80-110 The Nature of Mathematical Reasoning

Thursday, March 22, 2001

Quiz 7

    Name: _______________________________

  1. Every syllogism was given a particular name to identify it. Give an example of such a name that was given to a syllogism.

  2. Barbara. (Lecture).

  3. What is the biggest drawback of Aristotle's theory of syllogisms?

  4. It is not expressively complete. There are many valid inferences that cannot be expressed using syllogisms. (Lecture).

  5. What is the arity of a predicate?

  6. The arity of a predicate is the number of terms that it applies to, e.g., mother(x,y) has arity two. (Lecture).

  7. What is the difference between a sentence and a term?

  8. A sentence can be true or false, a term refers to an object. (Lecture).

  9. Is (1+1+1) a term in the first order language of arithmetic?

  10. No. ((1+1)+1) or (1+(1+1)) would be terms, since they are built up from the recursive rules for terms. (Lecture).