A. Analysis of Tosfos' Question
See Tosfos (s.v. Eelaima). Tosfos ask that considering the implication of our Gemara that there is no difference between moving the fire close to the item destroyed, or moving the item getting destroyed close to the fire, (as we see that moving produce to where the fire will consume it will obligate the perpetrator), why then does the Gemara in Sanhedrin 77a state that if one ties someone else in a place where the heat or cold will reach him and kill him, or, similarly, in front of a lion, he is not considered a direct murderer. He has merely caused the death of the victim. According to the opinion that holds Isho Mishum Chitzav (see beginning of previous post), then we should equate this to bringing the vehicle of death to the victim. Meaning, just as one who lights a fire that kills someone is a murderer according to this opinion, so too, based on this Gemara, should be someone who brings a victim to a place where fire (or, as in Sanhedrin, heat, cold, or wild animals) will kill him.
This requires explanation. In the case of bringing someone toward the fire, the fire was not propelled by the criminal, nor even ignited by him. How is there any way to consider the fire as "his arrows"?
Perhaps this can be explained based on R' Chaim Soloveitchik's comments to Hilchos Shecheinim (11:1) . In the matter of Isho Mishum Chitzav, there are two ways to define the novelty being conveyed by this formulation and categorization of Aish:
A - Although it is the wind that is transporting the fire, nevertheless, since he ignited it, we do not consider the wind's force as a mitigation of the human's action. On the contrary, we consider the wind as part of the human's action. Meaning, the Torah is telling us that when using the forces of nature in order to transport the Mazik created from point A to point B, this is considered the force of the human being. The reality of the ignition of the fire and its transportation are all traced back to be considered the force of the lighter of the fire. The Bircas Avraham adds somewhat more clarity to this by adding that just as the ability of the fire to burn and spread and consume is not considered extraneous, and hence exculpatory, to the human's input, but is considered part of the human's action, similarly the wind's intervention in transporation of the fire is considered to be employed by the human himself.
[It should be noted that the Chazon Ish in his glosses to R' Chaim there expresses difficulty with this interpretation of Isho Mishum Chitzav, and explains that when utilizes the force of the wind which is available immediately to propel the fire, this is considered Kocho]
B - Although in reality it is not the force of the human being used to propel the fire, nevertheless Halachah is informing us that just as when one shoots an arrow and utilizes his own force to propel it, he is culpable for the result, so too when one utilizes the force of nature to transport the fire he is just as responsible. These two cases, though distinct in terms of the reality of where the propellant forces are viewed as coming from, are treated Halachically without any difference.
It would seem that our Tosfos is following this second approach. Just as the Torah innovates that whatever the wind propels is Halachically synonymous with a shot arrow, despite the reality of the human involvement in propelling the arrow, since it is a force of nature being used to propel the fire and not a power source with any sort of cognitive input, similarly, when one brings the produce proximate to the fire, since he is using the forces of nature to damage the produce, this is also included in Chitzav.
[R' Chaim in Hilchos Shecheinim concludes that the first way of looking at Isho Mishum Chitzav is correct. R' Soloveitchik quotes R' Chaim as saying that indeed there is no application of Isho Mishum Chitzav in a situation of bringing something close to the fire, and that Tosfos' question is therefore moot. (See part B below) It seems clear that this is based on R' Chaim's conclusion. See also Bircas Avraham to 22b (Mahadura Basra) that R' Chaim explains Tosfos there (s.v. V'hayah) based on the second side of this Chakirah).]
[See Maharam Shiff to Tosfos that the question is inapplicable according to the view of Reish Lakish, Isho Mishum Mamono, since there is no question of culpability for murder even in a situation of lighting the fire.]
B. Additional Answers to Tosfos' Question
1) We brought R' Chaim earlier, and the Chochmas Shlomo (To Shulchan Aruch Choshen Mishpat 418) concurs, that there is the application of Isho Mishum Chitzav is limited to one igniting a fire, but when bringiing something close to the fire there is only Isho Mishum Mamono, and there is no culpability on grounds of Retzichah.
