Can't get previous_posts_link or next_posts_link to work

I am working on a custom theme, and I have these functions in my index.php

<?php previous_posts_link(); ?> <?php next_posts_link(); ?>

The links show up on the page, and when clicked take me to another page. However, the same posts show on the different pages. I have WP set to only show two posts on a page, and I have four posts. This works. So now when I click the link to view the older posts the page changes, but the posts that are displayed do not change.

What could be the problem?