When one is browsing through the comments to the above post the commenters' focus on eye colors and mathematical induction can be recognised very easily. I see other things:
A) Assumptions that are questionable and
B) Assumptions that are not stated explicitly, and are therefore unseen and
A1. Can a person be both highly logical and highly religious at the same time? If not, the Puzzle and its two alternative solutions are just a waste of our precious time?
A2. Who/what is logical (or illogical)? Is it the person or is it just some (not all) of his/her acts? For example, the most ‘logical’ person in the world – Kurt Gödel – tried to starve himself to death twice (and succeeded on the second attempt). What I imply is that a ‘logical’ person may sometimes act illogically and thus invalidate the logic of Solution 1 (where all islanders live) and Solution 2 (where all islanders die).
B1. Is the eye color what is important or is it the color perception? What
happens if the foreigner OR some/all islanders are color blind? They have eyes,
so they could be color blind, couldn’t they? What I mean is that the highly logical islanders won’t trust an unknown visitor’s word as he might be color blind. For the same reason they wouldn’t even trust the other islanders’ judgments and acts (and even their own ones). In this case, Solution 1 is the only possible solution.
The following pun may sound cheep but I think that (especially with respect to this puzzle) LOGIC IS IN THE EYE OF THE LOGICIAN.