It’s better, when asking, to give a link to the original source. כדאי to add here a link to the article you read.

I added a link, on the word “here” at the beginning. Don’t you see it?

Sorry, I didn’t notice.

After you saw what I’m talking about, I still didn’t understand your answer.

I understand why when a person creates a reality he prohibits, but I don’t understand how it can be that with thought he prohibits, even if it is the thought that causes the prohibition. Thought that effects the prohibition is not comparable to an act that effects the prohibition. Even though both of them themselves cause the prohibition, when it is an act the Torah has something to say about it, it has a reality to prohibit, but when it is thought there is nothing here to prohibit.

I didn’t see what is written there. Do you mean thought that creates a reality (like the speech of a Nazirite)? Spell out the question more (with an example).

No, Rabbi. What I mean is an act that prohibits the object, such as placing a yoke on a red heifer, except that for the act to prohibit you need the thought.
In the book To Perform Your Commandments, on Parashat Chukat, you bring in the name of Tosafot that the rule that a person cannot prohibit something that is not his applies only when the prohibition is because of a disqualifying thought (whereas where the prohibition takes effect because of the act, a person can indeed prohibit something that is not his, such as when he mixes milk with meat, since he created a reality that the Torah prohibits). And you ask, if so, why in the case of the red heifer, where willingness is required (on the part of the one doing the labor), despite this a person can still prohibit something that is not his; and you answer that in the case of the red heifer, the thought is not a condition for the act to prohibit the object, but rather it itself effects the prohibition.
But this is difficult for me, because as I understand it, even if the thought itself is what causes the prohibition, still a person cannot prohibit something that is not his, since he simply has no standing to prohibit something that is not his. That is unlike a person who performed an act on something not his that caused a prohibition, because there it is not the person who imposed the prohibition; rather the Torah imposed a prohibition on the reality that the person created.
You even write that thought that causes a prohibition is similar to an act that causes a prohibition, but apparently I disagree, because in the case of an act it is the Torah that initiates the prohibition (and therefore a person cannot prohibit something that is not his), whereas in the case of thought it is the person (and therefore in my opinion a person cannot prohibit something that is not his, since he has no standing to do so).

Even in the short summary on page 298 you write: “However, the opinions remain that on the Torah level one can prohibit another person’s item through an act. But as we saw, even this is only because in these situations it is not he who prohibits, but the Torah.” Exactly! I agree! So how can it be that when thought itself is what causes the prohibition (and the circumstances are only a condition, as in the red heifer, according to your suggestion), a person can indeed prohibit something that is not his? Here it is he who prohibits, not the Torah!

And another question:
Why, really, can a person not prohibit something that is not his? Is it because he has no power over what is not his, or is it because it is not moral to prohibit my fellow’s property? What is your practical conclusion on this question?

The thought here is not a condition for the act that imposes the prohibition, but a condition for the Torah to impose a prohibition (just as an act serves as a condition for that). Therefore, even in the case of thought, it is the Torah that imposes the prohibition.

I think I explained this in the article you linked to. A person has no ability to act outside his own territory.

Yes, but you explained that this is a moral territory… so it’s kind of an intermediate thing: on the one hand it’s territory (he has no power to act outside his domain), and on the other hand it’s a moral territory:
Why does he have no power? Because the Torah did not want someone to ruin his fellow’s things. Not because a person lacks the power to act on someone else’s things. As the other later authorities explained.
Am I understanding correctly, or am I mistaken?

Obviously. In the end, the prohibition is imposed by the Torah. Therefore, when a person does something outside his territory, the Torah does not impose a prohibition. So this is not simply a matter of the person lacking power, since in the end it is the Torah’s decision not to impose a prohibition.

At the end of the article on Parashat Chukat in the book To Perform Your Commandments, if I understood correctly, you think (or “rule,” if you like) that a person cannot prohibit something that is not his because it is outside his territory; that is, what determines the matter is the owner’s objection, not the absence of ability and control. And from this it follows that a person can indeed prohibit ownerless property, since there is no owner’s objection.
Is that the conclusion that, in your opinion, one should remember and keep in mind, and act accordingly? Because I saw that this is actually an inquiry discussed by the later authorities: in the law that a person cannot prohibit something that is not his, in order to prohibit does one need positive ownership of the object, or is it enough that there be no owners who object to the prohibition taking effect?
And more than that, it seems that this is a dispute among the medieval authorities throughout the whole topic.
In other words, your explanation of the rule based on the principle of territory fits well with the side that says lack of objection is enough, and not with the side that says effective ownership is required. Right?

Not necessarily. On the contrary, it seems to me by logic that only when there is someone else’s ownership is this a different territory. There has to be someone else’s control in order to say that I have no control. In other words: in order to say that I cannot prohibit something, a positive condition must exist (ownership), and therefore I can prohibit when that positive condition is absent. It is not correct that in order for me to be able to prohibit, a positive condition is needed (namely, my ownership).

Good, I accept that.
But that wasn’t really the question. The question was more about the learning methodology.
There is an inquiry by the later authorities (in our case: whether a person cannot prohibit something that is not his only when the thing positively belongs to someone else, or even when it has no owner, since it still is not his; and a practical difference would be ownerless property). They explained a number of Talmudic passages and medieval authorities according to the two sides of that inquiry.
So how do you decide between the two sides of the inquiry? I don’t really know how to formulate the question well, but as I wrote above, at the end of your article it really sounds like you go with one side of the inquiry, and you write that therefore regarding ownerless property this rule does not apply, as though in the end you decided to keep to (to rule like) one side of the inquiry; and the question is first, is it correct that this is indeed how you rule in practice (that is, that a person can indeed prohibit ownerless property? a practical question now), and second, how did you decide to adopt this side rather than the other (after all, this is a dispute among Amoraim that continues down to the later authorities, etc.)?

I no longer remember my conclusion there, but I am inclined to think that with ownerless property, a person can indeed prohibit something that is not his, because someone else’s ownership is needed in order to remove his ability to do so.