Misplaced Pages

#878121

95-398: Anaximander (c. 610–546 BCE) believed that the ultimate substance of the universe, generally known as arche , was apeiron , an infinite and eternal substance that is the origin of all things. Aristotle (384–322 BCE) held that the unmoved mover "must be an immortal, unchanging being, ultimately responsible for all wholeness and orderliness in the sensible world" and that its existence

190-655: A celestial sphere . This invention undoubtedly made him the first to realize the obliquity of the Zodiac as the Roman philosopher Pliny the Elder reports in Natural History (II, 8). It is a little early to use the term ecliptic , but his knowledge and work on astronomy confirm that he must have observed the inclination of the celestial sphere in relation to the plane of the Earth to explain

285-479: A sentence , idea or formula refers to itself. Although statements can be self referential without being paradoxical ("This statement is written in English" is a true and non-paradoxical self-referential statement), self-reference is a common element of paradoxes. One example occurs in the liar paradox , which is commonly formulated as the self-referential statement "This statement is false". Another example occurs in

380-410: A body distinct from the elements). the infinite, and not air or water, in order that the other things may not be destroyed by their infinity. They are in opposition one to another. air is cold, water moist, and fire hot. and therefore, if any one of them were infinite, the rest would have ceased to be by this time. Accordingly they say that what is infinite is something other than the elements, and from it

475-460: A boundless stock from which the waste of existence is continually made good, "elements.". That is only the natural development of the thought we have ascribed to Thales, and there can be no doubt that Anaximander at least formulated it distinctly. Indeed, we can still follow to some extent the reasoning which led him to do so. Thales had regarded water as the most likely thing to be that of which all others are forms; Anaximander appears to have asked how

570-430: A contradiction, was instrumental in the development of modern logic and set theory. Thought-experiments can also yield interesting paradoxes. The grandfather paradox , for example, would arise if a time-traveler were to kill his own grandfather before his mother or father had been conceived, thereby preventing his own birth. This is a specific example of the more general observation of the butterfly effect , or that

665-417: A distinction between logical paradoxes and semantic paradoxes, with Russell's paradox belonging to the former category, and the liar paradox and Grelling's paradoxes to the latter. Ramsey introduced the by-now standard distinction between logical and semantical contradictions. Logical contradictions involve mathematical or logical terms like class and number , and hence show that our logic or mathematics

760-440: A few doxographers provide us with the little information that remains. However, we know from Aristotle that Thales, also from Miletus, precedes Anaximander. It is debatable whether Thales actually was the teacher of Anaximander, but there is no doubt that Anaximander was influenced by Thales' theory that everything is derived from water. One thing that is not debatable is that even the ancient Greeks considered Anaximander to be from

855-472: A horizontal plane. The position of its shadow on the plane indicated the time of day. As it moves through its apparent course, the Sun draws a curve with the tip of the projected shadow, which is shortest at noon, when pointing due south. The variation in the tip's position at noon indicates the solar time and the seasons; the shadow is longest on the winter solstice and shortest on the summer solstice. The invention of

950-519: A lasting "unity of opposites". In logic , many paradoxes exist that are known to be invalid arguments, yet are nevertheless valuable in promoting critical thinking , while other paradoxes have revealed errors in definitions that were assumed to be rigorous, and have caused axioms of mathematics and logic to be re-examined. One example is Russell's paradox , which questions whether a "list of all lists that do not contain themselves" would include itself and showed that attempts to found set theory on

1045-405: A less active fire to break free. Thunderbolts are the result of a thicker and more violent air flow. He saw the sea as a remnant of the mass of humidity that once surrounded Earth. A part of that mass evaporated under the Sun's action, thus causing the winds and even the rotation of the celestial bodies, which he believed were attracted to places where water is more abundant. He explained rain as

SECTION 10

#1732844973879

1140-481: A personal deity, while others have taken more abstract views. John Scotus Eriugena held that God's essence is uncaused and incomprehensible. Similarly, Maimonides believed that God is a perfect unity and is indescribable with positive attributes , and that anthropomorphic imagery in the Bible is metaphorical. Baruch Spinoza believed that God is the natural world , existing eternally and necessarily, and that everything

1235-465: A portrait of the man. Anaximander was an early proponent of science and tried to observe and explain different aspects of the universe, with a particular interest in its origins , claiming that nature is ruled by laws, just like human societies, and anything that disturbs the balance of nature does not last long. Like many thinkers of his time, Anaximander's philosophy included contributions to many disciplines. In astronomy , he attempted to describe

