gerard.caseyI am familiar with the term ‘presupposition’, David, but not as it’s used by van Til and Bahnsen. That being so, there’s nothing sensible I can say about the use of the term in those contexts.
More generally, the idea of presupposition arise in the context of real-life argument analysis. You are, let us say, reading a scholarly article and you come upon a particular argument. This argument may very well be internally valid but may be sound (i.e. valid with true premises) only upon certain things being taken for granted (presuppositions). Such a strategy is not necessarily unwarranted as we don’t always have time to prove everything to everybody and sometimes we just have to take things for granted. In particular, when our arguments are addressed to particular audiences, we are justified in taking their positions as starting points that do not need to be argued for.