Monday 2/17

Monday 2/17

Examination I

Today we take the first of our examinations. Please note that this examination counts the least of all five of the exams, a mere 50 points out of a total 1000 possible. So in theory it is possible to do very poorly on this exam and still do well in the class. In theory.

Also note that I'm allowing a single 4inch x 6inch handwritten note-card for the examination. To be sure, if you are spending all of your time looking up rules, you'll never be able to finish the exam. Your best bet is to work so many problems in preparation for the exam that you only once in awhile have to glance at the card to jog your memory.

I haven't written the exam as yet, but I expect it cover roughly the following topics.

  • The Turn to Naturalism
  • Socrates' Defense Against the Late Charges
  • The Early Charges Against Socrates
  • Basic Logic Concepts (Inductive vs Deductive, Strength vs Weakness, Validity vs Invalidity, Validity vs Soundness, etc.)
  • Defining PC Validity and PC Theoremhood by the Method of Truth Tables
  • Showing PC Arguments Valid by the Method of Truth Tables
  • Showing PC Theorems Necessarily True by the Method of Truth Tables
  • Defining PC Validity and PC Theoremhood by the Method of Analytic Tableaux
  • Showing PC Arguments Valid by the Method of Analytic Tableaux
  • Showing PC Theorems Necessarily True by the Method of Analytic Tableaux
  • Translating English Arguments into PC and testing for validity.

Finally, I will select essay questions from the following list. It would probably be a good idea to prepare by at least outlining the key points you would make in writing a response. Essays questions on the exam range from 1/2 to 2 pages in length, so it is important you compose answers which are concise yet explanatory. That is, you should always assume in writing an essay that your audience is not our grader or me, but some other student who, crucially, is not in the class; thus, special terminology is always explained and examples to illustrate explanations are plentiful and well-chosen.

  1. In class I suggested that the pre-socratics set us on a new and novel course of investigation about the world and our place in it by rejecting explanations which appeal to supernatural agency. Using examples from the rich history of supernatural and natural explanations, explain the differences between supernatural and natural explanations, and explain why supernatural explanations are problematic.
  2. Recall Socrates' claim that there were really two sets of charges being brought against him: The current charges by Meletus, of which he was found guilty and eventually executed, and the earlier charges, that he studies matters of the heavens and below the earth and he makes the weaker argument appear stronger and the stronger argument appear weaker. Socrates confesses that this latter charge—that he makes weak arguments appear strong and strong arguments weak—would be the most difficult of all the charges to refute. Briefly explain Socrates' dilemma in responding to the weak/strong arguments charge.
  3. In responding to the later charges, Socrates discovers that there was indeed a sense in which he truly was the wisest man of Athens, as the Oracle charged. What did Socrates discover, and how did he discover it?
  4. How does Aristotle's discovery of logic--that is, that language has truth-tropic and truth-phobic properties which can be objectively characterized--serve to defend Socrates on the early charges, albeit too late?
  5. Recall our general definition of 'validity': An argument is valid iff it is impossible for the conclusion to be false when all the premises are true. Further recall that a logic is any language on which validity has been defined. We've given two methods for determining the validity of arguments in the Propositional Calculus (PC)which also serve as definitions of validity on the language, thereby making PC a logic: Truth Tables and Analytic Tableaux. Explain how truth tables can be used to define validity on PC using the valid argument form Hypothetical Syllogism as an example. [Hint: Which rows do we circle when we complete the standard truth table for Hypothetical Syllogism, and what do they reveal?]
  6. Recall our general definition of 'validity': An argument is valid iff it is impossible for the conclusion to be false when all the premises are true. Further recall that a logic is any language on which validity has been defined. We've given two methods for determining the validity of arguments in the Propositional Calculus (PC)which also serve as definitions of validity on the language, thereby making PC a logic: Truth Tables and Analytic Tableaux. Explain how analytic tableaux can be used to define validity on PC using the valid argument form Hypothetical Syllogism as an example.. [Hint: What does it show when we succeed in killing the tree which asserts the two premises of Hypothetical Syllogism but denies the conclusion?]
  7. Using the example of DeMorgan's Theorem, explain how i) truth tables can be used to demonstrate theorems of PC and ii) analytic tableaux can be used to demonstrate theorems of PC.

That seems a whole lot more daunting than perhaps it should. Note that it all really boils down to the truth tropic properties of language. In addition to some of the above essay question, please note again that all the problems (valid arguments, theorems, and translations) will be taken directly from the handouts: you will have seen and worked all the problems on the exam in studying for the exam, provided you set out (as I think you should) to answer every question on the handouts. In lieu of answer keys, I am happy to meet to discuss any of this material (TR 11-2, FC-280--upstairs from Starbucks).

Next time we will begin examining the truth phobic properties of language. And how to identify and avoid them. Or use them, if we want to be evil.