For Thales, the arche was water and for his companions one his disciple and another his contemporary was the indefinite Anaximander and the air Anaximenes.
This theme, the search for the element or principle of all things would be a topic of discussion for many other philosophers after Thales and these are known as pre-Socratic, because after Socrates philosophy was responsible for seeking other questions and answers. Now, why water was considered as the arche?
Thales of Miletus thought that it was the beginning of things because it is found everywhere, between continents and around the Earth for him the earth was a flat disk floating in an infinite ocean. In addition, its importance has always been highlighted because everything is born of water, that idea, which later would be corroborated by evolution, did not have those scientific connotations, but Thales believed that giving life to plants could be a constitutive part of everything.
Another important characteristic of water as arche was its variability since it can be vapor, liquid and solid. Although other philosophers did not follow his proposal of water as an origin and part of everything, Thales is considered the father of philosophy for thinking, by means of deduction and observation, that there was a universal principle of things, thus giving an order to the chaos of reality.
Although not verifiable, there are some interesting stories about Thales of Miletus. It is said that in his youth he traveled to Egypt and he learned geometry and astronomy when he returned, he taught Greek astrosophy a mixture between both.
It is also believed that he ran a nautical school and came to give political advice. So, in the popular image that has been created by some mentions in ancient history, Thales of Miletus is consolidated as a man of many qualities and different jobs. Finally, he was a teacher of Pythagoras and Anaximenes. It is not possible to think about his knowledge and position before the world without relating it to geometry because after studying in Egypt he elaborated some theorems and deductive reasonings that Euclides later collected in his work Elements.
For this reason, he is considered, in addition to the father of philosophy, the first to introduce geometry to Greece. Even so, all we know about this character has come to us through books by Herodotus, Xenophanes, and Aristotle since none of his works survived time.
It is believed that he died at the age of 78, as Apolodoro wrote in Chronicles. Many historians accept that his death was about b.
C; that is, between his hypothesis of birth and death, Thales of Mileto lived 76 years. Throughout his career, Carnap served as a professor of philosophy in different universities Vienna and Prague. For his contributions concerning neo-positivism, the construction of logical systems and discourse analysis is considered one of the most relevant philosophers of the twentieth century.
Son of Johannes Carnap and Anna Dorpfeld. Carnap was born into a modest German-Western family, which provided him with a good education. He began his academic training at the Barmen Gymnasium. Between and he studied philosophy, mathematics and traditional logic at the universities of Jena and Freiburg.
After the outbreak of the First World War, he entered the University of Berlin, where he continued his philosophical training. Later he obtained his doctorate at the University of Jena with the thesis on the concept of space, which he divided into three types: space physical, intuitive space, and formal space.
Since then he began to carry out research in which he addressed topics such as time and causality, and also discussed theories of symbolic and physical logic. Towards the end of the s, he began to work as a professor of philosophy in Vienna , at which time he associated with the Vienna Circle.
Philosophical collective founded by the empiricist logical Moritz Schlick, who invited Carnap to participate in meetings and studies of the circle. At that time the group was trying to create a scientific perspective of the world, through which the rigor of the exact sciences could be applied in philosophical theories and their studies, an idea that contrasted with the philosophical approach of the time, which was carried out Verifications based on deductions through an unofficial or strict language, which opened space for any doubts.
In the circle presented the manifesto The scientific conception of the world: the Vienna Circle, written by Otto Neurath. This showed the signatures of Carnap and Hans Hahn. In the manifesto the circle set out the principles of neo-positivism and its opposition to meaningless metaphysics, emphasizing the importance of verifiability; these approaches were inspired by the work of Wittgenstein Tractatus logico-philosophicus logical-philosophical treatise.
During this period the philosopher delved into the philosophical problems and the language with which they are addressed. Because these problems derived from the inappropriate use of language, to test this approach he carried out various studies in which he tried to build logical systems that were capable of avoiding ambiguities and misuse of language.
In parallel, he focused on analyzing scientific discourse, among the most outstanding works that addressed these themes are: The logical structure of the world , the overcoming of metaphysics through the logical analysis of language and The logical syntax of the language Towards the middle of the s, he moved to the United States, motivated by the rise of Nazism in Germany. When he settled down, he began working as a professor at the University of Chicago, an institution where he worked until the early s.
In these years he wrote Investigations in semantics , Meaning and necessity and Logical foundations of probability In the first two books he studied the formal and conceptual aspect of language and in Logical Foundations of the probability in which he distinguished between statistics and logic, generating important contributions in the field of statistics.
Between and he taught at Princeton, followed by moving to California where he was hired as a professor at the University of California.
He worked until the s. Throughout his academic career, Carnap defended and promoted the principles of mathematical logic or symbolic logic, through which he tried to create a scientific perspective of the world. After a long and outstanding academic career Carnap, he died on September 14, , in Los Angeles, California. Philosopher and theologian considered one of the most relevant thinkers of his time.