1330-455: A pre-Socratic effort to demystify physical processes. His major contribution to history was writing the oldest prose document about the Universe and the origins of life; for this he is often called the "Father of Cosmology " and founder of astronomy. However, pseudo-Plutarch states that he still viewed celestial bodies as deities. He placed the celestial bodies in the wrong order. He thought that

1425-460: A product of the humidity pumped up from Earth by the sun. For him, the Earth was slowly drying up and water only remained in the deepest regions, which someday would go dry as well. According to Aristotle's Meteorology (II, 3), Democritus also shared this opinion. Anaximander speculated about the beginnings and origin of animal life, and that humans came from other animals in waters. According to his evolutionary theory , animals sprang out of

1520-416: A reason. According to Dadosky, the concept of "ultimate reality" is difficult to express in words, poetry, mythology , and art. Paradox or contradiction is often used as a medium of expression because of the "contradictory aspect of the ultimate reality". According to Mircea Eliade , ultimate reality can be mediated or revealed through symbols . For Eliade the " archaic " mind is constantly aware of

1615-431: A result that appears counter to intuition , but is demonstrated to be true nonetheless: A falsidical paradox establishes a result that appears false and actually is false, due to a fallacy in the demonstration. Therefore, falsidical paradoxes can be classified as fallacious arguments : An antinomy is a paradox which reaches a self-contradictory result by properly applying accepted ways of reasoning. For example,

1710-462: A slightly rounded metal surface. The centre or “navel” of the world ( ὀμφαλός γῆς omphalós gẽs ) could have been Delphi , but is more likely in Anaximander's time to have been located near Miletus. The Aegean Sea was near the map's centre and enclosed by three continents, themselves located in the middle of the ocean and isolated like islands by sea and rivers. Europe was bordered on the south by

1805-490: A sort of primal chaos . According to him, the Universe originates in the separation of opposites in the primordial matter. It embraces the opposites of hot and cold, wet and dry, and directs the movement of things; an entire host of shapes and differences then grow that are found in "all the worlds" (for he believed there were many). "Anaximander taught, then, that there was an eternal. The indestructible something out of which everything arises, and into which everything returns;

1900-438: A statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true or apparently true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion. A paradox usually involves contradictory-yet-interrelated elements that exist simultaneously and persist over time. They result in "persistent contradiction between interdependent elements" leading to

1995-413: A system of hollow concentric wheels, filled with fire, with the rims pierced by holes like those of a flute. Consequently, the Sun was the fire that one could see through a hole the same size as the Earth on the farthest wheel, and an eclipse corresponded with the occlusion of that hole. The diameter of the solar wheel was twenty-seven times that of the Earth (or twenty-eight, depending on the sources) and

SECTION 20

#1732844973879

2090-430: A time-traveler killing his own grandfather, it is the inconsistency of defining the past to which he returns as being somehow different from the one that leads up to the future from which he begins his trip, but also insisting that he must have come to that past from the same future as the one that it leads up to. W. V. O. Quine (1962) distinguished between three classes of paradoxes: A veridical paradox produces

2185-410: A time-traveller's interaction with the past—however slight—would entail making changes that would, in turn, change the future in which the time-travel was yet to occur, and would thus change the circumstances of the time-travel itself. Often a seemingly paradoxical conclusion arises from an inconsistent or inherently contradictory definition of the initial premise. In the case of that apparent paradox of

2280-472: A tolerably elastic system. Some scholars see a gap between the existing mythical and the new rational way of thought which is the main characteristic of the archaic period (8th to 6th century BC) in the Greek city-states . This has given rise to the phrase "Greek miracle". But there may not have been such an abrupt break as initially appears. The basic elements of nature ( water , air , fire , earth ) which

2375-596: A world map comes from the late Babylonian Map of the World later than 9th century BC but is based probably on a much older map. These maps indicated directions, roads, towns, borders, and geological features. Anaximander's innovation was to represent the entire inhabited land known to the ancient Greeks. Such an accomplishment is more significant than it at first appears. Anaximander most likely drew this map for three reasons. First, it could be used to improve navigation and trade between Miletus 's colonies and other colonies around

