When one is mevateil chameitz, does he have to have in mind the chameitz he intends to be mevatel? If not, how could there be anything found on Pesach that he would have to burn?
According to this text, it would appear not, as this text of Bitul Chameitz covers chameitz he doesn't even know about [I recognize that one answer could be that one might use a text which doesn't explicitly mention unknown chameitz, but I'm working within the consequences of using this text]: כל חמירא וחמיעא דאכא ברשותי דלא חמתה ודלא בערתה ודלא ידענא לה לבטל ולהוי הפקר כעפרא דארעא
(Translation included here.)
But the Dirshu Daf HaYomi B'Halacha Daily Email - 21 Cheshvan/Nov 19 that I received today makes the following statement:
"According to many Rishonim, chometz found on Yom Tov which a person had not been mevatel, should be disposed of without burning (i.e. flushed down the toilet, or crumbled and thrown to the wind). "
(bolding and italics, mine)
It would seem that anything someone found would either be in someone else's reshut (sold to a non-Jew or originally belonging to someone else) or would have continued to belong to the Jew but would have been nullified had it not been sold (or known about).
Does bitul require knowledge and intention? Can one retain something in his reshut and not have nullified it?