Logic of LOST
In LOST, the characters often proceed from a certain premise, end up somewhere strange, and then discover the initial (bedrock or foundational) premise to have been false. This is a peculiar situation, and one typical of many modern problems, I find.
Locke, for instance, takes over care of the button because he believes the act of pushing it saves the world. Faith in the button leads him to the map, it breaks his leg, and even leads to a relationship with Not Henry Gale. And then he and Eko discover that the button is merely a psychological test -- yet John is where he is: belief in the button has become an inseparable part of the fabric of his life. Even if he were to stop believing immediately, it wouldn't erase the places his belief has taken him to.
To me, this recalls (though not in some heavy-handed allegorical way) the situation of an American soldier in Iraq: he's traveled there based on the assumption that the Iraqi government was in possession of WMDs -- an assumption long-since proven to be false. The premise that led our soldier to Iraq isn't true, but the consequences of his belief are very real.
Another way of coming at this is to consider Libby's role in the episode, "Dave." Hurley questions the basic reality of his being on the island (thinking he may instead be in a mental institution in a delusional state), and is about to throw himself off a cliff. It is connection with Libby that grounds him -- that leads him, literally, back from the precipice -- and then it is revealed that Libby was an inmate at the same asylum Hurley was at (throwing both her credibility and sanity into question).
In deductive logic, chains or threads of absolutely necessary logical deductions flow from an indisputable premise -- but what status do the chains have once the premise that gives them life is proven wrong? In the case of LOST and, perhaps, in the real world, the logical chains have been invested with our investment: we've followed along, and… that's where we are.
Related: Lost = TV, Lost in 'Lost', Others = Elves, Lost Notes