Simplistic tales are often those hardest to refute, not because they are true, but because they form a clear and understandable picture of the messiness of the real world. Take the neat story of how the ancient world turned to Middle Ages: Christians took over the kingdom of Rome, persecuted all the pagans doing real science, burned their writings and killed them, making Europe into a cultural wasteland, soon made into a real wasteland by the wandering barbarian tribes.
This particular story makes an essential mistake in supposing that Christians would have had any unified agenda. Instead, we have on the level of church governance, many sects competing on what the official dogma should be, and even within the sect that finally became the Catholic church, there were many actors with diverse agendas. Individual outbreaks of violence against polytheists by Christians did occur - most famous being the murder of the mathematician and philosopher Hypatia - but these were not officially sanctioned and often these were even condoned as not in the spirit of Christianity.
The church wasn’t completely neutral toward polytheists: bishops were happy to hinder all public display of traditional polytheistic rites by removing altars for the old gods, and some books on magical rituals were ordered to be destroyed. Yet, the prevalent tendency toward classical culture, literature and learning was one of appreciation.
The main reason for the destruction of many of the ancient pieces of writing is simply that physical copies of them were not eternal - the material that they were written on might have deteriorated or it might have been cleaned of text for further use - and there was no long lasting attempt to preserve them all. If there weren’t a large number of copies of some work in circulation, it was highly probable that it wouldn’t survive into modern days.
Lot of classical works did survive in the eastern part of the Roman empire, but general histories of European thought often tend to forget this, since they are more interested in the developments in the western side of the empire. The two parts were, of course, differentiated by language, Greek being the major language in the East, Latin in the West. As we have noticed many times earlier, Latin part of the Roman empire was almost like an intellectual backwater, where ideas discussed in the Greek part flowed much later and in not so great abundance. When the two parts drifted finally apart and the communication between them diminished, the Latin-speaking part had on many fields of learning only few summarised compilations to lean on to.
Compilers like Martianus Capella were thus important for the development of western medieval thought, even if the content of their works was far from groundbreaking. Martianus’ work was also a literary example for many medieval allegories. His compilation is framed by a story of god Mercury, patron of rhetoric, marrying a mortal woman, Philology, representing scholarly expertise. The setting of the story combines traditional polytheism with Neoplatonic influences - mythological stories of gods are joined with a more philosophical account of divinely animated planets, and Jupiter especially plays also a role of the Neoplatonic Intellect or Nus. Particularly noteworthy is the idea that even humans can rise to the celestial rank of gods, if they just educate themselves enough.
The story of the marriage leads to the handmaidens of Philology, each named after some field of learning, giving a speech about her field. Somewhat surprisingly, given that their audience is supposed to be full of learned divinities, the content of these lectures is rather elementary. Thus, the first handmaiden, Grammar, speaks about Latin letters, possible syllables formed of them and different classes of inflections. The second handmaiden, Dialectics, speaks then of the semantic classes of the words, continues by indicating how words are combined into sentences, shows various simple logical relations between sentences and finishes by showing what new sentences can be deduced out of given assumptions. The third handmaiden, Rhetorics, indicates various situations, where sentences should be put together into convincing speeches, delineates the structure of such speeches and rounds off with tricks for making the speech sound eloquent.
Martianus’ account of the more mathematical disciplines is even less impressive. The fifth handmaiden, Geometry, spends most of her time telling about the geography of the known world, on the pretext that geometry is all about measuring land areas. Of the discipline proper, she manages to expound only few elementary definitions of basic shapes. Arithmetic fares a bit better, as she uses only relatively little time with Pythagorean numerology and then proceeds to expound with comprehensive detail some basic properties of numbers and their divisibility. Even so, she does not really prove any arithmetical theorem she presents, but merely exemplifies them with some appropriate numbers.
The final chapters of the book concentrate mostly on some elementary facts of the disciplines in question. The account of Astronomy seems to contain no mention of any astrology, although we cannot be sure, since what has survived from her speech lacks the ending. Harmony does begin her speech by telling how the music guides the heavenly spheres, but then quickly continues with basics about rhythm and melody.
While Martianus’s book is an independent work, specifically dedicated to presenting basic information on a systematically chosen set of fields of learning, achievements of Greek scholars were transmitted to the early western medievals also through commentaries on works of philosophers from previous generations. As the prevailing character of the philosophy of the day was Platonist, so the philosophers chosen were also of Platonist schools of thought. So, while Martianus presented learning with a Platonist covering, these commentaries were completely soaked in Platonist teachings.
We’ve already seen one example of such a commentary, namely Calcidius’ work on Plato’s Timaeus, which contained, for instance, a section dedicated to astronomy. Another work of the same sort was written by Macrobius. He chose to comment on a work of Cicero on good republic. Cicero’s obvious reference point had been Plato’s seminal work on republic, and just like Plato had ended his work with a fable showing what happens to people after death, Cicero had also finished with a section describing how Scipio, a Roman general and statesman, had seen a dream describing what life after death was like.
It was this specific section in Cicero’s work that Macrobius wanted to deal with. Because ironically at least from Plato onward philosophers had been doubtful of the worth of doing philosophy through fables, Macrobius sees it fit to begin his commentary with an apology of philosophical fables. Macrobius notes that the highest levels of the ontological hierarchy cannot be dealt in fables, since these are completely detached from the world of perception and cannot be clothed in images, except through some inappropriate analogies. Then again, they are appropriate, he says, specifically, when dealing with divinities of common polytheism and the world-soul, because they are closely connected with the world of perception, but higher in status than mere earthly things and therefore should not be discussed openly, but with a reverent attitude.
Because Cicero’s work is a fable, and even more, a fable about a prophetic and revelatory dream, Macrobius appears to think that he can look through the external account of the story and find more substantial truths even in its minor details. This makes Macrobius’ commentary appear to be full of digressions not really connected with Cicero’s work. For instance, when Scipio is told by a soul of his dead relative that a certain event will occur to him when numbers determining his life are full, Macrobius takes this as an opportunity to explain Pythagorean numerology.
Although Macrobius’ account of the properties of numbers appears to be rather full of insignificancies, he seems to be particularly interested in the idea that numbers determine the cycles of human life. This does not mean, Macrobius continues, that everything in human life is preordained - some prophecies can be avoided - but certainly some of it is, and everyone will die eventually.
Now, Cicero had noted that what happens to a person after their death is dependent on their way of life, thus, Macrobius says, he had to study ethics. Particularly, Cicero had said that work for one’s commonwealth earned a person a place in heavens. Macrobius is adamant to reconcile Cicero’s statement with a later Neoplatonic idea that political life is not the highest form of life. Macrobius thus sees life dedicated toward the well-being of other people as a stepping stone toward life where one is completely removed from earthly worries.
Indeed, Macrobius is dedicated to the Platonist idea that real death is actually the earthly life where a human soul is imprisoned by the body and its passions and desires, while death as the separation of a soul from its body gives it a chance to return to a disembodied life. This does not mean that a human being should try to actively look for death, Macrobius says, because passion for death would merely lock the soul back to a bodily life.
In addition to ethics, Macrobius says, Cicero studied physics or the structure of the world of perception. Macrobius incorporates the physical world in the common Neoplatonist hierarchy, where the incomprehensible primal source of all being creates an intelligence that both imitates the source by thinking it and in looking away from its source creates the world-soul. The world-soul, again, both imitates the intelligence and merely thinks, but also looks away from it and creates a number of bodies to which it entangles itself, dividing into a number of individual souls.
This is the place where Macrobius introduces his account of astronomy. Lot of the details Macrobius goes through are, of course, same as in Martinus’ account of astronomy, although there are some significant differences (for instance, Martinus upholds a more sophisticated theory where Mercurius and Venus circle around the Sun, not the Earth). Yet, there is an even more important difference in the reason why Macrobius is interested in astronomy. Firstly, it provides a map of the journey the human soul takes when landing from the remotest sphere of the world to Earth, gaining new and more embodied capacities at each planet. Secondly, it shows the greatness of heavens and insignificance of Earth in comparison.
Macrobius continues with an account of the geography of the Earth. His main idea is that the area of lands accessible to Roman civilization is minuscule in proportion to all the inhabited lands on Earth. Connected with the cosmological fact that the heavens circle the Earth eternally and the consequent historical fact that the human civilizations have again and again risen and fallen this idea leads Macrobius to emphasise the insignificance of earthly life.
