Logic: famous argument evaluation I am finishing a section of a book about logic and math and I am very confused by one famous argument evaluation present in a few books (Thinking Mathematically, SAT Critical Reading and Writing Prep Course etc.) that is based on some famous part of the the Bible. I will paste the original:
problem:
This is an excerpt from a 1967 speech in the U.S. House of Representatives by Representative Adam Clayton Powell:
He who is without sin should cast the first stone. There is no one here who does not have a skeleton in his closet. I know, and I know them by name.

Powell’s argument can be expressed as follows:
A. No sinner is one who should cast the first stone.
B. All people here are sinners.
---------------
∴ Therefore, no person here is one who should cast the first stone.

Use an Euler diagram to determine whether the argument is valid or invalid

solution
argument is valid
questions
At first glance, I was thinking that the argument and its conclusion is of course valid, but then I tried to write it in Euler diagrams and also in some standard form and that is where it all failed apart.
Lets use


*

*S for "sinner"

*C for "should cast the first stone"

*P for "people here"
Euler Diagram Approach
First of all, it seems like the first premise No sinner is one who should cast the first stone is not a valid statement but someones opinion, it can not be true or false it seems so thats kind of a weak point of it.
Question 1: is the premise "No sinner is one who should cast the first stone" a valid statement?


*

*~S is inside of C - which does not say anything about S and since the first premise is an opinion I can not determine that S must be outside of C

*All P are inside of S - which again can be both inside of C or can be outside of C.
Therefore conclusion is not valid and argument is not valid, since there can be sinners who should cast the first stone (it also make sense if we assume we are all sinners then someone should "throw a stone" when something terrible happens)


Question 2: Do I miss something here about Euler diagrams?
Standard Form Approach
Question 3: how should we represent the premise "No sinner is one who should cast the first stone"?
I tried one approach which is again incompatible results with the book solution.
"No sinner is one who should cast the first stone" seems to me like "If you are not sinner, then you should cast the first stone." Which is ~S --> C. So:
[(~S --> C) ^ (all P are S)] --> (no P --> C)
which is an invalid argument since the premise only talks about no sinners not about sinners, so the conclusion seems like the fallacy of inverse ~S --> C ≠ S --> C

In the end, it feels like I have to read someones mind, if the first premise would be ONLY No sinner is one who should cast the first stone then I would probably did not go this way and draw the S outside of C in Euler diagram or evaluate it as ~S <--> C, which would all be fine.
Thank you all in advance.
 A: I'm writing from the Aristotelian perspective, here.
The two premises and conclusion are propositions. You might disagree with the truth value of them (I don't, actually), but they are propositions. They are sentences that are either true or false, and therefore qualify as propositions or statements.
I don't see any terms changing meaning in the course of the argument, so the fallacy of four terms doesn't seem to be in play.
It's a valid argument, though the terms might be better re-written to be clearer. The standard Aristotelian criteria all work:


*

*The number of negative premises (1) equals the number of negative conclusions (1).

*Both terms in the conclusion are distributed, and both of those terms are also distributed in the premises. Note that the E type statement (No A are B) distributes both A and B terms.

*The middle term, sinners, is distributed. 


Therefore the argument is valid. I would, though, rewrite the second premise like this:
All persons here are sinners.
A: I can see my own mistake now: I have thought that the conclusion is ( no P <---> C), but it is no (no P --> C) (!) maybe because it was rooted in my head like so from the childhood.