2470-485: Is an effect of God's nature. He defined God as a metaphysical substance rather than a personal being, and wrote in Ethics that "blessedness" comes from the love of God, meaning knowledge of reality as it is. Contemporary philosophy notes the possibility that reality has no fundamental explanation and should be seen as a brute fact . Adherents of the principle of sufficient reason reject this, holding that everything must have

2565-411: Is an example of the well-known liar paradox : it is a sentence that cannot be consistently interpreted as either true or false, because if it is known to be false, then it can be inferred that it must be true, and if it is known to be true, then it can be inferred that it must be false. Russell's paradox , which shows that the notion of the set of all those sets that do not contain themselves leads to

2660-506: Is derived in the last resort from Theophrastos, who certainly knew his book. He seems once at least to have quoted Anaximander's own words, and he criticised his style. Here are the remains of what he said of him in the First Book: "Anaximander of Miletos, son of Praxiades, a fellow-citizen and associate of Thales, said that the material cause and first element of things was the Infinite, he being

2755-468: Is described as the source of existence , an ineffable mystery, and something that can be individually harnessed for the good. It is thought of as being "the flow of the universe" and the source of its order and its qi , but it is not considered a deity to be worshipped , even if some interpretations believed it had the power to bless or illuminate. Abrahamic conceptions of ultimate reality show diversity, in which some perspectives consider God to be

2850-535: Is easy to understand that religious man deeply desires to be , to participate in reality , to be saturated with power. Common symbols of ultimate reality include world trees , the tree of life , microcosm , fire , children. Paul Tillich held that God is the ground of being and is something that precedes the subject and object (philosophy) dichotomy . He considered God to be what people are ultimately concerned with, existentially , and that religious symbols can be recovered as meaningful even without faith in

2945-480: Is impossible, since no document provides chronological references. Themistius , a 4th-century Byzantine rhetorician , mentions that he was the "first of the known Greeks to publish a written document on nature." Therefore, his texts would be amongst the earliest written in prose , at least in the Western world. By the time of Plato , his philosophy was almost forgotten, and Aristotle , his successor Theophrastus , and

Ultimate reality - Misplaced Pages Continue

3040-479: Is necessary to support everyday change. Democritus (c. 460–370 BCE) and Epicureanism (c. 307 BCE) rejected the idea of ultimate reality, saying that only atoms and void exist, but they do have the eternal, unbounded, and self-caused nature of non- materialistic views of the concept. In Neoplatonism (3rd century CE), the first principle of reality is "the One" which is a perfectly simple and ineffable principle which

3135-399: Is no contradiction, the doctor is the boy's mother.). Paradoxes that are not based on a hidden error generally occur at the fringes of context or language , and require extending the context or language in order to lose their paradoxical quality. Paradoxes that arise from apparently intelligible uses of language are often of interest to logicians and philosophers . "This sentence is false"

3230-548: Is non-terminating recursion , in the form of circular reasoning or infinite regress . When this recursion creates a metaphysical impossibility through contradiction, the regress or circularity is vicious . Again, the liar paradox is an instructive example: "This statement is false"—if the statement is true, then the statement is false, thereby making the statement true, thereby making the statement false, and so on. The barber paradox also exemplifies vicious circularity: The barber shaves those who do not shave themselves, so if

3325-691: Is not an independent authority, and the only question is what Theophrastos wrote." For him, it became no longer a mere point in time, but a source that could perpetually give birth to whatever will be. The indefiniteness is spatial in early usages as in Homer (indefinite sea) and as in Xenophanes (6th century BC) who said that the Earth went down indefinitely (to apeiron ) i.e. beyond the imagination or concept of men. Burnet (1930) in Early Greek Philosophy says: "Nearly all we know of Anaximander's system

3420-579: Is problematic. Semantical contradictions involve, besides purely logical terms, notions like thought , language , and symbolism , which, according to Ramsey, are empirical (not formal) terms. Hence these contradictions are due to faulty ideas about thought or language, and they properly belong to epistemology . A taste for paradox is central to the philosophies of Laozi , Zeno of Elea , Zhuangzi , Heraclitus , Bhartrhari , Meister Eckhart , Hegel , Kierkegaard , Nietzsche , and G.K. Chesterton , among many others. Søren Kierkegaard, for example, writes in

