Logic: Aristotle & The Syllogisms

Aristotle (380-320 BCE) was not originally from Athens, but he traveled there to study with the great Athenian philosopher Plato.  After Plato’s death (350 BCE) Aristotle left Athens, and then was offered the position of tutor to Alexander the Great.  As Alexander went on his campaigns of conquest, Aristotle returned to Athens and founded a school like the Academy of his teacher Plato named the Lyceum.  Upon Alexander’s death, Aristotle found himself unwanted in Athens and fled, as he was not Athenian and the Athenians were not too pleased to have been conquered by Alexander in the first place.

Aristotle is often praised as the father of Logic, but as we have seen with the Indian logicians it is far more reasonable (and logical) to say that Aristotle developed theories of debate and seeking truth just as earlier thinkers from many different cultures had done.  He is also called the father of the scientific method, but this is quite unobservant of the similarities his theories have with the cosmology shared by much of the ancient world (including Egypt, India and Persia).  He was not, in fact, primarily interested in logic or debate, but rather in cosmology, particularly what we would call today psychology, physics and biology.  In Indian terms, Aristotle was more like Kanada than Gotama.  The book he was most famous for up through the middle ages in Islamic lands and Christian Europe was his On The Soul (a psychology and biology text), but this book is hard to find in print today.

There are four of his texts that concern logic and debate: the Categories, On Interpretation, Prior Analytics and Posterior Analytics.  This first lecture will cover the Categories and On Interpretation, and the second lecture will cover the Prior and Posterior Analytics.


The Categories

Starting with the Categories we notice that Aristotle believes in the power of speech.  This lines up with the Zoroastrian and Abrahamic traditions.  Order is spoken downward, from the eternal mind into the particular beings or substances of changing matter the same way that a leader issues orders to subordinates and the mind issues orders to the body and the limbs.  Thus, ‘predicated’, something being said of a subject, is a central concept.  Aristotle assumes that things have purposes according to their natures, and these purposes correspond to concepts that can be put into words.

Aristotle believes that we must observe nature and say what can be said of things, based on their similarities and differences (the same method of his teacher Plato and others).  He believes that what can be said that is necessary of the thing must be what truly is.  Thus, as example, he says that ‘animal’ can be said, can be predicated, of both man and ox, just as ‘man’ and ‘animal’ can be predicated of any human individual (male, that is).

A Genera or Genus is the family to which a thing belongs.  Today, we think of this as the concept.  This is paired with Species, the sub group of the family.  He says (80) that if you are giving an account of a particular tree, you would say more with the species of tree than you would of the genus ‘plant’.

Aristotle gives us 10 categories, which he claims are in no way composite, meaning they are completely separate categories from each other, ‘categorically separate’: Substance, quantity, quality, relation, place, time, position, state, action, and affection.  Note that we saw several of these in Kanada, and that ‘relation, place, time, position, state, and affection’ are all quite confusingly interrelated, even though Aristotle says that they are all categorically separate.
Substances ‘underlie’ everything else.  This has led some to call Aristotle a materialist, but this is not so.  He thought there were motions above (mover) , immobile matter (the moved) below, so the substances are material, the receiver of motions (like Plato’s forms).  Aristotle argues that substances simply are, while ‘white’ or ‘beautiful’ or ‘warm’ can be more or less so in a thing.

(81) “The distinctive mark of substance is that it can admit contrary qualities.  Thus, a color cannot be both white and black, nor can the same act be good and bad: this is true for any non substance, but substances can at different times be white and black…The same individual person is at one time white, at another black, at one time warm, at another cold, at one time good, at another bad.”  (Note that by “white person” Aristotle means a pale or elderly person and nothing more, certainly not race).

Thus ‘he is sitting’ can be true, then false, then true of a person.  Aristotle denies that things can possess contrary qualities (be both white and black) or be in contrary states (good and evil) at the same time.  This is a major positivist point that any skeptic, before and after Aristotle, would deny.  Heraclitus, a major opponent that Aristotle argues against, thought that things were good and bad by perspective and positioning and so things can have contrary qualities and be in contrary states at the same time.  Aristotle completely denies the possibility of this: “If, then, someone says that statements and opinions are capable of admitting contrary qualities, his contention is unsound”.  For Aristotle, a person cannot be healthy and sick at the same time, but it can be one at one time, then another at another time.  (What if you have a healthy liver, but an eye infection?  What if you then get a liver problem?)


On Interpretation

Aristotle says that we must limit our discussion to propositions, sentences true OR false exclusively.  He argues that prayers and other requests are neither true nor false because they do not guarantee whether they will be fulfilled or not.  An affirmation is a positive statement of something, a denial a negative statement.  Thus, ‘I exist’ is positive, whereas ‘I do not exist’ or ‘I doubt that I exist’ are negative.

The Square of Opposition is a central concept for the ideas that follow.  In fact, Aristotle does not mention the concept himself but medieval Europeans created the square as a way of organizing his ideas.  In the same way, Aristotle did not use algebraic notation but his syllogisms which we will focus on in the next lecture were put in symbolic forms by Muslims and Christians in the middle ages to make them simpler to digest.

A says there are universals and individuals.  This corresponds to the eternal sphere and the temporal sphere.  Universals are the forces and motions of the stars and planets above, individuals are the particular substances acted upon on and in the earth below.  We saw this before in Kanada and Gotama’s texts.  Cows is the universal group of all cows, while a particular cow is an individual.  Thus, ‘All people are pale’ and ‘No people are pale’ is a universal proposition, whereas ‘Some people are pale’ and ‘Some people are not pale’ are particular propositions.

Notice that ‘men are white’ becomes the central example used, and how this can be misperceived by later cultures.  Muslims and Christians mistook this to be speaking about themselves equally, and unfortunately Aquinas in the 1200s uses “Socrates was a white man” as a central example for teaching Aristotle’s On Interpretation.  Yes, Aquinas is thinking that he and Aristotle are “white men”, and that this refers to the European race.  Muslim logicians assumed that Aristotle was a “white” Asiatic man like themselves earlier, and Aquinas is getting his Aristotle from Persians like Al Farabi and Al Ghazali.
To come back to the subject, Aristotle tells us (and this is critical for understanding the Square of Opposition) that particular propositions can contradict each other but both be true, whereas universal propositions can not contradict each other and both be true.

