Answer
Valid. The major and minor premises are diagrammed. There is only one way to compose the diagrams which is also diagrammed. Given true premises, the conclusion is always true. Hence the argument is valid.
Work Step by Step
Alternatively, the argument is true by universal modus tollens. The statement, "Nothing intelligible ever puzzles me" can be rewritten as: "$\forall x$, x is intelligible, then x does not puzzle me."
Universal modus tollens: $\forall x, $ if $P(x)$ then $Q(x)$.
~$Q(a)$ for a particular $a$.
~$\therefore P(a)$.
In this case P(x) is: x is intelligible.
Q(x) is: x does not puzzle me.
a is logic.
~Q(a), $\therefore$ ~P(a) is: Logic puzzles me, $\therefore$ logic is unintelligible.
