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Category: metaphysics

A principle of something is merely prior related to pro- to it either chronologically or logically. If the arche is taken to be an origin, then specific causality is implied; that is, B is supposed to be characteristically B just because it comes from A, which dominates it. The archai that Aristotle had in mind in his well-known passage on the first Greek scientists are not necessarily chronologically prior to their objects, but are constituents of it.

For example, in pluralism objects are composed of earth, air, fire and water, but those elements do not disappear with the production of the object. They remain as archai within it, as do the atoms of the atomists. What Aristotle is really saying is that the first philosophers were trying to define the substance s of which all material objects are composed.


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As a matter of fact, that is exactly what modern scientists are attempting to accomplish in nuclear physics , which is a second reason why Thales is described as the first western scientist, [ citation needed ] but some contemporary scholars reject this interpretation. Thales was known for his innovative use of geometry. His understanding was theoretical as well as practical. For example, he said:. The greatest is space, for it holds all things. Topos is in Newtonian-style space , since the verb, chorei, has the connotation of yielding before things, or spreading out to make room for them, which is extension.

Within this extension, things have a position.

Points , lines , planes and solids related by distances and angles follow from this presumption. Thales understood similar triangles and right triangles , and what is more, used that knowledge in practical ways. The story is told in DL loc. A right triangle with two equal legs is a degree right triangle, all of which are similar.

The length of the pyramid's shadow measured from the center of the pyramid at that moment must have been equal to its height. This story indicates that he was familiar with the Egyptian seked , or seqed , the ratio of the run to the rise of a slope cotangent. More practically Thales used the same method to measure the distances of ships at sea, said Eudemus as reported by Proclus "in Euclidem". One stick goes vertically into the ground. A second is made level. With the third you sight the ship and calculate the seked from the height of the stick and its distance from the point of insertion to the line of sight Proclus, In Euclidem , There are two theorems of Thales in elementary geometry , one known as Thales' theorem having to do with a triangle inscribed in a circle and having the circle's diameter as one leg, the other theorem being also called the intercept theorem.


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  • In addition Eudemus attributed to him the discovery that a circle is bisected by its diameter, that the base angles of an isosceles triangle are equal and that vertical angles are equal. According to a historical Note, [46] when Thales visited Egypt , [17] he observed that whenever the Egyptians drew two intersecting lines, they would measure the vertical angles to make sure that they were equal. Thales concluded that one could prove that all vertical angles are equal if one accepted some general notions such as: all straight angles are equal, equals added to equals are equal, and equals subtracted from equals are equal.

    The evidence for the primacy of Thales comes to us from a book by Proclus who wrote a thousand years after Thales but is believed to have had a copy of Eudemus' book.

    Proclus wrote "Thales was the first to go to Egypt and bring back to Greece this study. They say that Thales was the first to demonstrate that the circle is bisected by the diameter, the cause of the bisection being the unimpeded passage of the straight line through the centre. This theorem, that when two straight lines cut one another, the vertical and opposite angles are equal, was first discovered, as Eudemus says, by Thales, though the scientific demonstration was improved by the writer of Elements. Eudemus in his History of Geometry attributes this theorem [the equality of triangles having two angles and one side equal] to Thales.

    For he says that the method by which Thales showed how to find the distance of ships at sea necessarily involves this method. Pamphila says that, having learnt geometry from the Egyptians, he [Thales] was the first to inscribe in a circle a right-angled triangle, whereupon he sacrificed an ox. Hieronymus held that Thales was able to measure the height of the pyramids by using a theorem of geometry now known as the intercept theorem , after gathering data by using his walking-stick and comparing its shadow to those cast by the pyramids.

    because all (Western) philosophy consists of a series of footnotes to Plato

    Dicks question whether such anecdotes have any historical worth whatsoever. Thales' most famous philosophical position was his cosmological thesis, which comes down to us through a passage from Aristotle 's Metaphysics. Aristotle then proceeded to proffer a number of conjectures based on his own observations to lend some credence to why Thales may have advanced this idea though Aristotle did not hold it himself.

    Aristotle laid out his own thinking about matter and form which may shed some light on the ideas of Thales, in Metaphysics b6 8—11, 17— The passage contains words that were later adopted by science with quite different meanings. That from which is everything that exists and from which it first becomes and into which it is rendered at last, its substance remaining under it, but transforming in qualities, that they say is the element and principle of things that are.

