Thomas:

EVERY "kind" of infinity (of numbers, points, lines, shapes, etc.) you cite is NOT truly infinity at all, but is limited in at least some respect, even if only by its own deFINITion (finite, hence not IN-finite). This is why G. Cantor termed ALL of these so-called infinities transfinites so as to distinguish them from true infinity, to which the term infinity alone properly applies. Your error lies in your lack of proper application of this term, and is based on a laxity of logic that undercuts your arguments fundamentally. So, in TRUTH, any definition, any distinguishability means no infinity. This indeed is simple logic and is indubitably TRUE.

As to your later attempt to use logic to equate the freedom from distinguishability of Infinity with pantheism, it founders completely upon the falsity of your premise No. 2: If something is distinguishable from God, then God is not in that thing. For, what is distinguishable in your syllogism is something, not G-d hence, the proper then to your if is then that something is not G-d, not then G-d is not in that thing. Your switch of subject in the syllogism creates a non sequitur fallacy. Before you critique logic, perhaps you should first learn how to use it properly.

And in fact, if G-d is truly Infinite, then G-d is not distinguishable from anything (Judaism), but that does NOT logically mean that nothing is distinguishable from G-d (pantheism) for the truly Infinite is free to remain indistinguishable even in the midst of the finites inherent distinguishability, else it wouldn't be truly Infinite.