Taharos, Chapter 8, Mishnah 4. This chapter is occupied with the question of when we must suspect that our taharos were handled by someone whose touch renders them tamei, and when we may confidently assume that nothing happened at all. Our Mishnah applies that question to a man's own home: he leaves it in a certain state and returns to find it in another.
The three tahor cases
"Hamani'ach es beiso pasu'ach umatza pasu'ach, na'ul umatza na'ul, pasu'ach umatza na'ul, tahor." One who leaves his house open and finds it open; who leaves it locked and finds it locked; or who leaves it open and finds it locked. In all three of these cases the taharos inside remain tahor.
In each of them there is nothing to point to an intruder having entered and gone about the house. A house left open and found open shows no sign of anyone having come; a house left locked and found locked was plainly never breached; and a house left open and found locked gives us no reason to imagine that whoever closed the door had first walked inside among the vessels.
Left locked and found open
"Na'ul umatza pasu'ach": here is the case that divides the Tannaim. The owner locked his house, and when he came back the door stood open. Something clearly happened: someone opened that door. The question is whether we assume that he also went in.
Rabbi Meir metamei. Rabbi Meir holds that the contents are tamei. A person brazen enough to force open a locked house is certainly brazen enough to walk inside once the door has given way. Having gone that far, why would he stop at the threshold?
Vachachamim metaharin, shehayu gannavim venimlechu vehalchu lahen. The chachamim rule that everything is tahor. Yes, there were thieves, and yes, they broke the door open. But there is no evidence inside the house of anyone having walked about among the vessels. So we say that after breaking in, they reconsidered and went on their way, perhaps they even had a change of heart, and in any case we cannot presume that they entered and rendered anything tamei.
The halachah of the chachamim reflects the pattern of this whole chapter: a suspicion must be anchored in something real. An open door proves that a door was opened; it does not prove that a man walked through it.