Earlier within the context of his epistle, Paul said that we are to teach and proclaim the gospel in a state of wisdom (Colossians 1:27-28). He emphasizes properly knowing the mystery of God, which is the Person of Jesus Christ (Colossians 2:2-3). Philosophy necessarily involves the acquisition of wisdom.
There exists good philosophy and bad philosophy, with the former being in accordance with biblical doctrine. In other words, philosophy is not to be developed apart from or against the content of divine revelation. So, what type of philosophy was the Apostle Paul speaking against? Colossians 2:8 give us the answer: "according to the tradition of men, according to the elementary principles of the world, rather than according to Christ."
Paul was exhorting the church in Colossae not to be deceived into embracing various customs and practices that were rooted in Jewish and pagan mysticism (Colossians 2:16-23). In so doing, he was very much setting forth a philosophical proposition. The truth of the matter is that there no escaping philosophy. Everybody does it. Consequently, those who oppose philosophy are living by a self-defeating philosophy.