Malebranche was one of the followers of the thought of Rene Descartes , whose work he read avidly. Eventually became one of the main drivers of occasionalism, a doctrine created by the followers of the French philosopher. Malebranche revitalized the doctrine by including ideas based on Augustinianism.
According to this philosophy, the body and the mind are separate entities, which are connected by the intervention of God, also, for these the cause-effect relationship is determined by divine intervention, turning the cause into an occasion for God to act. His most outstanding works are The search for truth and Christian and metaphysical meditations His father was a prominent public official. This is known as Thales' Theorem. The Egyptians and Babylonians must have understood the above theorems, but there is no known recorded proof before Thales.
He used two of his earlier findings -- that the base angles of an isosceles triangle are equal, and the total sum of the angles in a triangle equals two right angles -- in order to prove theorem 5.
According to Diogenes Laertius, when Thales discovered this theorem, he sacrificed an ox! Thales bridged the worlds of myth and reason with his belief that to understand the world, one must know its nature 'physis', hence the modern 'physics'.
He believed that all phenomena could be explained in natural terms, contrary to the popular belief at the time that supernatural forces determined almost everything.
Thales professed it was "not what we know, but how we know it" the scientific method. His contributions elevated measurements from practical to philosophical logic. There are many recorded tales about Thales, some complimentary and others critical: Herodotus noted that Thales predicted the solar eclipse of BC, a notable advancement for Greek science. Aristotle reported that Thales used his skills at recognizing weather patterns to predict that the next season's olive crop would be bountiful.
A similar statement is made by Pliny see [ 8 ] :- Thales discovered how to obtain the height of pyramids and all other similar objects, namely, by measuring the shadow of the object at the time when a body and its shadow are equal in length.
Plutarch however recounts the story in a form which, if accurate, would mean that Thales was getting close to the idea of similar triangles This is in line with the views of Russell who writes of Thales contributions to mathematics in [ 12 ] :- Thales is said to have travelled in Egypt, and to have thence brought to the Greeks the science of geometry.
What Egyptians knew of geometry was mainly rules of thumb, and there is no reason to believe that Thales arrived at deductive proofs, such as later Greeks discovered.
On the other hand B L van der Waerden [ 16 ] claims that Thales put geometry on a logical footing and was well aware of the notion of proving a geometrical theorem. However, although there is much evidence to suggest that Thales made some fundamental contributions to geometry, it is easy to interpret his contributions in the light of our own knowledge, thereby believing that Thales had a fuller appreciation of geometry than he could possibly have achieved.
In many textbooks on the history of mathematics Thales is credited with five theorems of elementary geometry:- A circle is bisected by any diameter. The base angles of an isosceles triangle are equal. The angles between two intersecting straight lines are equal. Two triangles are congruent if they have two angles and one side equal. An angle in a semicircle is a right angle.
What is the basis for these claims? Proclus , writing around AD, is the basis for the first four of these claims, in the third and fourth cases quoting the work History of Geometry by Eudemus of Rhodes , who was a pupil of Aristotle , as his source. The History of Geometry by Eudemus is now lost but there is no reason to doubt Proclus. The fifth theorem is believed to be due to Thales because of a passage from Diogenes Laertius book Lives of eminent philosophers written in the second century AD [ 6 ] :- Pamphile says that Thales, who learnt geometry from the Egyptians, was the first to describe on a circle a triangle which shall be right-angled, and that he sacrificed an ox on the strength of the discovery.
Others, however, including Apollodorus the calculator, say that it was Pythagoras. A deeper examination of the sources, however, shows that, even if they are accurate, we may be crediting Thales with too much. For example Proclus uses a word meaning something closer to 'similar' rather than 'equal- in describing ii.
It is quite likely that Thales did not even have a way of measuring angles so 'equal- angles would have not been a concept he would have understood precisely. He may have claimed no more than "The base angles of an isosceles triangle look similar". The theorem iv was attributed to Thales by Eudemus for less than completely convincing reasons.
Proclus writes see [ 8 ] :- [ Eudemus ] says that the method by which Thales showed how to find the distances of ships from the shore necessarily involves the use of this theorem. Heath in [ 8 ] gives three different methods which Thales might have used to calculate the distance to a ship at sea. Thales is said to have been the first to describe the underlying principles of bisecting circles, and he may have been the first to demonstrate mathematically that the angles at the base of an isosceles triangle are equal.
Thales also showed that triangles having two angles and one side equal share equality. This was more than just lofty theory since these principles could be used for practical purposes, such as finding the distance of ships at sea.
Without these kinds of fundamental understandings of geometry, so much of what we take for granted today would be impossible. The mathematical developments of Thales spurred forward a variety of practical disciplines, from navigation and architecture to engineering and a deeper understanding of astronomy.
Thales is famous for an important theorem that is named after him. The greatest philosophers of modern times have debated the influence of Thales with enthusiasm, but also considerable disagreement.
0コメント