Logic question, How to determine truth value of categorical statements?
August 14, 2009 - 3:12 am
When the conclusion does not seem to follow the premise, but it isn’t negated by it either, what is the truth value of the statement, Specifically for statements that involve contraposition and obversion? For example the statement:
" All non frogs are snakes"(Assume this were true) with a contraposition of "all non snakes are frogs."
Would the truth value of the new statement be true, false or undetermined?
Try a categorical claim that works:
"All non-even numbers are odd."
The contraposition:
"All non-odd numbers are even"
Given the truth of a premise, the contraposition must also be true. It’s a fact of First Order Logic.
August 14th, 2009 at 8:57 am
Try a categorical claim that works:
"All non-even numbers are odd."
The contraposition:
"All non-odd numbers are even"
Given the truth of a premise, the contraposition must also be true. It’s a fact of First Order Logic.
References :
August 14th, 2009 at 9:02 am
The contraposition is allways equivalent to the first sentence.
This means they have the same value of truth.
References :
August 14th, 2009 at 9:49 am
The new statement is true.
The original statement, "All non-frogs are snakes" is an ‘A’ statement (universal affirmative).
Contraposition gives logically equivalent results for ‘A’ and ‘O’ statements. So, if the original statement is true, the contrapositive ("All non-snakes are frogs") is also true. Both statements mean the same thing.
References :