Reshaping the religion

Until now, almost no mention of religion has been necessary. True, I have described some philosophers as dealing with essentially religious themes, and some religious topics, like the question of divinities, have cropped up regularly. Yet, only now does religion truly start to interact with philosophy. But what then is religion and how did religions and especially religious texts come about?

This will not be a proper historical or anthropological study of actual religious developments, but more like a rough general outline of certain tendencies that may be discerned in the religious life of the environment of Mediterranean. Still, from this general standpoint, we might first note it is a common practice to explain events and happenings through likely scenarios of what might have happened. Some of these scenarios are based on known facts, while others are more speculative, but the common element is that we tell a story of proceedings leading up to the fact to be explained.

Many religious texts abound with such scenarios. ”Why is this mountain called as it is? Because some of our ancestors came to this mountain in certain circumstances, which suggested then this as a proper name for the mountain.” Some of these scenarios were based on more or less reliable historical knowledge, others on mere hearsay and unreliable traditions.

We may note two important types of these scenarios. First type tried to explain certain natural phenomena, such as raining, thundering, blossoming and wilting of flowers etc. - and of course, ultimately, the final existence of the world around us. Second type, on the other hand, tried to make certain habits and customs of a society or culture more comprehensible – why do we act in such and such manner, why do we celebrate certain days of the year etc.?

Almost no human culture has lived in a splendid isolation, thus, it has been quite natural that some of these scenarios or their aspects have traversed from one culture to another. One might have just switched the names of the characters to fit their own store of scenarios. Thus, life stories of certain mythical and even historical persons became confused with all types of stories.

Before these scenarios were put to writing, they were obviously quite modifiable, and one tribe might have quite a bit of variation in their scenarios, when compared to a neighboring tribe. Indeed, when these scenarios were transferred from oral tradition to written form, the writers were forced to make compromises between various relevant versions of these scenarios.

It was also quite common that under new circumstances old scenarios were reinterpreted. If a nation congratulated itself as a chosen nation in its days of glory, a fall of that nation might have required an emendation that the nation was punished because of its bad behaviour. Practices that once were held to be of greatest importance might be ridiculed by later religious innovators as mere superfluity. Layers upon layers of reinterpretation heaped up.

An important element in many of these scenarios was formed by certain human-like personalities with powers beyond human capacities – it makes little difference in this context, whether these personalities were called gods, angels, demons or something else. The main point is that these superhuman persons gave a convenient reason for explaining natural phenomena that were clearly beyond human capacities.

These superhuman persons were not just shaped like any ordinary human being. Because of their power, these persons were often considered regal – kings above kings. And just like with human kings, their whims were something that one ought to obey. Gifts were given to appease divinities or to show gratitude for their grace.

Just like with other scenarios, the scenarios about superhuman persons became layered, when cultures converged and cultural environment changed. When nations with different superhuman persons came in contact, there were different strategies for synthesising the different scenarios. The divinities of other cultures could be incorporated as new gods, unknown before contact, or they could be identified with divinities of one's own culture. In any case, list of superhuman persons would keep on developing.

Unwieldy collections of divinities would require establishing some sort of hierarchy. Different gods and spirits could be taken as having been generated from one another, in a temporal ordering. Then again the gods could also be arranged according to their power and importance in the divine hierarchy and according to their appearance in the supposed history of divinities. In best cases, these two orderings might coincide at least partially and the gods with most power would be earlier in time also – in the most extreme case, the most powerful, highest or even the only god would be the ultimate source of everything else.

In time, the superhuman persons or divinities would be used to back up moral and legal statements. If a person acted in a manner not in line with some moral or legal standards, one could always say that the divinities would punish her: immediately, in the future or even after her death. In this fashion, the divinities would once again play the role of earthly rulers, who had also a duty of upholding the laws of the nation.

The role of superhuman persons as righteous judges in some scenarios and their role as powerful beings with some mischievous whims in other scenarios were in clear contradiction. Sometimes it was easy just to assign these roles to different persons. In a religion like Zoroastrianism, we see two juxtaposed forces, a good creator god battling against a destructive spirit.

