appeal to possibility?

As your attorney, I recommend you watch Village of the Damned twice and call me in the morning. :)

I'm trying to parse this out as this is something I've thought a lot about.

If someone said:

P1:  Volunteering to work in a soup kitchen (or some other charitable work) can make the world a better place.

P2:  I want the world to be a better place.

C:    Therefore, I should volunteer to work in a soup kitchen (or other charity). 

Is that different from the children example?  

Is there a name for the fallacy in the children example?
Thanks

Yes, same reasoning error. It is only possible that it will make the world a better place, so the conclusion does not follow. This is mostly just a non sequitur .

Not sure if it’s Ok to dissent but I’m having trouble accepting what you wrote.  

You’re saying it’s a non sequitur to conclude that I should do something that may have a certain result if it’s only possible that it will. 

(Note that the conclusion isn’t that I must do the thing, only that I should)

Here’s another example:

P1 Being kind to others can make the world a better place.

P2: I want the world to be a better place.

C: Therefore, I should be kind to others.

Without going into the ethical questions this brings up, I just don’t see how this can be a non sequitur or other fallacy.   Perhaps it all has to do with what “should” means.  Per the Collins Dictionary on the Internet I got:  “You use "should" when you are saying what would be the right thing to do or the right state for something to be in.”  

With this definition, I don’t see how the conclusion doesn’t follow from the premises (and even less how it’s fallacious).    The conclusion isn’t “I must be kind to others”, or  “the only acceptable course of action is to be kind to others”.  It’s that  “I should be kind to others”.

One final example:

P1:     Wearing a seatbelt could avoid injury.

P2:     I want to avoid injury.

C:      Therefore, I should wear a seatbelt.

How is that different than the other examples?  (Or is it?)

The problem is with equivocation . The word "can" (or "could") has at least two distinct meanings in the contexts used, possibly 3three

1) "can" as is "possible."
2) "can" as in  "probable."
3) "can" as in the probability is unknown/unknowable.

Consider:

"I can win the $900m jackpot in the lottery. Therefore, you should pay me $1m to buy your tickets."

"Can" in this context, refers to a remote probability (or possibility), thus the conclusion does not follow.

"The God of the Bible could exist, so we better follow the Bible."

"Could" refers to an unknown/unknowable probability, so the conclusion does not follow.

"Wearing a seatbelt could avoid injury. Therefore, I should wear a seatbelt."

"Could" is not the right word... wearing a seatbelt does help people avoid injury. This has been well demonstrated, so the conclusion is reasonable (generally speaking). Same thing with being kind to others... it either does make the world a better place or it is probable that it makes the world a better place.

In summary, the conclusion does not follow when "can" mean a remote or unknown/unknowable probability.

OK, I get your distinction and I think it's a valid one.

I still think, however, that it is an overstatement to call it a non sequitur.  The following doesn't follow in my opinion:

A:    Doing charity work could help my community.  I want to help my community.

B:    You should do some charitable work.

A:    That's a non sequitur!

--I think the problem is one of equivocation but with the word "should".  Does "should" mean it's something I recommend you do based on your desire to help, vs. it'd be unacceptable (a wrong thing to do) not to do this (such as, unacceptable not to buckle your seat belt).

Getting into the nitty gritty, but "Doing charity work could help my community" is ambiguous. If we mean, the charity work might be in the community, or outside the community, then "can" means "we don't know." If this were more clear such as:

A:    Doing charity work for my town could help my community.  I want to help my community.

B:    You should do some charitable work.

Then this is a reasonable conclusion.

I agree with how you understand the appeal to possibility. I would add an explanation on why this appeal occurs.

I think that it results by confusing the sense of the words "probable" and "possible." When we say that something is probable, we mean that that something has a good chance of happening. When we say that something is possible, we mean that that something has a chance of happening. The lack of  use of the word "good" on the second interpretation makes the term "possible" super ambiguous. 

Why do I think that those interpretations are the usual sense of the words? I think because if we substitute the word "probable" with "possible," we're trying to have more leeway than to committing to an actual probability. This would be some sort of cognitive bias I think. 

There's probably (no pun intended) an equivocation with "possible" but it may come from enthymemes. 

Example:

P1. It is possible that children make the world a better place.
P2. I want to make the world a better place.
C. Therefore, it is probable that if I have children, I will make (or help make) the world a better place.

The enthymeme would have the next premise:
E: If it is possible that children make the world a better place, then it is probable that children make the world a better place.

Here, E does commit the fallacy of appeal to possibility. Also, there's a flat out switch of meanings of a single term: possible means probable. 

We may be strict and say that technically no equivocation is made since the same name needs to take on different meanings, but I would respond by saying that intentionality is what captures the fallacy. There is an intention of referring to the same thing when we switch names.

I think that this enthymeme does both: it appeals to possibility and it is a non sequitur.

I think we're pretty much on the same page here.  While I can agree that there's a case to be made for appeal to possibility , I see the case for non sequitur as much stronger.  In either case, it seems important to understand that neither probability nor possibility is a dichotomy; rather, each is a continuum so it's important to make sure there's a shared understanding of how possible or how probably things are.  (Having said that, it's important for me to note that I seem much closer to seeing "possible" and "probable" as synonyms than I understand you to be.  If they are, in fact, synonymous, the case for equivocation goes away; if they mean different things, then equivocation can certainly become part of the issue if one party were to switch between the two meanings.)

Regardless of what it's called, one thing that the example points out for me is the importance of making sure all parties to the discussion (or debate, or argument, or ...) share the same understanding of the terms used.  Without that shared understanding, we're open to either (a) one party innocently understanding one thing from a term while the other party understands something else, or (b) one party intentionally switching meanings in the middle of the discussion.  The former can happen without any intention to deceive ... but it's something we need to guard against by being clear on our meanings at the outset; the latter is an example of manipulative strategies that, although frequent as we listen to debated around us, are far from ideal.

I agree with most of what you said. When you mention that there is an "...importance of making sure all parties to the discussion (or debate, or argument, or ...) share the same understanding of the terms used..." that's something I agree with depending on the situation. But the way I understand what the sense of a word is, is a shared understanding on the use of that word and many times that includes heuristics. 

I kind of place a heuristic as part of making assumptions to make educated guesses. For example, if somebody tells you that there is a probability of winning the lottery, you might heuristically assume that those chances are low and not worth your money. But if they say that there is a possibility of winning the lottery, you might heuristically assume that the chances are low, but it is worth your money; possibility sounds more optimistic than probability. Probability sounds like a statistician is giving you advise rather than some close friend.

So, what is all this about? Many times heuristic thinking is very good because it's less stressful. It all depends on how deep you want to dive into a topic. On the flip side, we might get used to that and apply it to situations were you suggest it is important to not do that. So, I believe that that's what I meant with "the usual sense of the words" as an explanation on why the appeal occurs.