80-110 The Nature of Mathematical Reasoning

Tuesday, August 1 2000

Quiz 7

Name: _______________________________

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

2. A sentence is either true or false, a term refers to an object.

3. Is truth a semantic or syntactic concept?

4. We understand truth to be a relation between sentences and worlds, so it is a semantic concept.

5. Determine whether the propositional formula `A --> ( B --> A )' is a tautology or not.

6. A B | A --> ( B --> A )
--+----
T T | T
T F | T
F T | T
F F | T
Yes, it is a tautology.

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

8. The syllogism of figure 1 with `All' quantifiers is called Barbara. The other names are on page 50 of Handout #19.

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

10. It is not expressively complete, i.e., it is not general enough to represent all forms of argument. For example, neither `modus ponens', nor the proof of Euclid's first proposition can be formulated as syllogisms.