Consider the four propositions, “I like all cows”, “I dislike all cows”, “I like some cows”, and “I dislike some cows”.  The first two are universal propositions, as they refer to the group of all cows, while the second two are particular propositions, as they only refer to some individual cows.  These propositions correspond to the four corners of a square.  The top is universal (All and None), the bottom is particular (Some and Some Not), the left is positive (All and Some), and the right is negative (None and Some Not).  If we want to put the four corners in an algebraic form with X and Y, they would be:  All X is Y, No X is Y, Some X is Y, Some X is not Y.

Aristotle notes that the cross corners cannot both be true, and neither can the top two corners (ALL and NONE).  Also, he argues that one or the other of the bottom must be true, but there are counter examples to this (like we saw with Nagarjuna’s neither Y or not Y).

At end of the reading, Aristotle gets himself into another problem given what he has said.  He argues that he has a problem with things that are neither y nor not y, with the example of neither good nor bad person.  Is ‘x is good’ the contradiction of ‘x is bad’ or ‘x is not good’?  If x is neither good nor bad, the first is false, the second false, but the third is true.  This is an interesting problem, as it shows two sets of contraries.  Good and bad are contraries, but they are BOTH contrary to neither good nor bad (neutral, like Swiss).  Aristotle says, strangely, that ‘not good’ is MORE REALLY FALSE than ‘bad’, the contrary quality.  This seems to reverse his position from before, where he was saying that if something is good, it can be bad at some other time, but cannot be bad, because he is now saying that it is more that it cannot be good.  He says, ‘it SEEMS more contrary’.  Aristotle has already said that prayers (also commands) are neither true nor false, as are statements about the future (‘There will be a sea-battle tomorrow’).  Are these, then, more the contradiction of truths?  Or are false statements more?  Now Aristotle seems to be saying that True means not not true, and not false is simply a byproduct, an accident, even though the duality of true and false is central to his system.

Aristotle has founded everything on two things, what is later called the PRINCIPLE OF BIVALENCE (a proposition must be either true or false, not neither true nor false) and the PRINCIPLE OF NONCONTRADICTION (a proposition must be true or false, not both).  We will see with later European thinkers that positivism tends to support these principles while skepticism denies them.


INCLUSIVE OR VS. EXCLUSIVE OR

The top and bottom of the square are a good way of introducing the concept of Exclusive OR and Inclusive OR which will become important for understanding how truth tables function for the second half of the course after the midterm.

There are two different ways that the conjunction OR can function: inclusively and exclusively.  Let us say you are at a buffet, and the sign says, “You can have eggs, toast, bacon, soup, or salad”.  At a buffet, you can have as much of any number of things as you want, so the OR in the sign is being used INCLUSIVELY here.  Now let us say someone is buying you a car, and says “You can have an A, a B or a C”.  Since you only get to have one item, the OR is being used EXCLUSIVELY by the generous person who is buying you a (single) car.  When you can have your choice of more than one, OR is used inclusively.  When you can have ONLY one choice, not more, OR is used exclusively.

Notice that the top of the Square of Opposition, the Universal and General side, functions like an exclusive OR because both “All X is Y” and “All X is not Y” cannot both be true.  If all trees are green, then it can’t be that all trees are not green and vice versa.  The bottom of the Square of Opposition, the particular and individual side, functions like an inclusive OR because both “Some X is Y” and “Some X is not Y” can’t both be false but one, the other or both can be true.  If some trees are green, it is possible that some trees are not green.

Notice also that positivist and categorical thinking (black & white) functions like the top of the square, and skeptical and relative thinking (grey between black & white) functions like the bottom of the square of opposition.  Aristotle, a positivist thinker, wants universal all or nothing truths to have necessary and certain knowledge, while skeptical thinkers (like Heraclitus from Greece who we will examine after Aristotle) want relative some and some not truths to have perspective and wisdom.


SWITCHING TERMS:

Aristotle notes that SOME and NONE can have terms switched, but not ALL.  If some X is Y, then some Y is X (ex: if some trees are green things, then some green things are trees, and if some people are secret agents, then some secret agents are people).  Likewise, if no X is Y then no Y is X (if no trees are happy, then no happy things are trees, and if no planets are friendly, then no friendly things are planets).  However, if all X is Y it is not necessarily the case that all Y is X (ex: if all humans are animals, it does not mean that all animals are humans, and if all trees can scream it does not follow that all things that can scream are trees).


DEMONSTRATION VS. DIALECTIC

Aristotle says that true science or knowledge starts from starts from first principles to deduce necessary conclusions, and he says that this originated in ancient Babylon (modern day Iraq).  While he includes consideration of some and some not, notice that nothing is known certainly about X if we only know that some X is Y or not Y.  To know something certain about X, we would have to know that all X is Y or no X is Y.

Aristotle describes the difference between DEMONSTRATION, which starts from certain principles to deduce and conclude additional certain principles (If A, B, and C, therefore D) and DIALECTIC, which argues back and forth about a thing to see which side is more certain (Is A B or not B, just like the Nyaya Form of Debate).  While his teacher Plato thought dialectic was the ultimate device for achieving certain knowledge (like Hegel, whose dialectics we will learn about in the second half of the course) Aristotle believed that demonstration is superior to dialectic even though he uses both throughout his texts.  While some have said this makes Aristotle the first scientist, he himself believes that it originated in Babylon and it is also true that scientific study and daily reasoning make constant use of both forms.


THE FOUR PERFECT FORMS OF SYLLOGISM:

Aristotle presents us with many forms of argument that can be used in debate, but he only believes that the first four require no additional conditions, outside inferences or evidence.  For this reason, Aristotle’s four “perfect” syllogisms were studied as the forms of logic up until Wittgenstein replaced them with truth tables.  Aristotle does not put it in the easiest way, so we will reorder this like the Nyaya proof to make it easier to digest and recreate by keeping the order of A-B, B-C therefore A-C.  Notice there is one for each of the four corners of the square.

