For the purposes of this post, I define classical apologetics as apologetic argumentation which treats premises as neutral, that is, which treats the starting point for reasoning as unproblematically shareable between reasoning parties. Likewise, I define presuppositional apologetics as apologetic argumentation which recognizes that premises differ between reasoners, and regards its job as arguing for itself from within itself, and against the other from within the other. Dialectical apologetics is apologetic argumentation which recognizes that premises differ between reasoners, and which attempts to show why the other positions' own resources provide compelling reasons to adopt itself.
Thus, a Christian dialectical apologetic would endeavor to show that Christianity hits the mark which other views are implicitly aiming at. It would show how a variety of forms of life are best understood in the context which Christianity presents. It would take what others worship and show how they do what they are finally wanted for best when subjugated by Christ.
This approach requires a sensitivity to why people do what they do, why they are seeking what they are seeking which goes in detail enough to show--not merely tell--how people's aims are misdirected in being directed away from God, and to show how the form of life in which the fundamental desire is redirected back to God is more fulfilling. That is, we are trying to uncover the existentially affirmed premises which the others accept, and find in them some germ of truth, and then to show how the gospel speaks to that germ of truth which they existentially acknowledge.
The notion of "showing" here is intentionally broad. It is meant to include a kind of lived apologetics, whereby ones life exhibits the truth of the gospel to a watching world. It is also meant to include the potential for a role for poetry and novels, film and music. It must include exhibiting the reasoning, the logic of the gospel, in such a way that it strikes. The gospel must not be left as a mere set of propositions, but must be presented as something from which to live, something to trust in. In some sense, then, I am arguing that the gospel must be made visible to the soul. This requires speaking in a variety of modes, of speaking almost bi-lingually, trans-lingually, as it were, between the speech of church and the speech of the street, the office, the home, and all those other forms of discourse about life.
On the one hand, I aim to speak after the Bible--I want to bleed Bible. On the other hand, I want to speak only in language which the unchurched person can understand. This latter requires that I make the gospel explicit. I cannot leave the gospel in terms of redemption, of reconciliation of God and humanity, or salvation, of sin, of sacrifice, of forgiveness. I must speak in those terms, yet I must make those terms sensible, comprehensible, to one who has not heard them, or who has assumed a distorted meaning for them. I must speak the gospel in the terms the Bible sets, and I must ensure that what I say is rightly understood, not mistranslated, and this must all be said in such a way that the hearer knows what it means, not only abstractly, but to their lives. The call to repent and believe in the gospel, that is, the call to follow this crucified and risen Lord must be a possible call, one which would be distinguishable from living on one's own. That is, in presenting the gospel, we must make it possible for others to enter into the kingdom of God.