3515-566: Is the material, efficient, formal and final cause of all that exists. It is the pervasive, genderless, infinite, eternal truth and bliss which does not change, yet is the cause of all changes. Brahman as a metaphysical concept is the single binding unity behind diversity in all that exists in the universe. In Taoism , the Tao is the impersonal principle that underlies reality . It is a metaphysical principle and process that refers to how nature develops, being an enigmatic process of transformation. It

3610-405: Is the source of the universe, and exists without multiplicity and beyond being and non-being. Stoic physics (c. 300 BCE–3rd century CE) called the primitive substance of the universe pneuma or God, which is everything that exists and is a creative force that develops and shapes the cosmos. In Theravada Buddhism, Nirvana is ultimate reality. Nirvana is described in negative terms; it

3705-557: Is unconstructed and unconditioned. In some strands of Mahayana Buddhism , the Buddha-nature or the Dharmakaya is seen as ultimate reality. Other strands of Buddhism reject the notion of ultimate reality, regarding any existent as empty ( sunyata ) of inherent existence ( svabhava ). In Hinduism, Brahman connotes the highest universal principle, the ultimate reality in the universe . In major schools of Hindu philosophy , it

3800-570: Is very likely that leaders of Miletus sent him there as a legislator to create a constitution or simply to maintain the colony's allegiance. Anaximander lived the final few years of his life as a subject of the Persian Achaemenid Empire . Anaximander's theories were influenced by the Greek mythical tradition, and by some ideas of Thales  – the father of Western philosophy  – as well as by observations made by older civilizations in

3895-476: The Philosophical Fragments that: But one must not think ill of the paradox, for the paradox is the passion of thought, and the thinker without the paradox is like the lover without passion: a mediocre fellow. But the ultimate potentiation of every passion is always to will its own downfall, and so it is also the ultimate passion of the understanding to will the collision, although in one way or another

Ultimate reality - Misplaced Pages Continue

3990-535: The Grelling–Nelson paradox points out genuine problems in our understanding of the ideas of truth and description. Sometimes described since Quine's work, a dialetheia is a paradox that is both true and false at the same time. It may be regarded as a fourth kind, or alternatively as a special case of antinomy. In logic, it is often assumed, following Aristotle , that no dialetheia exist, but they are allowed in some paraconsistent logics . Frank Ramsey drew

4085-814: The Mediterranean Sea and was separated from Asia by the Black Sea, the Lake Maeotis , and, further east, either by the Phasis River (now called the Rioni in Georgia ) or the Tanais . The Nile flowed south into the ocean, separating Libya (which was the name for the part of the then-known African continent) from Asia. The Suda relates that Anaximander explained some basic notions of geometry. It also mentions his interest in

4180-624: The Monist school which began in Miletus, with Thales followed by Anaximander and which ended with Anaximenes . 3rd-century Roman rhetorician Aelian depicts Anaximander as leader of the Milesian colony to Apollonia on the Black Sea coast, and hence some have inferred that he was a prominent citizen. Indeed, Various History (III, 17) explains that philosophers sometimes also dealt with political matters. It

4275-409: The barber paradox , which poses the question of whether a barber who shaves all and only those who do not shave themselves will shave himself. In this paradox, the barber is a self-referential concept. Contradiction , along with self-reference, is a core feature of many paradoxes. The liar paradox, "This statement is false," exhibits contradiction because the statement cannot be false and true at

4370-404: The politics of Miletus and was sent as a leader to one of its colonies. Anaximander, son of Praxiades, was born in the third year of the 42nd Olympiad (610 BC). According to Apollodorus of Athens , Greek grammarian of the 2nd century BC, he was sixty-four years old during the second year of the 58th Olympiad (547–546 BC) and died shortly afterwards. Establishing a timeline of his work

4465-415: The " intermediate " with the something " distinct from " the elements ." "It is certain that he [Anaximander] cannot have said anything about elements, which no one thought of before Empedokles, and no one could think of before Parmenides. The question has only been mentioned because it has given rise to a lengthy controversy, and because it throws light on the historical value of Aristotle's statements. From

4560-583: The "Infinite" with a "material cause", Theophrastos is following the Aristotelian tradition of "nearly always discussing the facts from the point of view of his own system". Aristotle writes ( Metaphysics , I.III 3–4) that the Pre-Socratics were searching for the element that constitutes all things. While each pre-Socratic philosopher gave a different answer as to the identity of this element ( water for Thales and air for Anaximenes), Anaximander understood