BARBARA, the Positive Universal Syllogism:
If All A are B, and All B are C, then All A are C.
If all humans are animals, and all animals are alive, then all humans are alive.
In the Venn diagram form, if a circle A is entirely within a circle B, and this circle B is entirely in a third circle C, then circle A must be entirely inside circle C.

CELARENT, the Negative Universal Syllogism:
If All A are B, and No B are C, then No A are C.
If all humans are animals, and no animals are made of stone, then no humans are made of stone.
As a Venn diagram, if A is entirely within B, and no B is inside C, then no A can be inside C.

DARII, the Positive Particular Syllogism:
If Some A are B, and All B are C, then Some A are C.
If some animals are humans, and all humans are funny, then some animals are funny.
As a Venn diagram, if some A is inside B and all B is inside C then some A must be inside C.

FERIO, the Negative Particular Syllogism:
If Some A are B, and No B are C, then Some A are not C.
If some animals are humans, and no humans are reptiles, then some animals are not reptiles.
As a Venn diagram, if some A is in B and no B is in C then some of A is outside C.

Aristotle believed that you could derive pure knowledge from chaining these.  He argues in the text that since the Scythians have no vines, thus no grapes, thus no intoxication, thus no flute players.  He gives another example: If it is metal, then it will cut, Hatchets are made of metal, therefore hatchets will cut.  He argues, just like Gotama, that the eternal is uncreated and the temporal is created, and, just like Kanada, that lightning is fire that passes down into water which then rises with the fire from sun up into the clouds until it falls as rain.

In the 1600s, Sir Francis Bacon rejected the syllogism as fallible, just as Islamic scholars and scientists had before.  Aristotle’s forms thus became forms of logic but were too simple for science.  Consider that all metal things do not cut, nor do all knives, the butter knife being an example of something metal and a knife that does not cut.

Aristotle sometimes goes back on his earlier statements and gives us examples when things that are normally universal and certain can be conditional, can be different in certain situations and circumstances.  He says that it is never right to kill your father, but among the Triballi tribe, the gods sometimes demand it.  Since the gods are one’s super-parents and one’s obligations to them supersedes one’s obligations to ones parents, he says that the Triballi rightly sacrifice their fathers.  Notice that Aristotle believes that the polytheistic gods are real and that this is logical.

Interestingly Aristotle like the Nyaya provides us with defenses against syllogisms.  He says that in order to avoid having a syllogism drawn against one’s own argument, one should not let the opponent give the same term twice over.  This is an interesting place where arguing what is right blends with tactics and strategy for winning debates.  If one’s opponent argues that A is B, and B is C, therefore A is C, one should attack the twice used middle term (B that links A and C in the syllogisms) to attack the syllogism.  For example, if one’s opponent argues the war is American, what is American is good, therefore the war is good, one should argue that the war is only somewhat American or that only some of America is good because America is being used to link the war to the good.  We naturally know to do this in arguing, just like using the forms.

Funny enough, this makes Aristotle look like a skeptic, a person who argues that absolute knowledge is only some and some relative, and he calls skeptics “destroyers” and “no better than plants” in the text.  He says that we should conceal our syllogisms to prevent our opponent attacking our middle terms, which makes him sound like a sophist, someone who argues (like a lawyer) for a living and thus can’t be trusted with true science and knowledge above mere temporary, imperfect and uncertain opinions.

Logic: Aristotle Assignment

BCC Logic                                                   NAME:____________________________
Instructor: Eric Gerlach

ARISTOTLE LOGIC ASSIGNMENT

1) Recreate the Square of Opposition below.  For each corner, label each with X and Y (such as All X is Y), and then below that give an example (such as, “All cars have wheels”).  Make sure to draw the three arrows between corners that contradict, and put ‘can’t both be true’ and ‘can’t both be false’ on the two appropriate sides.










2) Describe the difference between inclusive and exclusive uses of OR.









3) Give examples (complete sentences) of a Barbara (All, All, All), Celarent (All, None, None), Darii (Some, All, Some) and Ferio (Some, None, Some Not) Syllogism.
Use new examples, not the examples from class or Aristotle. You can use the back of this sheet.

Asian Philosophy: Buddhism in India

This lecture covers Buddhism in India, including the major two traditions of Buddhism that originated in India, the Theravada and the Mahayana.  Next time, we will cover Mahayana Buddhism in Tibet, China, Korea and Japan.

The Life of the Buddha

According to the tradition and legend, Buddha, the awakened or conscious one, was the son of a king who ruled the Gotama region of Northern India, the same region and living at the same time as Gotama, founder of the Nyaya school of Logic and Debate.  When the Buddha was born, the king’s wise advisor told him that his son would be either a great king or a great holy man.  The king did not want his son to be a holy man, but rather the next king, so to control his son he hid his son away in his palace and gave him all the luxuries in the world, hiding death, disease and pain from him, surrounding him with dancing girls and servants and only healthy, happy, obedient people.  At 29, the Buddha had become bored of this, and snuck out to see the city, taking along his trusted servant.  In succession, the Buddha saw the Four Sights (an old man, a sick man, a dead man, and a holy man).  When he saw the first three, his servant each time told him that old age, disease and death are unfortunately inevitable for everyone, but when he got to the fourth, the holy man (likely a Jain or proto-Jain), his servant told him that the sage was working on the first three.

The Buddha was immediately envious of something more wonderful than he had ever possessed in the palace, and so he escaped into the jungle where he found sages practicing austerities.  The Buddha did these proto-Jain austere practices in the jungle for six years, but he found that this brought no great enlightenment and in fact brought him self-hatred.  Buddhism is famous for long periods of meditation, and this is quite like Jain austerities of standing in postures, fasting and concentration exercises, but Buddhism teaches that it is through balance and not extremes that one will be liberated.  The Buddha found Jain asceticism to be promoting of self hatred which is still attachment and duality.  In other words, the Buddha found Jainism to be ekantavada, one sided, and not in accord with the Jain principle of anekantavada, non-one-sidedness.

