Tuesday, December 4, 2012

Logic: Review for the Final Exam

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.