One thing that strikes me about Rabshakeh (2 Kings 18:26-35) is that he uses tactics similar to Job's three comforters (Job 3). He takes veracious statements and draws unwarranted inferences from them. His arguments are, in a word, irrelevant (another logical fallacy). Rabshakeh could have written a textbook on how not to do logic: he was a sophist, pure and simple. Furthermore, like Job's buddies, such "plausible talk" defamed the name of the only true God by misrepresenting Jehovah's purpose for Judah.
I also checked James D.G. Dunn's commentary on Colossians (NIGTC) to see if he could shed any additional light on πιθανολογία (Colossians 2:4). He observes that πιθανολογία and its cognates signify: "the persuasiveness and plausibility particularly of popular speakers" (133). However, Dunn adds that Plato makes a vital distinction between πιθανολογία and ἀπόδειξις, with the latter word being a terminus technicus in rhetoric that denotes: "a compelling conclusion drawn from accepted premises" (ibid). See Theaetetus 162E; Ethica Nicomachea 1.3.4 and Philo's De Cherubim 9.
πιθανολογία, in contrast to ἀπόδειξις ("demonstration") thus comes to mean "plausible discourse" (Rotherham), "specious arguments" (NJB) or "fine-sounding arguments" (NIV).