Paul tells the Colossians: See to it that no one takes you captive through philosophy and empty deceit (Col 3.8).
Philosophy in the ancient world was as much an ethical enterprise as anything else; for the ancients, philosophy was a way of becoming a better person and living a better life, morally and spiritually and otherwise. Of course, each philosophical school differed on its conception of the good life: the Epicureans taught that the good life was one of pleasure, which was best achieved through a life of simplicity and contentment in austere living; the Stoics thought that the good life was one lived in conformity with virtue, even if it may also be painful or pleasant; the Platonists thought a good life meant adhering to the values of the soul (moral development, knowledge and thought, etc.) and paying only as much attention to the body as is necessary for the proper and easy functioning of the soul. What was constant and shared among the schools, however, was a recognition of the necessity of intense personal effort to better oneself. You had to admit your initial state was a bad one, and that nothing but yourself was going to lift you up out of the mire. See the Plotinus quote at the head of this page: Never stop sculpting your own statue (Enn. I.6, 9).
Paul, on the other hand, is convinced that philosophy on its own will not save you. He does not deny that there is anything of value at all in philosophy, but he doesn't think that it will issue in saving transformation. Paul's preferred method of transformation is a christocentric one, a method which takes the focus of the human person from herself and puts it on Christ and what he has accomplished for her.
Paul affirms that in [Christ] the whole fullness of deity dwells bodily (v. 9), so that Christ is not just some mere teacher or man. He is not even like the "divine Plato," who was divine only by participation and some great wisdom. Rather Christ is God himself, the Good Itself come down to us for our salvation. Consequently he is above all teaches, above all masters; he is the head of every ruler and authority (v. 10) and to him all must bow the knee.
Moreover he says that you have come to fullness in him (v. 10). This is the first of Paul's critical uses of the phrase in him. For Paul Christ has come and taken the whole totality of the created order in himself (see 1.19; πᾶν τὸ πλήρωμα) and reconciled it to God (v. 20). This all occurs in the person of Christ himself, but it is a reality for all, and it is something from which all can and must benefit. In an important way, this is Paul's gospel: what humanity was unable to do, God himself accomplished in Christ's person, so that the fellowship between humanity and God may be restored to that which God had intended from the beginning. We benefit from this and experience that fellowship when we come and unite ourselves to Christ, who has already done everything for us.
The argument against philosophy implicit in all this is relatively obvious. Whereas the philosophical schools insisted that each man work out his own salvation in fear and trembling, Paul affirms that God has already accomplished our salvation for us. The Good does not remain infinitely far off, attained only through extreme ascetic living and a rupture from all that is human and earthly, as in the case of Plotinus. No, the Good has come to us, has become a human Itself, and has sanctified humanity for us.
Paul's point, moreover, is that the Christian's mind ought to be focused on what Christ has accomplished, and on what is hers in Christ, rather than on herself. There is a difference of mental orientation. Whereas the philosophers said to Withdraw into yourself, as far as you can (Seneca, Epistolae morales ad Lucilium I, 7), Paul says, Turn and see what is already yours in Christ!
The Platonists spoke of disregarding the body. Socrates, somewhere in the Phaedo, speaks of the pleasures of the body as rivets that keep the soul in bondage in its prison, when it would rather fly free in its more natural state. Porphyry said of Plotinus that he was like one who was ashamed to be in a body. Paul is not ignorant of the miserable condition of the body and the spiritual obstacle it can be, of course, but his solution is not asceticism -- it is the resurrection of Christ. I take it that the reference is to the resurrection and reconstitution of Christ's body when he says, In [Christ] also you were circumcised with a spiritual circumcision, by putting of the body of the flesh in the circumcision of Christ (v. 11). Christ was resurrected from the dead, and his new body is no longer subject to sin (cf. Rom 6.10). When we unite ourselves with him in baptism, we benefit from this and live a new life, even if in the old body: when you were buried with him in baptism, you were also raised with him through faith in the power of God, who raised him from the dead (Col 3.12; cf. Rom 6.5-11).
Whereas the ancient philosophers put the burden of salvation squarely upon the individual, who had to bring himself to life upon the realization of his miserable state, Paul insists that God accomplished salvation for us even when we were dead: And when you were dead in the trespasses and uncircumcision of your flesh, God made you alive together with him (Col 3.13). Christ's resurrection meant your resurrection already before you believed; it occurred while we were still sinners (Rom 5.8).
There is yet a further thing. I don't know what the ancient philosophical schools would have said about the forgiveness of sins. There are passages describing judgment in Plato, but there is hardly ever mention of the forgiveness of the gods of our sins. Very possibly they did not think that this was an actual problem. But arguably there is something deep within the psychology of humanity, a kind of deep-seated guilt for wrongs done, and we know that God's forgiveness alone can resolve the problem of the eternity of our guilt, to use a Nietzschean notion. The gospel of Christ is therefore superior to philosophy in this respect, because it affirms that God forgave us all our trespasses, erasing the record that stood against us with its legal demands (Col 3.13-4).
I like philosophy. I think it is very useful to know, especially as regards metaphysics. I enjoy medieval philosophy, I enjoy Platonic philosophy, I enjoy the arguments for the existence of God, and I enjoy the moral exhortation. I have an undergraduate degree in philosophy, and I don't regret getting it one bit. But there is a difference between philosophy and Christianity, especially as regards salvation. Philosophy, Paul insists, will not save anyone; only God can save, and he has done this in Christ. Therefore, if we want to be delivered, we need to unite ourselves to Christ, who has already accomplished all that is necessary for us.