The term “Hogarthian diver” generally refers to a minimalist diving style devised William Hogarth Main who believed, essentially, that if a piece of equipment isn’t needed, it’s a liability. It’s not simply the practice of diving with as little as possible, however, which sets apart the Hogarthian diver. (Indeed, if you look at some of their
gear set-ups, you’ll quickly see that Hogarthians are rarely accused of carrying very little.) Instead, the Hogarthian style strives to
“eliminate the unnecessary while configuring the necessary in the most streamlined manner possible.” Arguably, for the Hogarthian diver -- who are typically cave divers -- the means are an end unto themselves. For an excellent, articulate elaboration of the Hogarthian system, check out Jarrod Jablonski’s treatment of the practice.
If you’re interested in learning a bit more about Hogarthian diving, I found a fairly regimented list of “acceptable” Hogarthian rules. Moreover, the Woodville Karst Plain Project is widely considered to be the strictest adherents to Hogarth’s system. They’ve got plenty of images and suggestions for Hogarthian rigs for the curious.