Question

In column 366 you brought a Talmudic passage and the Pnei Yehoshua about someone setting a dog on another person, and you used it to illustrate an idea. There it is described that according to the Pnei Yehoshua, the inciter is exempt and the owner of the dog is exempt, and therefore even someone who sets his own dog on another person is exempt. I would suggest understanding the Pnei Yehoshua to mean that the inciter is exempt and the owner of the dog is exempt, but someone who sets his own dog on another person is liable.
In that column all the quotations are there, but I’ll quote them here too for completeness. In a comment there I briefly wrote my understanding of the Pnei Yehoshua, and here I’ll lay out the two possibilities in more detail. I’ve gone on at length as much as I could so it will be easy to put a finger on the differences.
 
The Talmud, Bava Kamma 24b: “They asked: If one sets his fellow’s dog on another person” (Levi sets Reuven’s dog on Shimon), “what is the law? The inciter is certainly exempt; what about the owner of the dog? Come and hear: If one set the dog on him, he is exempt. What, is it not that the inciter is exempt and the owner of the dog is liable? No; say: even the inciter is exempt.”
 
The underlying question is: where did the one raising the initial suggestion get the idea to invent that the inciter is exempt but the owner of the dog is liable, such that he tries to bring a proof? After all, everyone took it as obvious that the inciter is exempt, and the only doubt was about the owner of the dog. But the owner of the dog does not appear in the baraita at all. And what exactly is the dispute between the one raising the initial suggestion and the one rejecting it? The Pnei Yehoshua explains.
 
The wording of the Pnei Yehoshua: “In the Gemara: ‘What, is it not that the inciter is exempt and the owner of the dog is liable,’ etc.? It appears that the initial assumption was that since it says, ‘he set the dog on him,’ and does not say, ‘he set his dog on him,’ which would have implied a great novelty—that even though the dog is his, he is nevertheless exempt—rather, certainly in such a case he would be liable. And the respondent rejected this reasoning. This is straightforward.”
 
Understanding 1 in the Pnei Yehoshua (for example Ayelet HaShachar that you cited, and he leaves the Pnei Yehoshua as requiring further study):
A. From the baraita one can infer: “He set the dog on him” — he is exempt; but if he set his own dog on him, meaning that the inciter and the owner of the dog are one and the same person, then he is liable.
B. From here the one raising the initial suggestion (“What, is it not that the inciter is exempt and the owner of the dog is liable?”) draws the conclusion that if one who sets his own dog is liable, and one who sets another person’s dog is exempt, then it follows that the owner of the dog is always liable. The Gemara explicitly says that the conclusion the one raising the initial suggestion is trying to infer in order to resolve the question is that the owner of the dog is liable, and that is the main practical dispute between him and the one rejecting it, not merely the dispute about one who sets his own dog [this is an important point].
C. Meaning: according to the one raising the initial suggestion, if the inciter by himself is exempt and the owner of the dog by himself is exempt, then by logic someone who is both the inciter and the owner of the dog should also be exempt. Therefore the owner of the dog by himself must indeed be liable, and so someone who is both inciter and owner is liable.
D. The one rejecting it (“No; say: even the inciter is exempt”) jumps in to dispute the inference of the one raising the initial suggestion (without giving a reason), and tells him that even one who sets his own dog is exempt, because each one separately is exempt. And from that you know that the owner of the dog is exempt.
E. Meaning: according to the one rejecting it, the inciter by himself is exempt and the owner of the dog by himself is exempt, and even one who sets his own dog is exempt.
F. No one disputes the logic that if the inciter by himself is exempt and the owner of the dog by himself is exempt, then someone who sets his own dog should also be exempt. According to the one raising the initial suggestion, the owner of the dog is always liable. According to the one rejecting it, even one who sets his own dog is exempt.
 
