Monday, November 30, 2015

Aristotle (384-322 BC)

Posted by Unknown On 2:29 AM
Aristotle Altemps Inv8575.jpg     
 Aristotle, whose name means "the best purpose", was born in 384 BC in Stagira, Chalcidice, about 55 km (34 miles) east of modern-day Thessaloniki. His father Nicomachus was the personal physician to King Amyntas of Macedon. Although there is little information on Aristotle's childhood, he probably spent some time within the Macedonian palace, making his first connections with the Macedonian monarchy.

       At about the age of eighteen, Aristotle moved to Athens to continue his education at Plato's Academy. He remained there for nearly twenty years before leaving Athens in 348/47 BC. The traditional story about his departure records that he was disappointed with the Academy's direction after control passed to Plato's nephew Speusippus, although it is possible that he feared anti-Macedonian sentiments and left before Plato died.

 "Aristotle" by Francesco Hayez (1791–1882)
                  Aristotle then accompanied Xenocrates to the court of his friend Hermias of Atarneus in Asia Minor. There, he traveled with Theophrastus to the island of Lesbos, where together they researched the botany and zoology of the island. Aristotle married Pythias, either Hermias's adoptive daughter or niece. She bore him a daughter, whom they also named Pythias. Soon after Hermias' death, Aristotle was invited by Philip II of Macedon to become the tutor to his son Alexander in 343 BC.

          Aristotle was appointed as the head of the royal academy of Macedon. During that time he gave lessons not only to Alexander, but also to two other future kings: Ptolemy and Cassander.Aristotle encouraged Alexander toward eastern conquest and his attitude towards Persia was unabashedly ethnocentric. In one famous example, he counsels Alexander to be "a leader to the Greeks and a despot to the barbarians, to look after the former as after friends and relatives, and to deal with the latter as with beasts or plants".

        By 335 BC, Artistotle had returned to Athens, establishing his own school there known as the Lyceum. Aristotle conducted courses at the school for the next twelve years. While in Athens, his wife Pythias died and Aristotle became involved with Herpyllis of Stagira, who bore him a son whom he named after his father, Nicomachus. According to the Suda, he also had an eromenos, Palaephatus of Abydus.

        This period in Athens, between 335 and 323 BC, is when Aristotle is believed to have composed many of his works. He wrote many dialogues of which only fragments have survived. Those works that have survived are in treatise form and were not, for the most part, intended for widespread publication; they are generally thought to be lecture aids for his students. His most important treatises include Physics, Metaphysics, Nicomachean Ethics, Politics, De Anima (On the Soul) and Poetics.

     Aristotle not only studied almost every subject possible at the time, but made significant contributions to most of them. In physical science, Aristotle studied anatomy, astronomy, embryology, geography, geology, meteorology, physics and zoology. In philosophy, he wrote on aesthetics, ethics, government, metaphysics, politics, economics, psychology, rhetoric and theology. He also studied education, foreign customs, literature and poetry. His combined works constitute a virtual encyclopedia of Greek knowledge.

        Near the end of his life, Alexander and Aristotle became estranged over Alexander's relationship with Persia and Persians. A widespread tradition in antiquity suspected Aristotle of playing a role in Alexander's death, but there is little evidence.

      Following Alexander's death, anti-Macedonian sentiment in Athens was rekindled. In 322 BC, Eurymedon the Hierophant denounced Aristotle for not holding the gods in honor, prompting him to flee to his mother's family estate in Chalcis, explaining: "I will not allow the Athenians to sin twice against philosophy" – a reference to Athens's prior trial and execution of Socrates. He died in Euboea of natural causes later that same year, having named his student Antipater as his chief executor and leaving a will in which he asked to be buried next to his wife.

         Charles Walston argues that the tomb of Aristotle is located on the sacred way between Chalcis and Eretria and to have contained two styluses, a pen, a signet-ring and some terra-cottas as well as what is supposed to be the earthly remains of Aristotle in the form of some skull fragments.

         In general, the details of the life of Aristotle are not well-established. The biographies of Aristotle written in ancient times are often speculative and historians only agree on a few salient points.

Logic
     Aristotle portrayed in the 1493 Nuremberg Chronicle as a scholar of the 15th century AD.
Main article: Term logic
For more details on this topic, see Non-Aristotelian logic.
With the Prior Analytics, Aristotle is credited with the earliest study of formal logic,and his conception of it was the dominant form of Western logic until 19th century advances in mathematical logic. Kant stated in the Critique of Pure Reason that Aristotle's theory of logic completely accounted for the core of deductive inference.

History
       Aristotle "says that 'on the subject of reasoning' he 'had nothing else on an earlier date to speak of'".However, Plato reports that syntax was devised before him, by Prodicus of Ceos, who was concerned by the correct use of words. Logic seems to have emerged from dialectics; the earlier philosophers made frequent use of concepts like reductio ad absurdum in their discussions, but never truly understood the logical implications. Even Plato had difficulties with logic; although he had a reasonable conception of a deductive system, he could never actually construct one, thus he relied instead on his dialectic.

     Plato believed that deduction would simply follow from premises, hence he focused on maintaining solid premises so that the conclusion would logically follow. Consequently, Plato realized that a method for obtaining conclusions would be most beneficial. He never succeeded in devising such a method, but his best attempt was published in his book Sophist, where he introduced his division method.

Analytics and the Organon
Main article: Organon
What we today call Aristotelian logic, Aristotle himself would have labeled "analytics". The term "logic" he reserved to mean dialectics. Most of Aristotle's work is probably not in its original form, because it was most likely edited by students and later lecturers. The logical works of Aristotle were compiled into six books in about the early 1st century CE:

Categories
  • On Interpretation
  • Prior Analytics
  • Posterior Analytics
  • Topics

On Sophistical Refutations
       The order of the books (or the teachings from which they are composed) is not certain, but this list was derived from analysis of Aristotle's writings. It goes from the basics, the analysis of simple terms in the Categories, the analysis of propositions and their elementary relations in On Interpretation, to the study of more complex forms, namely, syllogisms (in the Analytics) and dialectics (in the Topics and Sophistical Refutations). The first three treatises form the core of the logical theory stricto sensu: the grammar of the language of logic and the correct rules of reasoning. There is one volume of Aristotle's concerning logic not found in the Organon, namely the fourth book of Metaphysics.

Aristotle's epistemology
         Plato (left) and Aristotle (right), a detail of The School of Athens, a fresco by Raphael. Aristotle gestures to the earth, representing his belief in knowledge through empirical observation and experience, while holding a copy of his Nicomachean Ethics in his hand, whilst Plato gestures to the heavens, representing his belief in The Forms, while holding a copy of Timaeus
      Like his teacher Plato, Aristotle's philosophy aims at the universal. Aristotle's ontology, however, finds the universal in particular things, which he calls the essence of things, while in Plato's ontology, the universal exists apart from particular things, and is related to them as their prototype or exemplar. For Aristotle, therefore, epistemology is based on the study of particular phenomena and rises to the knowledge of essences, while for Plato epistemology begins with knowledge of universal Forms (or ideas) and descends to knowledge of particular imitations of these. For Aristotle, "form" still refers to the unconditional basis of phenomena but is "instantiated" in a particular substance (see Universals and particulars, below). In a certain sense, Aristotle's method is both inductive and deductive, while Plato's is essentially deductive from a priori principles.

         In Aristotle's terminology, "natural philosophy" is a branch of philosophy examining the phenomena of the natural world, and includes fields that would be regarded today as physics, biology and other natural sciences. In modern times, the scope of philosophy has become limited to more generic or abstract inquiries, such as ethics and metaphysics, in which logic plays a major role. Today's philosophy tends to exclude empirical study of the natural world by means of the scientific method. In contrast, Aristotle's philosophical endeavors encompassed virtually all facets of intellectual inquiry.

            In the larger sense of the word, Aristotle makes philosophy coextensive with reasoning, which he also would describe as "science". Note, however, that his use of the term science carries a different meaning than that covered by the term "scientific method". For Aristotle, "all science (dianoia) is either practical, poetical or theoretical" (Metaphysics 1025b25). By practical science, he means ethics and politics; by poetical science, he means the study of poetry and the other fine arts; by theoretical science, he means physics, mathematics and metaphysics.

         If logic (or "analytics") is regarded as a study preliminary to philosophy, the divisions of Aristotelian philosophy would consist of:  Logic; Theoretical Philosophy, including Metaphysics, Physics and Mathematics; Practical Philosophy and  Poetical Philosophy.

       In the period between his two stays in Athens, between his times at the Academy and the Lyceum, Aristotle conducted most of the scientific thinking and research for which he is renowned today. In fact, most of Aristotle's life was devoted to the study of the objects of natural science. Aristotle's metaphysics contains observations on the nature of numbers but he made no original contributions to mathematics. He did, however, perform original research in the natural sciences, e.g., botany, zoology, physics, astronomy, chemistry, meteorology, and several other sciences.

         Aristotle's writings on science are largely qualitative, as opposed to quantitative. Beginning in the 16th century, scientists began applying mathematics to the physical sciences, and Aristotle's work in this area was deemed hopelessly inadequate. His failings were largely due to the absence of concepts like mass, velocity, force and temperature. He had a conception of speed and temperature, but no quantitative understanding of them, which was partly due to the absence of basic experimental devices, like clocks and thermometers.

        His writings provide an account of many scientific observations, a mixture of precocious accuracy and curious errors. For example, in his History of Animals he claimed that human males have more teeth than females.In a similar vein, John Philoponus, and later Galileo, showed by simple experiments that Aristotle's theory that a heavier object falls faster than a lighter object is incorrect.On the other hand, Aristotle refuted Democritus's claim that the Milky Way was made up of "those stars which are shaded by the earth from the sun's rays," pointing out (correctly, even if such reasoning was bound to be dismissed for a long time) that, given "current astronomical demonstrations" that "the size of the sun is greater than that of the earth and the distance of the stars from the earth many times greater than that of the sun, then ... the sun shines on all the stars and the earth screens none of them."