The Buddha left the jungle disappointed.  He decided to sit beneath a large tree, known as the Boddhi Tree (which one can go see in India today, a tree supposed to have been grown from the original in the original spot), and he vowed not  to rise until he found complete and total truth or he would give up his life.  After 49 days, at the age of 35, he realized complete enlightenment, the goal of moksha and nirvana that the Hindus and Jains also revere.  This is defined in the tradition as the total extinction of greed (raga), hate (dosa), and delusion (moha), obtainable in this life by any being through the overcoming duality and desire.  Just as Jains call their sages Tirthankaras, one who fords the stream to get to stability on the other side, the Buddha is often called the Tathagatha, the ‘Thus Come One’ or the ‘having arrived guy’.  While Hinduism and Buddhism competed against each other, they also incorporated each other: Hinduism recognizes the Buddha as an incarnation of Vishnu, while some Buddhist texts speak of the Buddha going to high heaven realms and teaching the Hindu gods, who rejoice upon being enlightened more than they apparently already were.

On a related note, Buddha is never depicted as fat in spite of how many Europeans and Americans who believe that he often is.  Gautama Siddhartha, the original Buddha, is always depicted in India, Tibet, China, Japan and South East Asia as tall and slender, particularly because when he was enlightened under the Boddhi Tree he had been practicing Jain-like austerities and fasting for some time.

The happy laughing and fat Buddha is Budai (in Chinese, Hotei in Japanese) the laughing Chan/Zen monk and good luck saint/bodhisattva who supposedly lived around 900 CE.  His name means ‘cloth sack’, and he is often depicted holding a sack, and orange, or a ball of butter up in the air.  It is said that he loves playing with children and giving them gifts and candy from his bag, just like the sort of people I was warned about by Nancy Reagan as a child in the eighties.  He appears in one Zen koan story, the sort we will concentrate on two weeks from now.  It is said that a monk approached him as he was distributing candy, and asked, “What is the meaning of Zen?”, a common koan question, and Budai dropped his bag to the ground.  The monk then asked, “How does one realize this?”, and Budai picks up his bag and wanders off.

Budai is extremely popular in Chinese culture, and it is believed that he brings good luck and fortune to lay people and shop owners.  Rubbing his belly is supposed to bring good luck, which is why the gold paint or red die on the belly of Budai statues in restaurants is often word away.  People saw Budai in the Chinatowns of Europe and America, and assumed this Buddhist monk to be the Buddha himself.  Yes, but only in the way that all of us are the original Buddha, Budai and the entire cosmos.

The Core Philosophical Teachings of Buddhism

The Four Noble Truths (or Four Truths of Nobles, or Four Ennobling Truths)

1) Existence is suffering.
2) The cause of suffering is desire.
3) There is liberation from suffering
4) The liberation is the Dharma, the Buddha’s Teaching, or the Eightfold Path

While these are supposed to be the realization of the Buddha under the Boddhi Tree, it seems strange to say that the Buddha suddenly realized that liberation is his teaching.  Sometimes it is said that the fourth is following Buddha’s teaching, but often it is said that it is following the Eightfold Path.

The Eightfold Path is similar to the Three Jewels of Jainism, which are right body, right speech and right mind.  Notice that the three correspond cosmologically to earth/desire, air/breath, and fire/thought.  The Buddha added more to the list to make eight:  right view, right intention, right speech, right action, right livelihood, right effort, right mindfulness, and right concentration.

The Five Abilities

The five abilities or faculties that are to be developed through study and practice are dedication, strength, mindfulness, concentration, and wisdom.  The final ability, wisdom, is the most prized.  Just as the lion is king of the animals, wisdom is king of the virtues and identified with the lion.  It is also symbolized by the sword or the ‘sword of wisdom’.  Some bodhisattvas such as Manjusri, bodhisattva or saint/buddha of wisdom, is often pictured holding the sword upright or above the head ready to cut off attachments and destroy the obstacles of ignorance, often personified as demons.

The Doctrine of the Middle Way

In all things, as the mind splits things into opposites and prefers one while rejecting the other, one should always practice moderation between the extremes.  As a criticism of Jainism, this means that one should balance pain and pleasure, being attached to neither, rather than chase pain and difficulty to liberate the self.  The Buddha found Jain practice to be immoderate: too much de-emphasis of self is attachment to self hate, not detachment from particular things (as self-hate is particular and bound up with particular things just as much as self-love or pride is).  One must love and hate the self, bringing the two together, to find detachment from many and complete identity in the One, the All.

Doctrine of Impermanence

The Buddha taught that all things are impermanent.  Thus, everything is constantly evolving, never the same twice.  Only the great All is eternal, the One to which we all belong, but as soon as you say this it becomes a conception, a particular being separated from other particular beings, and then is simply another temporary and limited being in your mind.  Just like Jains, Buddhists believe that because of suffering there is attachment and bondage to particular things, to ‘this versus that’, such that we come to have one-sided views of ourselves, of particular things, and of the cosmos as a whole.  The Buddhists, like the Jains, believe that one does not have a permanent self, and this constant transformation is a central cause of the fear and clinging of the mind to particular things outside of the self in order to seek stability.  However, because the things are not themselves permanent, the mind must jump from one thing to another, seeking ideal stability in each thing and then leaping to the next with the same hope, endlessly without rest unless wisdom is developed.

The Buddhists use the metaphor of the monkey mind, of a monkey leaping from branch to branch in a frenzy.  The liberation from desire is simultaneously the liberation of ignorance, a finding stability in the whole tree rather than seeking stability in any particular branch.  One can desire or thirst for an end to particular things or everything as well, but this is does not bring satisfaction either.  In another related monkey metaphor, one similar to the enchantingly racist Brer Rabbit and the Tar Baby story from Tales of Uncle Remus (which is nice in retelling African wisdom tales in the context of the American South, but plenty racist in their presentation by today’s standards), a hunter sets a trap for a monkey with pitch.  The monkey takes the bait and gets his hand stuck.  To get his hand out, he uses his other hand, then legs, then tail, getting more and more stuck in the trap as he tries to escape.  It is similar to the Chinese finger trap puzzle, where getting free means doing the opposite of trying to pull away.

