First, we look at the rise of Islamic civilization and its relationship to medieval European civilization with regard to logic, technology, science and scholarship. This is important to know, especially today. Second, we will look at central Islamic and medieval European philosopher/logicians (especially Avicenna and Aquinas).
America is particularly bad at Islamic Scholarship, though it is hard to beat out Europe. The United States has very few scholars who have contributed to the field. Because of this, there are few good comprehensive books about Islam published in the US, so books from the 50s and 60s are republished and taught (this is true of ancient Babylon and Persia as well). Centers for Islamic or ‘Near Eastern’ Studies focus on Islamic cultures in modern times, after the rise of Europe, so there is little opportunity for the American student to study the golden age of Islamic civilization and its massive influence on European civilization. In addition, philosophy departments rarely offer courses on Islamic philosophy or logic, and few departments of any subject study Islamic literature, philosophy, or science.
Islamic civilization was the world’s most powerful and advanced civilization before European civilization rose, so it is the natural place to look for the progression and development of philosophy, technology, and culture. It was the great multi-cultural, scientific, and philosophical culture before Europe and it gave Europe an astonishing amount of education and technology. In spite of this, most scholars remain entirely ignorant as we rarely look outside of ancient Greek or Roman history to find influences on European and modern society.
There is a greater appreciation of India and China in American scholarship, one that does not acknowledge equality with Europe but which acknowledges some depth. It is a good example of what has been called the “grandfather effect”: the grandfather (China and India) has tension with the father (Islam), the father has tension with the son (Europe) but the grandfather and grandson get along great because there is no direct relationship or conflict. Because Islam has always shared a border with Europe, Islam has been portrayed in a negative light as warlike and despotic. This is not because Muslims and Middle Eastern people are illogical, violent or authoritarian compared to Christians and Western people, but because Christian Europe viewed Islam as the enemy.
Here are some excellent ahadith, sayings of the prophet Mohammed, the second source of Islam after the Koran, which compliment this one-sided view.
Go in quest of knowledge, even unto China.
It is better to teach knowledge one hour in the night than to pray straight through it.
A moment’s reflection is better than 60 years devotion.
The ink of the scholar is holier than the blood of the martyrs.
Many times after quoting lines such as these, I have been asked by students, and even some of my professors, how it is that Muslims can say such things if they also behave in such violent and authoritarian ways. The unfortunate truth is that this paradox makes Muslims our close relatives more than either the intelligence of these verses or the brutality of warfare alone. Humanity is always capable, and in each civilization openly displays, both intelligence and ignorance, both discovery and brutality. We should use the best and the worst of Islamic civilization to better understand the best and the worst of our own.
Algebra is possibly the most useful device (if it can be called a device, though it is part device and part language) in human history. It is important for us to examine algebra because in the second half of the course logic like mathematics becomes an algebraic language of equations. In the ancient world, logic was intended to reveal the foundations of debate, but with Islamic and European developments it gradually became a specialized form of mathematics that was intended to reveal the foundations of not debate but mathematics itself.
It was assumed that the practice of mathematics was grounded in a simple form, a set of rules, and logic became the attempt to simplify and clarify these rules. Debate had proved too complicated and tricky to distill, but mathematics seemed simple, elegant, and symmetrical compared to human arguments and situations. Unfortunately, as Wittgenstein came to realize in his later thought, and as Godel asserted with his two Incompleteness theorems, mathematics, like debate, is too complicated to simplify into a single coherent and thoroughly deductive set of proven rules. Debate, logic and mathematics are useful tools we can use for discovery and innovation, but we can not use them to fully prove anything, neither about the complex and chaotic situations of our world, nor about our consistent use of debate, logic, or mathematics.
Let us take the simplest and most obvious algebraic equation, “1 = 1”. We learn this in kindergarten, if not before. We can write this down, and we all can assume that it is true, but can it be proved? At first, we assume (note, assume) that because it is so obvious and useful, that there is a way of proving it to be true, but any further proof complicates the matter. “1 = 1” is as simple as things get. To prove it would be to involve additional rules and adopt a system for the purpose of proving it. This makes sense, as if we need a system to prove “1 = 1”, what will prove the system is true? We must assume elementary rules and forms, such as “1 = 1” and “x = x”, to create any system. Similarly, we must use a hammer and screwdriver because they consistently work, not because we have proved without any doubt that they are the best tools for the job. A screwdriver need not be THE perfect screwdriver, let alone an unbreakable or immortal screwdriver, as long as it is a decently effective screwdriver.
