Monday, February 22, 2010

Logic Lecture Feb 24: Aristotle, the Categories and On Interpretation

BCC Logic
Eric Gerlach

First Lecture on Aristotle: The Categories and On Interpretation

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. 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.