*Originally posted by iamatiger*

**"If my third question is 'which path leads to truth town?', which way might you point?"**

I like this suggestion, but I can see multiple counter-arguments against your analysis of both the liar and the waverer (false).

As far as I can tell (correct me if I am wrong), your analysis basically assumes that such a person would think of the following disjunction: "I might point to lie or I might point to wavering". Then, your analysis assumes that in order to lie to you here, he has to basically give you the negation of the disjunction which is "It is not the case that I might point to lie and it is not the case that I might point to wavering", which translates here to his pointing only to truth town.

I can think of at least 2 counters to this analysis:

(1) In order to lie to you, it is not necessary that they give you the full negation of the disjunction. The point is that these persons function as deceivers, and they can try to deceive you in multiple ways. One way is simply to withhold one part of the disjunction and thereby not give you the full truth. In this case "I might point to lie" does not give you the full truth, and neither does "I might point to wavering". Both can be deceptive, just as "I might point to truth town" is deceptive. Then, under this construal, the liar or the waverer (false) can point to ANY of the towns in response to your question. (Or, else, it can be countered that your question presupposes only one way they might point, whereas there are multiple ways they might point.)

(2) The liar or waverer (false) would not think the above disjunction but rather would think the following conjunction: "I might point to lie and I might point to wavering". Then the negation of the conjunction is "It is not the case that I might point to lie or it is not the case that I might point to wavering". But, in this case, again in order to lie to you, it seems he can point to ANY of the towns in response to your question. (Or, else, it can be countered that your question presupposes only one way they might point, whereas there are multiple ways they might point.)