From physics, Macrobius says, Cicero moved finally to a study of the divine. He especially pointed out the only spark of the divine on Earth, namely, the human souls. The essence of soul, Cicero said, following Plato, lies in self-movement. Macrobius defends this notion against the criticism of Aristotle that mover always differs from moved, that self-movement is therefore impossible and that all movement has begun from an unmoved mover. Macrobius follows earlier Neoplatonists in insisting that self-movement does not mean that the soul would somehow act upon itself, but simply that the soul is by nature active, just like fire does not need something outside itself to become warm. This self-motion of the soul, Macrobius explains, is not literal change of place, but closer to such activities like thinking, emoting and wanting, and through such activities human souls move.their bodies, just like the world soul moves with such activities the stars and planets
What Macrobius finds in Cicero’s work is the whole philosophy. What medievals would find in Macrobius is something else. For them, important things would be the astronomical facts and such interesting details like categories of dreams. The overarching philosophy they would get elsewhere.
Näytetään tekstit, joissa on tunniste rhetoric. Näytä kaikki tekstit
Näytetään tekstit, joissa on tunniste rhetoric. Näytä kaikki tekstit
keskiviikko 30. maaliskuuta 2022
perjantai 1. heinäkuuta 2016
Science and learning in antiquity
The general tendency of ancient Greek and Roman thought has been to associate philosophy with the practice of good life and the ability to pursue such a life, although we have seen Aristotle instead relating the highest philosophy to theoretical knowledge of certain key elements of the world. Still, philosophy of the ancients was not completely separate from the questions of science, or learning in general, and for instance, early Stoics thought that full knowledge of the world and its ways was at least a necessary precondition of perfectly good life. Thus, it is justifiable to investigate Greek science and learning to shed some light on the ancient philosophy.
By far the most developed science of ancient times was mathematics. We often hear of the external form of Euclidean mathematics, which supposedly derives everything from self-evident axioms and definition through incontestable demonstrations. All of this sounds like Greek mathematics would have been quite formal and removed from ordinary experience. Yet, when we look at e.g. Euclid's Elements, we quickly find that Greek mathematics was quite heavily linked to experience. Just think about some key proofs at the beginning of the first book: Euclid asks us to move one triangle on top of another triangle and thus to conclude that the two triangles coincide. This is a primary manner in which the similar magnitude of areas is seen – through quite concrete experiment. In fact, many of the more complex proofs dealing with areas work by cutting compared areas to pieces that we could then know to be similar by relying on some previous propositions – and ultimately on direct observation. This is in fact the manner in which Euclid proves the most famous theory of elementary geometry, the Pythagorean formula.
Although Euclid called his book Elements, an average modern reader would probably find only the first book filled with recognisable questions of elementary geometry: when are triangles similar, what is the sum of the angles in a triangle, how are the angles generated by parallel line related etc.? The second book already opens up avenues unfamiliar from geometry. The book apparently deals with rectangles, but the true topic of the book are certain equations of algebra. Ancient mathematicians had as yet no way to express complex calculations in any other way than through geometric means – squaring through actual squares, multiplication through rectangles. Thus, a simple task of squaring the sum of two magnitudes was represented as a square made out of a line combined of two smaller lines – and the result was then shown to consist of two smaller squares, with sides equal to the smaller lines, together with two rectangles formed by same two lines.
The need to express such equations explains also certain uses of circle by ancient mathematicians. Circle was, of course, important because it provided a way to copy a length of one line to another place. It was also a source for more intricate tools. At the very end of the third book of Elements, Euclid proves that no matter what sort of lines you draw, from a spot outside the circle, towards the circle and cutting it in two places, the rectangle formed by the first line between the spot and the first cutting place and the second line between the two cutting places is always of the same size – and if the line merely touches the circle, the square formed by the line between the spot and the touching place equals all these rectangles. This at first somewhat uninteresting result works in many proofs as a convenient trick e.g. to express some multiples as squares.
The fourth book of Elements continues the study of circles, and its topic is especially drawing figures of certain shape within and around circles. While at first this might seem rather unimportant pursuit, fit only for decorative purposes, it is actually of utmost importance at least in two cases. Firstly, it gives a convenient manner to divide the circumference of circle to equal parts – something which is especially useful for astronomical purposes. Secondly, it can be used to estimate the area of circle. The latter case deserves a more thorough explanation.
Elements is not precisely meant to provide for exact formulas for measurement. Instead, it gives exact means for measuring relations between different geometrical objects. In fact, the fifth book contains a theory of ratios between different magnitudes – that is, it tells us when a pair of number is related exactly in the same manner as another pair and when the pair has a larger or smaller ratio than the other pair. This is convenient in case of estimating magnitude of figures that one cannot express through simple algebraic means. For instance, in the sixth book Euclid can show that two circles have the exactly same ratio as squares on their diameters. Here Euclid is helped by what is called a method of exhaustion. By drawing polygons within and around the circles, he points out that their ratios provide limits between which the ratios of the circles must fall – and because every other ratio exceeds limits given by some of these polygons, the only alternative is the one already mentioned.
Elements is then a book on two-dimensional geometry, but it is also a book on arithmetics – or at least for certain arithmetical principles. Euclid doesn't go so far as to do exact calculations, but we do know from other sources that actual counting at antiquity was rather cumbersome. Instead, in the seventh, eighth and ninth book of Elements Euclid explicates such trivialities as ”odd times even is even”, but also goes through very intricate truths about number, for instance, that there is no highest prime number.
This theory of numbers provides also a ground for Euclid's theory of rational and irrational quantities, which is developed in the tenth book. The notion of ratios provides again a starting point: we just choose some magnitude as rational and then all magnitudes of same type that have the same ratio to the rational magnitude as a number has to another number are rational, while other magnitudes of same type are irrational. Since it is especially geometric magnitudes, or lines and areas, Euclid deals with, he makes the somewhat confusing choice that even all lines with rational squares should be called rational. Going through various relations between lines and areas, Euclid provided a crude classification of all irrationals, only to conclude that his classification fails to account for all irrationals.
The final three books of Elements extend the geometrical account to three-dimensional cases. What is most intriguing is perhaps the manner in which Euclid defines the various three-dimensional shapes through a method for their construction, for instance, when a circle is thought as moving around one of its diameters, a sphere is formed. The actual propositions of the last books are mostly rather uninspiring: we are shown in a similar manner to two-dimensional cases what are the relations of e.g. pyramids and rectangular solids with same bases and same height and we see that relations of cones and cylinders can then be determined through the method of exhaustion. The final book still closes with a true high note, when Euclid shows how to inscribe all the five Platonic shapes into balls and demonstrates that the sides of these shapes must be certain irrationals.
All the things in the two-dimensional part of Elements are accomplished through circles and straight line. In later mathematics, this was made a sort of virtue, but it seems clear that at least not all ancient mathematicians did not put as strict limits to mathematics. This is shown even by Euclid's three-dimensional mathematics and its method of constructing three-dimensional shapes, but even more clearly by the ancient treatises of various types of curves, most interesting of which are possibly the conic sections, which get their names from being generated by planes cutting the cones in different angles. The use of conic section is, once again, not arbitrary, but important e.g. for expressing relations between one- and two-dimensional magnitudes.
Another interesting point in ancient mathematics is Arhcimedes' account of how to calculate various curvilinear areas and volumes. On some level, not much has changed from Euclidean account of finding relations that hold e.g. between circles. In many cases Archimedes even uses the same method of exhaustion Euclid had applied. For instance, when trying to determine the segment of a parabola, Archimedes shows that we can limit the area of the segment through sums of triangles, and by making the triangles smaller and smaller the limits become closer and closer to a certain area. But Archimedes had also another type of proof for such theories – he showed that when put to a lever the segment could be balanced with a triangle of a certain area, which was then equal to the segment. In other words, Archimedes used mechanical principles to determine an answer to a mathematical problem. As he himself testifies, this mostly just helped him to discover the areas, but he didn't accept it as a proper proof, which could be determined only through mathematical means.