Many might say here, “OK, I can’t prove the simplest elements, but it makes NO SENSE to question the use of “1 = 1” or “x = x” as they work in our systems with no contradictions or complications. This, unfortunately, is also often assumed, but there are problems and counter examples in our use of algebraic mathematics. Take the famous example of the Proof that One Equals Two, taught to me by my algebra teacher in eighth grade. It begins with the equally simple and intuitive equation, “a = b”.
a = b We multiply both sides by a.
a^2 = a*b We subtract b squared from both sides.
a^2-b^2 = a*b-b^2 We do difference of squares from the left and factor b from the right.
(a+b)(a-b) = b(a-b) We divide both sides by ‘a - b’.
(a+b) = b We substitute a for b, as they are equal.
a+a = a We substitute 2a for a + a.
2a = a Finally, we divide by a.
2 = 1
Typically, people think that there has been some wrong use of a rule and they focus on the fourth step because it is the most complex and try to find the error. The trick, however, is in the next fifth step. The rules of algebra work well, but sometimes they do not work and additional rules need to be invented, such as the rule, “Never divide by zero”. While it seems perfectly fine to divide both sides by ‘a - b’, as it is the next move to make to simplify both sides, in this particular case, because we started with ‘a = b’, you can not divide by ‘a - b’ because if you do the rules of algebra no longer work in this case. When you divide by ‘a - b’, you are in this case deducing that two infinities equals one infinity, which is true, but the equations work as if you have deduced that a + b is equal to b, which is where two seems to become equal to one. Algebra is a fine system, but when the rules do not work new rules need to be patched onto the system.
Before algebra, much of the world used the Egyptian doubling method (including ancient Greece and Rome) to do mathematics. Unfortunately, this method could not keep track of remainders and could not take account of series and other functions critical to the growth of math, trade and mechanical technology. Islamic mathematicians and logicians (some of whom are listed below) took the Indian base 10 system, along with the Indian numerals that became our Indian-Arabic numerals we use today, and began doing math in the form of equations we are all taught by law.
Algebra allowed trade caravans to keep greater accounts of goods, as well as sophisticated forms of insurance and banking. Islamic merchants traded by caravan all the way up through Russia and Scandinavia, as coins discovered attest. In dark age Europe, Islamic culture was passing through cities and towns with the latest things and systems of thought (books and printing come this way too into Europe from China). European Castles are modeled on Islamic Questles, the Persian word for fort. Medieval dress and decoration are not modeled on Roman but rather Islamic Persian and Turkish society. Consider hospitals with many beds, dosages measured with algebra, mechanical innovations such as gears, the chain and belt drive, pistons and clocks were all passed from Islamic to European hands before Europe became wealthy and successful. Europe owes very much to Islamic mechanics and mathematics.
While it is not central to the study of logic, it should be mentioned that law and protections for a diverse population were developed the most in Islam before Europe rose and took over. A woman had the right to sue her husband for divorce, and use algebra to get a percentage of his income and wealth. Jews and Christians who were not Catholic such as Nestorians fled to Islamic lands from European persecutions. Islam thrived as a multicultural and ‘cosmopolitan’ society. It would be centuries before Europe passed them. Consider that the year 1492 was not simply the year Columbus sailed the ocean blue, but the year that Spain and Portugal were reconquered from Muslims by Christian kings, as well as the first year of the Spanish Inquisition, the infamous persecution of Jews and other groups deemed heretical by the Catholic Church. Jews went from thriving and contributing much scholarship in Islamic Spain to outright persecution and secrecy underground in a year’s time. Maimonides (1135 - 1204 CE), the most famous Jewish medieval philosopher who lived much of his life in Cordoba, Spain, wrote that he read Aristotle but could not understand him until he read Al-Farabi.
Central to logic, it was with Islamic mathematics, logic and science that equations became the language for mathematical structures. The ancient Greeks such as Euclid and Aristotle talked out problems in long spoken form. Today, many scholars use algebraic logic to explain ancient Greek ideas, but it can be quite anachronistic and misleading to do this without acknowledging Islamic contributions. For instance, the syllogisms of Aristotle seem much clearer and cleaner when presented in variables and equations of first India and then Islamic algebra.
