Either arithmetic and logic are both necessary or logic and geometry are both necessary. If all knowledge is experiential, then even logic is not necessary. So, not all knowledge is experiential.
-Consider assuming 'E' for indirect proof of the given argument. Which of the following
Propositions is a likely last line of the indented sequence?
A) (A $ \lor $ G) • ∼(A $ \lor $ G)
B) E • ∼E
C) L • ∼L
D) All of the above
E) Options B and C, but not option A

Question

Quizplus · Accepted Answer

Assume E for indirect proof. If all knowledge is experiential, then logic would not be necessary. However, we know that either arithmetic and logic are both necessary or logic and geometry are both necessary. Therefore, logic is necessary regardless of whether knowledge is experiential or not. This contradicts the assumption that all knowledge is experiential, so we can conclude that not all knowledge is experiential.

Option A is not a likely last line because it simply represents a contradiction and does not tie in directly with the argument. Option B and C are both valid contradictions to E, which is the assumption made for indirect proof. Therefore, option E is the best choice. Option D is not a valid choice because option A is not likely the last line.

Either Arithmetic and Logic Are Both Necessary or Logic and Geometry