Although Archimedes did use then mechanics as a tool in mathematics, more familiar is his application of mathematics in mechanics. There was considerable interest on mechanical questions even before Archimedes, as shown by a work on mechanical problems, attributed to Aristotle, but in a sense, in Archimedes the ancient tradition of mechanics culminated. Especially important in this context is the notion of a centre of gravity, that is, a place to which we can think that the whole weight of a body is concentrated. Through this notion Archimedes can prove a number of important mechanical principles, such as the lever law – the longer the stick the more weight you can lift. Note how close to practice the Archimedean practice of mechanics is – it is all about making machines, like levers and pulleys.
Even more important field of application for mathematics was the study of stars and their comings and goings. Here especially the study of circles and angles was of primary importance. Earth and the universe were pictured as a sphere within a sphere. By carefully noting the distances between places, measuring differences of shadows and the places of stars in the sky, one could get a reasonable model of the place of the Earth in relation to the universe. Then by following the changes in the positions of the stars, and especially of the strangest of these, that is, planets, and by assuming that the movements of all heavenly objects must be somehow based on circles, Ptolemy constructed a reasonably accurate model of planetary movement.
Ancient thinkers were not satisfied with mere modelling of planetary movement, but they also tried to explain this phenomenon. The basic notions were simplistically mechanical or then compared the movement of stars to movements of animal things. Whatever the case, the stars themselves and their movement was supposed to have an effect on Earthly things through their pressure on Earth's atmosphere. Such influences were also felt to be a justification for attempts to predict key events in human life.
In addition to these astrological considerations, study of stars was quite useful in making maps – one can use the positions of stars in the night sky for approximating one's position on the globe. Here ancient mathematical learning came in contact with ancient empirical knowledge. One cannot say that Greeks and Romans would not have appreciated empirical learning. Quite the contrary, as Strabo's geographical writings and Pliny's collection of all sorts of interesting factoids show.
What was lacking was such technological advances like telescope and microscope, which have allowed us to see farther and in more detail. Also, the lack of trustworthy and fast communications often made it impossible to verify the facts collected, which makes these empirical compilations into an often tantalising mix of truths and fairy tales. One can see that there was e.g. great technological expertise on various special subjects, such as metallurgy, but this expertise was dispersed to many different individuals – while one person could know everything of, say, gold and its behaviour, he might have no idea about forging iron.
While ancient culture did have empirically discovered information on many questions of nature, the role of theoretical foundation of such information was rather ambiguous, reflecting the conflicts between various philosophical schools. The complex interactions between theory and empiria and many viewpoints on these interactions can be well exemplified through the difference of ancient schools of medicine. We have methodists, who were affiliated with the Pyrrhonic school and who accepted only some rules of thumb that had appeared to work in previous occasions. We have empiricists, who accepted immediate appearances and experiences as a tool for suggesting treatment, but who denied the possibility of any knowledge on the hidden causes of various diseases. And there were various rationalist schools, who attempted to justify their procedures through some theoretical framework, although what was a correct theory of human body was a point hotly debated.
Probably the most famous of these researchers of medicine was Galen, whose position was somewhere between empirical and rational schools. Galen despised methodists, whom he thought as mere bunglers and frauds. He was quite sympathetic of empiricists and admitted that in many cases empirical observations were enough for discovering a good treatment. He endorsed the rationalist ideal of a science of medicine based on certain foundations, but only if the foundations were correct. His preferred theory of human body was quite Aristotelian: the constituents of human body were characterised by four qualities (hotness, dryness, coldness and wetness), and if some quality took a too forceful position in some part of the body, causing imbalance and disharmony, a proper treatment was to apply opposed quality.
While Galenian medicine thus offered a comprehensive account of the biological make-up of human body, rhetoric was at least advertised as a comprehensive account of the cultural side of human beings. On the superficial level, the topic of the rhetoric is much more restricted – the production of speeches, and especially of speeches meant to be used in a court setting. Thus, the central aim of ancient rhetoric was to show how to invent good arguments for one's position, how to arrange these arguments into a coherent whole, how to express this whole in a good style, how to memorise the written speech and how to present it in a compelling manner.
Yet, writers like Cicero and Quintilian were eager to suggest that rhetoric was something more, namely the lost half of philosophy. That is, they pictured a time, when philosophical study of truths and especially of truths concerning good human life and rhetorical expertise of expressing those truths were an undivided unity. A conclusion they both draw was that a good rhetorician should also be a good person and know all the intricacies of human life.
An important part in rhetoric, Quintilian suggested was then the education of a future rhetoric. As it should be evident from his wide definition of rhetoric, Quntilian plans a careful curriculum for his imaginary students who wish to learn ,not just the tricks of the trade, but also the rudiments for becoming an ideal speaker. It appears that an ideal speaker should learn as much a possible from every topic – even if her skills are to be used in the courthouse, it is a definite possibility that some case would require expertise knowledge of some special topic. In addition to specialised knowledge, the rhetorician-to-be should also learn history, since past events often play part in modern cases. A special place in the curriculum is given to literature, which at the same time teaches the students the basics of good language, but also suggests various examples of human behaviour.
Quintilian's school of rhetoric incorporates then two important pieces of humanist learning: history and literature, both of which were important fields of study in antiquity. Study of history in ancient Greece and Rome was in a sense something quite different from academic history of our time. The ancient historians had progressed not much beyond mere chronicling of events. Often their standards of criticism were quite suspect. As a case in point, we might raise the historian of philosophy, Diogenes Laërtius, whose work is at worst a rambling collection of anecdotes from the lives of philosophers, without a proper explanation of their philosophies. The main historical guide line of Diogenes is the notion of one philosopher being a student of another, which allows him to create two lines of thinkers, but fails in explaining how the ideas of earlier philosophers led to ideas of future philosophers.
As for study of different types of literature, a scholarly criticism was quite developed. As an example, we might pick out the investigation of works of Aristotle, ancient commentaries on which could have filled libraries. An important example of this tradition is Alexander of Aphrodisias, who apparently set out to explain all of Aristotle's extant works, although only a handful of his commentaries have been passed down to us. And explain he does. Following through Aristotle's account of different types of deductions, Alexander goes carefully through every reasoning and every example Aristotle uses, expanding Aristotle's sometimes rather summarised sentences.
In some cases, Alexander picks on details that Aristotle probably did not mean as important. Why did Aristotle choose to present the three different figures of syllogisms in a certain order, Alexander asks. Pretty clearly the first figure is most important, because it is the only one allowing us to prove universal and affirmative propositions, required in scientific reasoning. Alexander takes this line of thought further and suggests that second figure, leading only to negative conclusions, is second best, because it can be used in philosophical debates, meant for refuting the ideas of opponents – and the third figure is then worst, leading only to particular conclusions and thus useful only in sophistical reasoning, in which propositions applying merely for particular cases are deceptively presented as holding in general.
At times, Alexander defends Aristotle against later critics. For instance, some Stoics had claimed that Aristotle went wrong in assuming that one cannot deduce impossibilities out of possibilities, because a possible statement ”Dion is dead” implied a statement ”he is dead” (”he” referring to Dion), but since the Greek term for ”he” could be used only of living persons, the implied statement was always an impossibility. Alexander noted that, if Stoics were correct in their grammar, then the first statement simply did not imply the latter. Furthermore, he pointed out that since Stoics believed in eternal recurrence of all things, death was always only a temporary state and one could refer to a dead person with a pronoun.
Alexander also opposed Stoics on their understanding of negation. Stoics had suggested that ”Socrates is not white” is not the negation of ”Socrates is white”, because both of these presuppose that Socrates exist, while ”It is not so that Socrates is white” does not, making it the sought-out negation. Alexander pointed out that a proper name did not necessarily refer to an existing entity, like in a sentence ”My future son will be called Eric”, which made Stoic assumption doubtful.
At other times, Alexander tried to show that certain innovations of later logicians were already accounted for by Aristotle. Thus, he attempts to show that a deduction consisting of nothing else but conditionals (”if A then B, if B then C, thus, if A then C”) must still follow syllogistic rules, because the premisses must have been ultimately deduced syllogistically.
Sometimes Alexander went clearly too far in his attempt to speak for Aristotle. A good example is latter's attempt to add necessity and possibility in his logic. Aristotle's efforts become quickly a hopeless muddle, when he distinguished many different meanings of possibility or contingency and then himself confused these various meanings from time to time. Alexander's valiant effort to make sense out of it manages just to muddle the issue even further.
