Makes sense. And you don’t distinguish between a case where the poison is definitely in the syringe and it kills with a one-in-five chance, and a case where the poison is in the syringe with a one-in-five chance and then certainly kills?
By the way, from the standpoint of Jewish law, if someone takes such a syringe (where there is a one-in-five chance that it contains poison that certainly kills), injects it, and kills in the presence of witnesses and prior warning, is he a full-fledged murderer?

I don’t think so.
It depends on the law of uncertain warning.

Every pursuer is a case of doubt—who says he’ll manage to kill?

The question of degree is important here—what level of probability are we talking about? If we don’t draw reasonable threshold lines, then it would come out, for example, that anyone who doesn’t follow the corona guidelines should be killed as a pursuer.

There is another difference between the cases as well: with the syringes, you intend to put me into a death lottery, but not necessarily to chase me in order to murder me. In the ordinary case of a pursuer, he intends to murder, except that maybe he won’t succeed. To be sure, that is a difference regarding the degree of wickedness, and it is not clear that it is relevant to the law of a pursuer.

Is there any connection between “your life takes precedence” and saving a life? That is, just as on the Sabbath saving a life includes saving a limb, would the law of a pursuer also apply to someone who wants to amputate another person’s limb? And if not, is there a distinction between the victim, who can kill the pursuer, and any other person?

You mean “and live by them,” not “your life takes precedence.” Saving a life on the Sabbath does not include danger to a limb alone (except for an eye).
As for the law of a pursuer in the case of someone who wants to amputate another person’s limb, it seems obvious to me that the full law of a pursuer applies to him, up to killing him if there is no other choice. I wrote in an article that even someone who comes to steal from me may be killed by me if there is no other choice (this is the law of one who breaks in, according to my interpretation; see the debates there). But in the case of pursuing a limb, it seems one may kill him even without the framework of the law of a burglar breaking in (which does not apply where it is absolutely clear that he will not kill him). The Sages also ruled this way regarding someone who informs on another’s property, that he is killed as a pursuer.
Note that in light of what I wrote here, there is no room at all for comparison to the laws of saving life on the Sabbath, because there the discussion is about the importance and value of a limb (as against Sabbath desecration)—whether its value is like the value of life or not—and the answer is no. Here, by contrast, I am arguing that even though a limb is not equal to a life, the law of a pursuer still applies in pursuit of a limb (just as it applies to property). Because in a case of pursuit we do not make a comparison between the values of what is being saved and what is being harmed. If we did make such a comparison, the law of a pursuer would never apply at all, since the rule is: “Who says your blood is redder?”—one life is not set aside for another.
A more fitting comparison than “your life takes precedence” is the reasoning “what difference does it make whether it is all killing or half killing,” which we find in several places.

I read it; I’ll correct myself. If a person wants to harm only another person’s limb (for example by blinding him with laser beams), such that it is known with absolute certainty that there is no danger to life, would the law of a pursuer apply to him? If not, would the victim be allowed to kill the attacker? And if not, what is the law in a case of absolute certainty that the victim can be saved (the victim is in the hospital) and the attacker is not going to kill him, but the act of injury itself, were it not for the hospital treatment, could have killed him?
(P.S. A person who wants to commit suicide would have the law of a pursuer apply to him, and it would therefore be incumbent on everyone to kill him 🙂 )

P.S. That wasn’t serious.

You corrected the analogy, not the question. But I did answer the question.
In a case where it can be repaired, it seems to me that he still has the law of a pursuer, just like in pursuit of a limb. Someone who wants to send me to the hospital—I have the right to defend myself. It is like someone who threatens me that I must give him a shekel, and if not he will kill me. There is no doubt that I am allowed to get up first and kill him, even though I could give him a shekel and save both of us. I do not owe him a shekel, and I do not owe him surgery in the hospital.

It’s not an analogy—I corrected the question. I read your article about the burglar breaking in. It is explained there that there has to be at least some saving-of-life concern, even if it is fictitious; and conversely, we see that if there is no aspect of saving life at all, it is forbidden to kill him. And regarding an informer, there are many intricate arguments there as to whether it is a special enactment, etc.
So that’s why I asked: what happens in our case when there is no element of danger to life, such as blinding with laser beams? What is the permission, if any, for the victim to defend himself—or for any person who wants to save him—at the cost of killing the attacker? If you think you answered me on this, say so and I’ll let it go, because I didn’t find an answer.

I’ll repeat myself hoarsely once again: the law of a pursuer applies also in the pursuit of property and of a limb, even without danger to life. If you can save the property or the limb without killing, then of course it is forbidden to kill. And in my opinion that is also the law in the case of a burglar breaking in. In any case I save the property, and if I cannot, I kill him. I explained that the exception of his father (where it is as clear as the sun that he would not kill) was intended only for declarative purposes. Any other thief in any situation may be killed.