1 tn BDAG 812 s.v. πιθανολογία states, “persuasive speech, art of persuasion (so Pla., Theaet. 162e) in an unfavorable sense in its only occurrence in our lit. ἐν πιθανολογίᾳ by specious arguments Col 2:4 (cp. PLips 40 III, 7 διὰ πιθανολογίας).”
2 sn Paul’s point is that even though the arguments seem to make sense (sound reasonable), they are in the end false. Paul is not here arguing against the study of philosophy or serious thinking per se, but is arguing against the uncritical adoption of a philosophy that is at odds with a proper view of Christ and the ethics of the Christian life.