         In places, Aristotle goes too far in deriving 'laws of the universe' from simple observation and over-stretched reason. Today's scientific method assumes that such thinking without sufficient facts is ineffective, and that discerning the validity of one's hypothesis requires far more rigorous experimentation than that which Aristotle used to support his laws.

      Aristotle also had some scientific blind spots. He posited a geocentric cosmology that we may discern in selections of the Metaphysics, which was widely accepted up until the 16th century. From the 3rd century to the 16th century, the dominant view held that the Earth was the rotational center of the universe.

     Because he was perhaps the philosopher most respected by European thinkers during and after the Renaissance, these thinkers often took Aristotle's erroneous positions as given, which held back science in this epoch.[30] However, Aristotle's scientific shortcomings should not mislead one into forgetting his great advances in the many scientific fields. For instance, he founded logic as a formal science and created foundations to biology that were not superseded for two millennia. Moreover, he introduced the fundamental notion that nature is composed of things that change and that studying such changes can provide useful knowledge of underlying constants.

Geology
     He [Aristotle] refers to many examples of changes now constantly going on, and insists emphatically on the great results which they must produce in the lapse of ages. He instances particular cases of lakes that had dried up, and deserts that had at length become watered by rivers and fertilized. He points to the growth of the Nilotic delta since the time of Homer, to the shallowing of the Palus Maeotis within sixty years from his own time ... He alludes ... to the upheaving of one of the Eolian islands, previous to a volcanic eruption. The changes of the earth, he says, are so slow in comparison to the duration of our lives, that they are overlooked; and the migrations of people after great catastrophes, and their removal to other regions, cause the event to be forgotten.

     He says [12th chapter of his Meteorics] 'the distribution of land and sea in particular regions does not endure throughout all time, but it becomes sea in those parts where it was land, and again it becomes land where it was sea, and there is reason for thinking that these changes take place according to a certain system, and within a certain period.' The concluding observation is as follows: 'As time never fails, and the universe is eternal, neither the Tanais, nor the Nile, can have flowed for ever. The places where they rise were once dry, and there is a limit to their operations, but there is none to time. So also of all other rivers; they spring up and they perish; and the sea also continually deserts some lands and invades others The same tracts, therefore, of the earth are not some always sea, and others always continents, but every thing changes in the course of time.
  • Physics
  • Main article: Aristotelian physics
  • Five elements
  • Main article: Classical element
  • Aristotle proposed a fifth element, aether, in addition to the four proposed earlier by Empedocles.
  • Earth, which is cold and dry; this corresponds to the modern idea of a solid.
  • Water, which is cold and wet; this corresponds to the modern idea of a liquid.
  • Air, which is hot and wet; this corresponds to the modern idea of a gas.
  • Fire, which is hot and dry; this corresponds to the modern ideas of plasma and heat.
  • Aether, which is the divine substance that makes up the heavenly spheres and heavenly bodies (stars and planets).

          Each of the four earthly elements has its natural place. All that is earthly tends toward the center of the universe, i.e., the center of the Earth. Water tends toward a sphere surrounding the center. Air tends toward a sphere surrounding the water sphere. Fire tends toward the lunar sphere (in which the Moon orbits). When elements are moved out of their natural place, they naturally move back towards it. This is "natural motion"—motion requiring no extrinsic cause. So, for example, in water, earthy bodies sink while air bubbles rise up; in air, rain falls and flame rises. Outside all the other spheres, the heavenly, fifth element, manifested in the stars and planets, moves in the perfection of circles.

Motion
Main article: potentiality and actuality
        Aristotle defined motion as the actuality of a potentiality as such.Aquinas suggested that the passage be understood literally; that motion can indeed be understood as the active fulfillment of a potential, as a transition toward a potentially possible state. Because actuality and potentiality are normally opposites in Aristotle, other commentators either suggest that the wording which has come down to us is erroneous, or that the addition of the "as such" to the definition is critical to understanding it.

Causality, the four causes
Main article: Four causes
    Aristotle suggested that the reason for anything coming about can be attributed to four different types of simultaneously active causal factors:

      Material cause describes the material out of which something is composed. Thus the material cause of a table is wood, and the material cause of a car is rubber and steel. It is not about action. It does not mean one domino knocks over another domino.
The formal cause is its form, i.e., the arrangement of that matter. It tells us what a thing is, that any thing is determined by the definition, form, pattern, essence, whole, synthesis or archetype. It embraces the account of causes in terms of fundamental principles or general laws, as the whole (i.e., macrostructure) is the cause of its parts, a relationship known as the whole-part causation. Plainly put, the formal cause is the idea existing in the first place as exemplar in the mind of the sculptor, and in the second place as intrinsic, determining cause, embodied in the matter. Formal cause could only refer to the essential quality of causation. A simple example of the formal cause is the mental image or idea that allows an artist, architect, or engineer to create his drawings.
The efficient cause is "the primary source", or that from which the change under consideration proceeds. It identifies 'what makes of what is made and what causes change of what is changed' and so suggests all sorts of agents, nonliving or living, acting as the sources of change or movement or rest. Representing the current understanding of causality as the relation of cause and effect, this covers the modern definitions of "cause" as either the agent or agency or particular events or states of affairs. So, take the two dominoes, this time of equal weighting, the first is knocked over causing the second also to fall over.
        The final cause is its purpose, or that for the sake of which a thing exists or is done, including both purposeful and instrumental actions and activities. The final cause or teleos is the purpose or function that something is supposed to serve. This covers modern ideas of motivating causes, such as volition, need, desire, ethics, or spiritual beliefs.
       Additionally, things can be causes of one another, causing each other reciprocally, as hard work causes fitness and vice versa, although not in the same way or function, the one is as the beginning of change, the other as the goal. (Thus Aristotle first suggested a reciprocal or circular causality as a relation of mutual dependence or influence of cause upon effect). Moreover, Aristotle indicated that the same thing can be the cause of contrary effects; its presence and absence may result in different outcomes. Simply it is the goal or purpose that brings about an event. Our two dominoes require someone or something to intentionally knock over the first domino, because it cannot fall of its own accord.

       Aristotle marked two modes of causation: proper (prior) causation and accidental (chance) causation. All causes, proper and incidental, can be spoken as potential or as actual, particular or generic. The same language refers to the effects of causes, so that generic effects assigned to generic causes, particular effects to particular causes, operating causes to actual effects. Essentially, causality does not suggest a temporal relation between the cause and the effect.

Optics
       Aristotle held more accurate theories on some optical concepts than other philosophers of his day. The second oldest written evidence of a camera obscura (after Mozi c. 400 BC) can be found in Aristotle's documentation of such a device in 350 BC in Problemata. Aristotle's apparatus contained a dark chamber that had a single small hole, or aperture, to allow for sunlight to enter. Aristotle used the device to make observations of the sun and noted that no matter what shape the hole was, the sun would still be correctly displayed as a round object. In modern cameras, this is analogous to the diaphragm. Aristotle also made the observation that when the distance between the aperture and the surface with the image increased, the image was magnified.

Chance and spontaneity
       According to Aristotle, spontaneity and chance are causes of some things, distinguishable from other types of cause. Chance as an incidental cause lies in the realm of accidental things. It is "from what is spontaneous" (but note that what is spontaneous does not come from chance). For a better understanding of Aristotle's conception of "chance" it might be better to think of "coincidence": Something takes place by chance if a person sets out with the intent of having one thing take place, but with the result of another thing (not intended) taking place.

        For example: A person seeks donations. That person may find another person willing to donate a substantial sum. However, if the person seeking the donations met the person donating, not for the purpose of collecting donations, but for some other purpose, Aristotle would call the collecting of the donation by that particular donator a result of chance. It must be unusual that something happens by chance. In other words, if something happens all or most of the time, we cannot say that it is by chance.

     There is also more specific kind of chance, which Aristotle names "luck", that can only apply to human beings, because it is in the sphere of moral actions. According to Aristotle, luck must involve choice (and thus deliberation), and only humans are capable of deliberation and choice. "What is not capable of action cannot do anything by chance".

Metaphysics
Main article: Metaphysics (Aristotle)
Aristotle defines metaphysics as "the knowledge of immaterial being," or of "being in the highest degree of abstraction." He refers to metaphysics as "first philosophy", as well as "the theologic science."

Substance, potentiality and actuality
See also: Potentiality and actuality (Aristotle)
         Aristotle examines the concepts of substance and essence (ousia) in his Metaphysics (Book VII), and he concludes that a particular substance is a combination of both matter and form. In book VIII, he distinguishes the matter of the substance as the substratum, or the stuff of which it is composed. For example, the matter of a house is the bricks, stones, timbers etc., or whatever constitutes the potential house, while the form of the substance is the actual house, namely 'covering for bodies and chattels' or any other differentia (see also predicables) that let us define something as a house. The formula that gives the components is the account of the matter, and the formula that gives the differentia is the account of the form.

With regard to the change (kinesis) and its causes now, as he defines in his Physics and On Generation and Corruption 319b–320a, he distinguishes the coming to be from:

  • growth and diminution, which is change in quantity;
  • locomotion, which is change in space; and
  • alteration, which is change in quality.
  • The coming to be is a change where nothing persists of which the resultant is a property. In that particular change he introduces the concept of potentiality (dynamis) and actuality (entelecheia) in association with the matter and the form.


       Referring to potentiality, this is what a thing is capable of doing, or being acted upon, if the conditions are right and it is not prevented by something else. For example, the seed of a plant in the soil is potentially (dynamei) plant, and if is not prevented by something, it will become a plant. Potentially beings can either 'act' (poiein) or 'be acted upon' (paschein), which can be either innate or learned. For example, the eyes possess the potentiality of sight (innate – being acted upon), while the capability of playing the flute can be possessed by learning (exercise – acting).

          Actuality is the fulfillment of the end of the potentiality. Because the end (telos) is the principle of every change, and for the sake of the end exists potentiality, therefore actuality is the end. Referring then to our previous example, we could say that an actuality is when a plant does one of the activities that plants do.

