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.
3 tn For the various views on the translation of ἐμβατεύων (embateuwn), see BDAG 321 s.v. ἐμβατεύω 4. The idea in this context seems to be that the individual in question loves to talk on and on about his spiritual experiences, but in reality they are only coming out of his own sinful flesh.
4 tn Grk “by the mind of his flesh.” In the translation above, σαρκός (sarkos) is taken as an attributive genitive. The phrase could also be translated “by his sinful thoughts,” since it appears that Paul is using σάρξ (sarx, “flesh”) here in a morally negative way.