The
final exam will cover the material we studied for the second half of
the course (Islam, Hegel, Modern Logic, Early and Late Wittgenstein,
truth tables and fallacies). Just like the midterm exam, There will be
multiple choice questions taken from the lectures and 18 short answer
questions (5 points each) largely taken from the weekly assignments
(primarily the truth tables and fallacies).
Islam
Islam
as a civilization gave European civilization very much (Math, Logic,
trade, technologies) but this is quite under-appreciated. Cryptography,
algebraic code-breaking, is a key culture related to scientific
analysis. Avicenna says that universals are mental conceptions, while
Averroes says that universals are the true essences of things.
Hegel
Hegel’s
major advancement was historical explanation, explaining the structures
of things as arising by process over time. Hegel’s dialectic is a
three stage process as positive, negative and synthesis. First, when
the individual or history has an idea, there is an initial stage of
positing that stands for the idea and completely opposes skepticism.
Second, there is the stage of negation, skepticism and doubting the
idea that is completely opposed to the first stage. Third and finally,
there is a synthesis between the two positions that becomes the positive
for the next cycle. In Hegel’s Logic, he attempts to trace the entire
path of consciousness up through modernity.
Russell & Mill
Like
Gautama (Nyaya Sutra), Aristotle and Averroes, Russell says we must use
induction to come up with necessary and basic principles from which we
can then deduce certain knowledge. Otherwise, we only have mere
opinion. With Frege, Russell believed that there was a inner truth
structure hidden within grammatical propositions and mathematics that
could be brought out by analysis. Russell at first believed
Wittgenstein would complete this project for him and give mathematics a
fully clarified foundation, but Wittgenstein eventually abandoned the
project to become quite like Mill. Mill, the one to whom Russell was
most opposed, believed that the meaning of a thing is its use or
positioning in situations. A thing does not have an essence besides its
use in its situation. Wittgenstein came to embrace this view in his
later thought.
Early Wittgenstein & the Tractatus
Reality
consists of atomic facts, states of affairs that are true. Thought,
expressed grammatically in language, ‘pictures’ the world, thus these
facts. These facts must be composed of several tautological structures
(p, not, and, or) that in themselves say nothing at all. If a statement
is meaningful, it must be possible and contingent, but neither certain
nor impossible. Wittgenstein introduced Truth Tables in his Tractatus.
Late Wittgenstein & the Philosophical Investigations
In
his later thought, Wittgenstein believed that the meaning of a thing
consisted in its use in language games or forms of life. He used many
thought experiments to demonstrate that meaning is not contained in
mental states or in rules of the world exclusively, but rather in the
use of the things (involving both the head and the world inseparably).
His metaphors include converting someone to ash in an oven, names as
signposts and labels, the game of catch that arises between people in a
field, rules as controls in a train cabin, and the child at the
blackboard. Wittgenstein argued that we should give complex
descriptions of things and resist the urge to explain things in terms of
a single factor or set of rules.
Truth Tables & Tautologies
For
Truth Tables, we assume BOTH the principle of Non Contradiction (p
cannot be both true and false), and the principle of the Excluded Middle
(p must be either True or False).
If
p is true, then it has T as its truth value. If it is false, it has F
as its truth value. We first used truth tables to determine the truth
values for propositions. We next used truth tables to prove
tautologies, equivalent statements that can then be used in substitution
for one another. You know you have proved a tautology right when you
have all T’s as the result. In addition, you will be asked to prove
that certain functions are NOT tautologies, which simply means you
should NOT get 4 T’s as the result.
Fallacies
You
should understand and be able to give examples of appeals to emotion
(including appeals to authority, force, pity, and ignorance), straw men,
slippery slopes, red herrings, personal attacks, and the fallacies of
composition and division.