        "For that for the sake of which a thing is, is its principle, and the becoming is for the sake of the end; and the actuality is the end, and it is for the sake of this that the potentiality is acquired. For animals do not see in order that they may have sight, but they have sight that they may see."

         In summary, the matter used to make a house has potentiality to be a house and both the activity of building and the form of the final house are actualities, which is also a final cause or end. Then Aristotle proceeds and concludes that the actuality is prior to potentiality in formula, in time and in substantiality.

         With this definition of the particular substance (i.e., matter and form), Aristotle tries to solve the problem of the unity of the beings, for example, "what is it that makes a man one"? Since, according to Plato there are two Ideas: animal and biped, how then is man a unity? However, according to Aristotle, the potential being (matter) and the actual one (form) are one and the same thing.

Universals and particulars
Main article: Aristotle's theory of universals
        Aristotle's predecessor, Plato, argued that all things have a universal form, which could be either a property, or a relation to other things. When we look at an apple, for example, we see an apple, and we can also analyze a form of an apple. In this distinction, there is a particular apple and a universal form of an apple. Moreover, we can place an apple next to a book, so that we can speak of both the book and apple as being next to each other.

       Plato argued that there are some universal forms that are not a part of particular things. For example, it is possible that there is no particular good in existence, but "good" is still a proper universal form. Bertrand Russell is a 20th-century philosopher who agreed with Plato on the existence of "uninstantiated universals".

     Aristotle disagreed with Plato on this point, arguing that all universals are instantiated. Aristotle argued that there are no universals that are unattached to existing things. According to Aristotle, if a universal exists, either as a particular or a relation, then there must have been, must be currently, or must be in the future, something on which the universal can be predicated. Consequently, according to Aristotle, if it is not the case that some universal can be predicated to an object that exists at some period of time, then it does not exist.

      In addition, Aristotle disagreed with Plato about the location of universals. As Plato spoke of the world of the forms, a location where all universal forms subsist, Aristotle maintained that universals exist within each thing on which each universal is predicated. So, according to Aristotle, the form of apple exists within each apple, rather than in the world of the forms.

Biology and medicine
     In Aristotelian science, especially in biology, things he saw himself have stood the test of time better than his retelling of the reports of others, which contain error and superstition. He dissected animals but not humans; his ideas on how the human body works have been almost entirely superseded.

  • Empirical research program
  • Octopus swimming
  • Torpedo fuscomaculata


Leopard shark
       Aristotle is the earliest natural historian whose work has survived in some detail. Aristotle certainly did research on the natural history of Lesbos, and the surrounding seas and neighbouring areas. The works that reflect this research, such as History of Animals, Generation of Animals, and Parts of Animals, contain some observations and interpretations, along with sundry myths and mistakes. The most striking passages are about the sea-life visible from observation on Lesbos and available from the catches of fishermen. His observations on catfish, electric fish (Torpedo) and angler-fish are detailed, as is his writing on cephalopods, namely, Octopus, Sepia (cuttlefish) and the paper nautilus (Argonauta argo). His description of the hectocotyl arm, used in sexual reproduction, was widely disbelieved until its rediscovery in the 19th century. He separated the aquatic mammals from fish, and knew that sharks and rays were part of the group he called Selachē (selachians).

      Another good example of his methods comes from the Generation of Animals in which Aristotle describes breaking open fertilized chicken eggs at intervals to observe when visible organs were generated.

  He gave accurate descriptions of ruminants' four-chambered fore-stomachs, and of the ovoviviparous embryological development of the hound shark Mustelus mustelus.[40]

Classification of living things
         Aristotle distinguished about 500 species of birds, mammals and fishes.His classification of living things contains some elements which still existed in the 19th century. What the modern zoologist would call vertebrates and invertebrates, Aristotle called 'animals with blood' and 'animals without blood' (he did not know that complex invertebrates do make use of hemoglobin, but of a different kind from vertebrates). Animals with blood were divided into live-bearing (mammals), and egg-bearing (birds and fish). Invertebrates ('animals without blood') are insects, crustacea (divided into non-shelled – cephalopods – and shelled) and testacea (molluscs). In some respects, this incomplete classification is better than that of Linnaeus, who crowded the invertebrata together into two groups, Insecta and Vermes (worms).

       For Charles Singer, "Nothing is more remarkable than [Aristotle's] efforts to [exhibit] the relationships of living things as a scala naturae" Aristotle's History of Animals classified organisms in relation to a hierarchical "Ladder of Life" (scala naturae or Great Chain of Being), placing them according to complexity of structure and function so that higher organisms showed greater vitality and ability to move.

        Aristotle believed that intellectual purposes, i.e., final causes, guided all natural processes. Such a teleological view gave Aristotle cause to justify his observed data as an expression of formal design. Noting that "no animal has, at the same time, both tusks and horns," and "a single-hooved animal with two horns I have never seen," Aristotle suggested that Nature, giving no animal both horns and tusks, was staving off vanity, and giving creatures faculties only to such a degree as they are necessary. Noting that ruminants had multiple stomachs and weak teeth, he supposed the first was to compensate for the latter, with Nature trying to preserve a type of balance.

       In a similar fashion, Aristotle believed that creatures were arranged in a graded scale of perfection rising from plants on up to man, the scala naturae. His system had eleven grades, arranged according "to the degree to which they are infected with potentiality", expressed in their form at birth. The highest animals laid warm and wet creatures alive, the lowest bore theirs cold, dry, and in thick eggs.

       Aristotle also held that the level of a creature's perfection was reflected in its form, but not preordained by that form. Ideas like this, and his ideas about souls, are not regarded as science at all in modern times.

       He placed emphasis on the type(s) of soul an organism possessed, asserting that plants possess a vegetative soul, responsible for reproduction and growth, animals a vegetative and a sensitive soul, responsible for mobility and sensation, and humans a vegetative, a sensitive, and a rational soul, capable of thought and reflection.

     Aristotle, in contrast to earlier philosophers, but in accordance with the Egyptians, placed the rational  soul in the heart, rather than the brain.[47] Notable is Aristotle's division of sensation and thought, which generally went against previous philosophers, with the exception of Alcmaeon.[48]

Successor: Theophrastus
Main articles: Theophrastus and Historia Plantarum (Theophrastus)
            The frontispiece to a 1644 version of the expanded and illustrated edition of Historia Plantarum (ca. 1200), which was originally written around 300 BC.
Aristotle's successor at the Lyceum, Theophrastus, wrote a series of books on botany—the History of Plants—which survived as the most important contribution of antiquity to botany, even into the Middle Ages. Many of Theophrastus' names survive into modern times, such as carpos for fruit, and pericarpion for seed vessel.

      Rather than focus on formal causes, as Aristotle did, Theophrastus suggested a mechanistic scheme, drawing analogies between natural and artificial processes, and relying on Aristotle's concept of the efficient cause. Theophrastus also recognized the role of sex in the reproduction of some higher plants, though this last discovery was lost in later ages.

Influence on Hellenistic medicine
For more details on this topic, see Medicine in ancient Greece.
After Theophrastus, the Lyceum failed to produce any original work. Though interest in Aristotle's ideas survived, they were generally taken unquestioningly. It is not until the age of Alexandria under the Ptolemies that advances in biology can be again found.

               The first medical teacher at Alexandria, Herophilus of Chalcedon, corrected Aristotle, placing intelligence in the brain, and connected the nervous system to motion and sensation. Herophilus also distinguished between veins and arteries, noting that the latter pulse while the former do not. Though a few ancient atomists such as Lucretius challenged the teleological viewpoint of Aristotelian ideas about life, teleology (and after the rise of Christianity, natural theology) would remain central to biological thought essentially until the 18th and 19th centuries. Ernst Mayr claimed that there was "nothing of any real consequence in biology after Lucretius and Galen until the Renaissance."Aristotle's ideas of natural history and medicine survived, but they were generally taken unquestioningly.

Psychology
      Aristotle's psychology, given in his treatise On the Soul (peri psyche, often known by its Latin title De Anima), posits three kinds of soul ("psyches"): the vegetative soul, the sensitive soul, and the rational soul. Humans have a rational soul. This kind of soul is capable of the same powers as the other kinds: Like the vegetative soul it can grow and nourish itself; like the sensitive soul it can experience sensations and move locally. The unique part of the human, rational soul is its ability to receive forms of other things and compare them.

     For Aristotle, the soul (psyche) was a simpler concept than it is for us today. By soul he simply meant the form of a living being. Because all beings are composites of form and matter, the form of living beings is that which endows them with what is specific to living beings, e.g. the ability to initiate movement (or in the case of plants, growth and chemical transformations, which Aristotle considers types of movement).

Memory
        According to Aristotle, memory is the ability to hold a perceived experience in your mind and to have the ability to distinguish between the internal "appearance" and an occurrence in the past. In other words, a memory is a mental picture (phantasm) in which Aristotle defines in De Anima, as an appearance which is imprinted on the part of the body that forms a memory. Aristotle believed an "imprint" becomes impressed on a semi-fluid bodily organ that undergoes several changes in order to make a memory. A memory occurs when a stimuli is too complex that the nervous system (semi-fluid bodily organ) cannot receive all the impressions at once. These changes are the same as those involved in the operations of sensation, common sense, and thinking .The mental picture imprinted on the bodily organ is the final product of the entire process of sense perception. It does not matter if the experience was seen or heard, every experience ends up as a mental image in memory 

       Aristotle uses the word "memory" for two basic abilities. First, the actual retaining of the experience in the mnemonic "imprint" that can develop from sensation. Second, the intellectual anxiety that comes with the "imprint" due to being impressed at a particular time and processing specific contents. These abilities can be explained as memory is neither sensation nor thinking because is arises only after a lapse of time. Therefore, memory is of the past,  prediction is of the future, and sensation is of the present. The retrieval of our "imprints" cannot be performed suddenly. A transitional channel is needed and located in our past experiences, both for our previous experience and present experience.

