2. On an island, there are 10 people, some of whom are honest people who always tell the truth, and others are liars who always lie. Each of them has thought of an integer. Then, the first person says: “My number is greater than 1.” The second person says: “My number is greater than 2.”...... The tenth person says: “My number is greater than 10.” Afterwards, these ten people stand in a line in some order and say one by one: “My number is less than 1.” “My number is less than 2.” ..... “My number is less than 10.” (each person says exactly one sentence) Question: What is the maximum number of honest people among them?
2. There can be at most 8 honest people.

First, prove: No honest person will say "My number is greater than 9" or "My number is greater than 10."

In fact, if an honest person said either of these statements, it would mean that the number they are thinking of is not less than 10. Therefore, they would not be able to say any of the following: "My number is less than 1," "My number is less than 2," ... "My number is less than 10." This indicates that there cannot be more than 8 honest people.
Next, provide an example to show that there can be 8 honest people.
Assume the first honest person is thinking of the number 2, the second honest person is thinking of the number 3, ... the eighth honest person is thinking of the number 9, and the two liars are thinking of the numbers 5 and 6. Then, for \( k=1,2, \cdots, 8 \), the \( k \)-th honest person can say "My number is greater than \( k \)" and "My number is less than \( k+2 \)," while the first liar can say "My number is greater than 9" and "My number is less than 1," and the other liar can say "My number is greater than 10" and "My number is less than 2."