Tuesday, March 30, 2010

Logic Lecture March 29: Islamic and Early European Logic

BCC Logic
Eric Gerlach


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 no good comprehensive books about Islam published in the US, so books from the 50s and 60s are republished and taught (I have found this is true of 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 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 religion, literature, philosophy, or science.

Islamic civilization was the world’s great 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 multi-cultural, scientific, and philosophical culture before Europe and it gave Europe an astonishing amount of technology and study. In spite of this, most scholars remain entirely ignorant as we rarely look outside of ancient Greek or Roman history to find influences on 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 always been portrayed in a negative light as warlike and despotic.

Here are some awesome ahadith, sayings of the prophet Mohammed, the second source of Islam after the Koran:

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.

Algebra is possibly the most used device (if it can be called a device) in human history. It is important to consider algebra because in the second half of the course logic becomes an algebraic language (remember, logic used to be about debate in the ancient world, but it gradually became a highly specialized form of math that was intended to ground the foundations of mathematics). 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 and began doing math in the form of equations we are all familiar with today (taught by law to everyone up through college).

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 town with the latest things and systems of thought (books come this way too from China). Castles are Questles, the Persian word for fort. Medieval dress and decoration are not modeled on Roman but rather Islamic Persian 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.

While it is not central to the study of logic, it is important today to mention 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. Nestorians and Jews fled to Islamic lands from European persecutions. Islam thus thrived as a multicultural and ‘cosmopolitan’ society. It would be centuries before Europe passed them.

Central to logic, it was with Islamic mathematics, philosophy, logic and science that equations became the language for structures. The ancient Greeks such as Euclid and Aristotle talked out problems in paragraph form. Today, many scholars use algebraic logic to explain ancient Greek ideas but is quite anachronistic and misleading to do this.

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 philosopher/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.

Algebraic equations allowed for modern 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? Positivists say that the world is truly mathematical and provides us with true knowledge, while skeptics say that mathematics builds models and remains human perspective and opinion. To see an interesting problem, consider the “proof that one equals two” (found easily online).


Islam has a long history of debate, called “Qiyas” (translated most often as reasoning or argument). There were three types: Analogy, Induction and Deduction. A big issue for Islamic philosophy was which of these was primary, and which secondary. Ibn Hazm said Inductive is the only one, the others 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)
Pioneer of Islamic sciences, cryptography and the experimental method,
introduced Indian numerals and base ten system to Islam, where it was developed into Algebra. Wrote numerous medical treatises (including the memorable Treatise on Diseases caused by Phlegm). Unlike Galileo and Newton, who came much later, but like Einstein, argued that time and space were relative, as all things save Being or God are relative, subjective, and contingent. Avicenna took up this position powerfully later.
Argued that Islam and Philosophy/Logic are completely compatible. Our scholarship says that he mostly merged Neoplatonism and Aristotle, but he also incorporated Zoroastrianism and Indian/Buddhist 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)
Little is known about Farabi’s origins or ethnic background. It is argued by scholars that he was Turkish or Persian. Farabi took the Aristotelian tradition of Alexandria, Egypt and expanded beyond. Maimonides famously said he could not understand Aristotle at all until he read Al-Farabi’s commentary, and then got it. Paid much attention to Imagination, as this is central to science, philosophy and religious prophecy. He argued that if you learn and get right, you have visions of the cosmos and its workings. This is close to Wittgenstein’s thought experiments in his later thought.

Avicenna or Ibn Sina (980-1037)
Foremost doctor of his time. 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, neuropsychiatry (hallucinations, insomnia, mania, dementia, epilepsy), and the syndrome, as well as hypothesizing microscopic organisms as the cause of disease. The first to correctly show the workings of the eye. He learned Indian Arithmetic from and Indian grocer. This is ignored in most. 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’.

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. Today, in the wake of Islamic and European civilization, we understand universals to be concepts and mental rather than physical. Do our theories exist in the real world, or in our heads? This was the big issue. Avicenna asks: Does a unicorn exist? Does it exist in your head as one thing, the same way that a real horse is one thing? Does the horseness of the unicorn exist? Is it more or less real than the horseness of a real horse? Avicenna says that all are things (single beings) equally, but only the horse is real, while the unicorn and the universal ‘horseness’ are both mental. Avicenna uses the phoenix and unicorn as imaginary beasts to illustrate.

His floating man thought experiment, showing self-consciousness, shows imagination.
This is considered by some to be a source of Descartes’ ‘I think’ with demon.

After this, there was a split in his followers: which is primary, the essence or existence?
Essentialism (What it is 1st, the thing second) vs. Existentialism (thing first, what 2nd).

MOST IMPORTANT for this class: he pioneered propositional calculus, the medium of logic from here on out in this class (in most logic classes it is the only thing taught).

Al Ghazali (1058-1111), Persian
One of the most celebrated scholars of Sufism. A pioneer of skepticism and doubt.
His work ‘The Incoherence of the Philosophers’ criticized Kindi, Farabi and Avicenna as thinking too much of arriving at certain human knowledge. When he says ‘The philosophers say’ I have read authors say, ‘this means Plato and Aristotle’, but I trust the scholars who say he means ‘Avicenna says’ as the position he always attacks. 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 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) Cordoba, Spain
Wrote commentaries on all of Aristotle’s works, thus central for Europe Aristotle.
Wrote ‘The Incoherence of the Incoherence’, arguing against Ghazali and for Farabi etc.
He was another central author in Europe for science and philosophy. He turned back to Aristotle from Avicenna, and Europe followed him. He is credited more than anyone with turning Europe on to Aristotle. Our science is now more like Avicenna, but for the longest time it was Aristotleian thanks to Averroes. It was only with Sir Francis Bacon in the 1600s declaring the syllogism as necessary to be flawed that Europe swung back into a ‘all is contingent’ Avicenna direction.


Aquinas (1225-1274)
Lived just after Averroes, about 200 years after Avicenna.
Augustine is the bringer of Plato and Aristotle into medieval Europe thanks to his reading of Islamic authors. He studied at the University of Naples until he was 16. Showed he was brilliant, so 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. His brother’s brought him a prostitute, but ‘he drove her away’. Then the Pope intervened, and he went back to being a Dominican.

He seems influenced primarily by Al Ghazali and Averroes, both of whom we said were critics of Avicenna, Averroes a supporter of Aristotle. Three years after his death, Aquinas was excommunicated for heresy due to following Averroes’ interpretation of Aristotle’s works, but then 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 he was pronounced the central thinker of the Church (and thus Europe).

As an Averroist Aristotelian, Aquinas believed that universals are real beings that are even more real than physical objects. Thus, he is an essentialist. 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 European thought, Being is essence of essences (we will see this in Hegel next week). The Superman argument is often used today in philosophy classrooms to shoot this down, along with Descartes who follows Aquinas’ argument for highest, most necessary being as God.

William of Ockham (1288-1348)
An Avicenna style Existentialist: Only objects and individuals are real, all else is mental construction and conception. Often called the first modern thinker, we can see that he is putting forward Avicenna’s ideas. His nominalism says that concepts are just our names for things, our add-ons. Just like Avicenna, only Being (God) is not contingent and custom.

Ockham is also known for ‘Ockham’s razor’: the simplest explanation is often correct.
Notice how this does away with hierarchies of universals as real, to call them simply mental and thus the simplest reasoning is the best.