      Aristotle proposed that slow-witted people have good memory because the fluids in their brain do not wash away their memory organ used to imprint experiences and so the "imprint" can easily continue. However, they cannot be too slow or the hardened surface of the organ will not receive new "imprints". He believed the young and the old do not properly develop an "imprint". Young people undergo rapid changes as they develop, while the elderly's organs are beginning to decay, thus stunting new "imprints". Likewise, people who are too quick-witted are similar to the young and the image cannot be fixed because of the rapid changes of their organ. Because intellectual functions are not involved in memory, memories belong to some animals too, but only those in which have perception of time.

Recollection
        Because Aristotle believes people receive all kinds of sense perceptions and people perceive them as images or "imprints", people are continually weaving together new "imprints" of things they experience. In order to search for these "imprints", people search the memory itself. Within the memory, if one experience is offered instead of a specific memory, that person will reject this experience until they find what they are looking for. Recollection occurs when one experience naturally follows another. If the chain of "images" is needed, one memory will stimulate the other. If the chain of "images" is not needed, but expected, then it will only stimulate the other memory in most instances. When people recall experiences, they stimulate certain previous experiences until they have stimulated the one that was needed.

       Recollection is the self-directed activity of retrieving the information stored in a memory "imprint" after some time has passed. Retrieval of stored information is dependent on the scope of mnemonic capabilities of a being (human or animal) and the abilities the human or animal possesses . Only humans will remember "imprints" of intellectual activity, such as numbers and words. Animals that have perception of time will be able to retrieve memories of their past observations. Remembering involves only perception of the things remembered and of the time passed. Recollection of an "imprint" is when the present experiences a person remembers are similar with elements corresponding in character and arrangement of past sensory experiences. When an "imprint" is recalled, it may bring forth a large group of related "imprints".

          Aristotle believed the chain of thought, which ends in recollection of certain "imprints", was connected systematically in three sorts of relationships: similarity, contrast, and contiguity. These three laws make up his Laws of Association. Aristotle believed that past experiences are hidden within our mind. A force operates to awaken the hidden material to bring up the actual experience. According to Aristotle, association is the power innate in a mental state, which operates upon the unexpressed remains of former experiences, allowing them to rise and be recalled.

Dreams
Sleep
         Before understanding Aristotle's take on dreams, first his idea of sleep must be examined. Aristotle gives an account of his explanation of sleep in On Sleep and Wakefulness.Sleep takes place as a result of overuse of the senses or of digestion, so it is vital to the body, including the senses, so it can be revitalized. While a person is asleep, the critical activities, which include thinking, sensing, recalling and remembering, do not function as they do during wakefulness. Since a person cannot sense during sleep they can also not have a desire, which is the result of a sensation. However, the senses are able to work during sleep, albeit differently than when a person is awake because during sleep a person can still have sensory experiences. Also, all of the senses are not inactive during sleep, only the ones that are weary.

Theory of dreams
     Dreams do not involve actually sensing a stimulus because, as discussed, the senses do not work as they normally do during sleep. In dreams, sensation is still involved, but in an altered manner than when awake. Aristotle explains the phenomenon that occurs when a person stares at a moving stimulus such as the waves in a body of water. When they look away from that stimulus, the next thing they look at appears to be moving in a wave like motion. When a person perceives a stimulus and the stimulus is no longer the focus of their attention, it leaves an impression. When the body is awake and the senses are functioning properly, a person constantly encounters new stimuli to sense and so the impressions left from previously perceived stimuli become irrelevant. However, during sleep the impressions stimuli made throughout the day become noticed because there are not new sensory experiences to distract from these impressions that were made. So, dreams result from these lasting impressions. Since impressions are all that are left and not the exact stimuli, dreams will not resemble the actual experience that occurred when awake.

       During sleep, a person is in an altered state of mind.Aristotle compares a sleeping person to a person who is overtaken by strong feelings toward a stimulus. For example, a person who has a strong infatuation with someone may begin to think they see that person everywhere because they are so overtaken by their feelings. When a person is asleep, their senses are not acting as they do when they are awake and this results in them thinking like a person who is influenced by strong feelings. Since a person sleeping is in this suggestible state, they become easily deceived by what appears in their dreams.

       When asleep, a person is unable to make judgments as they do when they are awake Due to the senses not functioning normally during sleep, they are unable to help a person judge what is happening in their dream. This in turn leads the person to believe the dream is real. Dreams may be absurd in nature but the senses are not able to discern whether they are real or not. So, the dreamer is left to accept the dream because they lack the choice to judge it.

        One component of Aristotle's theory of dreams introduces ideas that are contradictory to previously held beliefs He claimed that dreams are not foretelling and that they are not sent by a divine being.Aristotle reasoned that instances in which dreams do resemble future events are happenstances not divinations. These ideas were contradictory to what had been believed about dreams, but at the time in which he introduced these ideas more thinkers were beginning to give naturalistic as opposed to supernatural explanations to phenomena.

      Aristotle also includes in his theory of dreams what constitutes a dream and what does not. He claimed that a dream is first established by the fact that the person is asleep when they experience it. If a person had an image appear for a moment after waking up or if they see something in the dark it is not considered a dream because they were awake when it occurred. Secondly, any sensory experience that actually occurs while a person is asleep and is perceived by the person while asleep does not qualify as part of a dream.For example, if, while a person is sleeping, a door shuts and in their dream they hear a door is shut, Aristotle argues that this sensory experience is not part of the dream. The actual sensory experience is perceived by the senses, the fact that it occurred while the person was asleep does not make it part of the dream. Lastly, the images of dreams must be a result of lasting impressions of sensory experiences had when awake.

Practical philosophy
Ethics
Main article: Aristotelian ethics
             Aristotle considered ethics to be a practical rather than theoretical study, i.e., one aimed at becoming good and doing good rather than knowing for its own sake. He wrote several treatises on ethics, including most notably, the Nicomachean Ethics.

       A   ristotle taught that virtue has to do with the proper function (ergon) of a thing. An eye is only a good eye in so much as it can see, because the proper function of an eye is sight. Aristotle reasoned that humans must have a function specific to humans, and that this function must be an activity of the psuchē (normally translated as soul) in accordance with reason (logos). Aristotle identified such an optimum activity of the soul as the aim of all human deliberate action, eudaimonia, generally translated as "happiness" or sometimes "well being". To have the potential of ever being happy in this way necessarily requires a good character (ēthikē aretē), often translated as moral (or ethical) virtue (or excellence).

      Aristotle taught that to achieve a virtuous and potentially happy character requires a first stage of having the fortune to be habituated not deliberately, but by teachers, and experience, leading to a later stage in which one consciously chooses to do the best things. When the best people come to live life this way their practical wisdom (phronesis) and their intellect (nous) can develop with each other towards the highest possible human virtue, the wisdom of an accomplished theoretical or speculative thinker, or in other words, a philosopher.

Politics
Aristotle's classification of constitutions
        In addition to his works on ethics, which address the individual, Aristotle addressed the city in his work titled Politics. Aristotle considered the city to be a natural community. Moreover, he considered the city to be prior in importance to the family which in turn is prior to the individual, "for the whole must of necessity be prior to the part".He also famously stated that "man is by nature a political animal" and also arguing that humanity's defining factor among others in the animal kingdom is its rationality. Aristotle conceived of politics as being like an organism rather than like a machine, and as a collection of parts none of which can exist without the others. Aristotle's conception of the city is organic, and he is considered one of the first to conceive of the city in this manner.

          The common modern understanding of a political community as a modern state is quite different from Aristotle's understanding. Although he was aware of the existence and potential of larger empires, the natural community according to Aristotle was the city (polis) which functions as a political "community" or "partnership" (koinōnia). The aim of the city is not just to avoid injustice or for economic stability, but rather to allow at least some citizens the possibility to live a good life, and to perform beautiful acts: "The political partnership must be regarded, therefore, as being for the sake of noble actions, not for the sake of living together." This is distinguished from modern approaches, beginning with social contract theory, according to which individuals leave the state of nature because of "fear of violent death" or its "inconveniences."

Excerpt from a speech by the character 'Aristotle' in the book Protrepticus (Hutchinson and Johnson, 2015 p. 22)

      For we all  agree that the most excellent man should rule, i.e., the supreme by nature, and that the law rul  es and alone is authoritative; but the law is a kind of intelligence, i.e. a discourse based on intelligence. And again, what standard do we have, what criterion of good things, that is more precise than the intelligent man? For all that this man will choose, if the choice is based on his knowledge, are good things and their contraries are bad. And since everybody chooses most of all what conforms to their own proper dispositions (a just man choosing to live justly, a man with bravery to live bravely, likewise a self-controlled man to live with self-control), it is clear that the intelligent man will choose most of all to be intelligent; for this is the function of that capacity. Hence it's evident that, according to the most authoritative judgment, intelligence is supreme among goods.

Rhetoric and poetics
Main articles: Rhetoric (Aristotle) and Poetics (Aristotle)
    Aristotle considered epic poetry, tragedy, comedy, dithyrambic poetry and music to be imitative, each varying in imitation by medium, object, and manner.For example, music imitates with the media of rhythm and harmony, whereas dance imitates with rhythm alone, and poetry with language. The forms also differ in their object of imitation. Comedy, for instance, is a dramatic imitation of men worse than average; whereas tragedy imitates men slightly better than average. Lastly, the forms differ in their manner of imitation – through narrative or character, through change or no change, and through drama or no drama. Aristotle believed that imitation is natural to mankind and constitutes one of mankind's advantages over animals.

      While it is believed that Aristotle's Poetics comprised two books – one on comedy and one on tragedy – only the portion that focuses on tragedy has survived. Aristotle taught that tragedy is composed of six elements: plot-structure, character, style, thought, spectacle, and lyric poetry.The characters in a tragedy are merely a means of driving the story; and the plot, not the characters, is the chief focus of tragedy. Tragedy is the imitation of action arousing pity and fear, and is meant to effect the catharsis of those same emotions. Aristotle concludes Poetics with a discussion on which, if either, is superior: epic or tragic mimesis. He suggests that because tragedy possesses all the attributes of an epic, possibly possesses additional attributes such as spectacle and music, is more unified, and achieves the aim of its mimesis in shorter scope, it can be considered superior to epic.

