There are several synonyms for the word "appallingness," which typically refers to a state of being extremely shocking or horrifying. Some alternatives that convey a similar sense of intensity include atrocity, horror, outrage, monstrosity, and abomination. These words all suggest a level of moral or ethical repugnance, as well as a deep emotional reaction to the events or circumstances being described. Other synonyms for "appallingness" might include disgust, revulsion, or abhorrence, each of which emphasizes a sense of visceral rejection or aversion to what is being depicted. Ultimately, the right synonym for "appallingness" will depend on the specific context in which the word is being used, as well as the nuances of the writer's intended meaning.