By far the most developed science of ancient times was mathematics. We often hear of the external form of Euclidean mathematics, which supposedly derives everything from self-evident axioms and definition through incontestable demonstrations. All of this sounds like Greek mathematics would have been quite formal and removed from ordinary experience. Yet, when we look at e.g. Euclid's Elements, we quickly find that Greek mathematics was quite heavily linked to experience. Just think about some key proofs at the beginning of the first book: Euclid asks us to move one triangle on top of another triangle and thus to conclude that the two triangles coincide. This is a primary manner in which the similar magnitude of areas is seen – through quite concrete experiment. In fact, many of the more complex proofs dealing with areas work by cutting compared areas to pieces that we could then know to be similar by relying on some previous propositions – and ultimately on direct observation. This is in fact the manner in which Euclid proves the most famous theory of elementary geometry, the Pythagorean formula.
Although Euclid called his book Elements, an average modern reader would probably find only the first book filled with recognisable questions of elementary geometry: when are triangles similar, what is the sum of the angles in a triangle, how are the angles generated by parallel line related etc.? The second book already opens up avenues unfamiliar from geometry. The book apparently deals with rectangles, but the true topic of the book are certain equations of algebra. Ancient mathematicians had as yet no way to express complex calculations in any other way than through geometric means – squaring through actual squares, multiplication through rectangles. Thus, a simple task of squaring the sum of two magnitudes was represented as a square made out of a line combined of two smaller lines – and the result was then shown to consist of two smaller squares, with sides equal to the smaller lines, together with two rectangles formed by same two lines.
The need to express such equations explains also certain uses of circle by ancient mathematicians. Circle was, of course, important because it provided a way to copy a length of one line to another place. It was also a source for more intricate tools. At the very end of the third book of Elements, Euclid proves that no matter what sort of lines you draw, from a spot outside the circle, towards the circle and cutting it in two places, the rectangle formed by the first line between the spot and the first cutting place and the second line between the two cutting places is always of the same size – and if the line merely touches the circle, the square formed by the line between the spot and the touching place equals all these rectangles. This at first somewhat uninteresting result works in many proofs as a convenient trick e.g. to express some multiples as squares.
The fourth book of Elements continues the study of circles, and its topic is especially drawing figures of certain shape within and around circles. While at first this might seem rather unimportant pursuit, fit only for decorative purposes, it is actually of utmost importance at least in two cases. Firstly, it gives a convenient manner to divide the circumference of circle to equal parts – something which is especially useful for astronomical purposes. Secondly, it can be used to estimate the area of circle. The latter case deserves a more thorough explanation.
Elements is not precisely meant to provide for exact formulas for measurement. Instead, it gives exact means for measuring relations between different geometrical objects. In fact, the fifth book contains a theory of ratios between different magnitudes – that is, it tells us when a pair of number is related exactly in the same manner as another pair and when the pair has a larger or smaller ratio than the other pair. This is convenient in case of estimating magnitude of figures that one cannot express through simple algebraic means. For instance, in the sixth book Euclid can show that two circles have the exactly same ratio as squares on their diameters. Here Euclid is helped by what is called a method of exhaustion. By drawing polygons within and around the circles, he points out that their ratios provide limits between which the ratios of the circles must fall – and because every other ratio exceeds limits given by some of these polygons, the only alternative is the one already mentioned.
Elements is then a book on two-dimensional geometry, but it is also a book on arithmetics – or at least for certain arithmetical principles. Euclid doesn't go so far as to do exact calculations, but we do know from other sources that actual counting at antiquity was rather cumbersome. Instead, in the seventh, eighth and ninth book of Elements Euclid explicates such trivialities as ”odd times even is even”, but also goes through very intricate truths about number, for instance, that there is no highest prime number.
This theory of numbers provides also a ground for Euclid's theory of rational and irrational quantities, which is developed in the tenth book. The notion of ratios provides again a starting point: we just choose some magnitude as rational and then all magnitudes of same type that have the same ratio to the rational magnitude as a number has to another number are rational, while other magnitudes of same type are irrational. Since it is especially geometric magnitudes, or lines and areas, Euclid deals with, he makes the somewhat confusing choice that even all lines with rational squares should be called rational. Going through various relations between lines and areas, Euclid provided a crude classification of all irrationals, only to conclude that his classification fails to account for all irrationals.
The final three books of Elements extend the geometrical account to three-dimensional cases. What is most intriguing is perhaps the manner in which Euclid defines the various three-dimensional shapes through a method for their construction, for instance, when a circle is thought as moving around one of its diameters, a sphere is formed. The actual propositions of the last books are mostly rather uninspiring: we are shown in a similar manner to two-dimensional cases what are the relations of e.g. pyramids and rectangular solids with same bases and same height and we see that relations of cones and cylinders can then be determined through the method of exhaustion. The final book still closes with a true high note, when Euclid shows how to inscribe all the five Platonic shapes into balls and demonstrates that the sides of these shapes must be certain irrationals.
All the things in the two-dimensional part of Elements are accomplished through circles and straight line. In later mathematics, this was made a sort of virtue, but it seems clear that at least not all ancient mathematicians did not put as strict limits to mathematics. This is shown even by Euclid's three-dimensional mathematics and its method of constructing three-dimensional shapes, but even more clearly by the ancient treatises of various types of curves, most interesting of which are possibly the conic sections, which get their names from being generated by planes cutting the cones in different angles. The use of conic section is, once again, not arbitrary, but important e.g. for expressing relations between one- and two-dimensional magnitudes.
Another interesting point in ancient mathematics is Arhcimedes' account of how to calculate various curvilinear areas and volumes. On some level, not much has changed from Euclidean account of finding relations that hold e.g. between circles. In many cases Archimedes even uses the same method of exhaustion Euclid had applied. For instance, when trying to determine the segment of a parabola, Archimedes shows that we can limit the area of the segment through sums of triangles, and by making the triangles smaller and smaller the limits become closer and closer to a certain area. But Archimedes had also another type of proof for such theories – he showed that when put to a lever the segment could be balanced with a triangle of a certain area, which was then equal to the segment. In other words, Archimedes used mechanical principles to determine an answer to a mathematical problem. As he himself testifies, this mostly just helped him to discover the areas, but he didn't accept it as a proper proof, which could be determined only through mathematical means.
Although Archimedes did use then mechanics as a tool in mathematics, more familiar is his application of mathematics in mechanics. There was considerable interest on mechanical questions even before Archimedes, as shown by a work on mechanical problems, attributed to Aristotle, but in a sense, in Archimedes the ancient tradition of mechanics culminated. Especially important in this context is the notion of a centre of gravity, that is, a place to which we can think that the whole weight of a body is concentrated. Through this notion Archimedes can prove a number of important mechanical principles, such as the lever law – the longer the stick the more weight you can lift. Note how close to practice the Archimedean practice of mechanics is – it is all about making machines, like levers and pulleys.
Even more important field of application for mathematics was the study of stars and their comings and goings. Here especially the study of circles and angles was of primary importance. Earth and the universe were pictured as a sphere within a sphere. By carefully noting the distances between places, measuring differences of shadows and the places of stars in the sky, one could get a reasonable model of the place of the Earth in relation to the universe. Then by following the changes in the positions of the stars, and especially of the strangest of these, that is, planets, and by assuming that the movements of all heavenly objects must be somehow based on circles, Ptolemy constructed a reasonably accurate model of planetary movement.
Ancient thinkers were not satisfied with mere modelling of planetary movement, but they also tried to explain this phenomenon. The basic notions were simplistically mechanical or then compared the movement of stars to movements of animal things. Whatever the case, the stars themselves and their movement was supposed to have an effect on Earthly things through their pressure on Earth's atmosphere. Such influences were also felt to be a justification for attempts to predict key events in human life.
In addition to these astrological considerations, study of stars was quite useful in making maps – one can use the positions of stars in the night sky for approximating one's position on the globe. Here ancient mathematical learning came in contact with ancient empirical knowledge. One cannot say that Greeks and Romans would not have appreciated empirical learning. Quite the contrary, as Strabo's geographical writings and Pliny's collection of all sorts of interesting factoids show.