     Aristotle was a keen systematic collector of riddles, folklore, and proverbs; he and his school had a special interest in the riddles of the Delphic Oracle and studied the fables of Aesop.

Views on women
Main article: Aristotle's views on women
      Aristotle's analysis of procreation describes an active, ensouling masculine element bringing life to an inert, passive female element. On this ground, feminist metaphysics have accused Aristotle of misogyny and sexism.However, Aristotle gave equal weight to women's happiness as he did to men's, and commented in his Rhetoric that the things that lead to happiness need to be in women as well as men.

Loss and preservation of his works
           First page of a 1566 edition of the Nicomachean Ethics in Greek and Latin
Modern scholarship reveals that Aristotle's "lost" works stray considerably in characterization from the surviving Aristotelian corpus. Whereas the lost works appear to have been originally written with an intent for subsequent publication, the surviving works do not appear to have been so. Rather the surviving works mostly resemble lecture notes unintended for publication. The authenticity of a portion of the surviving works as originally Aristotelian is also today held suspect, with some books duplicating or summarizing each other, the authorship of one book questioned and another book considered to be unlikely Aristotle's at all.

           Some of the individual works within the corpus, including the Constitution of Athens, are regarded by most scholars as products of Aristotle's "school," perhaps compiled under his direction or supervision. Others, such as On Colors, may have been produced by Aristotle's successors at the Lyceum, e.g., Theophrastus and Straton. Still others acquired Aristotle's name through similarities in doctrine or content, such as the De Plantis, possibly by Nicolaus of Damascus. Other works in the corpus include medieval palmistries and astrological and magical texts whose connections to Aristotle are purely fanciful and self-promotional.

      According to a distinction that originates with Aristotle himself, his writings are divisible into two groups: the "exoteric" and the "esoteric".Most scholars have understood this as a distinction between works Aristotle intended for the public (exoteric), and the more technical works intended for use within the Lyceum course / school (esoteric).Modern scholars commonly assume these latter to be Aristotle's own (unpolished) lecture notes (or in some cases possible notes by his students).However, one classic scholar offers an alternative interpretation. The 5th century neoplatonist Ammonius Hermiae writes that Aristotle's writing style is deliberately obscurantist so that "good people may for that reason stretch their mind even more, whereas empty minds that are lost through carelessness will be put to flight by the obscurity when they encounter sentences like these."

    Another common assumption is that none of the exoteric works is extant – that all of Aristotle's extant writings are of the esoteric kind. Current knowledge of what exactly the exoteric writings were like is scant and dubious, though many of them may have been in dialogue form. (Fragments of some of Aristotle's dialogues have survived.) Perhaps it is to these that Cicero refers when he characterized Aristotle's writing style as "a river of gold";it is hard for many modern readers to accept that one could seriously so admire the style of those works currently available to us.However, some modern scholars have warned that we cannot know for certain that Cicero's praise was reserved specifically for the exoteric works; a few modern scholars have actually admired the concise writing style found in Aristotle's extant works.

         One major question in the history of Aristotle's works, then, is how were the exoteric writings all lost, and how did the ones we now possess come to us The story of the original manuscripts of the esoteric treatises is described by Strabo in his Geography and Plutarch in his Parallel Lives. The manuscripts were left from Aristotle to his successor Theophrastus, who in turn willed them to Neleus of Scepsis. Neleus supposedly took the writings from Athens to Scepsis, where his heirs let them languish in a cellar until the 1st century BC, when Apellicon of Teos discovered and purchased the manuscripts, bringing them back to Athens. According to the story, Apellicon tried to repair some of the damage that was done during the manuscripts' stay in the basement, introducing a number of errors into the text. When Lucius Cornelius Sulla occupied Athens in 86 BC, he carried off the library of Apellicon to Rome, where they were first published in 60 BC by the grammarian Tyrannion of Amisus and then by the philosopher Andronicus of Rhodes.

     Carnes Lord attributes the popular belief in this story to the fact that it provides "the most plausible explanation for the rapid eclipse of the Peripatetic school after the middle of the third century, and for the absence of widespread knowledge of the specialized treatises of Aristotle throughout the Hellenistic period, as well as for the sudden reappearance of a flourishing Aristotelianism during the first century B.C." Lord voices a number of reservations concerning this story, however. First, the condition of the texts is far too good for them to have suffered considerable damage followed by Apellicon's inexpert attempt at repair.

      Second, there is "incontrovertible evidence," Lord says, that the treatises were in circulation during the time in which Strabo and Plutarch suggest they were confined within the cellar in Scepsis. Third, the definitive edition of Aristotle's texts seems to have been made in Athens some fifty years before Andronicus supposedly compiled his. And fourth, ancient library catalogues predating Andronicus' intervention list an Aristotelian corpus quite similar to the one we currently possess. Lord sees a number of post-Aristotelian interpolations in the Politics, for example, but is generally confident that the work has come down to us relatively intact.

      On the one hand, the surviving texts of Aristotle do not derive from finished literary texts, but rather from working drafts used within Aristotle's school, as opposed, on the other hand, to the dialogues and other "exoteric" texts which Aristotle published more widely during his lifetime. The consensus is that Andronicus of Rhodes collected the esoteric works of Aristotle's school which existed in the form of smaller, separate works, distinguished them from those of Theophrastus and other Peripatetics, edited them, and finally compiled them into the more cohesive, larger works as they are known today.

Legacy

"Aristotle" by Jusepe de Ribera

"Aristotle with a bust of Homer" by Rembrandt.
An thirteenth-century Islamic portrayal of Aristotle (right).
Statue by Cipri Adolf Bermann (1915) at the University of Freiburg Freiburg im Breisgau
More than 2300 years after his death, Aristotle remains one of the most influential people who ever lived. He contributed to almost every field of human knowledge then in existence, and he was the founder of many new fields. According to the philosopher Bryan Magee, "it is doubtful whether any human being has ever known as much as he did". Among countless other achievements, Aristotle was the founder of formal logic, pioneered the study of zoology, and left every future scientist and philosopher in his debt through his contributions to the scientific method.

      Despite these achievements, the influence of Aristotle's errors is considered by some to have held back science considerably. Bertrand Russell notes that "almost every serious intellectual advance has had to begin with an attack on some Aristotelian doctrine". Russell also refers to Aristotle's ethics as "repulsive", and calls his logic "as definitely antiquated as Ptolemaic astronomy". Russell notes that these errors make it difficult to do historical justice to Aristotle, until one remembers how large of an advance he made upon all of his predecessors.

Later Greek philosophers
The immediate influence of Aristotle's work was felt as the Lyceum grew into the Peripatetic school. Aristotle's notable students included Aristoxenus, Dicaearchus, Demetrius of Phalerum, Eudemos of Rhodes, Harpalus, Hephaestion, Meno, Mnason of Phocis, Nicomachus, and Theophrastus. Aristotle's influence over Alexander the Great is seen in the latter's bringing with him on his expedition a host of zoologists, botanists, and researchers. He had also learned a great deal about Persian customs and traditions from his teacher. Although his respect for Aristotle was diminished as his travels made it clear that much of Aristotle's geography was clearly wrong, when the old philosopher released his works to the public, Alexander complained "Thou hast not done well to publish thy acroamatic doctrines; for in what shall I surpass other men if those doctrines wherein I have been trained are to be all men's common property?"

Influence on Byzantine scholars
    Greek Christian scribes played a crucial role in the preservation of Aristotle by copying all the extant Greek language manuscripts of the corpus. The first Greek Christians to comment extensively on Aristotle were John Philoponus, Elias, and David in the sixth century, and Stephen of Alexandria in the early seventh century.John Philoponus stands out for having attempted a fundamental critique of Aristotle's views on the eternity of the world, movement, and other elements of Aristotelian thought. After a hiatus of several centuries, formal commentary by Eustratius and Michael of Ephesus reappears in the late eleventh and early twelfth centuries, apparently sponsored by Anna Comnena.

Influence on Islamic theologians
     Aristotle was one of the most revered Western thinkers in early Islamic theology. Most of the still extant works of Aristotle, as well as a number of the original Greek commentaries, were translated into Arabic and studied by Muslim philosophers, scientists and scholars. Averroes, Avicenna and Alpharabius, who wrote on Aristotle in great depth, also influenced Thomas Aquinas and other Western Christian scholastic philosophers. Alkindus considered Aristotle as the outstanding and unique representative of philosophy and Averroes spoke of Aristotle as the "exemplar" for all future philosophers. Medieval Muslim scholars regularly described Aristotle as the "First Teacher".The title "teacher" was first given to Aristotle by Muslim scholars, and was later used by Western philosophers (as in the famous poem of Dante) who were influenced by the tradition of Islamic philosophy.

   In accordance with the Greek theorists, the Muslims considered Aristotle to be a dogmatic philosopher, the author of a closed system, and believed that Aristotle shared with Plato essential tenets of thought. Some went so far as to credit Aristotle himself with neo-Platonic metaphysical ideas.

Influence on Western Christian theologians
      With the loss of the study of ancient Greek in the early medieval Latin West, Aristotle was practically unknown there from c. AD 600 to c. 1100 except through the Latin translation of the Organon made by Boethius. In the twelfth and thirteenth centuries, interest in Aristotle revived and Latin Christians had translations made, both from Arabic translations, such as those by Gerard of Cremona, and from the original Greek, such as those by James of Venice and William of Moerbeke.

