A commutative quantale is a complete lattice ordering \(\leq\) together with a commutative and associative binary operation \(\otimes\) that distributes over arbitrary supremums. Let \(a \multimap b\) be the supremum of those \(q\) such that \(a\otimes q\leq b\). A Girard quantale is a commutative quantale with an element \(\perp\) such that \((a \multimap \perp) \multimap \perp=a\). In a Girard quantale, \(\perp \multimap \perp\) is an identity element for \(\otimes\). This paper presents several interesting constructions of countable and finite Girard quantales, and uses them to prove that the rules of dismissed weakening and contraction are admissible for a formula in the multiplicative fragment of linear logic if and only if that formula has no propositional variables and is equivalent to the linear logical constant \(\perp\).