered. It could be regarded as a Law or a Conscious Mind or God, sometimes referred to under the name of the mythical god Zeus. Other gods (Archons?) were present in the differentiating substances and phenomena that emerged from the Arche, but this was arguably more metaphor than mythology, and certainly not religion. For Thales, the Arche or first Substance was Water from which all other matter condensed and differentiated. With ultimately life itself emerging from the sea. This related to the Greek Cosmos of a Great Ocean from which the Earth emerged and floated on. Thales began a school known as the Milesians.
Other influential Milesians were Anaximander and Anaximenes, the former refered to Arche as Aperion, an unknowable, undetectable primal matter (or energy) from which the elements emerged, but this seemed to confuse many. Anaximenes returned to an elemental Arche, but suggested it was Aether, a general term for air, mist and gases. For Anaximenes everything emerged from a primal mist, and life and mind was based on breath (the words psyche and pneuma are derived from 'breath'). The Aether was essentially a life force, much like the later concepts of the 'Etheric' that were derived from it.
A radical reformulation was inaugurated by Pythagoras, who argued that Mathematics not Substance came first and was the Arche on which all things were founded and which generated the all objects. It is difficult to fathom what was meant by this, as like most Greeks Pythagoras believed in material substance, abstract philosophies like ontological or mathematical Idealism were unknown to peoples who lived close to Nature. Pythagoras seems to have believed that before Mathematics there was just Void (nothingness) with random patches of Apeiron emerging in it and fading away again. But this universe was not stable or even knowable, so could not be said to exist. Mathematics emerged with Form, but was seen as the Arche instead of Matter as the first stable entity existed in it. A patch of Apeiron only became our world after it became a stable whole Monad, or identifiable as the number one. This meant its Form was based on Number. From then on Mathematics generates everything from this unified Aperion. The Monad was only momentary however because as soon as it formed organised substance appeared and so there was a Dyad - Form and Matter. Then the Void is sucked in forming bubbles of nothingness and division into parts. This multiplicity was caused by the emergence of number through continual dyadic division. From then on the universe built up geometrically culminating in the 'elements' represented by 3D geometrical solids. For Pythagoras Mathematics ensured stability, balance and harmony, and was closely associated with its pure manifestation in music.
Heracliteans (Late Ionic)
Heraclitus agreed with Pythagoras that a mathematical order existed within reality, but thought it had been over emphasised. He returned to an elemental Arche, but a new one, Fire, or more accurately perhaps energy, from which all things were formed, and which concretely replaced Pythagoras' unknowable Apeiron. But within it he maintained a Logos, a cosmic ordering principle, that ensured balance and generated cycles of transformation, from which both material manifestation and actual mathematics emerged. Within these cycles, in which Forms were constantly changing, Heraclitus argued the only thing that was permanent was change itself. He thus inaugurated an Ontology of Becoming rather than Being. His philosophy one of cyclic change through the tension between opposites, and has been described as hard Taoism. Heraclitus was a shadow Plato and equally influential in his own way giving rise to Process Philosophy (see also Heraclitus).
Parminedes wrote in part in opposition to the process philosophy of Heraclitus. He claimed he had a divine revelation from an unknown Goddess that nothing changes and everything is eternal. His perspective appears to be rooted in a mystical experience of an Eternal Now, which shaped his thought. His arguement was that Nothing could not Exist, by definition, therefore it was impossible for something to come into existence from something that did not exist. So it followed that Being could not have appeared out of Nothing, it must have appeared from Something, therefore Being was eternal. He also claimed this Being was Whole and Changeless but his arguements why are vague and poetic and partly rely on his gnosis. Parminedes distinguished between his 'Nous', or gnostic intuition and his 'Logos' or rationalising ability. He can be interpreted as saying that from his mystical experiences of an Eternal Now, Time could not exist. Worldly change was thus part of a general illusion of appearance for him and his Eleatic School.
A disciple, Melissus of Samos, attempted to elucidate more rational arguements for this vision. Melissus argued that something eternal could also be seen as an Infinite Continuum of Time, from a less mystical perspective, and what was also infinite in time was spatially infinite. Contentious points but Melissus uses them to prove the universe is a single, undivided Being that does not change. Einstein seems to have developed this notion into his Block Universe in which Time was just another dimension. Arguably if Melissus thought the same way he would have argued that Being was spatially infinite because if Time was the Space must be, given there was no Void, or Nothing, in existence.
Most other Philosophers, including Aristotle and Democritus, were very sceptical about the logic of these arguements. Thus the logician Zeno of Elea created his famous Paradoxes of Motion, as part of his refutation of Change. These have been solved in a variety of ways however.
Shortly before the time of Socrates Natural Philosophers were attempting to combine the ideas of the previous philosophers in synthetic world views. Fusions were particular sought between the Ionic and Eleatic schools. Two are noted for their originality.
Empedocles argued that four primal substances, called Roots, emerged from Chaos: Water, Air, Fire and Earth and that all Matter was based on different combinations of these eternal substances. Plato would adopt this and call them Elements. They were united by the force of Love and separated by the force of Strife. This became the dominant Greek Ontology, but had been challenged by Heraclitus who said both could unite or divide, but Love slowed change and Strife speeded it up.
Anaxagoras agreed that all things emerged from Chaos, which contained everything in potential, but they were differentiated and ordered by a Mind, which he called Nous, to differentiate it from Logos. The difference is obscure, and the Stoics considered them identical. But whereas Nous denotes the capacity for certainty, as it is the Divine Mind that differentiates and defines, thus creating a fixed meaning and Truth, Logos "rationalises" or develops possible meanings. For Heraclitus to rationalise meant 'to ratio-lize' a balencing and contingent synthesis between opposites on a metaphysical level that created possible forms in the world, whereas for Parmenides it is a vague human faculty that 'reasons', and for Aristotle it is logical reasoning through opposing opinions, similar to the dialectic arguements of Socrates, that produces possible truths or logical accounts, but not Truth. The human Nous in contrast is the faculty of gnosis that connects to the Divine Nous and perceives the Truth by intuition. Heraclitus' can thus be seen as more radical as his Divine Logos created contigent truths that are subject to change or evolution, a more fluid sense of meaning in keeping with his philosophy of Becoming over Being.
The later schools of all the previously outlined Pre-Socratic positions would also incorporate these synthetic speculations, particularly the Pythagoreans.
A maverick fringe school were the Atomists, whose philosophy was perfected by Democritus. He argued that only two types of fundamental components existed, the Void and many eternal Atoms. All other things that existed were composed of combinations of Atoms and change was simply their rearrangement