    Thales the founder of this type of philosophy says that it is water. In this quote we see Aristotle's depiction of the problem of change and the definition of substance. He asked if an object changes, is it the same or different? In either case how can there be a change from one to the other? Aristotle conjectured that Thales reached his conclusion by contemplating that the "nourishment of all things is moist and that even the hot is created from the wet and lives by it.

    Footnotes to Plato | because all (Western) philosophy consists of a series of footnotes to Plato

    Thales thought the Earth must be a flat disk which is floating in an expanse of water. Heraclitus Homericus states that Thales drew his conclusion from seeing moist substance turn into air, slime and earth. It seems likely that Thales viewed the Earth as solidifying from the water on which it floated and the oceans that surround it.

    In his dogma that water is the origin of things, that is, that it is that out of which every thing arises, and into which every thing resolves itself, Thales may have followed Orphic cosmogonies, while, unlike them, he sought to establish the truth of the assertion. Hence, Aristotle, immediately after he has called him the originator of philosophy brings forward the reasons which Thales was believed to have adduced in confirmation of that assertion; for that no written development of it, or indeed any book by Thales , was extant, is proved by the expressions which Aristotle uses when he brings forward the doctrines and proofs of the Milesian.

    According to Aristotle, Thales thought lodestones had souls, because iron is attracted to them by the force of magnetism. Aristotle defined the soul as the principle of life, that which imbues the matter and makes it live, giving it the animation, or power to act. The idea did not originate with him, as the Greeks in general believed in the distinction between mind and matter, which was ultimately to lead to a distinction not only between body and soul but also between matter and energy. This belief was no innovation, as the ordinary ancient populations of the Mediterranean did believe that natural actions were caused by divinities.

    Accordingly, Aristotle and other ancient writers state that Thales believed that "all things were full of gods. Zeus was the very personification of supreme mind , dominating all the subordinate manifestations. From Thales on, however, philosophers had a tendency to depersonify or objectify mind, as though it were the substance of animation per se and not actually a god like the other gods.

    The end result was a total removal of mind from substance, opening the door to a non-divine principle of action. Classical thought, however, had proceeded only a little way along that path. Instead of referring to the person, Zeus, they talked about the great mind:. Thales", says Cicero , [57] "assures that water is the principle of all things; and that God is that Mind which shaped and created all things from water.

    The universal mind appears as a Roman belief in Virgil as well:.

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    Due to the scarcity of sources concerning Thales and the discrepancies between the accounts given in the sources that have survived, there is a scholarly debate over possible influences on Thales and the Greek mathematicians that came after him. Historian Roger L. Cooke points out that Proclus does not make any mention of Mesopotamian influence on Thales or Greek geometry, but "is shown clearly in Greek astronomy, in the use of sexagesimal system of measuring angles and in Ptolemy 's explicit use of Mesopotamian astronomical observations.

    Historian B. Van der Waerden is among those advocating the idea of Mesopotamian influence, writing "It follows that we have to abandon the traditional belief that the oldest Greek mathematicians discovered geometry entirely by themselves…a belief that was tenable only as long as nothing was known about Babylonian mathematics.

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    This in no way diminishes the stature of Thales; on the contrary, his genius receives only now the honour that is due to it, the honour of having developed a logical structure for geometry, of having introduced proof into geometry. Some historians, such as D. Dicks takes issue with the idea that we can determine from the questionable sources we have, just how influenced Thales was by Babylonian sources. He points out that while Thales is held to have been able to calculate an eclipse using a cycle called the "Saros" held to have been "borrowed from the Babylonians", "The Babylonians, however, did not use cycles to predict solar eclipses, but computed them from observations of the latitude of the moon made shortly before the expected syzygy.

    He points out that Ptolemy makes use of this and another cycle in his book Mathematical Syntaxis but attributes it to Greek astronomers earlier than Hipparchus and not to Babylonians. Martini, J. Dreyer, O. Neugebauer in rejecting the historicity of the eclipse story altogether. Herodotus wrote that the Greeks learnt the practice of dividing the day into 12 parts, about the polos , and the gnomon from the Babylonians.

    The exact meaning of his use of the word polos is unknown, current theories include: "the heavenly dome", "the tip of the axis of the celestial sphere", or a spherical concave sundial.