If you don't like introducing the concept of person-hood to the discussion, then you should take it up with u/thenousman instead of me - for I see no way of interpreting his phrase 'people have the right to life' without invoking the notion of personhood. What else could it mean if it wasn't about assigning the right of life to entities belonging to the extension of the predicate that maps said entities to a group known as 'people'?

Although it is understandable that some may have no exposure to symbolic logic, it should be noted that my formalization of arguments is no mere exercise in theoretical mathematics - it uses first order logic to bring clarity to what I think the underlying logical structure of u/thenousman's argument looks like. OP should be able to look at it and give us a statement about whether that is what he meant or not - and propose a different formalization to describe the true form of his argument if he does not agree with it (I believe that OP should be able to comprehend it as it is quite clear that he is a student of philosophy in a university). Stating things in formal terms is also a tremendously useful technique in evaluating the validity of an argument - as I did with a proof by natural deduction.

It is difficult for me to understand how speculating on the likely beliefs of people who support capital punishment is somehow degrading to their status. I have never heard of calling someone a 'proponent of x' being understood as an insult before (assuming that whoever is stating this does not use other obviously offensive epithets in conjunction with it), but I shall use your preferred terminology for the sake of convenience if nothing else.

My issue here is that I don't think it is methodologically sound to discuss how various substantive issues (such as the issue of whether the right to life is absolute, as you've raised elsewhere) affect the implications of u/thenousman's argument without first getting a clear understanding of it - which we still haven't managed to do despite me expending quite a bit of effort to rectify the malformed nature of (1) . I will however acknowledge that if my interpretation of his argument is correct, and the formalization basically accurate, then your criticisms of it undoubtedly have merit.

I will note one more potential issue with (1) here (without saying that it actually is an issue due to the aforementioned problem of clear understanding): the use of "iff" means that aside from personhood being sufficient for having the right to life, personhood is now also a necessity of it - which would seem to be tremendously disagreeable to anyone in favor non-human animal rights who do not simultaneously believe that non-human animals are persons.

At this juncture, if OP would please tell us what he actually intended to express, it would be much appreciated.

I advanced no claims about the criteria of personhood as I merely wished to point out the fact that (1) cannot be translated into a well-formed formula (and thus its truth value would be indeterminate) without my modification - in which I rearranged the position of 'iff' such that it is between the two atomic propositions implicitly contained within the original premise.

To make my interpretation (the motivation of which is to sort out the logic) of what OPs malformed premise was trying to express even more clearly, I give the following formalization of the rectified argument:

Domain: all entities Predicates: person(x) - 'x is a person', righttolife(x) - 'x has a right to life', murderer(x) - 'x is a murderer"

1. ∀x (person(x) <-> righttolife(x)) (premise)
2. ∀x (murderer(x) -> person(x)) (premise)
3. murderer(a) -> person(a) (∀E 2)
4. person(a) <-> righttolife(a) (∀E 1)
5. person(a) -> righttolife(a) (<->E 4)
6. | murderer(a) (assumption: want righttolife(a))
7. | person(a) (->E 3)
8. | righttolife(a) (->E 5)
9. murderer(a) -> righttolife(a) (->I 6-8)
10. ∀x (murderer(x) -> righttolife(x)) (∀I 9)

I considered 'people in favor of capital punishment' broadly similar with 'capital punishment proponents' in terms of their moral intuitions and used these terms interchangeably. While there may be instances where drawing a distinction between these groups would be useful, I do not see the need to do so for the purposes of determining whether a given premise is likely acceptable to their moral intuitions.

(1) is malformed - the meaning is unclear. Are you sure you didn't mean something like "an entity has the right to life iff it is a person" instead?

But this would seem to be a premise that is still likely to suffer rejection in the minds of a capital punishment proponent, as the original disagreement about whether being a person suffices for having the right to life remains applicable.