In other cases, the assignment could not be done so easily. The Israelite god Yahweh acted sometimes like a dictatorial monarch, condemning all humanity for crimes that appeared to not deserve such a great punishment, yet he was still supposed to be a standard of morality. Gnostic sects did try to use the obvious solution and separate these two roles: Yaldabaoth, insane creator of human world thought himself to be the highest god, although he was only an accidental birth of higher and more benevolent divinities. Yet, the Gnostic rereading of Genesis remained an idea of mere sects, perhaps because the Yahweh scenarios were so deeply entrenched in the Jewish culture.

What is most important from my perspective is what happens when religious scenarios come in contact with philosophical ideas. A case in point is Philo, who read Torah in light of Greek philosophy, especially Platonism and Stoicism. Philo's strategy was to downplay the elements of Torah he finds too marvelous, such as the tales of giants. He even outright denied that e.g. tower of Babel could have been actually built, because the fiery air of the upper regions of the sky would have melted it. Of course, he still accepted things we might find quite fantastic, like the idea of souls as aerial entities descending from the heavens to snatch earthly bodies. Since this was something accepted by many philosophers of the day, Philo did not think it incredible, but quite a scientific story.

Philo also de-emphasised the role of Torah as a historical account, at least in a straightforward sense. Instead, he read Torah allegorically, so that each individual story contained hidden meanings, that could be applied universally to various cases. The basic idea behind this allegorical reading was to make Torah into a philosophically respectable text.

Thus, noting the somewhat confusing fact that Torah has two distinct creation stories, Philo had an explanation ready. God must have first created something akin to Platonic world of ideas, which served as a blueprint for the later, material creation – or actually ”first” refers only to the importance of various parts of creation, since Philo thought that the scenario of creation taking place in six days cannot be a literal truth, because God creates all at once.

This paradigmatic blueprint is a somewhat peculiar feature of Philo's reading. It is not quite clear, if it was meant to refer just to the mind of God or whether it was supposed to be something distinct from the God itself. Still, Philo described it with the Stoic word Logos, and like in Stoicism, it played the role of keeping the material world well-ordered.

Just like Plato had left the creation of earthly things to lower divinities, so did Philo suggest that God used lesser spiritual beings as helpers in the mundane creation. Thus, Philo was able to explain why Torah made God sometimes refer to himself in plural. Furthermore, Philo could then assume the common idea that stars and planets were actually living beings of a higher order than humans.

God created then both an ideal human being, or an ideal of how human should live their lives, and earthly human beings, who in many ways often fell short of this ideal. The scenario of the original sin, Philo read as a universal philosophical account of what led human mind (Adam) astray: it was senses (Eve), which were often beguiled by promises of pleasure (snake).

The true crime of human mind was still not its imperfection, but its arrogant assumption of being in possession of everything in the world (exemplified by Cain), while a better course of life would be to refer all back to God (like Abel did). Even worse than self-centered Cain were ”giants” or earth-bound people, like Epicureans, who followed nothing but their low desires. A counterpart to the giants was Noah, the first inventor of real agriculture, who tilled not only with soil, but with his fellow human beings, cultivating their education. Yet, Noah was just a symbol of a well-acting person, who still lacks the proper perfection of a human being, that is, wisdom.

Story of Abraham then recounts the life of a person learning true wisdom through teaching. Abraham left behind astrological speculations, which originated in Chaldea and which support the notion that world is self-sufficient and uncreated, and moved on to Haran, which symbolises reliance on sense perception that can be used as an evidence for God's existence. His further journies then represent further travails on the road to divine wisdom and his discussions with God show how a good man should let divine truth lead him in all circumstances. When Abraham conceived a child first with Hagar, the servant, and only afterwards with Sarah, Philo understood this to be just a description of the proper order of training – we should first train ourselves with disciplines that serve philosophy and only later with wisdom itself.

While Abraham was the symbolical man who learned wisdom, his son Isaac was supposedly something even higher, a person who is by nature wise. Their difference is symbolised by Abraham receiving a new name after his education, Philo said, while Isaac is always called by the same name. Somewhat less perfect than Abraham was his grandson Jacob or Israel, who was supposed to symbolise a person who learns wisdom – not through theoretical teaching, but through practice. Below all of the three was Joseph, whose knowledge lied in the material affairs of state.