Codependent Arising (Pratityasamutpada)

Another major teaching of Buddhism is the codependent arising of all things, also known as dependent origination and conditioned genesis.  All things are themselves in so far as they are interconnected to every other thing.  Opposites, such as heat and cold or self and other, do not anchor themselves or give things their meaning, but rather all things exist dependent on other things.  Not only do opposites arise codependent with each other (without good there can be no bad, and without cold there can be no heat) but each particular thing is a bundle or pile (skanda) of many things.  The self is a pile of many things, as is the meaning of a thing, the memory of a thing, or the cause of a thing.

Emptiness (Shunyata)

Buddha taught that all things are empty (shunya) of self or self-existence.  While this seems depressing or frightening to many, it should be understood more as openness, as not being closed off in the self as it first appears but being connected to and dependent on everything else.  Just like when studying Nietzsche or any decently skeptical thought, what first appears to be nihilism, belief in nothing, should rather be understood as belief in everything as a whole, as a rich abundance that means far too much to mean any specific thing in particular.  A set of talks by the Dalai Lama recently released is called Compassion in Emptiness.  He speaks about Nagarjuna, who we will study as well, and connects emptiness, openness, and compassion as the goal of Buddhist teaching and practice.  Being empty of self is not just lacking self-determination, but lacking selfishness and possessiveness.  An absence of selfishness or division of things does not mean one has nothing.  Rather one is not attached to the things one finds one has.  In an early text, the Buddha says that abiding in emptiness is abiding in fullness.

Mudras of the Buddha

We have already discussed mudras, hand positions such as the seed or essence mudra pinching of thumb and index finger together which is found in the Hindu Upanishads as well as early images and statues of the Buddha teaching that all is one without division and the essence of what deludes us and prevents us from realizing it is desire and attachment to particular things.  There are many mudras associated with the Buddha and his teachings, but there are two central mudras that form a paradoxical pair.  Buddha is often shown with his palm face down towards the earth, cutting off all desire and delusion, blocking the lower and detaching from the inferior.  Buddha is also often shown with his fingertips touching the earth, connecting with the lowest and purifying the inferior.  This is similar to dogmatic understanding which separates the true and good from the false and bad, and skeptical reason which seeks the union of the divided and oppositions into an integrated whole.  In so far as delusion is division, one should eliminate it.  In so far as division is delusion, one should integrate with it to get beyond it.

Meditation Practice

While I am not, in any way, an instructor in meditation, I have periodically practiced it based on the instructions of modern teachers and there are a few points to share with the average person who wishes to put a simplified and informal version into practice.  You can practice in the traditional lotus position or ‘sitting Indian style’ as it is sometimes called, but you can also sit straight in a chair, stand straight, stand in yoga postures, walk, or even jog according to post-eighties trendy teachers.  You can close your eyes (I would not while jogging), keep your eyes open, or, as many Zen teachers instruct, keep your eyes half open, half closed.  In the Zen tradition, there was debate about this similar to the opposing mudras just discussed.  With the eyes closed, it is easier (while not that easy) to concentrate but harder to integrate with everyday life.  One of my favorite short Buddhist stories tells of a monk who goes up to an isolated mountain top and becomes greatly enlightened, but then when he goes back down into the marketplace someone bumps into him and he is greatly angered.  With the eyes half open, it is easier to concentrate while integrated with experience of the world.  For human beings, visual experience is the most vivid and most processed in the brain.

While meditation is about clearing and calming the mind, it is very difficult if not impossible to empty the mind.  No matter how hard one tries, particularly if one is trying hard, things continue to pop into the head and take your mind away with them.  Jack Kornfield, an American meditation instructor and author, says we should watch as things rise continuously in the mind and let them fall away without following them, what he and his teachers in India call, “gazing at the waterfall”.  Other teachers, including those of early traditions, speak of holding compassion or particular images in mind.

Regardless of whether one concentrates on nothing, something in particular or whatever arises naturally, all instruct that one should also concentrate on the breath.  There are complex formulas for in and out counts for breath, as well as quick or slow inhalation versus exhalation, but the simplest is slowly breathing in with a count of four or five seconds followed by breathing out with the same count at the same speed.  You can count forward for both or count from one to five on inhaling and from five to one on exhaling.  At first it is awkward to switch from inhaling to exhaling and exhaling to inhaling while concentrating, but with practice and patience the sharp transition becomes smooth and rounded.  There have been numerous psychological and neurological studies that suggest regularly meditating in this or a similar way has mental and physical health benefits, particularly due to reduction of stress.


Schools of Buddhist Thought in India

The two largest groups of Buddhism are the Theravada and the Mahayana.  ‘Theravada’ means ‘The Way of the Elders’, the continuation of the initial orthodoxy from the time of the Buddha.  ‘Mahayana’, which  means ‘Greater Vehicle’, was a reformation in India in the first century CE that became the larger of the two schools, though there are still over 100 million practicing Theravadins.  The Mahayana call Theravada ‘Hinayana’, the ‘Lesser Vehicle’, though of course the Theravada never use this term to refer to themselves.

Today both can be found all over the world including Europe and America, but primarily Theravada is the official religion of several countries in South East Asia including Sri Lanka, Burma, Thailand, Cambodia and Laos, and Mahayana is found in many countries of East Asia including China, Mongolia, Korea, Vietnam and Japan.  Sometimes Tibetan Buddhism is considered part of Mahayana, but sometimes it is considered the third large school of Buddhism, Vajrayana, the ‘Diamond Vehicle’.  As with the terms ‘Mahayana’ and ‘Hinayana’, it is often only the Tibetans refer to themselves this way.


