An apparent majority of people claim that "the ends don't justify the means", that you can't do a small evil to cause a much greater good. If you think you can, you're a "consequentialist", and many opponents claim your position is somehow "relativism".
My article will mostly cover intuitive arguments for consequentialism and deal with the most powerful objection I've seen, but there is a logical problem with saying an evil means can never be justified by a good result, no matter how much bigger: it can't deal with the concept of probability. Michael Huemer explains this in "Risk Refutes Absolutism". I wouldn't normally outsource arguments, but he makes the point so well that I'm not going to write my own article on it, even though I could probably reduce his 10-minute length somewhat without losing much.
Besides the problem it faces with probability and that the rule seems very arbitrary, intuitive reasons to reject it are obvious. Surely you can steal some food in a pinch to save a starving person's life, but stealing is an evil means, no?
Some might argue it doesn't count as theft if it's justified, but that's a terrible answer because if being necessary for a better end makes a normally evil act count as not an evil means, then the claim that a good end can't justify an evil means is meaningless. (There's at least one other reason not to argue that: it prevents appealing to the difference between justifying and purifying the means, which I explore below.)
Another response might be that it's not theft because the person with the food is obligated to save the starving person's life. This is very similar to the previous, and is a bad idea for the same reasons: if people are obligated to make sacrifices for others when they can produce a large benefit at a small cost to themself, you lose the point of saying the ends don't justify the means, because you still think you could hurt an unwilling person if it produces enough benefit.
But if for whatever reason stealing doesn't count as an evil means but other things, like maiming or killing innocents, do, even if they're necessary to save more people, then just pick one of those. It might be easy to say you can't kill one person to save two others. But what about a thousand? A million? How many people would you let die to avoid committing one murder?
I think the only reason anyone believes that ends can't justify evil means besides being raised to is because of contrived examples that scare them. Often these examples are red herrings (consequentialism doesn't entail what the presenter says it does), but others are more honest. I'll give the strongest example I can think of by far:
A scenario I first read on philosophyexperiments.com titled "The Backpacker" (I've seen it discussed in a few other places since then). To preserve all details of the original statement, I'll copy-paste it here:
Dr Georgina Mouse is a truly great surgeon, so great that any organs she transplants always take. At the moment she has five patients who need organs (lungs, kidneys and a heart). If they do not get those organs today, they will all die; if organs are found for them today, Dr Mouse can transplant the organs and they will all live. The time is almost up when a report comes in that a young backpacker has come into the hospital for a routine checkup. It turns out he is in excellent health, and has exactly the right blood type to guarantee success if she transplants his organs into the patients. All she needs do is cut him up and distribute his parts among the five who need them. Assuming the backpacker doesn't consent to giving up his life to save five other people, is it morally permissible for Dr Mouse to take matters into her own hands, and operate anyway?
Most people - myself included, when I first read this - have a very strong intuition that the answer is no. First, I need to clarify something about my position.
There's a difference between the ends justifying the means and purifying them. Even if Dr Mouse is right to murder the backpacker, it is still murder, and if they were to meet in another world, she would owe him her life in restitution. The ends justify the murder, but they don't make it not a murder.
But I doubt that satisfies most people. So to bridge the enormous discrepancy between common intuition and consequentialist logic, I'll make an argument from both directions. First I'll explain why Protagonist consequentialism doesn't see this as a 5 to 1 - it's a lot closer than it looks (but I do stand by killing him). My complete moral system is described here; that's where I'm getting the principles I apply below.
Factor #1: there is a difference between killing and letting die; it's the value of consent. A way of looking at it is that (see how consent and compassion are two separate values that stack) you're not destroying one person's life and saving the others', but destroying one person's life and violating one person's right to their life to save the others. (The people who were already dying do not have a "right to life", because that's not how rights work.) So it takes more than a 1 to 1 ratio to justify this.
Factor #2: forcing him to make this sacrifice for the benefit of everyone else creates a very large benefactor-freeloader relationship, which is less just, all other things the same.
Factor #3: the difference in the quality of life they're likely to have if they live. The five patients are dying and it's as best not established that an organ transplant will restore them to full health and a normal life. The backpacker, on the other hand, is explicitly stated to be in excellent health. So you're destroying one probably enjoyable life to maintain five lives that are likely to be far less enjoyable for the people living them. (This factor should be disregarded if the scenario assumes that the patients will return to full health. I've heard it stated that way somewhere else, but this statement didn't say that, so I'm pointing out that it makes a difference.)
Factor #4: the backpacker is having this ultimatum laid on him out of nowhere, so he gets no closure if he ends his life here. Even if we believe it's right to murder him here, we must recognize that it's crueler than murdering someone with a few days' warning. Albeit, this is probably a small factor in the scheme of things.
Factor #-1, which works against my argment: the patients have presumably already suffered greatly at the hands of their illnesses, and so, by the factor of equality, compassion to them has more weight than compassion to the backpacker. These two probably mostly cancel out; but I saw fit to mention both to prevent your intuition from being biased by noticing only of them. (I noticed Factor #4 when I first wrote this article and only noticed the opposite effect while editing it years later.)
Another thing I want to say while I'm at it: try considering this from any perspective other than Dr Mouse's. Imagine if one of the patients had the choice. Would you find it equally obvious that the dying patient would be wrong to kill one person to save themselves and four other innocents? Or even the backpacker's perspective: wouldn't you agree that he's incredibly selfish to refuse (even if it's understandable)?
Factor #-2: according to my value system, refusing to make this sacrifice makes him a worse person and thus makes his life worth somewhat less.
But actually, due to the self-anchored perspective effect I mentioned in moral conflict, the backpacker may truly be justified in refusing to sacrifice his one life to save five strangers. He might consider himself important. And he might be right. Maybe he's involved in something that critically affects more than five people. But he doesn't know anything about these patients. For all he (or we) know, they're as likely to be bad people as they are to be good. But even if he's justified in refusing, that doesn't mean Dr Mouse shouldn't kill him - see the moral conflict article.
But this probably still isn't enough. I realize there's probably still a discrepancy between your intuition and what seems to be inevitable if the end justifies the means. So for the rest, I'm going to point out a significant amount of bias in the way the problem is stated.
The first hint of bias is that the 5 people are introduced as one entity. Every time they're referred to, it's as "the five" and not as individuals.
It's also worth mentioning that we don't know anything about any of the dying patients as people. They're just "patients" and that's all we know about them. Video game story writers and critics will be intimately familiar with this effect: we find it hard to value the lives of those we don't know anything about and thus can't easily feel for. But we know something about the backpacker as a person: he's a backpacker. It's not much, but it exists. He has also taken an action in the story (he came to the hospital for a routine checkup), which probably furthers this effect. Finally, he has an assigned gender, even if it's arguably the less advantageous one, which goes a long way toward humanizing him and biasing our emotions toward siding with him. We've been given a basis to imagine the backpacker's perspective, but the scenario hasn't done anything to help us imagine the patients' perspectives - it's done the opposite by collectivizing them.
Then there's the unnecessarily vivid way the murder is described. "Cut him up" is very gory language that suggests an image of Dr Mouse assaulting the backpacker with a knife and spilling his blood everywhere while he screams. To increase the relevance of the example to the principles at stake, we should assume that Dr Mouse has a way of killing him quickly and painlessly (since the suffering of the five patients isn't mentioned at all either).
Phew, that was a lot. I hope now you can see how it's not hard to accept that the answer to the question is "Yes".