Principles of Classical Logic

Question 1

Law of non-contradiction

Answer 1

A statement cannot be both true and false at the same time (consistency of truth values)
If (P) is true, then (not P) must be false and vice versa.
Denies possibility of statement of having two opposite truth values simultaneously.
eg “The cat is on the mat” cannot be both true and false simultaneously.

Question 2

Law of Excluded Middle

Answer 2

A statement is either true or false (exhaustiveness of truth evaluation)
For any statement either it is true, or its negation is true (either true or false).
There is no middle ground/middle option.
eg “It is raining” : either it is raining, or it is not raining. There is no middle state where it is “sort of raining.”

Question 3

Principle of Bivalence

Answer 3

Every declarative statement has exactly one truth value: either true or false.
Metalogical principle - claim on the nature of truth.
eg “The Earth orbits the Sun” : is either true or false. There is no third value like “unknown” or “indeterminate”