4655-421: The "immense ocean from which everything is born and upon which the Earth floats." Anaximander was then able to envisage the Earth at the centre of an infinite space, in which case it required no support as there was nowhere "down" to fall. In Rovelli's view, the shape – a cylinder or a sphere – is unimportant compared to the appreciation of a "finite body that floats free in space." Anaximander's realization that

4750-649: The Boundless " intermediate between the elements " than to say that it is " distinct from the elements." Indeed, if once we introduce the elements at all, the former description is the more adequate of the two. At any rate, if we refuse to understand these passages as referring to Anaximander, we shall have to say that Aristotle paid a great deal of attention to some one whose very name has been lost, and who not only agreed with some of Anaximander's views, but also used some of his most characteristic expressions. We may add that in one or two places Aristotle certainly seems to identify

4845-407: The Earth floats free without falling and does not need to be resting on something has been indicated by many as the first cosmological revolution and the starting point of scientific thinking. Karl Popper calls this idea "one of the boldest, most revolutionary, and most portentous ideas in the whole history of human thinking." Such a model allowed the concept that celestial bodies could pass under

SECTION 50

#1732844973879

4940-497: The Earth, opening the way to Greek astronomy. Rovelli suggests that seeing the stars circling the Pole star , and both vanishing below the horizon on one side and reappearing above it on the other, would suggest to the astronomer that there was a void both above and below the Earth. Anaximander's bold use of non- mythological explanatory hypotheses considerably distinguishes him from previous cosmology writers such as Hesiod . It indicates

5035-587: The Mediterranean Sea and Black Sea. Second, Thales would probably have found it easier to convince the Ionian city-states to join in a federation in order to push the Median threat away if he possessed such a tool. Finally, the philosophical idea of a global representation of the world simply for the sake of knowledge was reason enough to design one. Surely aware of the sea's convexity, he may have designed his map on

5130-494: The Near East, especially Babylon. All these were developed rationally. In his desire to find some universal principle, he assumed, like traditional religion, the existence of a cosmic order; and his ideas on this used the old language of myths which ascribed divine control to various spheres of reality. This was a common practice for the Greek philosophers in a society which saw gods everywhere, and therefore could fit their ideas into

5225-441: The assembly of demos in the agora which is lying in the middle of the city. The same rational way of thought led him to introduce the abstract apeiron (indefinite, infinite, boundless, unlimited ) as an origin of the universe, a concept that is probably influenced by the original Chaos (gaping void, abyss, formless state) from which everything else appeared in the mythical Greek cosmogony . It also takes notice of

5320-401: The barber does not shave himself, then he shaves himself, then he does not shave himself, and so on. Other paradoxes involve false statements and half-truths ("'impossible' is not in my vocabulary") or rely on hasty assumptions (A father and his son are in a car crash; the father is killed and the boy is rushed to the hospital. The doctor says, "I can't operate on this boy. He's my son." There

5415-406: The beginning or first principle to be an endless, unlimited primordial mass ( apeiron ), subject to neither old age nor decay, that perpetually yielded fresh materials from which everything we perceive is derived. He proposed the theory of the apeiron in direct response to the earlier theory of his teacher, Thales, who had claimed that the primary substance was water. The notion of temporal infinity

5510-421: The collision must become its downfall. This, then, is the ultimate paradox of thought: to want to discover something that thought itself cannot think. A paradoxical reaction to a drug is the opposite of what one would expect, such as becoming agitated by a sedative or sedated by a stimulant . Some are common and are used regularly in medicine, such as the use of stimulants such as Adderall and Ritalin in

5605-451: The cosmic order is not monarchic but geometric , and that this causes the equilibrium of the Earth, which is lying in the centre of the universe. This is the projection on nature of a new political order and a new space organized around a centre which is the static point of the system in the society as in nature. In this space there is isonomy (equal rights) and all the forces are symmetrical and transferable. The decisions are now taken by

5700-679: The countless worlds. This theory places Anaximander close to the Atomists and the Epicureans who, more than a century later, also claimed that an infinity of worlds appeared and disappeared. In the timeline of the Greek history of thought , some thinkers conceptualized a single world (Plato, Aristotle, Anaxagoras and Archelaus ), while others instead speculated on the existence of a series of worlds, continuous or non-continuous ( Anaximenes , Heraclitus , Empedocles and Diogenes ). Anaximander attributed some phenomena, such as thunder and lightning, to