But the highest figure in the eyes of Philo was the supposed writer of Torah, Moses, who was not just the perfect statesman, but also knew the mind of God best of all human beings. Torah was for Philo a book describing rules of conduct. The story of creation in Genesis confirmed the divine origin of these rules and the legendary figures before Moses showed how these rules could be put into practice. The four other books of Torah then stated the rules explicitly, firstly, in summarised form in Decalogue, and secondly, in form of particular laws. These latter laws fell under some general law of Decalogue and often had some symbolical meaning for Philo. For instance, circumcision Philo took to be symbolical expression for cutting away excessive pleasure.

Decalogue and the other laws of Torah thus served for Philo as a general guide of good conduct. The first two commands dealt with person's relation towards God. The created world belies the existence of a creator, and although finite human beings can never hope to completely understand what God is like, they can at least think of his powers, which were for Philo essentially the Platonic ideas giving unity and beauty to the whole material universe. Thus, one should not believe people denying the existence of either God or ideas and one should also not follow anyone who multiplies the number of gods. Furthermore, one should not put any created things, whether sensible or rational, above God, because they are imperfect in comparison.

The three following commands made further demands on a person's behaviour towards God, but on a more symbolical level. Because God is the most constant thing possible, Philo explained, one should avoid swearing to do anything by his name, since such promises must be kept. Since Philo's God had created world that follows certain simple numerical relationships, he also demanded his followers to have celebrations and special occasions according to a strict numeric scheme. Many of these holidays were meant for training our intellect, thus, anyone (even servants) should not need to do any bodily work at those times. Finally, parents were to Philo a symbol of divinity among humans, since they have created life and therefore their children must respect them.

Rest of the commands concerned the behaviour of human beings, when it is not directly involved with God. One should avoid excesses of sensual pleasure, Philo said, and so justified the strict rules governing sexuality in Torah. The only true purpose of sex for Philo was procreation – otherwise sex is merely gratification of one's sensuous desires – and Philo followed this view to its logical conclusion, denying even marriage with a person who is known to be barren.

Although sensuous or material side of a human being was lower for Philo than her intellect, Philo did admit that human body is the highest pinnacle of natural world. Hence, destroying such a body or killing a human being could not be tolerated. Indeed, any attempt to harm a living human being through violence, poison or other means was strictly forbidden.

After quickly condemning thievery and describing correct court proceedings. Philo returned to his pet peeve, the sensuous desire. This time, he was especially interested of the various restrictions on eating. Philo suggested that their purpose was to diminish the pleasure one gets from eating – you shouldn't ear pork, because pork just tastes too good. This was all part of Philo's conviction that material side of our existence is not to be overindulged.

This concluded Philo's attempt to rationalise the laws of Torah. Yet, he also wanted to show that Torah agreed with traditional Greek ideals of living, embodied in Platonic notion of four primary virtues. With some of these virtues Philo had an easy task – he also thought that we should follow wise teachers who know the ways of good living and that we should control our sensuous desires. Justice or the virtue of communal living was embodied especially in the commands of Torah on appointment of the kings and their duties and rights.

Courage was a more difficult thing, because warfare between city states was not so relevant thing anymore in Philo's own lifetime, although he did have the biblical tales of warfare to follow. Thus, it was more boldness at times of peace Philo concentrated on – something Cicero did also. It was especially a certain notion of masculinity Philo was after with his idea of courage – and he was very anxious to point out that Torah forbids men to dress in women's clothing.

Yet, Philo was not quite willing to let the Greek standards of good life to rule over the guidance of Torah. While Plato had thought that respect of divinities was no independent virtue, since divinities really wanted us just to live well, Philo thought that Torah guides us toward respecting God as the most important thing, for instance, through sacrifices. Another important element by which Philo modified Greek and especially Platonic ethics was his suggestion that repentance and humility is something to be respected – if one can admit one's faults, one is at least on a way toward better life.

Furthermore, Philo suggested a quite new way to evaluate worth of person's action, namely, their gentleness in dealing with other living beings. We should treat everyone with respect, even if their condition in life belies of a low social status or even slavery, he said. Indeed, Philo had no respect for supposed nobility by birth, because good persons have had bad children and vice versa. Even animals must be respected and one should not kill or destroy them in an improper fashion.

Philo was then an example of a philosopher trying to rationalise religious texts, but he was definitely not the only one in late antiquity combining philosophy and religion. Indeed, there was one important group of philosophers interested in religions - Platonists - and an important religious group with philosophically inclined thinkers - the Christian Church Fathers.

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.