The difficulties with this understanding:

• On this reading, the flow of the Gemara does not explain how the one rejecting it escapes the correct inference from the baraita made by the one raising the initial suggestion.
• And one of the sides has a strange position, even as practical Jewish law: that one who sets his own dog is exempt. The later authorities objected to this, and so did you.
• And in the end it still has not been explained what their conceptual dispute is.
• And it is not clear why the one rejecting it volunteered to reject more than he needed to. He could have rejected only the reasoning and not the inference, as below. And why would the Pnei Yehoshua load onto the one rejecting it that he volunteered to reject more than he had to, and where does the Pnei Yehoshua get that from?
• [And the Pnei Yehoshua too should have felt that the matter was strange, and concluded that this is how it seems to him he must explain it under pressure, while sadly noting that it still requires further study—not as though he doesn’t feel the thorn and only the later authorities had to cry out.]

 
Understanding 2 in the Pnei Yehoshua.
A. From the baraita one can infer: “He set the dog on him” — he is exempt; but if he set his own dog on him, meaning that the inciter and the owner of the dog are one and the same person, then he is liable. This is a correct inference with no dispute about it.
B. From here the one raising the initial suggestion (“What, is it not that the inciter is exempt and the owner of the dog is liable?”) draws the conclusion that if one who sets his own dog is liable, and one who sets another person’s dog is exempt, then it follows that the owner of the dog is always liable. The Gemara explicitly says that this is the conclusion the one raising the initial suggestion is trying to infer in order to resolve the question.
C. Meaning: according to the one raising the initial suggestion, if the inciter by himself is exempt and the owner of the dog by himself is exempt, then someone who is both the inciter and the owner of the dog should also be exempt. Therefore the owner of the dog by himself must indeed be liable, and so someone who is both inciter and owner is liable.
D. The one rejecting it (“No; say: even the inciter is exempt”) cannot dispute the correct inference, but he disputes the conclusion of the one raising the initial suggestion. He tells him that indeed one who sets his own dog is liable, but not because he is the owner of the dog; rather because he is both the inciter and the owner of the dog, while each of those taken separately is always exempt.
E. Meaning: according to the one rejecting it, indeed the inciter by himself is exempt and the owner of the dog by himself is exempt, but someone who is both the inciter and the owner is liable.
F. No one disputes the practical ruling that one who sets his own dog is liable. Their dispute is conceptual: does separate exemption imply combined exemption, or not?
 
All the wrinkles smooth out:

• On this reading the flow of the Gemara is clear. And no one disputes the correct inference.
• And there is no strange practical position at all, certainly not in the conclusion.
• And the view of the two sides is clear: they are disputing the subtle conceptual question of whether it is possible that each one separately is exempt but together they are liable.
• And the one rejecting it did not volunteer on his own to reject too much.
• [And therefore the Pnei Yehoshua was not especially troubled by his explanation, writes it matter-of-factly, and concludes that it is easy to understand.]

And according to this, this is how the Pnei Yehoshua should be read, with the necessary completions:
In the Gemara: “What, is it not that the inciter is exempt and the owner of the dog is liable,” etc.? It appears that the initial assumption was that since it says, “he set the dog on him,” and does not say, “he set his dog on him,” which would have implied a great novelty—that even though the dog is his, he is nevertheless exempt—rather, certainly in such a case he would be liable [and by logic, if one who sets his own dog is liable, then the owner of the dog must always be liable, since that is what the one raising the initial suggestion is trying to prove]. And the respondent rejected this reasoning [and says: one who sets his own dog is indeed liable, but in general the owner of the dog is exempt]. And this is easy to understand.
 
 
So my questions, in summary:

1. Is it indeed correct that this is how the later authorities (whom you mentioned in that column) understood the Pnei Yehoshua — Understanding 1?
2. Is it correct that Understanding 2 as I wrote it is a more plausible explanation of the Gemara?
3. In your opinion, is the correct reading intended by Rabbi Yaakov Yehoshua Falk, author of Pnei Yehoshua, Understanding 1? And why?