Despite the numerous scholarly attempts to ascertain both the nature of the disease and the author’s precise definition of “healthy teaching,” the issue remains unresolved because the author’s purpose was not to draw a profile of this disease, but to warn against it. The primary focus is not the nature of the heresy, but the moral consequences of both healthy and unhealthy instruction. [Thompson, Moral Formation according to Paul, 200-1.]
The origin of this "disease" is found in those who are commonly referred to as the "opponents". The opponents of Paul/Timothy/Titus in these letters are addressed throughout the letters, but more specifically in 1 Tim 1:3-7; 1:19-20; 4:1-3, 7; 6:3-5; 6:20-21; 2 Tim 2:14-18; 2:22-26; 3:1-9; 4:3-5; Titus 1:10-16; 3:9-11. While we are not able to draw a profile of the details of the false teaching and the opponents, there are certain things that we can know about them. What follows is an engagement with the evidence and argument presented by Paul Trebilco in The Early Christians in Ephesus from Paul to Ignatius.
Trebilco, notes that “Much of what the Pastor writes about the opponents is general; in fact it seems very likely that much of the language used in a number of passages against the opponents is typical of the polemic that philosophers used against the Sophists” [Trebilco, 209-10].
The conclusion Trebilco draws from this similarity, with Towner, is that we therefore cannot be certain that the description given, for example in 2 Tim 3:2-5, actually describes said opponents because this is a standard description. Towner notes that "By and large the purpose of this catalogue was to identity the opponents as belonging to the apostates of 'the last days'" [Towner, The Goal of Our Instruction, 28].
While these conclusions are sound, I wonder if there is not more to the comparison. What if the author of these writings is using a standard critique of the Sophists in an analogous way. Perhaps the author wants the audience to realise that he is a true "philosopher" unlike the Sophists who seek to take advantage of people. Perhaps the author wishes to denounce the opposition by this very comparison, that his Philosophy is "sound" and "healthy" (using language from the Philosophers (see Malherbe, "Medical Imagery in the Pastoral Epistles"), and that his opponents teaching is a "disease" that stems from a corrupt source, and produces corrupt lives.
Perhaps these descriptions are not merely part of the standard critique, but do help us to understand the author's reasons for using this specific polemic.