I thought to suggest an explanation for the difference between a melakhah not needed for its own purpose and psik reisha by using the example of opening a refrigerator door on the Sabbath. The act of opening the door is an act that has no “melakhah-like” character; it’s just that a melakhah is caused as a result, and therefore it is a psik reisha. But when one does an act that does have a “melakhah-like” character (that is, the act itself changes a state), only one is doing it for a different purpose than the change of state, that is a melakhah not needed for its own purpose.

As proof, Maimonides writes as follows (the opening words of each section are the important ones that support my distinction):

ו ***He performed an act***, and because of it a labor was done that would certainly be done on account of that act—even though he did not intend it, he is liable, for it is known that it is impossible that that labor not be done. How so? If one needed a bird’s head to play with for a child, and he cut off its head on the Sabbath—even though his ultimate purpose was not merely to kill the bird, he is liable, for it is known that it is impossible for the head of a living creature to be cut off without death resulting. And the same applies in all similar cases.

ז ***Whoever performs a labor on the Sabbath***—even though he does not need the labor itself, he is liable for it. How so? If he extinguished a lamp because he needed the oil so that it should not be lost, or so that the earthenware lamp should not burn through—he is liable, because extinguishing is a labor, and he intended to extinguish. Even though he does not need the extinguishing itself, and he extinguished only because of the oil, the earthenware, or the wick—he is liable. Likewise, one who carries a thorn four cubits in the public domain, or extinguishes a live coal so that the public should not be harmed by them, is liable—even though he does not need the extinguishing itself or the carrying itself, but only to remove the danger—he is liable. And the same applies in all similar cases.

The difference between an unintended act and a doubtful psik reisha is also understandable according to this distinction. An unintended act refers to actions with a “melakhah-like” character, while psik reisha refers to actions that do not have such a character. So it is also understandable why Rabbi Shimon and Rabbi Yehuda disagreed about an unintended act and a melakhah not needed for its own purpose, both of which relate to actions with a “melakhah-like” character, whereas regarding psik reisha they did not disagree (because there there is no melakhah-like character).

I think you are right that in an unintended act we are indeed always speaking of a situation where the action you intend to do is not itself a melakhah. But that is not a matter of the definition of an unintended act; it is a result of the very nature of the exemption. For if there were a melakhah here and you intended it, why should you be exempt? So by the nature of the exemption itself, this must be a case where the action you intend is not a melakhah, but together with it another action is done that you did not intend and that is a melakhah, and Rabbi Shimon’s novelty is that you are exempt for that melakhah because you did not intend it. By contrast, in a melakhah not needed for its own purpose only one action is done, not two, and therefore by definition this is an action that is a melakhah (otherwise there would be nothing for which to obligate). It is just done for a purpose different from the usual one, like digging a pit and needing only its dirt. Therefore, according to Rabbi Shimon, one is exempt.
So the distinction is not between an action and a melakhah versus two melakhot, but between one action and two actions (one of which is a melakhah). As far as I remember, Rabbi Abraham son of Maimonides already wrote this distinction (and it is also brought in the Magen Avraham or in the Kesef Mishneh; I don’t remember which).

I wanted to suggest a different distinction from the familiar distinction you mentioned, one based on the character of the action being done. There are actions that lack a “melakhah-like” character, like passing in front of a camera or an electronic sensor nowadays, and there I claim this is the classic example that defines psik reisha (even more fitting than cutting off the bird’s head). A melakhah not needed for its own purpose and an unintended act do not apply to actions that lack this melakhah-like character, like opening a refrigerator door and passing in front of the electronic sensor that I mentioned above. The invention of electricity makes it possible to grasp the nature of this distinction more clearly.

I understand, and I also agreed with the description. Indeed, in an unintended act we are dealing with an action that is not a melakhah, and in a melakhah not needed for its own purpose we are dealing with a melakhah. My claim, however, is that this distinction is not the conceptual essence of the difference between an unintended act and a melakhah not needed for its own purpose. As I explained, that difference follows from a technical reason (because there cannot be a case of an unintended act involving two melakhot). But the exemption in an unintended act is not because this is an action and not a melakhah, but because he does not intend the second action, which is in fact a melakhah.
Here is the practical difference between us: suppose there were a case of an unintended act involving two melakhot, one of which he intends and one of which he does not. I would claim that even in such a case he would be exempt for the second one under the rule of unintended act (though he would be liable for the first). By contrast, if I understood you correctly, you would say that such a case would be a melakhah not needed for its own purpose and not an unintended act (and therefore, for example, according to Maimonides he would be liable). I do not agree with that.
I thought perhaps this could be tied to a dispute among the medieval authorities (Rishonim), since Tosafot identifies a psik reisha that is not beneficial to him with a melakhah not needed for its own purpose. In its view these two are the same thing. But on the face of it they really are not the same, because of what I wrote (that an unintended act involves two actions, while a melakhah not needed for its own purpose involves one). But it seems to me that according to your approach Tosafot’s words are also hard to understand, because if a psik reisha that is not beneficial to him is part of the topic of unintended act, that means we are talking about an action and a melakhah, whereas a melakhah not needed for its own purpose is an actual melakhah, so how can the two be identified?!