        After Thomas Aquinas wrote his theology, working from Moerbeke's translations, the demand for Aristotle's writings grew and the Greek manuscripts returned to the West, stimulating a revival of Aristotelianism in Europe that continued into the Renaissance.  Aristotle is referred to as "The Philosopher" by Scholastic thinkers such as Thomas Aquinas. See Summa Theologica, Part I, Question 3, etc. These thinkers blended Aristotelian philosophy with Christianity, bringing the thought of Ancient Greece into the Middle Ages. It required a repudiation of some Aristotelian principles for the sciences and the arts to free themselves for the discovery of modern scientific laws and empirical methods. The medieval English poet Chaucer describes his student as being happy by havingat his beddes heedTwenty bookes, clad in blak or reed,Of aristotle and his philosophie,The Italian poet Dante says of Aristotle in the first circles of hell,

  • I saw the Master there of those who know,
  • Amid the philosophic family,
  • By all admired, and by all reverenced;
  • There Plato too I saw, and Socrates,
  • Who stood beside him closer than the rest.
  • Post-Enlightenment thinkers

      The German philosopher Friedrich Nietzsche has been said to have taken nearly all of his political philosophy from Aristotle.However debatable this is, Aristotle rigid separated action from production, and argued for the deserved subservience of some people ("natural slaves"), and the natural superiority (virtue, arete) of others. It is Martin Heidegger, not Nietzsche, who elaborated a new interpretation of Aristotle, intended to warrant his deconstruction of scholastic and philosophical tradition. Ayn Rand accredited Aristotle as "the greatest philosopher in history" and cited him as a major influence on her thinking. More recently, Alasdair MacIntyre has attempted to reform what he calls the Aristotelian tradition in a way that is anti-elitist and capable of disputing the claims of both liberals and Nietzscheans.

List of works
Main article: Corpus Aristotelicum
The works of Aristotle that have survived from antiquity through medieval manuscript transmission are collected in the Corpus Aristotelicum. These texts, as opposed to Aristotle's lost works, are technical philosophical treatises from within Aristotle's school. Reference to them is made according to the organization of Immanuel Bekker's Royal Prussian Academy edition (Aristotelis Opera edidit Academia Regia Borussica, Berlin, 1831–1870), which in turn is based on ancient classifications of these works.

Archimedes (287-212 B.C.)

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     Archimedes
     (287-212 B.C.) 
Archimedes Thoughtful by Fetti (1620)  
       Archimedes of Syracuse Greek (287 BC – c. 212 BC) was an Ancient Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Generally considered the greatest mathematician of antiquity and one of the greatest of all time,Archimedes anticipated modern calculus and analysis by applying concepts of infinitesimals and the method of exhaustion to derive and rigorously prove a range of geometrical theorems, including the area of a circle, the surface area and volume of a sphere, and the area under a parabola.

           Other mathematical achievements include deriving an accurate approximation of pi, defining and investigating the spiral bearing his name, and creating a system using exponentiation for expressing very large numbers. He was also one of the first to apply mathematics to physical phenomena, founding hydrostatics and statics, including an explanation of the principle of the lever. He is credited with designing innovative machines, such as his screw pump, compound pulleys, and defensive war machines to protect his native Syracuse from invasion.

              Archimedes died during the Siege of Syracuse when he was killed by a Roman soldier despite orders that he should not be harmed. Cicero describes visiting the tomb of Archimedes, which was surmounted by a sphere and a cylinder, which Archimedes had requested to be placed on his tomb, representing his mathematical discoveries.

               Unlike his inventions, the mathematical writings of Archimedes were little known in antiquity. Mathematicians from Alexandria read and quoted him, but the first comprehensive compilation was not made until c. 530 AD by Isidore of Miletus in Byzantine Constantinople, while commentaries on the works of Archimedes written by Eutocius in the sixth century AD opened them to wider readership for the first time. The relatively few copies of Archimedes' written work that survived through the Middle Ages were an influential source of ideas for scientists during the Renaissance,while the discovery in 1906 of previously unknown works by Archimedes in the Archimedes Palimpsest has provided new insights into how he obtained mathematical results.

Biography

Archimedes was born c. 287 BC in the seaport city of Syracuse, Sicily, at that time a self-governing colony in Magna Graecia, located along the coast of Southern Italy. The date of birth is based on a statement by the Byzantine Greek historian John Tzetzes that Archimedes lived for 75 years. In The Sand Reckoner, Archimedes gives his father's name as Phidias, an astronomer about whom nothing is known. Plutarch wrote in his Parallel Lives that Archimedes was related to King Hiero II, the ruler of Syracuse.A biography of Archimedes was written by his friend Heracleides but this work has been lost, leaving the details of his life obscure. It is unknown, for instance, whether he ever married or had children. During his youth, Archimedes may have studied in Alexandria, Egypt, where Conon of Samos and Eratosthenes of Cyrene were contemporaries. He referred to Conon of Samos as his friend, while two of his works (The Method of Mechanical Theorems and the Cattle Problem) have introductions addressed to Eratosthenes.
         Archimedes died c. 212 BC during the Second Punic War, when Roman forces under General Marcus Claudius Marcellus captured the city of Syracuse after a two-year-longsiege. According to the popular account given by Plutarch, Archimedes was contemplating a mathematical diagram when the city was captured. A Roman soldier commanded him to come and meet General Marcellus but he declined, saying that he had to finish working on the problem. The soldier was enraged by this, and killed Archimedes with his sword. Plutarch also gives a lesser-known account of the death of Archimedes which suggests that he may have been killed while attempting to surrender to a Roman soldier. According to this story, Archimedes was carrying mathematical instruments, and was killed because the soldier thought that they were valuable items. General Marcellus was reportedly angered by the death of Archimedes, as he considered him a valuable scientific asset and had ordered that he not be harmed. Marcellus called Archimedes "a geometrical Briareus".
             The last words attributed to Archimedes are "Do not disturb my circles", a reference to the circles in the mathematical drawing that he was supposedly studying when disturbed by the Roman soldier. This quote is often given in Latin as "Noli turbare circulos meos," but there is no reliable evidence that Archimedes uttered these words and they do not appear in the account given by Plutarch. Valerius Maximus, writing in Memorable Doings and Sayings in the 1st century AD, gives the phrase as "...sed protecto manibus puluere 'noli' inquit, 'obsecro, istum disturbare'" - "... but protecting the dust with his hands, said 'I beg of you, do not disturb this.'" The phrase is also given in Katharevousa Greek as "μὴ μου τοὺς κύκλους τάραττε!" (Mē mou tous kuklous taratte!).

      The tomb of Archimedes carried a sculpture illustrating his favorite mathematical proof, consisting of a sphere and a cylinder of the same height and diameter. Archimedes had proven that the volume and surface area of the sphere are two thirds that of the cylinder including its bases. In 75 BC, 137 years after his death, the Roman orator Cicero was serving as quaestor in Sicily. He had heard stories about the tomb of Archimedes, but none of the locals was able to give him the location. Eventually he found the tomb near the Agrigentine gate in Syracuse, in a neglected condition and overgrown with bushes. Cicero had the tomb cleaned up, and was able to see the carving and read some of the verses that had been added as an inscription.A tomb discovered in the courtyard of the Hotel Panorama in Syracuse in the early 1960s was claimed to be that of Archimedes, but there was no compelling evidence for this and the location of his tomb today is unknown.

The standard versions of the life of Archimedes were written long after his death by the historians of Ancient Rome. The account of the siege of Syracuse given by Polybius in his Universal History was written around seventy years after Archimedes' death, and was used subsequently as a source by Plutarch and Livy. It sheds little light on Archimedes as a person, and focuses on the war machines that he is said to have built in order to defend the city.
Archimedes' principle
      The most widely known anecdote about Archimedes tells of how he invented a method for determining the volume of an object with an irregular shape. According to Vitruvius, a votive crown for a temple had been made for King Hiero II, who had supplied the pure gold to be used, and Archimedes was asked to determine whether some silver had been substituted by the dishonest goldsmith.[16] Archimedes had to solve the problem without damaging the crown, so he could not melt it down into a regularly shaped body in order to calculate its density. While taking a bath, he noticed that the level of the water in the tub rose as he got in, and realized that this effect could be used to determine the volume of the crown. For practical purposes water is incompressible,so the submerged crown would displace an amount of water equal to its own volume. By dividing the mass of the crown by the volume of water displaced, the density of the crown could be obtained. This density would be lower than that of gold if cheaper and less dense metals had been added. Archimedes then took to the streets naked, so excited by his discovery that he had forgotten to dress, crying "Eureka!" (Greek: "εὕρηκα,heúrēka!", meaning "I have found [it]!"). The test was conducted successfully, proving that silver had indeed been mixed in.

            The story of the golden crown does not appear in the known works of Archimedes. Moreover, the practicality of the method it describes has been called into question, due to the extreme accuracy with which one would have to measure the water displacement.Archimedes may have instead sought a solution that applied the principle known in hydrostatics as Archimedes' principle, which he describes in his treatise On Floating Bodies. This principle states that a body immersed in a fluid experiences a buoyant force equal to the weight of the fluid it displaces. Using this principle, it would have been possible to compare the density of the golden crown to that of solid gold by balancing the crown on a scale with a gold reference sample, then immersing the apparatus in water. The difference in density between the two samples would cause the scale to tip accordingly. Galileo considered it "probable that this method is the same that Archimedes followed, since, besides being very accurate, it is based on demonstrations found by Archimedes himself." In a 12th-century text titled Mappae clavicula there are instructions on how to perform the weighings in the water in order to calculate the percentage of silver used, and thus solve the problem.The Latin poem Carmen de ponderibus et mensuris of the 4th or 5th century describes the use of a hydrostatic balance to solve the problem of the crown, and attributes the method to Archimedes.

