Form of the Midterm: First
20 – 30 multiple choice questions about the lectures (ex: Aristotle
thinks that skeptics like Heraclitus are no better than PLANTS, Kanada
believes there are 6 categories, including KARMA/action, etc). Second, 8
short answers that demonstrate your knowledge of the forms that we have
learned so far (ex: recreate the square of opposition, the forms of
syllogisms, Nyaya proof), essentially the questions from the
assignments. No essay.
Logic,
Magic and Riddles: We read in Malinowski’s Rational Mastery by Man of
His Surroundings that tribes use all of the grammatical forms and pieces
of reasoning that we all use. We saw difference of practice and
theory, constantly intertwined, in the difference between shallow water
fishing and deep sea fishing. We saw in the next article that in
baseball, the same sort of split occurs between hitting/pitching and
fielding. In wisdom tales, understanding contradiction. Logic switched
from the study of debate in early cultures to foundations of
mathematics in modern times with the rise of algebra.
Kanada:
Karma as action/energy. We saw the basic structure of IF-THEN
hypothetical statements. The Modus Tollens transformation: (If p then
q), means also (if not q then not p). Ex: If we know “If there are
clouds then there is rain”, we know “If there is no rain then there are
no clouds”.
Nyaya:
We saw the Nyaya form of the two sided debate: (X is Y) vs. (X is not
Y). We saw that there are four sources of knowledge: perception,
inference, comparison, and testimony.
Inference shows us induction leading to deduction, gathering leading to rules/principles.
The Nyaya proof: Rule, Example, Reason, Conclusion
Wherever there is smoke, there is fire, as in a kitchen.
Because there is smoke on the hill, there is fire on the hill.
Whatever is produced is not eternal, as a pot. (If p, then n, pot is both)
Because it is produced, Sound is not eternal. (Because s is p, s is n)
Note the subtle attack on the older tradition of the Vedas in the last two examples.
While
Nyaya scholars believe X is Y or not Y, exclusively, we see that Jains
think it must be some Y and some not Y, neither ALL or None. Buddhists
argue that X can in some part, sometimes and somewhere be Y but also in
other parts, other times and other places not be Y. Nagarjuna’s
Catuskoti (is, is not, is and is not, neither is nor is not)
Aristotle:
Genus and Species (ex: animal, human), substances can have contrary
qualities but only at different times, “if someone admits contrary
qualities, his contention is unsound”, skeptics are destroyers, plants.
Square of opposition, All X is Y, No X is Y, Some X is Y, Some X is not Y as four corners.
Top pair (universals) can’t both be true, bottom pair (particulars) can’t both be false.
If we know All X is Y is true, then we know two things are false: No X is Y & Some X is not Y.
If we know No X is Y, then we know All X is Y and Some X is Y are false.
If we know Some X is Y, then we know No X is Y is false.
If we know Some X is not Y, then we know All X is Y is false.
Exclusive and Inclusive OR:
Inclusive Or: X or Y and you can choose more than one.
Exclusive Or: X or Y but you can only choose one exclusively.
The Four Forms of the Perfect Syllogism:
First, the Positive Universal, ‘Barbara’:
All A are B, All B are C, therefore All A are C.
Example: If it’s a human, animal, living thing.
(Venn diagram of A within B, B within C, or partially/fully collapsed)
Second, the Negative Universal, ‘Celarent’
All A are B, No B are C, therefore No A are C.
Ex: All men are animals, No animals are stone, therefore No men are made of stone.
Third, the Positive Particular, ‘Darii’
Some A are B, All B are C, therefore Some A are C.
Ex: Some animals are humans, All humans are funny, therefore some animals are funny.
Fourth, the Negative Particular, ‘Ferio’:
Some A are B, No B are C, therefore Some A are not C.
Ex: Some animals are humans, No humans are reptiles, therefore Some animals are not reptiles.
Greek
Skepticism: Heraclitus says do not trust experts, we are all a bunch of
apes. Pyrrho argues anything against anybody, then the opposite.
Sextus Empiricus says inference can be wrong.
Chinese
Paradox: Laozi’s Wheel (positive, negative, both), Zhuangzi’s
perspective, sage’s this always has a that, Hui Shi’s left today arrived
yesterday and greater and lesser similarity and difference, Gongsun
Long’s white horse is not a horse argument and two uses of “is”.