One of the sources of algebraic science was code-breaking or cryptography (also cryptanalysis). Between questles, codes had to be sent and algebra was used to make and break these codes. As nature was studied with mathematics, the philosophers and scientists discovered that algebra is an amazing tool for CODE BREAKING NATURE. What we call “science” is still very much this today. Consider the constant of gravity as a hidden code or message to be discovered and phrased in algebraic language. Remember that in ancient cosmology, as well as medieval Islamic and European thought, the order of things was thought to be spoken downwards from the heavens. As Islamic scientists began using algebra to crack the codes of nature, they believed that they were finding the numbers that were the thoughts and speech of God. Islamic art, which makes much use of geometric patterns, reflects this too.
Algebraic equations allowed for Wittgenstein’s later truth table logic and other forms that we study as Logic today. However, equations present us with a new problem that was recognized by the central philosophers of the golden age of Islamic civilization: Is the world truly structured by equations, or are they a model in the human mind? Dogmatists and positivists say that the world is truly mathematical and we can acquire true knowledge of it, while skeptics and relativists say that mathematics is human modeling and it remains human perspective and opinion. Consider again the One Equals Two example, and how equations seem to function on their own until we find cases in which they break down.
ISLAMIC LOGIC AND THE GREAT PHILOSOPHERS:
Islam has a long history of debate, called ‘Qiyas’ (translated most often as reasoning or argument). There were three types of reasoning debated in the Islamic world: Analogy, Induction and Deduction. Notice that the Nyaya of India use all three in their proofs, and that Islamic thought and mathematics gathered much from India. A big issue for Islamic philosophy was which of these three was primary, and which secondary. Ibn Hazm said inductive is the only one, rather skeptical of deduction and analogy as misleading, arguing the other two are illusions of the mind, while Al Ghazali (Aquinas’ favorite author and source) says Analogy is first, then Deductive second. We will see more of analogy as central to analysis today with Avicenna, and near the end of the course in the later thinking of Wittgenstein.
Al Kindi (801-873) was a pioneer of Islamic sciences, cryptography and the experimental method. He was also one of the scholars that introduced Indian numerals and base ten system to Islam, where it was developed into Algebra. He wrote numerous medical treatises (including the memorable Treatise on Diseases caused by Phlegm). Unlike Galileo and Newton, who came much later, but like Einstein, he argued that time and space are relative, as all things save Being or God are relative, subjective, and contingent. Avicenna took up this position powerfully later. Modern scholarship often says that he merged Neo-platonism and Aristotle, but he also incorporated Zoroastrianism and Indian Logic. Even though Christians in Europe followed Islamic Alchemy and Astrology for centuries, he was an early voice against both, saying they were both pseudo-sciences and the best method of knowledge was strictly observation and experimentation.
Al Farabi (872-950), who was either Turkish or Persian, took the Aristotelian tradition of Alexandria, Egypt and expanded beyond. Maimonides was much indebted to his work, and read his commentaries to understand Aristotle. Farabi paid much attention to imagination, as this is central to science, philosophy and religious prophecy. He argued that if you learn and think critically, you can have greater and greater visions of the cosmos and its workings.
Avicenna or Ibn Sina (980-1037) was the foremost doctor of his time. As a boy he learned Indian Arithmetic from an Indian grocer in his neighborhood. His Cannon of Medicine was used as a text book for Europe in translation until the 1700s. His medicine was based on experimentation and clinical trials, fusing Persian, Greek, Indian and other texts together. He is credited with formulating the nature of infectious disease, randomized control trials, psychiatry (hallucinations, insomnia, mania, dementia, epilepsy), the syndrome, as well as hypothesizing that microscopic organisms are the cause of disease. He was the first to correctly show the workings of the eye. He was one of the key authors for understanding Aristotle and scientific investigation, even as he argued against Aristotle Europeans often took up his ideas as genuine fruit of Aristotle’s tradition of thought, thus ‘Aristotelian’. He was also a pioneer of equations and propositional algebra, which would be developed later by Europeans into calculus.
