Knights, Knaves, and an Inhabitant's Hat

[wany]

Homework Statement

You are on an island where there are two types of people knights and knaves. Knights always tell the truth and knaves always lie.
Suppose one of the inhabitants tells you:
"If I am a knave, I will eat my hat."

Must this inhabitant be a knave?
Must this inhabitant eat his/her hat?

Homework Equations

The Attempt at a Solution

Looking at this problem, I tried to break it down.
First assume that the person is a knight. The statement "If I am a knave, I will eat my hat." is true since the first part will fail.

Now assume that the person is a knave. The statement "If I am a knave, I will eat my hat." is false since the first part is true and a knave will always lie. Therefore, from this the knave will not eat his/her hat.

However, I feel that this is a loop, since a knight would never lie, whereas a knave always lies. So I feel that we cannot determine whether or not the inhabitant is a knave or knight. Furthermore, I do not believe we can conclude if he/she must eat her hat.

Is this correct?

 

[HallsofIvy]

You are correct. If A is false in a statement of the form "if A then B", the statement is true, whether B is true or not. Thus a knight can, in fact, make that statement, telling the truth. And a knave could also make the statement, not eating his hat of course. It is impossible to tell whether the person is a knight or a knave.

 

[wany]

Alright that is what I thought. Thank you.