Taharos, Chapter 7, Mishnah 3. From beginning to end this perek is occupied with the am ha'aretz, the amaratzim as they are commonly called: people who are not scrupulous when it comes to tumah and taharah. Again and again the Mishnah asks the same practical question: what stance should someone who is careful take toward such a person, and where does that person fit within the system of purity and impurity? Since whatever a tamei person touches becomes tamei, the instant he is left by himself among your utensils you are facing a genuine difficulty.
The Case of the Workers
"Hamani'ach umanim betoch beiso": one who leaves workers inside his house. Picture painters, or whatever tradesmen you like, left on their own in the house while the owner is away. On this the Mishnah records, "habayis tamei, divrei Rebbi Meir." According to Rebbi Meir, the entire house is tamei.
The logic behind Rebbi Meir's ruling is simple, and it would be hard to call it unreasonable. A worker is not a visitor. He entered the house in order to accomplish something, and having a task to accomplish makes him feel he may put his hands on anything standing in his path. Leave a crew of painters in a room and they will push the table aside if the table is in the way, take items off it, rest their own things on it, and then move along to the next wall. Given that this is how such men operate, every object in the house has been touched, and every object in the house has therefore contracted tumah.
The Chachamim Hold Their Line
Against this comes the second opinion: "Vachachamim omrim," and the chachamim say otherwise. In their formulation, "ein tamei" nothing has become tamei, "ela ad makom" other than as far as the point "shehem yecholim lifshot es yadam veliga," that is, the distance within which a worker could reach out an arm and make contact.
The chachamim are being perfectly consistent here. Their principle is that we do not assume a person handled what was not his to handle, and they apply that principle even to hired workers. In their view the workers do not feel entitled or comfortable touching anything the homeowner did not explicitly give them permission or instructions to touch. What is treated as tamei is therefore only what lies within arm's reach of where they were, whatever they might have brushed against without meaning to.
There is almost a tone of debate audible in the exchange, as if Rebbi Meir were pressing the chachamim: "Really? Even workmen? You still say so?" He is pushing their position to its limit, testing it as one tests an argument by carrying it to an extreme case. And the chachamim do not flinch. Their measure holds even here, and that is exactly how we pasken, like the chachamim.