I'm also going to begin this thread by posting some additional resources and very brief remarks.
One observation that took me by surprise was that the ONLY place in the Bible where the word "philosophy" φιλοσοφία occurs is Colossians 2:8 where the author is talking about a "philosophy" luring away the Christians in Colossal:
Quote from Colossians 2:8Beware lest any man spoil you through philosophy and vain deceit, after the tradition of men, after the rudiments of the world, and not after Christ.
Troy Martin identified that "philosophy" with Cynicism:
I've seen a source saying that the "philosophy" was Gnosticism, but more research and available Gnostic texts has made this position much less likely.
This Christian professor states that it can't be determined which Greco-Roman philosophy is being referred to in Colossians 2:8:
QuotePaul does not give us enough information to identify precisely what sect or “philosophy” he is describing. There are some clues, however, that suggest that it was perhaps a syncretistic hybrid of Jewish mystical practices and popular pagan folk-belief: he mentions the observance of special days, including the Sabbath (v. 16); visionary experience and the worship of angels (v.18); submission to the “elemental spirits of the world” (v. 20);6 and abstinence (vv. 21, 23). Paul clearly is attacking a peculiar form of religious speculation, but it is impossible to identify it with any of the major schools of philosophy known to us from the Greco-Roman world. In fact, it is important to keep in mind that the Greek word philosophia (and its Latin cognate) had a variety of meanings in this period, and, depending on the context, might be translated “religion,” “speculation,” or “investigation.” (excerpt)
Meyer's NT Commentary notes a couple candidates for the philosophy of 2:8:
Quotewe are under no necessity to infer from the word φιλοσοφία a reference to Greek wisdom, as Grotius did, suggesting the Pythagorean (Clemens Alexandrinus thought of the Epicureans, and Tertullian of such philosophers as Paul had to do with at Athens).
One last general comment: The authorship of Colossians is debated by scholars with opinions about evenly split on whether it was Paul or someone else claiming to be Paul who wrote it. The scholarly phrase is "Deutero-Pauline letters" for Ephesians, Colossians, 2 Thessalonians. 1 & 2 Timothy, Titus, and Hebrews are not accepted as authentically written by Paul by any mainstream academic scholars today (and have not been for quite some time).
The 7 undisputed letters are:
Romans
1 Corinthians
2 Corinthians
Galatians
Philippians
1 Thessalonians
Philemon
I will add that the fact that the "philosophy" isn't named opens up interpretation to anyone with an agenda or preconception of what they want to see or find. Dewitt is no different in that. It's just a question of whether there's any there there.