What was lacking was such technological advances like telescope and microscope, which have allowed us to see farther and in more detail. Also, the lack of trustworthy and fast communications often made it impossible to verify the facts collected, which makes these empirical compilations into an often tantalising mix of truths and fairy tales. One can see that there was e.g. great technological expertise on various special subjects, such as metallurgy, but this expertise was dispersed to many different individuals – while one person could know everything of, say, gold and its behaviour, he might have no idea about forging iron.
While ancient culture did have empirically discovered information on many questions of nature, the role of theoretical foundation of such information was rather ambiguous, reflecting the conflicts between various philosophical schools. The complex interactions between theory and empiria and many viewpoints on these interactions can be well exemplified through the difference of ancient schools of medicine. We have methodists, who were affiliated with the Pyrrhonic school and who accepted only some rules of thumb that had appeared to work in previous occasions. We have empiricists, who accepted immediate appearances and experiences as a tool for suggesting treatment, but who denied the possibility of any knowledge on the hidden causes of various diseases. And there were various rationalist schools, who attempted to justify their procedures through some theoretical framework, although what was a correct theory of human body was a point hotly debated.
Probably the most famous of these researchers of medicine was Galen, whose position was somewhere between empirical and rational schools. Galen despised methodists, whom he thought as mere bunglers and frauds. He was quite sympathetic of empiricists and admitted that in many cases empirical observations were enough for discovering a good treatment. He endorsed the rationalist ideal of a science of medicine based on certain foundations, but only if the foundations were correct. His preferred theory of human body was quite Aristotelian: the constituents of human body were characterised by four qualities (hotness, dryness, coldness and wetness), and if some quality took a too forceful position in some part of the body, causing imbalance and disharmony, a proper treatment was to apply opposed quality.
While Galenian medicine thus offered a comprehensive account of the biological make-up of human body, rhetoric was at least advertised as a comprehensive account of the cultural side of human beings. On the superficial level, the topic of the rhetoric is much more restricted – the production of speeches, and especially of speeches meant to be used in a court setting. Thus, the central aim of ancient rhetoric was to show how to invent good arguments for one's position, how to arrange these arguments into a coherent whole, how to express this whole in a good style, how to memorise the written speech and how to present it in a compelling manner.
Yet, writers like Cicero and Quintilian were eager to suggest that rhetoric was something more, namely the lost half of philosophy. That is, they pictured a time, when philosophical study of truths and especially of truths concerning good human life and rhetorical expertise of expressing those truths were an undivided unity. A conclusion they both draw was that a good rhetorician should also be a good person and know all the intricacies of human life.
An important part in rhetoric, Quintilian suggested was then the education of a future rhetoric. As it should be evident from his wide definition of rhetoric, Quntilian plans a careful curriculum for his imaginary students who wish to learn ,not just the tricks of the trade, but also the rudiments for becoming an ideal speaker. It appears that an ideal speaker should learn as much a possible from every topic – even if her skills are to be used in the courthouse, it is a definite possibility that some case would require expertise knowledge of some special topic. In addition to specialised knowledge, the rhetorician-to-be should also learn history, since past events often play part in modern cases. A special place in the curriculum is given to literature, which at the same time teaches the students the basics of good language, but also suggests various examples of human behaviour.
Quintilian's school of rhetoric incorporates then two important pieces of humanist learning: history and literature, both of which were important fields of study in antiquity. Study of history in ancient Greece and Rome was in a sense something quite different from academic history of our time. The ancient historians had progressed not much beyond mere chronicling of events. Often their standards of criticism were quite suspect. As a case in point, we might raise the historian of philosophy, Diogenes Laërtius, whose work is at worst a rambling collection of anecdotes from the lives of philosophers, without a proper explanation of their philosophies. The main historical guide line of Diogenes is the notion of one philosopher being a student of another, which allows him to create two lines of thinkers, but fails in explaining how the ideas of earlier philosophers led to ideas of future philosophers.
As for study of different types of literature, a scholarly criticism was quite developed. As an example, we might pick out the investigation of works of Aristotle, ancient commentaries on which could have filled libraries. An important example of this tradition is Alexander of Aphrodisias, who apparently set out to explain all of Aristotle's extant works, although only a handful of his commentaries have been passed down to us. And explain he does. Following through Aristotle's account of different types of deductions, Alexander goes carefully through every reasoning and every example Aristotle uses, expanding Aristotle's sometimes rather summarised sentences.
In some cases, Alexander picks on details that Aristotle probably did not mean as important. Why did Aristotle choose to present the three different figures of syllogisms in a certain order, Alexander asks. Pretty clearly the first figure is most important, because it is the only one allowing us to prove universal and affirmative propositions, required in scientific reasoning. Alexander takes this line of thought further and suggests that second figure, leading only to negative conclusions, is second best, because it can be used in philosophical debates, meant for refuting the ideas of opponents – and the third figure is then worst, leading only to particular conclusions and thus useful only in sophistical reasoning, in which propositions applying merely for particular cases are deceptively presented as holding in general.
At times, Alexander defends Aristotle against later critics. For instance, some Stoics had claimed that Aristotle went wrong in assuming that one cannot deduce impossibilities out of possibilities, because a possible statement ”Dion is dead” implied a statement ”he is dead” (”he” referring to Dion), but since the Greek term for ”he” could be used only of living persons, the implied statement was always an impossibility. Alexander noted that, if Stoics were correct in their grammar, then the first statement simply did not imply the latter. Furthermore, he pointed out that since Stoics believed in eternal recurrence of all things, death was always only a temporary state and one could refer to a dead person with a pronoun.
Alexander also opposed Stoics on their understanding of negation. Stoics had suggested that ”Socrates is not white” is not the negation of ”Socrates is white”, because both of these presuppose that Socrates exist, while ”It is not so that Socrates is white” does not, making it the sought-out negation. Alexander pointed out that a proper name did not necessarily refer to an existing entity, like in a sentence ”My future son will be called Eric”, which made Stoic assumption doubtful.
At other times, Alexander tried to show that certain innovations of later logicians were already accounted for by Aristotle. Thus, he attempts to show that a deduction consisting of nothing else but conditionals (”if A then B, if B then C, thus, if A then C”) must still follow syllogistic rules, because the premisses must have been ultimately deduced syllogistically.
Sometimes Alexander went clearly too far in his attempt to speak for Aristotle. A good example is latter's attempt to add necessity and possibility in his logic. Aristotle's efforts become quickly a hopeless muddle, when he distinguished many different meanings of possibility or contingency and then himself confused these various meanings from time to time. Alexander's valiant effort to make sense out of it manages just to muddle the issue even further.
Tunnisteet:
Alexander of Aphrodisias,
Archimedes,
astronomy,
Diogenes Laertius,
Euclid,
geography,
history,
history of philosophy,
mathematics,
mechanics,
Pliny,
Ptolemy,
Quintillian,
rhetoric,
science,
Strabo
sunnuntai 2. elokuuta 2015
Philosophy translated
All the
philosophers thus far have spoken and written in Greek, even if they
lived far away from Greek mainland. Philosophy, as we have faced it –
this strange mix of a search for meaningful life and an investigation of truth – has been a unique part of Greek culture. This changed, when
philosophical schools started to translate their theories to Rome.
At first,
philosophy did not fair well in these new surroundings. There is a
well known story of a group of philosophical ambassadors arriving in
Rome. Carneades the Academic was one member of this group, and upon
the day of their arrival, he made a touching speech about the
usefulness of military prowess – a topic close to the heart of
Romans. True to his habit of not asserting anything, Carneades made
another speech the following day and this time insulted military
prowess as the ultimate evil. Needless to say, Roman authorities were
not pleased and banned the arrival of philosophers to Rome.
It is not
certain how fabulous the story is, but it probably reflects a real
tendency in Roman society. Greeks in general were considered
effeminate and thus suspicious in the eyes of the masculine culture
of Romans. Philosophy was considered nothing more than a further
evidence of the perversity of Greeks – who on earth would spend
considerable time in thinking such frivolities?
Of course,
as time went by, Romans started to warm up to Greek learning. Thus,
in few generations we find representatives of major philosophical
schools using Latin in their writings. Even such highly infamous
school as Epicureanism had its Roman follower, Lucretius. Basic
opinions of Lucretius remained same as those of Epicurus, but some
interesting differences of emphasis had occurred. While Epicurus
himself was against too flowery teaching, Lucretius used his poetic
skills for teaching philosophy. Indeed, he concentrated on the most
epic theme in Epicurean philosophy, that is, physics or the study of
the world and its birth, instead of the usual emphasis on ethical
matters.
