Based on your description here of your reaction, I get the impression that you mistook the structure of the argument. Specifically, you note, as if it were sufficient, that you disagree with several of the premises. Engel was not attempting to build on the conjunction (p1*p2*...*p16) of the premises; he was building on their disjunction (p1+p2+...+p16). Your credence in p1 through p16 would have to be uniformly very low to keep their disjunction also low. Personally, I give high credence to p1, p9, p10, and varying lower degrees of assent to the other premises, so the disjunction is also quite high for me, and therefore the conclusion has a great deal of strength; but even if I later rejected p1, p9, and p10, the disjunction of the others would still be high. It’s that robustness of the argument, drawing more on many weak points than one strong one, that convinced me.
I don’t understand your duck/troll response to the quote from Engel. Everything he has said in that paragraph is straightforward. It is important that beliefs be true, not merely consistent. That does mean you oughtn’t simply reject whichever premises get in the way of the conclusions you value. p1-p16 are indeed entangled with many other beliefs, and propagating belief and value updates of rejecting more of them is likely, in most people, to be a more severe change than becoming vegetarian. Really, if you find yourself suspecting that a professional philosopher is trolling people in one of his most famous arguments, that’s a prime example of a moment to notice the fact that you’re confused. It’s possible you were reading him as saying something he wasn’t saying.
Regarding the edit: the argument does not assume that you care about animal suffering. I brought it up precisely because it didn’t make that assumption. If you want something specifically about animal suffering, presumably a Kantian argument is the way to go: You examine why you care about yourself and you find it is because you have certain properties; so if something else has the same properties, to be consistent you should care about it also. (Obviously this depends on what properties you pick.)
(Hi, sorry for the delayed response. I’ve been gone.)
Just the standard stuff you’d get in high school or undergrad college. Suppose we have independent statements S1 through Sn, and you assign each a subjective probability of P(Si). Then you have the probability of the disjunction P(S1+S2+S3+...+Sn) = 1-P(~S1)*P(~S2)*P(~S3)*...*P(~Sn). So if in a specific case you have n=10 and P(Si)=0.10 for all i, then even though you’re moderately disposed to reject every statement, you’re weakly disposed to accept the disjunction, since P(disjunction)=0.65. This is closely related to the preface paradox.
You’re right, of course, that Engel’s premises are not all independent. The general effect on probability of disjunctions remains always in the same direction, though, since P(A+B)≥P(A) for all A and B.
OK, yes, you’ve expressed yourself well and it’s clear that you’re intepreting him as having claimed the opposite of what he meant. Let me try to restate his paragraph in more LW-ish phrasing:
“As a rationalist, you are highly interested in truth, which requires consistency but also requires a useful correspondence between your beliefs and reality. Consequently, when you consider that you believe it is not worthwhile for you to value animal interests and you discover that this belief is inconsistent with other of your beliefs, you will not reject just any of those other beliefs you think most likely to be false. (You will subject the initial, motivated belief to equal, unprivileged scrutiny along with the others, and tentatively accept the mutually consistent set of beliefs with the highest probability given your current evidence.)”
If you’re interested in reconsidering Engel’s argument given his intended interpretation of it, I’d like to hear your updated reasons for/against it.