5795-593: The element of origin was often revisited afterwards, notably by Aristotle, and by the Greek tragedian Euripides : "what comes from earth must return to earth." Friedrich Nietzsche , in his Philosophy in the Tragic Age of the Greeks , stated that Anaximander viewed "... all coming-to-be as though it were an illegitimate emancipation from eternal being, a wrong for which destruction is the only penance." Physicist Max Born , in commenting upon Werner Heisenberg 's arriving at

SECTION 60

#1732844973879

5890-407: The elements arise.'⁠—Aristotle Physics. F, 5 204 b 22 (Ritter and Preller (1898) Historia Philosophiae Graecae, section 16 b)." Anaximander maintains that all dying things are returning to the element from which they came ( apeiron ). The one surviving fragment of Anaximander's writing deals with this matter. Simplicius transmitted it as a quotation, which describes the balanced and mutual changes of

5985-439: The elements: Whence things have their origin, Thence also their destruction happens, According to necessity; For they give to each other justice and recompense For their injustice In conformity with the ordinance of Time. Simplicius mentions that Anaximander said all these "in poetic terms", meaning that he used the old mythical language. The goddess Justice ( Dike ) keeps the cosmic order. This concept of returning to

6080-521: The first Greek philosophers believed made up the universe in fact represent the primordial forces imagined in earlier ways of thinking. Their collision produced what the mythical tradition had called cosmic harmony. In the old cosmogonies – Hesiod (8th – 7th century BC) and Pherecydes (6th century BC) – Zeus establishes his order in the world by destroying the powers which were threatening this harmony (the Titans ). Anaximander claimed that

6175-574: The first to introduce this name of the material cause. He says it is neither water nor any other of the so-called elements, but a substance different from them which is infinite" [apeiron, or ἄπειρον ] "from which arise all the heavens and the worlds within them.—Phys, Op. fr. 2 (Dox. p. 476; R. P. 16)." Burnet's quote from the "First Book" is his translation of Theophrastos' Physic Opinion fragment 2 as it appears in p. 476 of Historia Philosophiae Graecae (1898) by Ritter and Preller and section 16 of Doxographi Graeci (1879) by Diels. By ascribing

6270-580: The form of images or other media. For example, M.C. Escher featured perspective-based paradoxes in many of his drawings, with walls that are regarded as floors from other points of view, and staircases that appear to climb endlessly. Informally, the term paradox is often used to describe a counterintuitive result. Self-reference , contradiction and infinite regress are core elements of many paradoxes. Other common elements include circular definitions , and confusion or equivocation between different levels of abstraction . Self-reference occurs when

6365-526: The geographer Eratosthenes , Anaximander was the first to publish a map of the world . The map probably inspired the Greek historian Hecataeus of Miletus to draw a more accurate version. Strabo viewed both as the first geographers after Homer . Maps were produced in ancient times, also notably in Egypt , Lydia , the Middle East , and Babylon . Only some small examples survived until today. The unique example of

6460-467: The gnomon itself cannot be attributed to Anaximander because its use, as well as the division of days into twelve parts, came from the Babylonians . It is they, according to Herodotus ' Histories (II, 109), who gave the Greeks the art of time measurement. It is likely that he was not the first to determine the solstices, because no calculation is necessary. On the other hand, equinoxes do not correspond to

6555-421: The idea that humans had to spend part of this transition inside the mouths of big fish to protect themselves from the Earth's climate until they could come out in open air and lose their scales. He thought that, considering humans' extended infancy, we could not have survived in the primeval world in the same manner we do presently. Both Strabo and Agathemerus (later Greek geographers) claim that, according to

6650-426: The idea that the elementary particles of quantum mechanics are to be seen as different manifestations, different quantum states, of one and the same "primordial substance,"' proposed that this primordial substance be called apeiron . Anaximander was the first to conceive a mechanical model of the world. In his model, the Earth floats very still in the centre of the infinite, not supported by anything. It remains "in

6745-433: The identification of sets with properties or predicates were flawed. Others, such as Curry's paradox , cannot be easily resolved by making foundational changes in a logical system. Examples outside logic include the ship of Theseus from philosophy, a paradox that questions whether a ship repaired over time by replacing each and all of its wooden parts one at a time would remain the same ship. Paradoxes can also take

