Ever met an antagonist?
Generally speaking, drugs are divided in agonist and antagonist molecules. Basically, the agonist triggers a biological response, while the antagonist doesn't.
Pharmacologists have always tried to explain how the biological effect is correlated with the binding of the molecule to its target. During their studies, scientists have pointed out differences among the agonists and, therefore, two subtypes of agonists were defined: partial and inverse agonists. Antagonists were subclassified too.
Partial agonists are unable to trigger the maximum response; inverse agonists, on the other hand, reduce the baseline activity of the target.
Clark was one of the first to formulate a theory that explained the aforementioned relationship: he said there is a linear dependence between responce and number of receptors occupied by the molecule (or, in other words, its concentration).
Clark's theory has been corrected, as time passed:new discoveries showed, in particular, that proteins are actually in a dynamic equilibrium between an active and an inactive form.
Consistently, an agonist(A) will bind to the active form of the receptor R (R*), while an antagonist will form an adduct with the inactive form.

Basal activity will be due to the number of receptors normally in the active form.
Let's go back to the definition of inverse agonist, now. We said these molecules bind to the receptor and REDUCE its basal activity.
Since the chances of a response are tightly linked to the active form, inverse agonists have an extremely higher affinity for the inactive form R, rather than R*.
Inverse agonists will bind to R, reducing the number of active receptor.
To sum up, agonists move the equilibrium to R*, inverse agonists to R.
According to its definition, an antagonist will not reduce the basal activity: it'll solely NOT trigger any additional biological effect, but it will leave unaltered the basal activity of the protein.
We should therefore consider our antagonist as the fulcrum of a balance, on whose plates agonism (hence, R*, in order to trigger the biological respose) and inverse agonism (hence, R, in order to decrease the baseline response) were placed.

This can lead to the conclusion that antagonism doesn't REALLY exist, but is a mere pharmacologic, theoretical artifact, with no correspondence in a real biological system.
Your post is really interesting. I suggest you to read: Efficacy as a vector: the relative prevalence and paucity of inverse agonism.Kenakin T.
Mol Pharmacol. 2004 Jan;65(1):2-11.
It is an intriguing article that that shows that the 85% of the ligands former known as antagonists actually are inverse agonists. Thermomodynamic supports that observation, since it is really unlikely that a ligand binds to its receptor without making any change. In fact, I think the relevant question is the mechanism by wich such ligands exert their effects. It can be theoretically predicted several means by which inverse agonists decreases basal responses, with very large implications to receptor theory and clincal practices. If you like we can discuss this topic thoroughly.