Tony Lumpkin serenades his fellow drinkers at the Three Pigeons pub with a song he wrote called "The Three Pigeons." A pigeon in slang, then and now, is one who is easily deceived, a fool.
One would imagine that a song about three pigeons would attack three types of foolish people, but Tony only attacks scholars and Methodist preachers. Scholars are fools, according to Tony, because they have their heads in the clouds, thinking about the classical world of Greece and Rome and not enjoying what life has to offer at a pub. They "brag of their Heathenish Gods" but are in reality pigeons or fools.
Methodists preachers (as opposed to Church of England ministers) gain Tony's scorn because of the Methodist faith's attack on drinking. Sitting in a pub, drinking ale with his friends, Tony can easily laugh at this kind of oddity.
Another form of pigeon or fool Tony does not attack is upper-class men of leisure like Hastings and Marlow, who will soon descend on the pub, having lost their way to the Hardcastle estate. Rather than sing about them as fools, Tony uses the fact of these men's presence in the pub to play them for fools, telling them that Hardcastles are far away and directing them to the "inn" that is in fact the Hardcastle manor house.
Tony plays the fool himself, but his song suggests that he is well aware of classical learning while his knowledge of Methodism indicates he knowledgeable of current news and trends.