6840-426: The image as such, as a whole bundle of meaning, that is "true" (faithful, trustworthy). Eliade says : the sacred is equivalent to a power , and, in the last analysis, to reality . The sacred is saturated with being . Sacred power means reality and at the same time enduringness and efficacy. The polarity sacred-profane is often expressed as opposition between real and unreal or pseudoreal . [...] Thus it

6935-420: The intervention of elements, rather than to divine causes. In his system, thunder results from the shock of clouds hitting each other; the loudness of the sound is proportionate with that of the shock. Thunder without lightning is the result of the wind being too weak to emit any flame, but strong enough to produce a sound. A flash of lightning without thunder is a jolt of the air that disperses and falls, allowing

7030-496: The lunar wheel, whose fire was less intense, eighteen (or nineteen) times. Its hole could change shape, thus explaining lunar phases . The stars and the planets, located closer, followed the same model. Anaximander was the first astronomer to consider the Sun as a huge mass, and consequently, to realize how far from Earth it might be, and the first to present a system where the celestial bodies turned at different distances. Furthermore, according to Diogenes Laertius (II, 2), he built

7125-458: The measurement of time and associates him with the introduction in Greece of the gnomon. In Lacedaemon , he participated in the construction, or at least in the adjustment, of sundials to indicate solstices and equinoxes . Indeed, a gnomon required adjustments from a place to another because of the difference in latitude . In his time, the gnomon was simply a vertical pillar or rod mounted on

7220-463: The mechanics of celestial bodies in relation to the Earth. In physics, his postulation that the indefinite (or apeiron ) was the source of all things, led Greek philosophy to a new level of conceptual abstraction . His knowledge of geometry allowed him to introduce the gnomon in Greece. He created a map of the world that contributed greatly to the advancement of geography . Anaximander was involved in

7315-502: The middle point between the positions during solstices, as the Babylonians thought. As the Suda seems to suggest, it is very likely that with his knowledge of geometry, he became the first Greek to determine accurately the equinoxes. In his philosophical work De Divinatione (I, 50, 112), Cicero states that Anaximander convinced the inhabitants of Lacedaemon to abandon their city and spend

7410-439: The mutual changes between the four elements. Origin, then, must be something else unlimited in its source, that could create without experiencing decay, so that genesis would never stop. The Refutation attributed to Hippolytus of Rome (I, 5), and the later 6th century Byzantine philosopher Simplicius of Cilicia , attribute to Anaximander the earliest use of the word apeiron ( ἄπειρον "infinite" or "limitless") to designate

7505-475: The night in the country with their weapons because an earthquake was near. The city collapsed when the top of the Taygetus split like the stern of a ship. Pliny the Elder also mentions this anecdote (II, 81), suggesting that it came from an "admirable inspiration", as opposed to Cicero, who did not associate the prediction with divination. Paradox A paradox is a logically self-contradictory statement or

7600-467: The opposites found in nature — for example, water can only be wet, never dry — and therefore cannot be the one primary substance; nor could any of the other candidates. He postulated the apeiron as a substance that, although not directly perceptible to us, could explain the opposites he saw around him. "If Thales had been right in saying that water was the fundamental reality, it would not be easy to see how anything else could ever have existed. One side of

7695-650: The opposition, the cold and moist, would have had its way unchecked, and the warm and dry would have been driven from the field long ago. We must, then, have something not itself one of the warring opposites, something more primitive, out of which they arise, and into which they once more pass away." Anaximander explains how the four elements of ancient physics ( air , earth , water and fire ) are formed, and how Earth and terrestrial beings are formed through their interactions. Unlike other Pre-Socratics, he never defines this principle precisely, and it has generally been understood (e.g., by Aristotle and by Saint Augustine ) as

7790-431: The original principle. He was the first philosopher to employ, in a philosophical context, the term archē ( ἀρχή ), which until then had meant beginning or origin. "That Anaximander called this something by the name of Φύσις is the natural interpretation of what Theophrastos says; the current statement that the term ἀρχή was introduced by him appears to be due to a misunderstanding." And "Hippolytos, however,

7885-513: The personal God of traditional Christianity. Anaximander Anaximander ( / æ ˌ n æ k s ɪ ˈ m æ n d ər / an- AK -sih- MAN -dər ; Ancient Greek : Ἀναξίμανδρος Anaximandros ; c.  610  – c.  546 BC ) was a pre-Socratic Greek philosopher who lived in Miletus , a city of Ionia (in modern-day Turkey). He belonged to the Milesian school and learned