Archimedes' screw
          A large part of Archimedes' work in engineering arose from fulfilling the needs of his home city of Syracuse. The Greek writer Athenaeus of Naucratis described how King Hiero II commissioned Archimedes to design a huge ship, the Syracusia, which could be used for luxury travel, carrying supplies, and as a naval warship. The Syracusia is said to have been the largest ship built in classical antiquity.According to Athenaeus, it was capable of carrying 600 people and included garden decorations, a gymnasium and a temple dedicated to the goddess Aphrodite among its facilities. Since a ship of this size would leak a considerable amount of water through the hull, the Archimedes' screw was purportedly developed in order to remove the bilge water. Archimedes' machine was a device with a revolving screw-shaped blade inside a cylinder. It was turned by hand, and could also be used to transfer water from a low-lying body of water into irrigation canals. The Archimedes' screw is still in use today for pumping liquids and granulated solids such as coal and grain. The Archimedes' screw described in Roman times by Vitruvius may have been an improvement on a screw pump that was used to irrigate the Hanging Gardens of Babylon.The world's first seagoing steamship with a screw propeller was the SS Archimedes, which was launched in 1839 and named in honor of Archimedes and his work on the screw.
Claw of Archimedes
The Claw of Archimedes is a weapon that he is said to have designed in order to defend the city of Syracuse. Also known as "the ship shaker," the claw consisted of a crane-like arm from which a large metal grappling hook was suspended. When the claw was dropped onto an attacking ship the arm would swing upwards, lifting the ship out of the water and possibly sinking it. There have been modern experiments to test the feasibility of the claw, and in 2005 a television documentary entitled Superweapons of the Ancient World built a version of the claw and concluded that it was a workable device.
Heat ray
          Archimedes may have used mirrors acting collectively as a parabolic reflector to burn ships attacking Syracuse. The 2nd century AD author Lucian wrote that during the Siege of Syracuse (c. 214–212 BC), Archimedes destroyed enemy ships with fire. Centuries later, Anthemius of Tralles mentions burning-glasses as Archimedes' weapon.The device, sometimes called the "Archimedes heat ray", was used to focus sunlight onto approaching ships, causing them to catch fire.
        This purported weapon has been the subject of ongoing debate about its credibility since the Renaissance. René Descartes rejected it as false, while modern researchers have attempted to recreate the effect using only the means that would have been available to Archimedes.It has been suggested that a large array of highly polished bronze or copper shields acting as mirrors could have been employed to focus sunlight onto a ship. This would have used the principle of the parabolic reflector in a manner similar to a solar furnace.
            A test of the Archimedes heat ray was carried out in 1973 by the Greek scientist Ioannis Sakkas. The experiment took place at the Skaramagas naval base outside Athens. On this occasion 70 mirrors were used, each with a copper coating and a size of around five by three feet (1.5 by 1 m). The mirrors were pointed at a plywood mock-up of a Roman warship at a distance of around 160 feet (50 m). When the mirrors were focused accurately, the ship burst into flames within a few seconds. The plywood ship had a coating of tar paint, which may have aided combustion. A coating of tar would have been commonplace on ships in the classical era.
          In October 2005 a group of students from the Massachusetts Institute of Technology carried out an experiment with 127 one-foot (30 cm) square mirror tiles, focused on a mock-up wooden ship at a range of around 100 feet (30 m). Flames broke out on a patch of the ship, but only after the sky had been cloudless and the ship had remained stationary for around ten minutes. It was concluded that the device was a feasible weapon under these conditions. The MIT group repeated the experiment for the television show MythBusters, using a wooden fishing boat in San Francisco as the target. Again some charring occurred, along with a small amount of flame. In order to catch fire, wood needs to reach its autoignition temperature, which is around 300 °C (570 °F).

