In the form you've presented the claims, there would be a fallacy of denying the antecedent. If free, then responsible. Not free. So, not responsible. But I don't think philosophers typically agree with the conditional claim, which says that having free will (or doing A freely) is sufficient for moral responsibility (or being responsible for A). And we should not agree with it. After all, I might freely decide to back my car out of the driveway and in doing so run over the sleeping cat I could not be expected to have seen. If so, I do not seem to be responsible (blameworthy) for killing the cat. There might be ways to fix up the terms, but there is likely an epistemic condition (a justified belief requirement) for responsibility that goes beyond the free will (or control) condition. However, it is more plausible to say that moral responsibility (being responsible for A) requires free will (that one did A freely, or did some earlier action freely that one should have known would lead to...

I think your argument is logically valid--that is, IF the premises were true, then the conclusion would be true. And I don't think it commits any formal or informal fallacies (except perhaps equivocation in the sense I'll explain shortly). The problem is that it is unsound , because it has at least one false premise; hence the conclusion is not "made true" by the premises. Premise 3 is false. The government does not tell us not to kill no matter what . As you point out, it tells us not to break specific laws against specific types of killing. Typically, citizens are not breaking the law (and are morally justified) in killing in self-defense or to protect others from an immediate and deadly threat. And (legal) killing in war and use of the death penalty (where it is legal) are also not forms of killing the government tells us not to commit. Now, we may have reasons to think that some or even all killing in war is morally problematic and even more reasons to think the death penalty is...

The syllogism is still valid (i.e., if the two premises were true, the conclusion would have to be true). But you have just found a case (Mushmush) that falsifies the first premise. It turns out John does not really believe that all green people should be killed, but he believes (at least) one green person (Mushmush) should not be killed. Good for logic and good for Mushmush!

This is a nice case of what can go wrong when you (i.e., I) do philosophy too quickly! As Richard charitably suggests, (I think) I was reading the argument (too quickly) to say: 1. John believes that all green people should be killed, and 2. John believes that Mushmush is a green person, 3. Thus, John believes that Mushmush should be killed. Mitch is right that the original question left "John believes" out of premise 2, so it's clearly not formally valid: 1 could be true, but if John does not believe Mushmush is green (even though he is), then clearly 3 would not follow. With premise 2 written as here, with "John believes," then it looks much "closer to valid" but "valid" is not like horseshoes or hand grenades, so close does not count. It's hard to see how John could miss the inference, but perhaps he is like some racists in literature who sincerely hold universal derogatory beliefs about another race and sincerely reject that belief about their friend or neighbor who they...