The focus of the selection of Avicenna I gave you was whether or not universals exist. Consider that Aristotle believed that universals are motions or forms of the eternal cosmos coming down from the stars, so the universal group ‘cows’ or ‘numbers’ is up in the sky and is embodied in substances on the earth. Islamic philosophers increasingly turned to the human mind and imagination as the source of universals, though this was highly debated. Today, we understand universals to be concepts and mental rather than physical, but it is still highly debatable. Do our theories exist in the real world, or in our heads? Does the group ‘cows’ exist primarily in the physical set of animals, or in the line we draw around several animals in our heads? This was the big issue, and it still is. Avicenna asks about unicorns and the phoenix, which he knows to be fictional animals made by the imagination out of the parts of real animals. He asks many probing questions about the reality of imagination, concepts and universals. Does a unicorn exist? Does it exist in your head as one thing, the same way that an imaginary horse does? Does the horse-ness of the unicorn exist? Is it more or less real than the horse-ness of a real horse? Avicenna says that all are things (single beings) equally, but only the horse is real and physical, while the unicorn and the universal ‘horse-ness’ are mental.
Al Ghazali (1058-1111) was Persian and one of the most celebrated scholars of Sufism, Islamic mysticism. Like Heraclitus and Pyrrho, he was skeptical of human expertise and the ability to acquire absolute knowledge. His work ‘The Incoherence of the Philosophers’ criticized Kindi, Farabi and Avicenna as thinking too much of arriving at certainty. He does say that Avicenna is beyond all doubt the most distinguished philosopher. He argued that atoms are the only true things, and all else in the world is accidental. In his ‘Alchemy of Happiness’, wrote of the negative theology of embracing the One. St. Thomas Aquinas, the great ethics teacher of Christianity, read Ghazali as his favorite and central author. Unfortunately, Aquinas is in spell check today, while Ghazali is not.
Averroes, Ibn Rushd (1126-1198) like Maimonides lived in Cordoba, Spain. he wrote commentaries on all of Aristotle’s works, and like Avicenna (notice that their two names are rendered in Latin) was central for Europe’s understanding of Aristotle. Against Ghazali, he wrote The Incoherence of the Incoherence, arguing against skepticism for the pursuit of universal knowledge. He turned back to Aristotle from Avicenna, and Europe largely followed him, arguing that universals are physical and not mental. He is credited more than anyone with turning Europe on to Aristotle. Our understanding and science is today more like Avicenna and conceives of the universal as a mental and psychological phenomena, but for the longest time it was Aristotelian thanks to Averroes. It was only with Sir Francis Bacon in the 1600s declaring the syllogism as uselessly rigid that Europe turned from Averroism.
THE GREAT MEDIEVAL EUROPEAN PHILOSOPHERS
Aquinas (1225-1274) lived just after Averroes, about 200 years after Avicenna. Augustine was the bringer of Plato back into Christian Europe, and Aquinas was the bringer of Aristotle into medieval Europe thanks to his reading of Islamic authors. He studied at the University of Naples until he was 16. Because he was brilliant, the Dominican order offered to support his scholarship. He became a Dominican, then was kidnapped by his parents who wanted him to come back home. According to the legend his brother’s brought him a prostitute, but he drove her away. Then the Pope intervened, and he went back to being a Dominican.
Aquinas was primarily influenced by Ghazali and Averroes, both of whom were critics of Avicenna. Three years after his death, Aquinas was excommunicated for heresy due to following Averroes’ interpretation of Aristotle’s works, but later the Church reversed its position. This is after Aquinas defended the Church again and again as the only source of true authority and knowledge. 50 years after his death, he was pronounced a Saint. Later, at the First Vatican Council (1868) he was pronounced the central thinker of the Catholic Church.
As an Averroist Aristotelian, Aquinas believed that universals are real beings that are even more real than physical objects. His argument for the existence of God shows this. He argues that all things are dependent on, possible because of, and less than a highest thing, which must be God, Being itself. Thus, like later European thought, Being is essence of essences (we will see this in Hegel later). Descartes follows Aquinas’ argument for a highest, most necessary being.
William of Ockham (1288-1348), unlike Aquinas, followed Avicenna and argued that only objects and individuals are real, all else is mental construction and conception. He is sometimes called the first modern thinker because of this, but Avicenna put this idea forward centuries earlier. His nominalism says that concepts are just our names for things, our labels. Just like Avicenna, he argued that only Being (God) is not contingent, not dependent on other things. Ockham is also known for ‘Ockham’s razor’: the simplest explanation is often correct. This fits with his Avicenna-like position: if how a thing works is a conception in our heads, then the simplest conception will often be the most useful.