       When MythBusters broadcast the result of the San Francisco experiment in January 2006, the claim was placed in the category of "busted" (or failed) because of the length of time and the ideal weather conditions required for combustion to occur. It was also pointed out that since Syracuse faces the sea towards the east, the Roman fleet would have had to attack during the morning for optimal gathering of light by the mirrors. MythBusters also pointed out that conventional weaponry, such as flaming arrows or bolts from a catapult, would have been a far easier way of setting a ship on fire at short distances.
     In December 2010, MythBusters again looked at the heat ray story in a special edition entitled "President's Challenge". Several experiments were carried out, including a large scale test with 500 schoolchildren aiming mirrors at a mock-up of a Roman sailing ship 400 feet (120 m) away. In all of the experiments, the sail failed to reach the 210 °C (410 °F) required to catch fire, and the verdict was again "busted". The show concluded that a more likely effect of the mirrors would have been blinding, dazzling, or distracting the crew of the ship.
Other discoveries and inventions
           While Archimedes did not invent the lever, he gave an explanation of the principle involved in his work On the Equilibrium of Planes. Earlier descriptions of the lever are found in the Peripatetic school of the followers of Aristotle, and are sometimes attributed to Archytas.According to Pappus of Alexandria, Archimedes' work on levers caused him to remark: "Give me a place to stand on, and I will move the Earth." (Greek: δῶς μοι πᾶ στῶ καὶ τὰν γᾶν κινάσω) Plutarch describes how Archimedes designed block-and-tackle pulley systems, allowing sailors to use the principle of leverage to lift objects that would otherwise have been too heavy to move. Archimedes has also been credited with improving the power and accuracy of the catapult, and with inventing the odometer during the First Punic War. The odometer was described as a cart with a gear mechanism that dropped a ball into a container after each mile traveled.
    Cicero (106–43 BC) mentions Archimedes briefly in his dialogue De re publica, which portrays a fictional conversation taking place in 129 BC. After the capture of Syracuse c. 212 BC, General Marcus Claudius Marcellus is said to have taken back to Rome two mechanisms, constructed by Archimedes and used as aids in astronomy, which showed the motion of the Sun, Moon and five planets. Cicero mentions similar mechanisms designed by Thales of Miletus and Eudoxus of Cnidus. The dialogue says that Marcellus kept one of the devices as his only personal loot from Syracuse, and donated the other to the Temple of Virtue in Rome. Marcellus' mechanism was demonstrated, according to Cicero, by Gaius Sulpicius Gallus to Lucius Furius Philus, who described it thus:
      Hanc sphaeram Gallus cum moveret, fiebat ut soli luna totidem conversionibus in aere illo quot diebus in ipso caelo succederet, ex quo et in caelo sphaera solis fieret eadem illa defectio, et incideret luna tum in eam metam quae esset umbra terrae, cum sol e regione. — When Gallus moved the globe, it happened that the Moon followed the Sun by as many turns on that bronze contrivance as in the sky itself, from which also in the sky the Sun's globe became to have that same eclipse, and the Moon came then to that position which was its shadow on the Earth, when the Sun was in line.
       This is a description of a planetarium or orrery. Pappus of Alexandria stated that Archimedes had written a manuscript (now lost) on the construction of these mechanisms entitled On Sphere-Making. Modern research in this area has been focused on the Antikythera mechanism, another device built c. 100 BC that was probably designed for the same purpose. Constructing mechanisms of this kind would have required a sophisticated knowledge of differential gearing. This was once thought to have been beyond the range of the technology available in ancient times, but the discovery of the Antikythera mechanism in 1902 has confirmed that devices of this kind were known to the ancient Greeks.
Mathematics
     While he is often regarded as a designer of mechanical devices, Archimedes also made contributions to the field of mathematics. Plutarch wrote: "He placed his whole affection and ambition in those purer speculations where there can be no reference to the vulgar needs of life." Archimedes was able to use infinitesimals in a way that is similar to modern integral calculus. Through proof by contradiction (reductio ad absurdum), he could give answers to problems to an arbitrary degree of accuracy, while specifying the limits within which the answer lay. This technique is known as the method of exhaustion, and he employed it to approximate the value of π. In Measurement of a Circle he did this by drawing a larger regular hexagon outside a circle and a smaller regular hexagon inside the circle, and progressively doubling the number of sides of each regular polygon, calculating the length of a side of each polygon at each step. As the number of sides increases, it becomes a more accurate approximation of a circle. After four such steps, when the polygons had 96 sides each, he was able to determine that the value of π lay between 31⁄7 (approximately 3.1429) and 310⁄71 (approximately 3.1408), consistent with its actual value of approximately 3.1416.[50] He also proved that the area of a circle was equal to π multiplied by the square of the radius of the circle (πr2). In On the Sphere and Cylinder, Archimedes postulates that any magnitude when added to itself enough times will exceed any given magnitude. This is the Archimedean property of real numbers.
      In Measurement of a Circle, Archimedes gives the value of the square root of 3 as lying between 265⁄153 (approximately 1.7320261) and 1351⁄780 (approximately 1.7320512). The actual value is approximately 1.7320508, making this a very accurate estimate. He introduced this result without offering any explanation of how he had obtained it. This aspect of the work of Archimedes caused John Wallis to remark that he was: "as it were of set purpose to have covered up the traces of his investigation as if he had grudged posterity the secret of his method of inquiry while he wished to extort from them assent to his results."[52] It is possible that he used an iterative procedure to calculate these values.
       In The Quadrature of the Parabola, Archimedes proved that the area enclosed by a parabola and a straight line is 4⁄3 times the area of a corresponding inscribed triangle as shown in the figure at right. He expressed the solution to the problem as an infinite geometric series with the common ratio 1⁄4:
\sum_{n=0}^\infty 4^{-n} = 1 + 4^{-1} + 4^{-2} + 4^{-3} + \cdots = {4\over 3}. \;
If the first term in this series is the area of the triangle, then the second is the sum of the areas of two triangles whose bases are the two smaller secant lines, and so on. This proof uses a variation of the series 1/4 + 1/16 + 1/64 + 1/256 + · · · which sums to 1⁄3.
       In The Sand Reckoner, Archimedes set out to calculate the number of grains of sand that the universe could contain. In doing so, he challenged the notion that the number of grains of sand was too large to be counted. He wrote: "There are some, King Gelo (Gelo II, son of Hiero II), who think that the number of the sand is infinite in multitude; and I mean by the sand not only that which exists about Syracuse and the rest of Sicily but also that which is found in every region whether inhabited or uninhabited." To solve the problem, Archimedes devised a system of counting based on the myriad. The word is from the Greek μυριάς murias, for the number 10,000. He proposed a number system using powers of a myriad of myriads (100 million) and concluded that the number of grains of sand required to fill the universe would be 8 vigintillion, or 8×1063.
Writings
     The works of Archimedes were written in Doric Greek, the dialect of ancient Syracuse.The written work of Archimedes has not survived as well as that of Euclid, and seven of his treatises are known to have existed only through references made to them by other authors. Pappus of Alexandria mentions On Sphere-Making and another work on polyhedra, while Theon of Alexandria quotes a remark about refraction from the now-lost Catoptrica.[b] During his lifetime, Archimedes made his work known through correspondence with the mathematicians in Alexandria. The writings of Archimedes were first collected by the Byzantine Greek architect Isidore of Miletus (c. 530 AD), while commentaries on the works of Archimedes written by Eutocius in the sixth century AD helped to bring his work a wider audience. Archimedes' work was translated into Arabic by Thābit ibn Qurra (836–901 AD), and Latin by Gerard of Cremona (c. 1114–1187 AD). During the Renaissance, the Editio Princeps (First Edition) was published in Basel in 1544 by Johann Herwagen with the works of Archimedes in Greek and Latin.[56] Around the year 1586 Galileo Galilei invented a hydrostatic balance for weighing metals in air and water after apparently being inspired by the work of Archimedes.
Surviving works
On the Equilibrium of Planes (two volumes)
The first book is in fifteen propositions with seven postulates, while the second book is in ten propositions. In this work Archimedes explains the Law of the Lever, stating, "Magnitudes are in equilibrium at distances reciprocally proportional to their weights."
Archimedes uses the principles derived to calculate the areas and centers of gravity of various geometric figures including triangles, parallelograms and parabolas.[58]
On the Measurement of a Circle
     This is a short work consisting of three propositions. It is written in the form of a correspondence with Dositheus of Pelusium, who was a student of Conon of Samos. In Proposition II, Archimedes gives an approximation of the value of pi (π), showing that it is greater than 223⁄71 and less than 22⁄7.
On Spirals
    This work of 28 propositions is also addressed to Dositheus. The treatise defines what is now called the Archimedean spiral. It is the locus of points corresponding to the locations over time of a point moving away from a fixed point with a constant speed along a line which rotates with constant angular velocity. Equivalently, in polar coordinates (r, θ) it can be described by the equation\, r=a+b\theta
with real numbers a and b. This is an early example of a mechanical curve (a curve traced by a moving point) considered by a Greek mathematician.
On the Sphere and the Cylinder (two volumes)
       In this treatise addressed to Dositheus, Archimedes obtains the result of which he was most proud, namely the relationship between a sphere and a circumscribed cylinder of the same height and diameter. The volume is 4⁄3πr3 for the sphere, and 2πr3 for the cylinder. The surface area is 4πr2 for the sphere, and 6πr2 for the cylinder (including its two bases), where r is the radius of the sphere and cylinder. The sphere has a volume two-thirds that of the circumscribed cylinder. Similarly, the sphere has an area two-thirds that of the cylinder (including the bases). A sculpted sphere and cylinder were placed on the tomb of Archimedes at his request.
On Conoids and Spheroids
     This is a work in 32 propositions addressed to Dositheus. In this treatise Archimedes calculates the areas and volumes of sections of cones, spheres, and paraboloids.
On Floating Bodies (two volumes)
      In the first part of this treatise, Archimedes spells out the law of equilibrium of fluids, and proves that water will adopt a spherical form around a center of gravity. This may have been an attempt at explaining the theory of contemporary Greek astronomers such as Eratosthenes that the Earth is round. The fluids described by Archimedes are not self-gravitating, since he assumes the existence of a point towards which all things fall in order to derive the spherical shape.
     In the second part, he calculates the equilibrium positions of sections of paraboloids. This was probably an idealization of the shapes of ships' hulls. Some of his sections float with the base under water and the summit above water, similar to the way that icebergs float. Archimedes' principle of buoyancy is given in the work, stated as follows:
    Any body wholly or partially immersed in a fluid experiences an upthrust equal to, but opposite in sense to, the weight of the fluid displaced.
The Quadrature of the Parabola
     In this work of 24 propositions addressed to Dositheus, Archimedes proves by two methods that the area enclosed by a parabola and a straight line is 4/3 multiplied by the area of a triangle with equal base and height. He achieves this by calculating the value of a geometric series that sums to infinity with the ratio 1⁄4.
(O)stomachion
    This is a dissection puzzle similar to a Tangram, and the treatise describing it was found in more complete form in the Archimedes Palimpsest. Archimedes calculates the areas of the 14 pieces which can be assembled to form a square. Research published by Dr. Reviel Netz of Stanford University in 2003 argued that Archimedes was attempting to determine how many ways the pieces could be assembled into the shape of a square. Dr. Netz calculates that the pieces can be made into a square 17,152 ways.[59] The number of arrangements is 536 when solutions that are equivalent by rotation and reflection have been excluded. The puzzle represents an example of an early problem in combinatorics.
   The origin of the puzzle's name is unclear, and it has been suggested that it is taken from the Ancient Greek word for throat or gullet, stomachos (στόμαχος). Ausonius refers to the puzzle as Ostomachion, a Greek compound word formed from the roots of ὀστέον (osteon, bone) and μάχη (machē – fight). The puzzle is also known as the Loculus of Archimedes or Archimedes' Box.
Archimedes' cattle problem
     This work was discovered by Gotthold Ephraim Lessing in a Greek manuscript consisting of a poem of 44 lines, in the Herzog August Library in Wolfenbüttel, Germany in 1773. It is addressed to Eratosthenes and the mathematicians in Alexandria. Archimedes challenges them to count the numbers of cattle in the Herd of the Sun by solving a number of simultaneous Diophantine equations. There is a more difficult version of the problem in which some of the answers are required to be square numbers. This version of the problem was first solved by A. Amthor in 1880, and the answer is a very large number, approximately 7.760271×10206544.
The Sand Reckoner
        In this treatise, Archimedes counts the number of grains of sand that will fit inside the universe. This book mentions the heliocentric theory of the solar system proposed by Aristarchus of Samos, as well as contemporary ideas about the size of the Earth and the distance between various celestial bodies. By using a system of numbers based on powers of the myriad, Archimedes concludes that the number of grains of sand required to fill the universe is 8×1063 in modern notation. The introductory letter states that Archimedes' father was an astronomer named Phidias. The Sand Reckoner or Psammites is the only surviving work in which Archimedes discusses his views on astronomy.
The Method of Mechanical Theorems
     This treatise was thought lost until the discovery of the Archimedes Palimpsest in 1906. In this work Archimedes uses infinitesimals, and shows how breaking up a figure into an infinite number of infinitely small parts can be used to determine its area or volume. Archimedes may have considered this method lacking in formal rigor, so he also used the method of exhaustion to derive the results. As with The Cattle Problem, The Method of Mechanical Theorems was written in the form of a letter to Eratosthenes in Alexandria.
Apocryphal works
      Archimedes' Book of Lemmas or Liber Assumptorum is a treatise with fifteen propositions on the nature of circles. The earliest known copy of the text is in Arabic. The scholars T. L. Heath and Marshall Clagett argued that it cannot have been written by Archimedes in its current form, since it quotes Archimedes, suggesting modification by another author. The Lemmas may be based on an earlier work by Archimedes that is now lost.

       It has also been claimed that Heron's formula for calculating the area of a triangle from the length of its sides was known to Archimedes.However, the first reliable reference to the formula is given by Heron of Alexandria in the 1st century AD.

Archimedes Palimpsest
      The foremost document containing the work of Archimedes is the Archimedes Palimpsest. In 1906, the Danish professor Johan Ludvig Heiberg visited Constantinople and examined a 174-page goatskin parchment of prayers written in the 13th century AD. He discovered that it was a palimpsest, a document with text that had been written over an erased older work. Palimpsests were created by scraping the ink from existing works and reusing them, which was a common practice in the Middle Ages as vellum was expensive. The older works in the palimpsest were identified by scholars as 10th century AD copies of previously unknown treatises by Archimedes.[68] The parchment spent hundreds of years in a monastery library in Constantinople before being sold to a private collector in the 1920s. On October 29, 1998 it was sold at auction to an anonymous buyer for $2 million at Christie's in New York.[69] The palimpsest holds seven treatises, including the only surviving copy of On Floating Bodies in the original Greek. It is the only known source of The Method of Mechanical Theorems, referred to by Suidas and thought to have been lost forever. Stomachion was also discovered in the palimpsest, with a more complete analysis of the puzzle than had been found in previous texts. The palimpsest is now stored at the Walters Art Museum in Baltimore, Maryland, where it has been subjected to a range of modern tests including the use of ultraviolet and x-ray light to read the overwritten text.
      The treatises in the Archimedes Palimpsest are: On the Equilibrium of Planes, On Spirals, Measurement of a Circle, On the Sphere and the Cylinder, On Floating Bodies, The Method of Mechanical Theorems and Stomachion.
Legacy
      Galileo praised Archimedes many times, and referred to him as a "superhuman". Leibniz said "He who understands Archimedes and Apollonius will admire less the achievements of the foremost men of later times."
    There is a crater on the Moon named Archimedes (29.7° N, 4.0° W) in his honor, as well as a lunar mountain range, the Montes Archimedes (25.3° N, 4.6° W).
     The asteroid 3600 Archimedes is named after him.
       The Fields Medal for outstanding achievement in mathematics carries a portrait of Archimedes, along with a carving illustrating his proof on the sphere and the cylinder. The inscription around the head of Archimedes is a quote attributed to him which reads in Latin: "Transire suum pectus mundoque potiri" (Rise above oneself and grasp the world).
      Archimedes has appeared on postage stamps issued by East Germany (1973), Greece (1983), Italy (1983), Nicaragua (1971), San Marino (1982), and Spain (1963).
      The exclamation of Eureka! attributed to Archimedes is the state motto of California. In this instance the word refers to the discovery of gold near Sutter's Mill in 1848 which sparked the California Gold Rush.