Deck 17: Axiom Systems

Question 1

True or False

-There are complete and consistent axiom systems for both sentential and predicate logic.

Answer 1

True

Question 2

True or False

-There is a complete and consistent axiom system for arithmetic.

Answer 2

False

Question 3

True or False

-It is possible to construct an inconsistent axiom system for arithmetic in which all truths of arithmetic would be derivable.

Answer 3

True

Question 4

True or False

-There are decision procedures both for sentential and predicate logic.

Question 5

True or False

-Truth table analysis constitutes a decision procedure for sentential logic.

Question 6

True or False

-There can be no decision procedure for any consistent formulation of arithmetic.

Question 7

True or False

-An axiom system for predicate logic is complete if either every well-formed formula or its negation is derivable as a theorem.

Question 8

True or False

-An axiom system for arithmetic is complete if either every well-formed formula or its negation is derivable as a theorem.

Question 9

Theory
-If an axiom system is not complete, can we say whether it is consistent? (Defend your answer.)

Question 10

Theory
-Can we say that an axiom system for predicate logic is complete if every formula or its negation is derivable as a theorem? If so, why? If not, why not?

Question 11

Theory
-a. Roughly, how does one prove that a given consistent axiom system is consistent?
b. Roughly, how does one prove that a given inconsistent axiom system is inconsistent?