Ben Askins commented on a podcast done by RazorsKiss about Fristianity styled counters. I’m going to post my own responses here, and work out some of the ways we think about these kinds of objections.
“The Fristianity objection is calculated to consider the assertion of the Trinity as the resolution of the “one-and-many problem,” in consideration of the strong modal claim in Greg Bahnsen’s formulation of a transcendental argument (i.e. “God is the *necessary* precondition for X” where X is some moral, metaphysical or epistemic given.).
So step  with respect to Fristianity would require presenting reasons why a trinitarian worldview is coherent – with particular reference to distinguishing it from quadrinitarianism (i.e. the aforementioned reasons must be available to the trinitarian in a way which is not available to the quadrinitarian). I haven’t seen anyone do this and I can’t think of any way to do it myself (or I would just present that for consideration).”
According to Ben, what is required of the Christian theist, being mindful now of fristianity, is to distinguish between the Christian God, and demonstrate why YHWH is the precondition for the things mentioned above, and not the Fristian god.
This may be a simplistic way of understanding it, but let’s go off of this. I will post a quick response, (I have to go back to work soon).
the quadrinity is a hypothetical, posited to deal with “TAG”, on the basis of the “Boise Bible”. Now, if we are going to be “presuppositionalists” even after the Bahnsen stripe. One thing that you’d have to consider is that even in hypothetical arguments, you are arguing from somewhere. At least in Fristianity (and I’ve not read the boise bible, It’s just been purported to exist, like the Injeel of Islam, or the golden tablets of Mormonism) . Just as the Mormon, and the Muslim, the Fristian purports to be a continuation of God’s special revelation. Unlike mormonism (which argues polytheism) and Islam (which argues Unitarianism ) Fristianity purports a 4th Person.
But it can’t do so on the basis of Christian theism, if Christian theism is true, God has spoken in these last days through His Son, who is God and man. (Heb 1:1-3). He is the culmination of all of the revelation of God, because He was with God from the beginning. (John 1:1-3). In that sense, there is no reason to expect anything else, especially when it contradicts what has already been given. This isn’t just an appeal to piety, but it’s just that our arguments (such as TAG) is grounded in revelation. Given that the Fristian has self-consciously foisted himself smack dab in the middle of the Christian worldview, an internal critique would be showing him how he doesn’t belong on his own terms (which is God’s revelation). That’s the internal critique.
In any case, this will hopefully provide some readers, and Ben, understanding on where we are coming from. Perhaps I will continue to respond more if time allows it