The Theravada Tradition

First we consider the original early tradition, the Theravada, which formed as a religion at the same time as Jainism and Hinduism were gathering and codifying their own religious traditions.  This was centered in the sangha, the community or monasteries.  To become or convert to Buddhism, traditionally one takes the three vows: “I take refuge in the Buddha, the Dharma (the Buddha’s teaching) and the Sangha (the Buddhist community or tradition of the faithful).  Sometimes monasteries were founded in remote locations to promote meditation and withdrawal from the bustle of life, but often they served as religious, educational and medical sites for local communities the same way that Christian monasteries did in the Middle East and Europe.  Both were centers for learning to write and copying texts, first by hand and then printed after block printing was invented in China.  The first block printed text is a Chinese scroll of the Diamond Sutra, printed in 878 CE and held today in the British Museum.

There are three ways one can be involved in the sangha, though the third is only vaguely involved.  First, one could be a common lay person who is educated by monks or self-educated in Buddhist teachings, meditation and devotional worship.  Buddhist monks of the Theravada tradition wander from house to house, collecting alms and food to eat.  Monks often have only two possessions, a robe and a begging bowl.  To the horror of many Jains, Buddhists will eat donations of meat, rare in most households of India not only because of diet but because it is expensive.  When challenged on this by Jains, the Buddha replies that it is perfectly alright to eat meat if it has not been killed particularly for the monk to eat.  This is similar to eating fruit after it has already fallen from the tree, but the Jains of course were not satisfied with this answer.  Much later, an emperor of China asked the Indian Buddhists for texts that prescribed vegetarianism, and when they said there was no text that made the diet a requirement, the emperor had one written up and made law for Buddhist monks of China because Daoism had already convinced Chinese culture that vegetarianism is required of great sages.

The second way one can become involved with the sangha is to quit being a lay person and join the monastery as a monk or a nun.  In one early text, Buddha uses a parable identical to one used by Jesus, the parable of sowing seeds on good and bad soil, explaining that while teachings should be shared with everyone, those monks and nuns who have committed their lives to monastic living are rich with potential to use the teachings the most.  While this did give women as well as low caste and poor individuals the opportunity to seek a better life outside of their circumstances and become educated, it is also true that nuns were still considered subordinate to monks.  Monks could instruct nuns, but nuns could not instruct monks.  The same was true of Christian monasteries in Europe, which is why nuns often teach children in schools but not adult men.  In one text, Buddha prescribes this sexist social order but when asked by Prajapati, the legendary founding Buddhist nun, how nuns should train and practice compared to monks, Buddha replies ‘as monks do’ twice, explicitly mentioning no difference.

The third way one can be involved, though not very involved, with the sangha is to become an arhat.  Remember that Jainism and Buddhism developed from individuals who were not yet bound in communities and monastic orders but were rather practicing meditation and austerities individually in the jungle.  Both Jainism and Buddhism recognize that some individuals who practice on their own are indeed sages who achieve greatness, though typically the traditions advocate joining the traditions and the community within the walls.  One can go off on one’s own, but it is often better to seek instruction and discipline within the community.  In early texts, the title arhat means little more than a buddha, but in the later tradition the term increasingly refers to individuals on their own or only marginally involved with the monastic community.

In one early text, an evil monk tries to take over the community and when the Buddha sends him away he returns and argues with Buddha in front of the sangha about how staying near the outside community and seeking alms and food will necessarily involve monks in evil so monks should dwell in the forest apart from lay people.  Buddha replies that one can go into the forest if one wants, or dwell in the community if one wants, and enlightenment can be gained either way.  The evil monk uses this as a devise to cause a schism in the sangha, a story that explains to early Buddhists both how Buddha accepts arhats as well as how early on there were competing Buddhist schools with various dogmas and interpretations.  Just before this final trick that worked, the monk had tried to kill Buddha by releasing a crazed elephant on the path where Buddha was walking, but he sooths the elephant with his unsurpassed compassion mind and strokes its pacified forehead, and the elephant cleans the dust off Buddha’s feet with his trunk, anoints his own head with the dust and wanders off, no longer a crazed but now an enlightened elephant.


The Mahayana Tradition

One of the major differences between the Theravada and Mahayana traditions is that the Theravadins believe that one can possibly become enlightened on one’s own or outside the monastery, but typically it is monks who gain enlightenment and liberation.  This meant that lay people as well as nuns were taught that they should work hard to reposition themselves such that they could be born a monk and achieve nirvana in the next rebirth or one soon to come.  The Mahayana tradition grew in reaction against this rigid formula.  Increasingly, stories and texts were circulated telling of lay people, including old women and young children, becoming enlightened without needing monastic training.  In one story, a snake/dragon (naga) princess becomes enlightened upon hearing Buddha’s teachings, but when she goes to have her enlightenment confirmed, the monks do not believe her because she is a woman and argue that it is not possible.  To refute them, she transforms into a male in front of their eyes and shoots off to a high heaven realm.  Notice that one could read this story in the community as a progressive or a conservative, as if it doesn’t matter or as if you still have to transform into a man first before total liberation.  When we read Zen koan stories in two weeks, there are many in which a mountain dwelling sage, or an old woman, or a girl with pigtails shows up a Zen master, who must acknowledge they are beaten by the understanding of an outsider.

Buddha Nature (Buddha Dhatu)

The Mahayana began teaching that, just as all particular beings are in fact one being, all conscious beings have Buddha nature and so it helps to be a monk but anyone can achieve great enlightenment no matter who they are.  Just as Jainism and Buddhism had appealed to individuals of all castes by putting enlightenment above caste duties, Mahayana Buddhism flourished and considerably outgrew the Theravada in numbers.  The Theravada tradition survived as the official religion of Sri Lanka, the island south of India, and was spread along Indian shipping trade routes of Southeast Asia along with the Ramayana and much Hindu culture.   The Mahayana thrived in central India and so it was the Mahayana tradition that spread through East Asia, through Tibet and China and then Korea and Japan.

