Rabbi Akiva Eiger wrote about the Ran's words (Responsa, First Edition, Siman 23): "I will add to what the Ran wrote, that the reason for searching is because nullification depends on people's thoughts, and their thoughts are not the same, and they might be lenient about it and not completely remove it from their minds. It seems difficult, since if one says with his mouth that he nullifies it, even if his heart is not in agreement, these are 'words of the heart' and his thoughts do not nullify his words. We must say that since the language of nullification is not actual abandonment but rather an expression of the heart, indicating that he considers it as dust, and since we judge based on what is in his heart, i.e., revealing what his intention is, if his intention is not aligned, the nullification is meaningless. And this is likely what the Ran emphasizes in his precise wording, that this nullification depends on their thoughts." This means that nullification is about expressing that the chametz has lost its value in his eyes and is considered as dust.