Thursday, December 9, 2010

Logic: Final Exam Review

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).

There will be 10 multiple choice questions (1 point each) 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 as a civilization gave European civilization very much (Math, Logic, trade, technologies) but this is quite underappreciated. Cryptography, algebraic code-breaking, is a key culture related to scientific analysis. Avicenna says that universals are mental conceptions and individual beings are primary existents, while Averroes says that universals are the true essences of things and primary over individuals.

Hegel’s major advancement was historical explanation, explaining the structures of things as arising by process over time and not immediately by type. 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 and 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. Logical structures deal with the certain and impossible, but all propositions they construct are contingent on the situation of the world. Wittgenstein introduced Truth Tables in his Tractatus. We use them to demonstrate tautologies or equivalencies between truth value equations.

Late Wittgenstein and 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 (rules leading to an infinite regress). Wittgenstein argued that we should give complex descriptions of things and resist the urge to essentialize things to a single factor or set of rules.

Truth Tables and 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.

Appeal to Authority: Ex: ‘The police chief said that those people are evil’.
Ex: ‘If you brush with whatever toothpaste, 9 out of 10 scientists we gathered into a list to look just that way think you are awesome’.

Straw Man: The ‘Straw Man’ refers to setting up a scarecrow as a fake person. One essentializes the opponent’s position in a bad way, setting up their argument or position in a way that makes it easy to knock down. This is one of the most common fallacies that people accuse each other of doing: ‘My opponent is misrepresenting my position on the issues’. If you pull particular details or properties out of an opponent’s argument to knock it down, it can lead to over-essentializing and simplifying the position to the degree that your opponent will claim that you are not adequately representing their position on the issue.

Slippery Slope: One takes a consequence of the opponent’s position and blows it out of proportion. Example: ‘Well, if you legalize drugs people will try them, see there is no consequences, and then everyone will be doing them and civilization will collapse’.
This person took the consequence of some new users and it slides all the way down the slippery slope of over-simplifying judgment to everyone becoming an addict. Another Example: ‘If you want to legalize homosexuality, then you want to legalize all sexual conduct, including pedophilia. Thus you must be evil and wrong.’

Appeal to Emotion: Many types- one for every sort of emotion or desired goal.
Advertising, of course, appeals to desires for success, for happiness, for respect and status, appealing to both the desire for the positive and fear of the negative.

Appeal to Force: Ex: If you don’t believe me, Islamic extremists will eat your baby.
Ex: If you are wrong about this, everything will unravel and society will collapse.

Appeal to Pity: Ex: ‘If we don’t do it like I say, small children will cry’.
Ex: ‘This particular country has been poor for hundreds of years, so we should totally sell them a bunch of weapons to make them feel better about themselves’.

Appeal to Ignorance: There are things about X we don’t know, so we should assume Y.
Ex: Bush head of AAS on global warming as ‘just a theory’

Red Herring: Also ‘Missing the point’, taking the argument after an issue that does not decide the original issue being argued. One type of Red Herring, certainly the most popular is the Personal Attack.

Personal Attack: When one attacks the opponent and not the opponent’s argument. This also applies to attacking the way the opponent always argues but not the argument itself. Ex: ‘You can not believe a word my opponent says, because she/he is a communist/Mormon/atheist/aquatic fowl etc.’

Fallacy of Composition and Fallacy of Division:
Wrongly attributing property of part to whole, and whole to part.
These are interlaced with the fallacies so far.

Ex of Fallacy of Composition: If water is wet, and water is 3/5ths the human, then the human being is essentially wet. If San Francisco and LA are very liberal, then California is very liberal.

Ex of Fallacy of Division: If water is wet, and water is H2O, then Hydrogen must be wet. If California is very liberal, then Fresno must be rocking liberal.