Bodhisattvas

The final major difference between the Theravada and Mahayana traditions, one of great importance for devotional worship, is the reverence of great saints or bodhisattvas.  These are often also understood to be buddhas in their own right.  Just as Mahayana increasingly involved lay people, devotional worship came to incorporate the honoring of great saints that could bestow particular blessings or help individuals achieve states of realization.  The bodhisattvas are understood to be great individuals who could have been fully released but decided to stay involved in the world for the sake of enlightening and liberating all conscious beings.

Buddhist devotional worshipers pray, chant and give offerings such as burning incense to implore the help of their power.  The most important and popular bodhisattva is Avalokitesvara, known as Guan Yin in China, the bodhisattva of compassion.  She plays a similar role to the Virgin Mary in Catholicism, a being one can implore for kindness and mercy.  Another central bodhisattva is Maitreya, the Buddha who will come at the end of this kalpa or cycle of the cosmos to signal the end of this world and its rebirth.  Maitreya is the Buddha to come, the one who will be as great as the Buddha who came at the high noon of this kalpa to teach the true way of things.  Another popular bodhisattva is Manjusri, the bodhisattva of wisdom who is often pictured holding the sword of wisdom above his head, ready to cut off attachments and the ignorance attached.

The Perfection of Wisdom (Prajnaparamita) Sutras

The earliest and most popular Mahayana sutra texts are called ‘perfection of wisdom’ sutras.  They are short compared to much of the Buddhist texts, and are chanted in devotional worship to Buddha and the bodhisattvas.  The two most central are the Diamond Sutra or Diamond Cutter (Vajracchedika) Sutra and the Heart (Hrdaya) Sutra, which I gave you in your readings.  Notice that vajra, ‘diamond’, is taken up by the Tibetans to specifically refer to their tradition as Vajrayana or ‘Diamond Vehicle’.

These texts repeat the message that the perfection of wisdom is emptiness and compassion, not for one’s own sake exclusively but for all conscious beings.  This is the vow of the bodhisattva, but it is also the aim of the lowest practitioner.  Wisdom is, as the Buddha taught according to much earlier Theravada texts, the highest virtue, seeing beyond selfishness and identity such that one cares for the liberation of all beings.  In the introduction of a book on the comparison of Psychoanalysis with Zen (a Mahayana school) called The Couch and the Tree, the author recalls a conversation as a therapist with a Zen monk, who says, “My religion can save rocks and trees…Can your religion do that?”.

As the Mahayana draw the focus away from salvation in the monastery to salvation of the community as a whole, the Buddha and bodhisattvas are presented as superior to arhats because they teach others rather than isolate themselves, concerned with their own achievement.  Rather than abstain from the world and suffering, the goal is to overcome the world, suffering and attachment by becoming them and thereby surpassing them.  As Zen master Joshu says in one koan story we will read, “Buddha is compulsive passions, and compulsive passions are Buddha”.  Similar to how the Buddha tried austerities but found it to be an attachment to self loathing in the attempt to get rid of attachment, by seeing one’s own goal of liberation as itself delusion you gain self liberation by giving up on self liberation and helping others.

In the Diamond Sutra, after Buddha goes to collect food and alms in a large city, he is asked about the bodhisattva path at an assembly of monks.  He replies that all beings are to be liberated and enlightened, and the merit or good karma generated from this is as invaluable as the sky is immeasurable (which is also, we are told, thus no particular merit at all, which will be important for Bodhidharma, the founder of Zen).  The Buddha can see with his ‘buddha eye’, the third eye that opens in the center of the forehead as in Hinduism symbolizing union of the duality of two eyes, that there have been countless buddhas so far and this is the root of countless buddhas in the future.  He questions Subhuti, a bodhisattva himself, and Subhuti answers correctly, demonstrating his right understanding, exactly as Chan/Zen monks will do in koan stories we will examine soon.  Many of his answers consist of saying that there is a teaching, but there isn’t, there is a galaxy, but there isn’t, there are the thirty two marks that traditionally identify the Buddha, and there aren’t, and many other things that do and do not exist as they are.  We will see with Nagarjuna and the Madhyamakas that this becomes foundational for Buddhist logic.  Buddha says that the universe is like a Ganges river for every grain of sand in the Ganges river, endlessly complex, yet there is one mind that can be known that contains all of it.  In the final lines, he says that even if a bodhisattva were to give innumerable galaxies of precious gems to him as a gift, this would not have the immeasurable merit that a humble woman or man would achieve by sharing the teaching with others.

In the Heart Sutra, the bodhisattva Avalokitesvara, filled with compassion, teaches that all things are empty, including the emptiness and negation of things.  How do you like them non-apples?


Buddhist Logic

The Buddhists, who enjoyed debate on the nature of reality, took Gautama’s teachings on logic and in dialogue and debate with Jains developed skeptical arguments against Nyaya atomic truth.  Until recently, it was believed that Buddhists took these developments from the Jains who developed them earlier, but today it is understood that Buddhism was forming and developing its doctrines at the same time as Jainism was, so it is not clear whether the Buddhists got the skeptical arguments from Jains or if both Jains and Buddhists get them from earlier Jain-like thinkers who were meditating and practicing disciplines in the Jungle as the Jains do.  Like Jains, Buddhists argued that a thing can be in some part but not others, in some place but not everywhere (universal) and at some time but not all times (eternal).

Things are not grounded in singular essences or elements, but in the network of elements and particular things as a whole complex.  The Buddhists, like the Vaisheshika and Nyaya, believe that things have causes, however they do not have singular causes but rather instrumental, dominant, significant or efficient causes that catch our focus such that the infinite network of causes is obscured.  It is true that particular things cause other particular things, but not in a simple exclusive ‘A to B’ relationship.  One can understand and recognize A to B causation while also maintaining awareness of the perpetual complexity of context.

According to the Buddhist tradition of logic, there are three kinds of inference, two positive and one negative.  The positive types of inference are identity (If there is fire then there  is flame) and perception of effect (if there is smoke then there is fire).  The negative type of inference is non-perception (There is no fire if we see no fire).  Buddhist logicians, like Jains, often use the same examples the Vaisheshika and Nyaya use, such as ‘If there is smoke on the hill, then there is fire on the hill’ to analyze types of inference and discussing whether or not a particular inference is valid.