The Shitah Mekubetzes quotes the Ra'ah, who distinguishes between murder and damage. wherein one is not culpable for murder unless it is done by the person's body or force generated by him - "and Isho, according to the opinion that it is Mishum Chitzav, as well as his actual arrows, is considered fully as his Koach, but generally speaking this is not so. And it also stands to reason that a rock, knife, or bundle placed atop of his roof, where they fell due to a common wind and damaged, which is considered a sub-category of Aish, cannot be considered Chitzav, but only Mamono.
It seems that the fundamental idea behind this Ra'ah is identical to R' Chaim, in that he holds like the first side of the Chakirah earlier - that Isho Mishum Chitzav is considered, in reality, to be his Koach, as is implied by the language of the Ra'ah - כוחו גמור חשבינן ליה - and therefore where the Koach of the perpetrator has already been expended, such as in the case of the rock and knife, or when bending the produce where he brings the produce proximate to the fire, there is no application of Isho Mishum Chitzav.
2) The Ran (Sanhedrin 77b, end of s.v. Zarak) holds that even if we were to assume Isho Mishum Chitzav, and the perpetrator ignites the fire, there is no culpability for murder. The reason for this is that it is not really a direct act of murder on the part of the person who lit the fire, since he merely lit the fire. It is not even like a case of מצמצם (Sanhedrin 76b - restricting someone to a place or situation where he will die, such as holding someone under water, where the victim went under the water initially on his own), where he is doing a direct act.
The difficulty with this position is the Gemara on 22b, that states that if one lights a haystack with a slave tethered to it, and a goat nearby, and everything was consumed by the fire - he is absolved from having to pay for the haystack, according to the opinion of Isho Mishum Chitzav, based on the rule of Kim Leih B'Derabbah Mineih - he has done an act worthy of the death penalty and therefore he does not have to pay for the monetary damage. The implication here is that the person lighting the fire is culpable for murder of the slave.
The Minchas Chinuch (Mitzvah 56) explains that since he is causing the person to die by his "arrows", he has the status of a Rodef (someone chasing after another to kill him), and a Rodef who breaks someone else's utensils is absolved since he is in a situation where someone else can legally kill him. [See the Minchas Chinuch there, who uses this idea to explain the Rambam's opinion, unlike our Tosfos, that even if the perpetrator moves the victim toward the heat or cold he is not culpable for murder. However, R' Chaim in Hilchos Shecheinim there. and the Brisker Rav in Hilchos Rotzeiach dispute the explanation of the Minchas Chinuch in the Rambam. They are of the opinion that the Rambam does hold one ignites a fire responsible for murder according to the approach of Isho Mishum Chitzav. This is beyond the scope of our discussion here]
3) The Tosfos Rid distinguishes between a situation of the heat or cold approaching, versus our case - in a case of sun or cold they do not kill immediately, but only after a great amount of timeh has elapsed, and even though the cold reaches the victim eventually, this is insufficient grounds for culpability for murder. But in the case of fire, the fire burns him immediately, and since it is going to come, there is no greater act of murder than this.
All of these answers, along with the answer of Tosfos, present interesting ramifications. For instance, throwing someone into oncoming traffic, or tying someone to the train tracks. Tosfos and Tosfos Rid would hold one responsible for murder in these cases (assuming the traffic is high-speed enough to kill upon impact, as per the Tosfos Rid criterion) whereas R' Chaim and the Ran would not.
4) Maharsha to Tosfos (Sanhedrin 77a) explains Tosfos there that Isho Mishum Chitzov applies only if the wind is transported with no wind at all, but if the wind is transporting the fire it is considered Koach Kocho, and therefore the person who lights the fire is not culpable for murder. However, the Chazon Ish (Bava Kama 2:2) explains this Tosfos along the lines of the Ra'ah above. See also B'ikvei Hatzon (7: 3-6)