In logic, sophistry was the use of an argument that appeared to be logical on the surface, but was, in reality, untrue.
In an attempt to subvert the Prime Directive and save Sarjenka and the Dremans from certain death in 2365, Data suggested that her transmissions could be considered a call for help. Picard recognized this as sophistry, and Worf agreed, saying that the girl could not ask for help from someone she did not know. Upon hearing her cry for help over the comms, Picard changed his mind. (TNG: "Pen Pals")
In 2372, Harry Kim argued that USS Voyager should contact a Vidiian convoy to ask about Kathryn Janeway and Chakotay's unknown disease because they had not gone out of their way to locate them, but rather had happened upon them coincidentally. Tuvok denied his suggestion, saying "That bit of sophistry is not terribly persuasive, Ensign". (VOY: "Resolutions")