Buddhists believe that reason, wisdom and enlightenment can be achieved through study, reflection and meditation.  Study is taking knowledge in, reflection is critical reasoning about the knowledge one has taken in, and meditation is practicing stillness and calm.  While most Indian schools of thought teach that study and reflection are paths to enlightenment and greater perspective, Buddhists emphasize the necessity of practicing meditation over long periods of time.


Nagarjuna

Nagarjuna (150-250 CE) is the central and most famous logician of Buddhism and, from a non-eurocentric view, one of the greatest logicians in all of human history.   He was likely the abbot of a Mahayana monastery where he wrote textbooks for monks on logic, meditation and compassion for all beings.  He is considered the founder of the Madhyamaka school of Mahayana Buddhism.  Nagarjuna’s work was important for many Chinese and Japanese schools of Buddhism.  Tibetan Buddhists, who wrote many commentaries on his work.  The Dalai Lama today teaches Nagarjuna to large audiences.

The Madhyamaka or ‘Middling’ school develops in response to other competing Buddhist schools of the time by attempting to get back to the fundamental concept of the middle way, the non-one-endedness that the Buddha found but not enough of in Jain practice.  To show that all things are interdependent, Nagarjuna and the Madhyamaka school argues that all things, in so far as they can mean and thus be particular things for us, are mental constructs that can always be opposed by their opposites.  In this way, Nagarjuna’s four things or modes are very similar to the Jain dogma of seven perspectives that are simultaneously true of each and every thing.

Nagarjuna attacks positions of other schools and debaters by showing contradictions that undo their position and conception.  If a position contradicts itself, it is not self sufficient but dependent on its opposite within its very self.  For example, if the ultimate truth is that there is no predominant ultimate truth, the ultimate truth is simultaneously its opposite.  To rephrase, if the meaning of life is that we can find all sorts of meaning in life, then the singular meaning of life is, at least to a decent degree, that there is no singular meaning of life.  This does not make life devoid of truth or meaning, but rather shows how fruitful truth and meaning can be.  As another example, if benefiting the self requires benefiting others, then true self-interest and self-investment is interest and investment in others.

Against Nagarjuna and the Madhyamaka school arose the Yogachara school who argued that the Madhyamakas were nihilists who did not understand the Buddha’s teachings about the essence of all things.  If everything is a mental construct, they argued, then what are mental constructs ultimately made out of?  They argued that there is mind, which is what mental constructs are made out of, and so their school is known as the ‘Mind Only’ school.  One could say this is simply rephrasing the Madhyamaka position that all things are mental constructs, but the Yogachara are arguing that all is Mind, one thing, and this itself is not a mental construct.  When mental constructs are cleared away, there is revealed the mind that is in all things.  Of course, many would call this nihilism as well.

Many of Nagarjuna’s  works attack the Nyaya school as well as competing schools such as the Yogacharans.  Like the Jains, Nagarjuna believed that the Nyaya were right about their views but they did not understand that viewpoints and descriptions can complement each other as opposites.  While Buddhists believe in classifying types of things in the world and mind, and teach these lists of categories as catechism, they believe in seeing things as temporary, dependent on other things, and lacking self-stability and self-determination.  Like the Nyaya and other Buddhist debaters, Nagarjuna typically argues for a proposition supported by both reason and analogy while pointing out fallacies in the argument of his opponents.

In one debate, his opponent argues that if Nagarjuna believes everything is empty, then his words and argument must be empty.  Nagarjuna replies that his words are, like all things, relatively empty, but this does not mean they are not relatively true and meaningful at the same time.  Nagarjuna’s opponent argues that if Nagarjuna believes that everything can be negated, then so can his argument.  Nagarjuna replies that he can negate his own argument, but he can also put it forward at the same time.  What will these words I use now mean in five years or 3000 years?  If we do not know this makes them quite meaningless to us sitting here today as far as we know, but does this make them quite meaningless here and now?

Buddhists believe in teaching particular things, but acknowledge that sometimes we need to hear a particular truth and be lead in a particular way, and other times we need its opposite.  Just like Jains believe, a teacher who knows there are many sides to truth is wiser at teaching particular things as true.  If a truth is quite true, this is dependent upon and interactive with the opposite truth being quite false but still in some ways true.  Nagarjuna taught that all Buddhist concepts are only valid for actual practice and not abstractly in theory, much like American pragmatism and John Stuart Mill’s Utilitarianism.  Like Wittgenstein in his later thought, Nagarjuna taught that things do not have singular essences, but arise out of the complex whole.  He argued this against other Buddhist schools of his time who taught that the essence of the self is non-existence as opposed to existence, that time is the essence of things, anger is the essence of duality, that compassion is the essence of practice, and matter is the essence of form.

Nagarjuna is a firm supporter of pratityasamutpada and Jain anekantavada, non-one-endedness.  This is displayed well in his Catuskoti (also called the Tetralemma, both meaning, ‘The Four Things’) show us another modal understanding of viewpoint and description that complements the Jain seven view understanding already discussed.  This is best symbolized as a cross or an X that cuts a space into four quadrants of is, is not , is and is not, and neither is nor is not.  This last case may be hard to understand at first, but if consider that the absolutist principle and strategy called the ‘principle of non-contradiction’ denies that something can be and not be at the same time.  Another different example is that the image of a fire on a television is not hot like a fire, but neither is it cold because it is not hot.  Rather, the image of a fire is neither hot nor cold in itself unless one has left the television on for far too long.  Another example of this type is an actor playing a villain is not bad because he does evil, but neither is he good because he is not evil as he appears.  The actor may be acting well or poorly regardless of what the role requires.

As a final example of the Catuskoti, one that fits well with the previous examples of Nagarjuna’s thought, consider that being, reality, is, is not, is and is not, and neither is nor is not.  If there are presences and absences, then being is (as plenty of things), being is not (as plenty of spaces), and so being both is and is not (together) and being neither is nor is not (exclusively, as it is both).