Lucretius
spins a dramatic tale starting from the idea of atoms of different
shapes flying around, all in straight line in infinite space.
Suddenly, an atom changes its course, due to no reason at all, and
bounces on other atoms, thus creating aggregates of atoms, like the
elements or earth, water, air and fire. At first the elements are
completely mixed, but the heavy earth finally takes up the middle
point and the lighter elements are left to the outer remnants. Thus
was finally born the world we know, and one day it will be destroyed,
when the fight of the elements is finally canceled.
Spirit
animating animals and humans is also in Epicurean theory an element
consisting of atoms, and furthermore, such that can live only within
a body – no afterlife in Epicurean philosophy, but then again,
there's also nothing to worry about, no eternal pain after death.
True, people do get visions of tormented souls, but these are just
freak combinations of atoms striking our mind. In the beginning of
the world, the earth itself had enough power to create combinations
of spirit and other matter or living beings, but in time its power
diminished and only those animals that could have offspring remained.
For humans, this meant the beginning of a long progress towards
civilization, through inventions like agriculture, metallurgy and
social life. But far more important Lucretius considers the
discoveries of Epicurus, who showed that many events apparently
caused by gods were actually natural occurrences and hence no reason
to fear divine wrath.
But it is
not Lucretius one should take as the most important link between
Greek and Latin philosophy. Instead, this epithet should be bestowed
on Marcus Tullius Cicero, who actually began his career as an orator
and a statesman in Roman republic and took to philosophy only later
in his life, when he was effectively prevented from taking part in
state life by machinations of Julius Caesar and his followers. His
first literary works concerned rhetoric, a topic he had plenty of
personal experience with, and therefore it is no wonder that he took
a considerably more positive view of it than many earlier
philosophers – rhetoric was a good instrument, if the user just was
an upright citizen. Indeed, Cicero was of the opinion that originally
rhetoric or oratory formed a complete whole with philosophy, as a
general capacity to know how to live and to present one's wisdom to
fellow citizens. Later philosophers had isolated some topics for pure
research and ignored the need for defending them, and some
(Epicureans) had even tried to escape the duty to serve others of
their communities in their search for personal peace and contentment.
True, philosophers like Stoics might have better arguments, but they
lacked the means of making the crowd convinced – a criteria that
was essential for evaluating the success of one's speech.
In
comparison with philosophers, Cicero thought that orators had nothing
to be shamed of. He even suggested that an ideal speaker, like the
famous Greek orator, Demosthenes, should know of all sorts of things
and be highly civilized. He should be well versed with logic and
ethics (for instance, he should know that there are basically two
sources of a decent human life: cultivation of one's intellectual
capacities and harmonisation of desires under the guidance of
intellect). Cicero still admitted that real speakers were often far
from this ideal, but maintained that even they had to have some
inkling of certain tricks of trade, like some basic human psychology
and capacity of finding convincing arguments, even if rhetoric is
more dependent on one having the capacities of a potential speaker.
Furthermore, Cicero was convinced that oratory as a whole had
developed in the sense that best speakers of earlier ages were mere
babblers in comparison with best speakers of Cicero's day.
Cicero was
in fact convinced that even in philosophy caring about the affairs of
community is far more appropriate than losing oneself to the study of
the wonders of nature. Indeed, he himself was highly interested of
the question of the shape of an ideal community. Cicero basically
accepted the Aristotelian idea of three paradigmatic forms of
community: monarchy, aristocracy and democracy. Of these, democracy
does retain the liberty of every citizen, but often leads to a state
of anarchy, when no one has a clear governing position, while
monarchy and aristocracy are more efficient, but are in danger of
being corrupted into tyrannies and oligarchies, just like happened
with Roman monarchy. True solution would be a balanced community,
with elements of all forms of government, which Cicero felt was
embodied in republican Rome, in which consuls retained some of the
monarchic power, while patrician senate and plebeian tribunal
expressed aristocratic and democratic elements.
Quite
traditionally, Cicero held that a balanced community – and indeed,
any community, if it was to be community and not just an enslavement
of people – would have to be based on justice, that is, on the
principle that everyone was due to what she deserved. While Greek
philosophers had to apply this principle in affairs of one city,
Cicero as a citizen of an empire had to consider what justice means
in international affairs. True to the mores of his time, Cicero could
defend aggression of a state over another with the Aristotelian
notion that some people just were more natural to rule, while the
fate of others was to be ruled. Cicero also had to face the problem
of different mores in different cultures, so obvious in an
international empire like Rome – if different cultures thought
different things good and evil, how could we defend justice as the
guiding principle of all communities? Cicero's answer was that deep
down all people must agree on some basic values, such as justice,
because they were based on the nature of things and not on arbitrary
cultural habits.
Just like
Greek philosophers before him, Cicero was also certain that the good
of a community relied not only on the structure of the society, but
also on harmonising the actions of the community members. This
harmonising then requires that the members have a state of mind
geared towards community life, instead of just caring for themselves.
As an incentive towards such a mindset, Cicero uses Plato's trick of
suggesting a reward in the afterlife for all those who have lived
well – a reason not to be intimidated of death nor of old age. Even
if death were a mere annihilation of life and so all sensation, it
would be nothing to be afraid of, since it would mean deliverance
from all pain and would resemble deep sleep. But, Cicero argues,
since human body appears to contain a divine element, as evidenced by
the mental powers of human beings, this spark must not be hindered by
the death of body. Instead, as it is made of finer elements than the
coarse body, it will get to fly away from the insignificant speck
that Earth is to the beauty of heavenly spheres. Thus, Cicero is
willing to incorporate religious rituals to state life and so gain
divine justification to it.
Cicero is
also insistent that the harmony of the state is dependent especially
on the state of its nobles – on the one hand, it's important that
there is a class that has the means to understand the affairs of
state better than the common people, on the other hand, this class
should also work for the common good instead of their own
advancement. Cicero especially emphasises the role of past great men
of Rome as examples of good life. These past heroes knew that true
worth of human life lies not in riches, but more in one's capacity to
control oneself – riches and earthly goods are something that comes
and goes and a person controlled by a desire for them is never
satisfied, while a self-controlled person can never become unhappy,
because of his ability to adjust to all circumstances. He would never
be anxious or depressed about anything, because he would understand
how small and meaningless all the seeming troubles of life are.
These
statements of what good life is sound like they could have come out
of the mouth of a Stoic. Indeed, like Stoics, Cicero was critical of
the Epicurean philosophy. Epicurean physics Cicero despised
completely. Atoms changing the direction of their movement just by
accidence and complete worlds coming to be through pure chance were
just too unbelievable doctrines in his eyes. And images of things far
away floating around, pinging our bodies and causing us imagine
things not actually present sounds convincing at first, but then
you'd have to accept the existence of all sorts of fables, like
centaurs and dragons.
Epicurean
idea of gods Cicero thought especially ridiculous. Epicureans thought
a god should be human in shape, because that was the only suitable
form for reasoning, but this just made human ignorance into a general
principle – and in any case, how could a thing in human form be
anything but mortal? Furthermore, Epicureans thought that gods would
do nothing and care for nothing and still be happy, but Cicero
insisted that only an active life would be a happy life. Even worse,
idea of such indifferent gods would mean end to all religion, because
no one would feel any need to worship such gods. In any case, Cicero
thought that it would have been easier if Epicureans had just denied
the existence of gods altogether, since they just appeared to accept
them because of common opinion.
Cicero had
learned from Epicurean teachers and so knew more of their ethics than
just the usual caricature – he was aware that Epicureans did not
search for mere temporary delights of flesh, but like other major
schools of philosophy, recommended a life of moderation, because only
such promised stable pleasures. Yet, Cicero thought, Epicurus was
trying to play with two sets of cards at the same time: on the one
hand, he spoke of pleasure to entice people wanting to spend their
life full of a variety of pleasant sensations, on the other hand, he
acted as if greatest pleasure was just a life without pain in order
to sound more respectable in philosophical circles. Epicurus even
says that traditional virtues are good for pleasures (for instance,
courage makes us feel less pain in adverse circumstances), but Cicero
thinks this view distorts the true purpose of virtues, which are
meant to serve the whole community, not just an individual. Indeed, a
true Epicurean would be a complete egoist, and because Epicurus
himself valued his friends, he must have been inconsistent.
