I saw the following questions left for me elsewhere on the Internet so I will take a moment to briefly respond.
1. “Van Til and Bahnsen claim that TAG is neither inductive nor deductive. Do the other things they say about TAG also imply this, and if so, how?”
To my knowledge, Van Til and Bahnsen never use the acronym ‘TAG,’ although Bahnsen repeats the phrase ‘Transcendental Argument for God.’ Searching this site reveals a fair amount of rather heated discussion and evidence regarding Van Til and Bahnsen’s claims to the effect that transcendental argument is neither inductive nor deductive.
2. “What is the logical structure of a transcendental (as opposed to a deductive or an inductive) argument? Is Van Til’s and Bahnsen’s view identical to Don Collett’s formulation?”
3. “We understand what it means for an inductive argument to be strong or weak. We know what validity and soundness is with regard to deductive arguments. What distinguishes a successful transcendental argument from an unsuccessful one?”
‘Strong’ and ‘weak’ inductive arguments can, presumably, both be ‘successful.’ ‘Validity’ and ‘soundness’ are more precise deductive categories than ‘successful.’ So although it is unclear what is meant by ‘successful,’ a ‘successful’ transcendental argument would likely demonstrate some precondition of knowledge and an ‘unsuccessful’ transcendental argument would fail to do so.