# Questions (1)

Here are questions that you might help you to prepare for the midterm exam.

Try first to answer the questions by yourself, before you look at the answers !

Questions regarding the second half of the course are here.

1. What did the Egyptians use to construct a right angle?
2. Describe in a sentence the relation between Pythagoras and the Pytagorean theorem.
3. Who is the "first philosopher"?
4. What is the explanation for the fact that Chinese children can in average recite longer series of numbers than American children of the same age?
5. Say when the last ice age was, and why was it mentioned in class.
6. When are two lengths commensurable?
7. What is so special about 60 that it has become the base of many number systems?
8. When is an argument deductively valid?
9. What is an inductive argument?
10. What is the general structure of an argument of the form of modus ponens?
11. When is a judgment objective (within a certain community)?
12. What is a formal argument?
13. What is the structure of an argument of the form reductio ad absurdum?
14. If you know that the premises of an argument are true, and the conclusion is true, what do you know about the argument? (Is is valid?)
15. Consider the following argument:
If taxes are lowered, my income rises.
My income rises.
Therefore, my taxes are lowered.
Assuming that all three statements are true, is this a valid argument? Justify your answer in one sentence.
16. What is a sound argument?
17. What entities can be true or false?
18. Name a theory (other than Geometry) that has been axiomatized.
19. When is an axiom system consistent?
20. If I say "X is valid", what does X have to be? (Statement, axiom system, proposition, argument, etc.)
21. When is an axiom independent of other axioms?
22. Is the axiom system consisting of Euclid's first four axioms and the negation of his fifth axiom consistent?
23. In what century where the axioms for arithmetic formulated?
24. In Tarski's World, can an object have more than one name? How about in our (the actual, real) world?
25. State the three axioms of probability theory.
26. State either the definition of Conditional Probability or Bayes' Theorem.
27. Assume you woke up this morning and had no idea whatsoever about what day of the week it was. It could be any of { Mon, Tue, Wed, Thu, Fri, Sat, Sun }. If P(Thu) stands for "the probability that today is Thursday", what is the value of P(Thu)?
28. Let 80-110 stand for "there's 80-110 lecture today". What is the value of P( Thu | 80-110 )?