Let's take each of these starting with the "assumption" claim.
First, presuppositions are not taken to be synonymous with "merely assumed." As used in presuppositionalism -- as Greg Bahnsen emphasized -- presuppositions are the basic, non-negotiable claims of a worldview. Also, a presupposition is a necessary belief to account for a "state of affairs." Neither of these carry the notion of "unprovable assumptions." In fact the characterization as a "necessary belief" carries with it the idea that such a presupposition is necessary because of the impossibility of the contrary, i.e. to deny it proves it by leading to self-contradiction. That is the essence of proof used in TAG (the "transcendental argument for God").
We note that the charge of circularity used by opponents is a case of special pleading on their part. They argue as if their worldview is not guilty of the "sin" of circularity. Yet their argumentation is circular in the most vicious sort of way. The most glaring example is the belief in the existence of an unproved disembodied universal abstract logic existing someplace in a materialist cosmos (or just as incoherent a platonic "heaven"). As Bahnsen pointed out it is unprovable on the basis of their presuppositions, citing the example: "How could one prove 'modus ponens' without using 'modus ponens'?" One can't. In other words, one has "modus ponens" because of "modus ponens" -- one can't get more tightly circular than that.
To elaborate, here is a more immediate example from linguistics that illustrates the use of presuppositions in the presuppositional approach of Van Til: "Have you stopped beating your wife?" That question presupposes that the person did in fact engage in wife beating. That is the necessary presupposition that renders the question meaningful. This does not mean the presupposition is true or false. Also, note in this case the presupposition is not of the unprovable variety. In fact, the truth of the presupposition is potentially testable by empirical investigation.
1 See Chapter 8.5, p.662 in "Van Til's Apologetic" by Greg Bahnsen for the critiques of Gordon H. Clark.↩
2 p.672 in "Van Til's Apologetic" by Greg Bahnsen.↩
3 N.B. Clark's writings are not devoid of value. His history of philosophy "Thales to Dewey" is an excellent text that thoroughly dismantles atheistic thought as being contradictory in all of its historical systems.↩
Above I mentioned that some treat a presupposition as an axiom. Unfortunately, that view was espoused by Gordon H. Clark in his version of presuppositionalism. I agree with Van Til and Greg Bahnsen that Gordon H. Clark's version of presuppositionalism is fatally flawed1. His defense of Christian theism had to ultimately rest on the "axiom of Scripture." This essentially reduced Clark's system to fideism. As Bahnsen summarized: "Clark ultimately left Christianity without a rational defense."2 Clark's system leaned heavily to rationalism and deductive proofs when it came to the positive defense of Christianity. He was vehemently opposed to empirical evidence -- deeming it not a path to any knowledge. So much so that he claimed that science has no cognitive content regarding nature. Only deductivism provided knowledge. These faults are serious, and actually are self destructive of Clark's system.3 One should be aware of the difference between Van Til's and Clark's versions of presuppositionalism and not confuse the two.
1 See Chapter 8.5, p.662 in "Van Til's Apologetic" by Greg Bahnsen for the critiques of Gordon H. Clark.↩
2 p.672 in "Van Til's Apologetic" by Greg Bahnsen.↩
3 N.B. Clark's writings are not devoid of value. His history of philosophy "Thales to Dewey" is an excellent text that thoroughly dismantles atheistic thought as being contradictory in all of its historical systems.↩