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
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.
MEDIEVAL EUROPEAN LOGIC
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.
