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1) To know anything there must be a god like the Christian God.
2) We do know something.
3) Therefore, there is a god like the Christian God.
This is a reasonable, abbreviated formulation of one version of TAG.
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I am disagreeing with (1). I do not think that the ability to know anything presupposes that there is a God. I can show this by giving hypothetical examples of knowing something where that knowledge does not presuppose God (e.g. such as in the case of the Platonic Forms).
This begs the question. You're just asserting something without argumentation or addressing the TAG arguments in support of (1). Platonic realism is a good place to start as Van Til used this as the earliest example of what he called the rational-irrational difficulty attendant on all non-theistic thought - it always reduces to abstract universals and abstract particulars and you can never bring the two into meaningful contact, thus human knowledge is impossible on that basis. He spends quite a lot of ink tracing this idea from Plato through many Western philosophers. He gives a very sharp critique of Plato and the Ideas in Survey of Christian Epistemology - remember, he did have a Ph.D. in philosophy from Princeton University and a Th.M. from Princeton Seminary - just dismissing the premise is what I meant by a massive overreach.
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Modal logic is not really relevant to my point here, at least, not in any way that I see.
You couched your first argument in possible world vocabulary, after mentioning you were dismissing the TAG argument involving necessity(which is often a modal term), so I assumed you were arguing from modal logic. If not then fine, it becomes a normal issue involving conventional logic and concepts of plausibility and probability.