7980-633: The point of view of his own system, these may be justified; but we shall have to remember in other cases that, when he seems to attribute an idea to some earlier thinker, we are not bound to take what he says in an historical sense." For Anaximander, the principle of things, the constituent of all substances, is nothing determined and not an element such as water in Thales' view. Neither is it something halfway between air and water, or between air and fire, thicker than air and fire, or more subtle than water and earth. Anaximander argues that water cannot embrace all of

8075-502: The presence of the Sacred , and for this mind all symbols are religious (relinking to the Origin). Through symbols human beings can get an immediate " intuition " of certain features of the inexhaustible Sacred. The mind makes use of images to grasp the ultimate reality of things because reality manifests itself in contradictory ways and therefore can't be described in concepts . It is therefore

8170-452: The primary substance could be one of these particular things. His argument seems to be preserved by Aristotle, who has the following passage in his discussion of the Infinite: "Further, there cannot be a single, simple body which is infinite, either, as some hold, one distinct from the elements, which they then derive from it, or without this qualification. For there are some who make this. (i.e.

8265-495: The same place because of its indifference", a point of view that Aristotle considered ingenious, in On the Heavens . Its curious shape is that of a cylinder with a height one-third of its diameter. The flat top forms the inhabited world. Carlo Rovelli suggests that Anaximander took the idea of the Earth's shape as a floating disk from Thales , who had imagined the Earth floating in water,

8360-471: The same time. The barber paradox is contradictory because it implies that the barber shaves himself if and only if the barber does not shave himself. As with self-reference, a statement can contain a contradiction without being a paradox. "This statement is written in French" is an example of a contradictory self-referential statement that is not a paradox and is instead false. Another core aspect of paradoxes

8455-516: The sea long ago, born trapped in a spiny bark, but as they got older, the bark would dry up and animals would be able to break it. The 3rd century Roman writer Censorinus reports: Anaximander of Miletus considered that from warmed up water and earth emerged either fish or entirely fishlike animals. Inside these animals, men took form and embryos were held prisoners until puberty; only then, after these animals burst open, could men and women come out, now able to feed themselves. Anaximander put forward

8550-443: The seasons. The doxographer and theologian Aetius attributes to Pythagoras the exact measurement of the obliquity. According to Simplicius, Anaximander already speculated on the plurality of worlds , similar to atomists Leucippus and Democritus , and later philosopher Epicurus . These thinkers supposed that worlds appeared and disappeared for a while, and that some were born when others perished. They claimed that this movement

8645-627: The stars were nearest to the Earth, then the Moon, and the Sun farthest away. His scheme is compatible with the Indo-Iranian philosophical traditions contained in the Iranian Avesta and the Indian Upanishads . At the origin, after the separation of hot and cold, a ball of flame appeared that surrounded Earth like bark on a tree. This ball broke apart to form the rest of the Universe. It resembled

8740-455: The teachings of his master Thales . He succeeded Thales and became the second master of that school where he counted Anaximenes and, arguably, Pythagoras amongst his pupils. Little of his life and work is known today. According to available historical documents, he is the first philosopher known to have written down his studies, although only one fragment of his work remains. Fragmentary testimonies found in documents after his death provide

8835-399: The treatment of attention deficit hyperactivity disorder (also known as ADHD), while others are rare and can be dangerous as they are not expected, such as severe agitation from a benzodiazepine . The actions of antibodies on antigens can rarely take paradoxical turns in certain ways. One example is antibody-dependent enhancement (immune enhancement) of a disease's virulence; another

8930-445: Was eternal, "for without movement, there can be no generation, no destruction". In addition to Simplicius, Hippolytus reports Anaximander's claim that from the infinite comes the principle of beings, which themselves come from the heavens and the worlds (several doxographers use the plural when this philosopher is referring to the worlds within, which are often infinite in quantity). Cicero writes that he attributes different gods to

9025-410: Was familiar to the Greek mind from remote antiquity in the religious concept of immortality, and Anaximander's description was in terms appropriate to this conception. This archē is called "eternal and ageless". (Hippolytus (?), Refutation , I,6,I;DK B2) " Aristotle puts things in his own way regardless of historical considerations, and it is difficult to see that it is more of an anachronism to call

#878121