Even
though Cicero did agree with Stoics that Epicureans were a really bad
school of philosophy and even used their terminology in a Latinized
form, he still was no straightforward Stoic, but appropriated
features of many philosophies into his worldview. Indeed, he didn't
have a high opinion of Stoic logic or Stoic ideas of the natural
world, thinking that Stoics had merely copied the ideas of their
predecessors and in some cases had even regressed. At some point, Cicero especially
criticized their ethics, which attempted to state paradoxical
conclusions, such as the indifference of all except virtuous
behaviour, but had to admit, like Platonists and Aristotelians had
done earlier, that even Stoics thought it preferable to be healthy
and of good means – in effect Cicero accused Stoics of using
terminological quibbles to distinguish themselves from more adequate
philosophers.
Cicero was
especially interested of the New Academy, and like them, accepted
that humans can usually achieve only probability, not true knowledge
– at least if knowledge is defined in the manner Stoics had. The
basis of all knowledge should be perceptions that accurately portray
things they appear to present, Stoics say, but there is no way to
discern such true perceptions from mere appearances, which might look
essentially same as true perceptions. This doesn't mean that one
should be completely blind about how to conduct one's live, Cicero
says, because probability is enough for a decent life – indeed,
even Stoics must admit that most people must do with mere
probability, because knowledge is so rare.
Still,
even in case of conduct Cicero finds at first that opinions of Plato and
Aristotle were far more probable than Stoicism – Plato and
Aristotle at least straightforwardly admitted that material things
are goods and part of a happy life, they just weren't as good as
mental fortitude. Stoics announced that pain was no evil, but such a
statement would not help anything when one was actually feeling it.
Far better in Cicero's opinion was to teach one to tolerate pain,
just like a manly man can do – and if pain turns too strong to
bear, there's always the possibility to escape to the netherworld.
And while Stoics were satisfied to say that wise men never felt any
distress, because they saw how unreasonable it is, this helps in no
manner anyone wallowing in grief who does not fulfill the ideal of
Stoic sage – instead, they should be led to reflect on the cause of
their grief and note themselves its insignificance.
Yet,
Cicero wouldn't have been a true Academician, if he couldn't have
seen the other side of the debate also. While Aristotle was to be
recommended for realizing the importance of sensuous goods and pains,
Cicero was highly critical of his idea of best life being a sort of
mean between two extremes. If someone was, say, even the slightest
bit agitated out of anger, he might well be overwhelmed, if the
emotion rose to a higher degree. Far better it would be, Cicero
thought, to follow the Stoic ideal, in which all emotions should fall
under perfect control of a person. Indeed, if even Epicureans, who
laid all happiness in pleasure, said that a true philosopher was
always happy and not shaken by anything, shouldn't disciples of
Socrates be equally capable?
Similarly
ambivalent was Cicero's attitude towards Stoic doctrine of gods. He
did find appealing the idea of gods governing the world and taking
care of human affairs. Yet, he found some severe inconsistencies in
the Stoic teachings, arising mostly from their attempt, on the one
hand, to base their notions of gods in clear reasoning, and on the
other hand, to accommodate common notions of divinities. Even this
dual attempt itself seems rather suspect in Cicero's eyes, since to
rely on the ideas of common people e.g. in matters of divine
existence appears so unphilosophical. Furthermore, to allow at least
some gods of tradition into a philosophical system opens up a can of
worms. Where to stop? Why accept only these gods and not all of those
lesser demons? And why just Greek and Latin gods and not also gods of
other people? In addition, as Greco-Roman religion had no accepted
consensus on the different origin stories and genealogies of the
gods, one could not form a consistent pantheon around them.
Even if
Stoics would disentangle their view of gods from the common
conceptions, it would face grave difficulties. Stoics thought that
the ultimate god must be the whole world itself, since there can not
be anything greater than world – world must, for instance, live and
think, because it contains parts that live and think. Yet, Cicero
noted, this type of reasoning is just false. A city or a nation is
clearly greater than the individuals that constitute it, but still we
do not admit that cities or nations would live or think. Cicero also
noted that how hard it was to believe that this Stoic world god
controlled all its parts perfectly and that it had arranged all the
parts of the world and even human affairs as well as it could be.
World god had given reason to humans, but these then went on to use
it for all sorts of evil deeds – why not make humans good at the
same time?
Cicero was
particularly critical of the Stoic acceptance of divination. Firstly,
Cicero thought that divination was either impossible or futile.
Either there are things that happen by chance and then divination
cannot happen, or then all events occur with utmost necessity and
then it makes no sense to e.g. know of any future dangers, since one
cannot avoid them in any manner. Furthermore, Cicero found all
alleged instances of divination rather unconvincing. True, sometimes
diviners and fortune tellers did make correct predictions, but at
least as often they were completely wrong. One couldn't argue for
divination from the acceptance of predictions of doctors, which also
might go wrong sometimes, because doctors could rely on their
knowledge of natural processes, while diviners could not really
explain the mechanism by which the divination was supposed to work.
Indeed, one could often hear one diviner interpreting some dream or
other sign in a completely opposite way as another diviner – so
flimsy is the connection between the supposed sign from gods and its
meaning. One might even ask if it is unbecoming to gods to present
their messages so unclearly.
In fact,
Cicero was rather skeptical of the whole Stoic notion of an
unyielding fate controlling everything that happens in the world.
Clear problem such a fatalism was, because it appeared to cancel all
possibility of humans freely choosing their actions. Cicero then
suggested that one might instead accept the possibility of free
actions and hence deny outright fatalism.
Cicero did
not remain satisfied with mere criticism of famous schools of
philosophy, but also developed his own stance on how one should live,
in his last published book on duties. The first and foremost question
in Cicero's eyes is what makes human life, not just distinct from,
but also better than mere animal life. Cicero suggests rather
traditionally that it is the human desire to know things that
separates us from beasts and that should therefore be cultivated in
greatest measure.
Yet,
Cicero was no advocate of the ideal of a hermit philosopher, as we
have clearly seen in his appraisal of community life. Indeed, as
human community is based on such matters like communication, it is
something that prominently separates us from beasts. Cicero thinks
that nature has given for human beings an instinct to contact their
fellows and make bonds with them, and this instinct should be
followed – one should communicate with one's relatives, but also
with friends and generally everyone in our community. Thus, people
who shy away from communal life, because of their own interests, fail
to do what they should, and even worse are people, like Caesar, who
work actively against common interest, because of their own
ambitions.
Respect
for the communal life gives then various particular rules for people
to follow, such as: we should respect the rights of other people for
their own property, but we should also be willing to part of our own
property for the benefit of others in our community. Yet, Cicero is
not willing to give any definite rules, since in some cases we must
break rules in order to avoid greater evil, just as when we must
break a promise if obeying it would actually do more harm.
Furthermore,
even though we should try to advance the interests of our own
community, we should still also not do anything immoral against other
communities, such as starting an unprovoked war against them. Indeed,
one should show respect even to one's enemies and to one's servants
and slaves, if one is to be a truly good person, Cicero continues.
Like many
thinkers before him, Cicero considered masculine ideal of brave and
unrelenting warrior, who despises all hardships and pains, to be
worthy of following, although, again just like many previous
thinkers, he would consider it a good thing only in service of the
community. Furthermore, Cicero would note that such a courageous and
stolid attitude could be shown even at times of peace, especially in
political arena.
Search for
knowledge, acknowledgment of the importance of social relations and a
manly behaviour are for Cicero important ingredients of good human
life, but in addition, one must also show a certain finesse in
behaviour that is not easy to put in definite rules. One important
element in Cicero's ideal is self-control – one should not be
carried away by pleasures of senses or mind, whether it be wine or
good humour, and especially one should shy away from things
considered indecent by the community. Then again, this behavioural
finesse requires also a possession of a clear character that one must
follow – one must be oneself and act according to one's station in
life. Here belong questions like what it is proper for one to wear
and what kind of professions one should pursue. In these questions
the social relations are also important, since one learns these
unspoken rules of conduct by observing the behaviour of one's fellow
citizens and especially of those considered to be especially good
examples.
