The philosophy being spoken of was the false teachings of pagan religions like the Gnostics.
The philosophy spoken of concerned traditions of men. Why do you say pagan? The "traditions of men" Were taught among the jews as well.
Mr 7:8 For laying aside the commandment of God, ye hold the
tradition of men, as the washing of pots and cups: and many other such like things ye do.
Col 2:8 Beware 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.
Josephus the first century Jewish historian wrote of three main philosophies among the Jews. He named them Pharisee's, Sadducee's, and Essene's. Sects of Judaism.
Mt 15:3 But he answered and said unto them, Why do ye also transgress the commandment of God
by your tradition?
Mt 15:6 And honour not his father or his mother, he shall be free. Thus have ye made
the commandment of God of none effect by your tradition.
Mr 7:13 Making
the word of God of none effect through your tradition, which ye have delivered: and many such like things do ye.
We are also warned of the "leaven" of the Pharisee's meaning their "doctrine"
several times we are warned concerning the "leaven" of the Pharisee, Sadducee, and even Herod (Herodians).
These were spoken of as Philosophies.
Mt 16:12 Then understood they how that he bade them not beware of the leaven of bread, but of
the doctrine of the Pharisees and of the
Sadducees.