One of the weaknesses I see in the Van Tillian presuppositionalist project is that it is possible for one to assume some worldview significantly similar to Christianity which differs from Christianity in some way which violates what Van Tillians take to be essential features of the Christian religion, such that the worldview presupposed has all of the supposed advantages which the Christian worldview has, without actually being Christian. Let’s call Van Tillian Christianity ‘Reformed Christianity’ and ask the question of whether I might presuppose a worldview which is relevantly similar to reformed Christianity, such that I escape the problem of induction and other supposed difficulties are dodged by reason of my approximately ‘Reformed Christian’ presupposed worldview. However, my version of Christianity, call it ‘Christianity 2.0’, may involve a significant difference in essential doctrine. For instance, perhaps Justification is infused rather than imputed (thus leading to ‘Catholic Christianity’). The point is that ‘Christianity 2.0’ differs significantly from ‘Reformed Christianity’ for which the Van Tillian project is intended to be an apologetic, without differing in such a way that it makes itself vulnerable to the challenge Van Tillians pose to Atheists.
The Calvinist is likely to respond to this in the same manner that Calvin himself responds to a similar objection: that the Holy Spirit will confirm one in the correct doctrine. The problem is, however, that their argument is nevertheless undermined even granting the truth of that hypothesis (which, of course, I deny). Since, there are any number of worldviews (‘Christianity 2.1, 2.2, …2.n’) which escape the charge of incoherence or unintelligibility, without actually satisfying the ‘Reformed Christianity’ thought to be logically inevitable given the Transcendental Argument for the existence of God. This leaves the Van Tillian with two options: either in some way shoring up their argument for a peculiarly ‘Reformed Christianity’ which it seems may be impossible to do, or else adopting a more ecumenical apologetic. Alternatively, of course, they could always abandon such a radical presuppositionalist approach to apologetics.