In
addition to the question of how one should live one's life, Cicero
also considers the question what is of benefit to a person. He
suggests that while many things do help us, like the inanimate and
animate goods of nature, it is especially other human beings who are
of use to us, especially as many of the goods of nature must be first
cultivated by humans. Of course, humans can also be of the greatest
disadvantage to one another, but this just means that we should spend
most of our time to get others co-operate with us. Indeed, in this
sense the most advantageous way of life is just the one described
above, in which one tries to live in service of one's community.
True to
this opinion, Cicero did not allow any real conflict exist between
the demands of how one should live and demands of what is truly
advantageous: he thus finally accepts the Stoic position. One must
think of one's friends, before trying to gain more wealth or power to
oneself, and one must think of one's community, before helping one's
friends. This still does not mean that one's duty would be always
straightforward. For instance, we usually must keep our promises, but
there appears to be cases where promises must be broken, such as when
someone's life depends on it – here, one duty is cancelled by a
higher duty. Cicero even notes that commitments to one's community
might be overridden, if the community at stake uses perverted means to
improve its positions, such as when it wages an unjust war against an
innocent opponent. Thus, Cicero overcomes the restricted patriotism
of a Roman gentleman and achieves a more cosmopolitan stand toward
questions of politics.
Tunnisteet:
ancient philosophy,
atomists,
Cicero,
history of philosophy,
Lucretius,
rhetoric,
Roman philosophy
lauantai 26. tammikuuta 2013
How to do things with words
The highest point in practical
investigations for Aristotle was investigating the final end of all
human endeavours that is, happiness of individuals and communities.
The final aim of such investigation was action for the sake of
action, but usually activities aim at producing something. Because
the end of these actions is something else than the action itself, a science
investigating such an action will be lower in status than the science
investigating happiness. Thus, we get a third class of sciences,
which Aristotle calls poetic.
Now, the easiest examples of such
productive activities are perhaps handicrafts: we do not pay for a
tailor to continue his activities indefinitely, but to make clothes
for us. Aristotle, like any good Greek gentleman, in all likelihood
felt that such menial activities are beneath him and thus worthy of
no interest. Still, he did study some productive activities, that is,
those to do with language.
In one sense we have already seen
Aristotle tackle one such productive science, namely, in his
methodological writings: after all, the point of scientific method is
not the method itself, but its result or science. Even more clear
example is provided by rhetoric or the investigation of how to make
eloquent and convincing speeches.
Rhetoric shares some features with
scientific methodology and even more with debating on scientific and
philosophic matters. Yet, the aim of rhetoric is not to find truth,
but to convince others that something is true. Hence, a speaker must
do something more than just spin out intricate proofs. The speaker
must, for instance, make the impression that she is a reliable and
trustworthy character. In order to do so, she must know what sort of
characters e.g. persons of different age or of different social
status have.
In addition to showing a good front to
her audience, the speaker must also use some proofs. Yet, the proofs
of a speaker must be less intricate than full scientific proofs.
Thus, a speaker often leaves some of the assumptions of her proofs
implicit, so that she will not appear a bore repeating self-evident
matters. Furthermore, a speaker must often rely on mere probabilities
and leave the search of certainty for philosophers. Finally, a
speaker cannot usually go through all possible individual cases, if
she wants to justify some general proposition, but she must be
satisfied with few paradigmatic examples.
Mere knowledge of argument forms is not
enough to set up a proof, and speaker must therefore be acquainted
with a variety of topics, depending on what she is speaking of.
Speeches were used in Aristotle's time for convincing citizens of a
community to decide on future actions in certain manner. Thus, a
speaker should know politics: she should understand what a community
and its citizens are striving for, how different communities work and
how to achieve desired ends. She should also have clear understanding
of what is possible and what is not.
Speeches could also be used to praise
or damn persons either living or dead. Because a speaker should
already have the ability to make her own character to look good, she
should have no trouble convincing people that a character of someone
else is good or bad. Furthermore, she should be able to augment or
diminish the worth of things and persons, whatever the case requires.
A third use of speeches beyond planning
for the future and praising of present persons is convincing court
officials that a certain event has or has not happened in the past,
e.g. that someone has committed a crime. Thus, speakers should know a
thing or two about motives of human beings, especially as it comes to
unjust actions, and also be acquainted with the laws in question. In
addition, some basic knowledge of how to establish past events is
required.
In addition to proving things through
their own speech, especially in courts the speakers can have
sometimes recourse to other sort of evidence. One example are
witnesses, but a good speaker must also know when to use witnesses,
how to make them look reliable and how to discredit witnesses of the
opponent.
A speaker should not just know human
character and modes of reasoning, but also human passions: that is,
how certain emotions arise and what are they targeted at. Thus, she
should be able to, for instance, make people pity a person and thus
look at him in favourable light, or on the contrary, envy and
therefore despise him.
The core of a speech should consist of
the justification of the statement to be defended. In addition to
this, usually just the statement itself is necessary, Aristotle
thinks. At least one does not need a long prologue just to awaken the
interest of the listener – usually the listener is most
apprehensive in the beginning, while the attention starts to lag only
after a while. The end of the speech might require a recapitulation
of the main points, if the justification has been long.
Aristotle also considers the style in
which the speech should be made. He is somewhat reluctant to speak of
the topic, because style is something extraneous to the matter to be
discussed. Still, the speaker must know stylistic issues, because
these affect the listeners. Even so, complex and too poetic style
should be avoided, as it just makes listeners confused.
If rhetoric is just hindered by too
ornate language, a second productive science studied by Aristotle or
poetic thrives in metaphors. Poetry is one species of activities
characterized by the desire to capture natural and social life in
presentations – nowadays we would speak of arts. Such arts use many
different media, Aristotle notes: for instance, some use musical
instruments, others painting. The medium specific for poetry is
language, which imitates events of real social life through words.
Now, poetry itself falls into different
categories. On the one hand, we can differentiate types of poetry or
literature through objects they imitate: some of them describe lives
of noble persons, such as legendary heroes, while others describe
lives of commoners and even rabble – Aristotle was apparently used
to seeing such characters only in comedies. On the other hand, we can
differentiate types according to the literary strategies used in
them. In this respect tragedies as dramatic texts are closer to
comedies than to epics, which described heroes as well as Greek
tragedies.
While Plato had disparaged poets and
denied letting them in his ideal society, Aristotle had a more
positive idea of poetry. As pieces of art poetic texts were meant to
imitate, but even imitations may have beneficial results. Indeed,
poetic works produced emotions of sympathy and thus purified human
mind from all repressed feelings.
Aristotle is interested not just to
describe poetic works, but also to find some rules how to make better
literature and especially dramas. His answer is that one should
concentrate on the most important element of dramas or the plot –
all other elements, such as character building are subservient to the
plot, and especially means for the actual theatrical production of a
play are completely superfluous in comparison. Because of the
importance of the plot, the play should be small enough so that the
spectator couldn't forget all the intricacies of the events. Thus,
good dramas should concentrate on one problematic and not use many
plot strands, unlike epics which allowed for a more variety.
The role of dramas and especially
tragedies was to purge emotions by showing events of tragic nature,
which then aroused feelings of pity toward the characters in play.
Aristotle noted that misfortunes of bad persons do not arouse pity,
because the spectator feels that bad person deserves bad luck.
Indeed, seeing bad persons get lucky is also not tragic, but an
outrage. Furthermore, when an incomparably good person faces
misfortune, we are bound to feel horrified instead of pitying him. It
is then only misfortunes of persons like or slightly more better than
us, caused by mistakes that we ourselves could have also made, which
cause most pity and thus form the most suitable topic of tragedies.
Aristotle also considered the problem
whether tragedies were of more value than epics. He admitted that the
theatrical form of tragedies appeared to hinder the true enjoyment of
their literary qualities. Yet, this is more of a question of bad
stagecraft, which concentrates on more spectacular aspects of
theater. Even tragedies merely as read fare better than epics,
Aristotle contested, because they could unravel and analyse one
incident more completely than epic, which had to use many different
plot strands to keep the reader awake. Thus, tragedies as a whole, as
pieces of literature and combined with stagecraft, are much more
dignified than epics.
Tunnisteet:
aesthetics,
ancient philosophy,
Aristotle,
poetry,
practical philosophy,
rhetoric
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