I think you did not fully understand what I meant. According to my suggestion, an “unintended act” is an act with the character of a melakhah, except that there is uncertainty regarding the side-effect of the act (such as a furrow in the ground), whereas a melakhah not needed for its own purpose is the same as an “unintended act,” only that the uncertainty becomes certainty. In other words, a melakhah not needed for its own purpose and an unintended act are both fairly similar things (actions with a melakhah-like character), and the whole difference between them is only the level of certainty that the problematic side-effect will occur (a furrow in the ground). On the other side there is psik reisha (and doubtful psik reisha), which is defined by an action lacking melakhah-like character (such as opening a refrigerator door). In that case Rabbi Shimon also agrees that it is forbidden. I think that this way of looking at it is also simpler and more intuitive.

So I really did miss your point. I thought you were distinguishing between an unintended act and a melakhah not needed for its own purpose. Then it seems to me that you first need to define unintended act and only afterward explain psik reisha, because psik reisha is a subcategory within unintended act.

You defined an unintended act as an action that does have the character of a melakhah. But dragging a bench is really not a melakhah. The furrow is the melakhah.

Dragging a bench is the act of dragging an object across the ground, which creates a furrow in the ground—that is exactly the melakhah of plowing. I am just doing it for a different purpose than plowing, namely to move the bench—meaning, I have no interest in the usual purpose of creating a furrow (the essence of the labor); my purpose is only to move the bench.

According to my suggestion, unintended act is a subcategory within a melakhah not needed for its own purpose, and that also fits with the dispute between Rabbi Yehuda and Rabbi Shimon, who disagreed over a melakhah not needed for its own purpose and unintended act, but did not disagree over psik reisha.

It is still not clear to me why dragging a bench when there is no certainty that a furrow will be created is an unintended act, given that this is an action with a melakhah-like character (plowing). Why would psik reisha turn that into a non-melakhic action?

According to my suggestion, “unintended act” is defined only by actions with a melakhah-like character, when there is uncertainty about their side-effect.

I did not understand the second question. What do you mean that psik reisha turns it into a non-melakhic action?
Psik reisha, according to my suggestion, is defined as an action with a non-melakhic character (a mere act, like opening a refrigerator door).

Exactly. So I ask: a person drags a bench and makes a furrow. If it is certain that a furrow will be made, that is psik reisha, and if it is not certain, that is a regular unintended act. But whether there is certainty or not, the action is making a furrow—that is, a melakhic action.

If it is certain that a furrow will be made, then according to my suggestion it is not psik reisha but a melakhah not needed for its own purpose.

It is explicit in the Talmud that psik reisha is a subcategory of the laws of unintended act (that Rabbi Shimon, who permits unintended act, agrees in the case of psik reisha). See Ketubot 6a and Bekhorot 25a, and also Shulchan Arukh Orach Chayim 337:1, and the Talmud in Shabbat 75a according to the explanation in Tosafot, s.v. “Mitasek,” there. See also at the beginning of Tosafot, s.v. “Tfei,” in Shabbat there, and many more places.
And from this it follows that in the very same case, if there is no certainty it is an unintended act, and if there is certainty it is psik reisha. Therefore it is clear that in dragging a bench, if there is no certainty it is an unintended act (Shabbat 29b), and from that it follows that if there is certainty it is psik reisha (and not a melakhah not needed for its own purpose). And so it is in all cases of psik reisha (which is why Tosafot there on Shabbat 75 comments regarding mitasek).
The same is true of cutting off the head of the chicken: if it were not certain that it would die, it would be an unintended act, and only because there is certainty is it psik reisha. Yet there one is indeed dealing with a melakhah (killing the chicken) and not with a mere action.

So it seems to me that you cannot be right. According to your view, the difference between unintended act and psik reisha is not at all on the axis of certainty, but on the axis of the character of the action (melakhah or not). In effect, according to your view unintended act and a melakhah not needed for its own purpose are the same category (depending on whether there is or is not certainty), while psik reisha is something different from both of them (when we are speaking of an action that is not a melakhah). That is really not like the Talmud and the medieval authorities (Rishonim).

True, Shabbat 29b is seemingly difficult for me, because there they want to distinguish between large benches and small benches, and the distinction is that small ones can be lifted without dragging. Seemingly, if I am right, it would have made more sense to distinguish the opposite way: with large ones it should be permitted because it is certain there will be a furrow and so it is psik reisha, and with small ones it should be permitted because there is no certainty there will be a furrow. But given the premises they are trying to reconcile there, it is explicit that with large ones it is permitted and with small ones forbidden, so the Talmud is forced to distinguish on the axis of possible or impossible.
In any case, whatever you say about that passage, from the whole Talmud and the medieval authorities (Rishonim) it is clear that the distinction between unintended act and psik reisha is based on the question of certainty.
By the way, I remember from many years ago an interesting Rabbi Akiva Eger who asks on the Talmud in Shabbat 117a, because the Talmud there speaks as though it is psik reisha, even though the case is a melakhah not needed for its own purpose and not unintended act. Rabbi Aharon Kotler (in his collected novellae, siman 12) resolved the question by distinguishing between psik reisha in a melakhah not needed for its own purpose and psik reisha in unintended act. But I saw this decades ago and do not remember it. I think it would be worthwhile for you to look there. I’ll send you by email a file with that section. It is very worthwhile reading for anyone dealing with this topic.

Sent.

Thank you very much!
Here is a link to the file for anyone interested:
https://drive.google.com/open?id=1DFMkIi1sSF3MlMBSbdGoxWJm9WUEDNWn