First, I doubt if we are willing to say that every contingent event in the world is a result of God's active willing it.

I specifically refrained from saying "active" will; Aquinas distinguishes between God's active will and His permissive will, and I am referencing His permissive will.

Therefore, the only way to construe my touching the stop button would be as a direct act of intervention.

It is precisely because we cannot know the mind of God, and whether He permissively wills a man die or become a cripple, that we must always act according to charity in all we do. The end of charity is God and eternal life, not temporal peace. If these ends are not obstructed through our action, and no probable danger will come to us by intervening, and we are able, then we should act to preserve life.

Yes there are many complicating factors in these scenarios, such that, depending on the details, it may be a prudential matter with no clear answer. This may be such a matter. But there are similar situations were the answer is clear, like active euthanasia, and this we must condemn.

Nor can we say that God necessarily willed that I be here to deliberate.

If you are there then it is part of God's Providence. It does not follow from this that a certain action of you is expected, but that you would be there He certainly did will.

I know that you'll be able to say that it is for God alone to issue mercy.

Men can of course be merciful also, but the ends of the action differ. To have mercy with respect to a life can be man's; with respect to a soul, God's alone.

I agree with your sense that it would be more merciful to "let someone die" then "force them to live" in certain situations. I guess in my envisioning of the scenario, especially originally, my idea was that it was a choice between stopping the machine before any mangling had occurred, rather than after. But even if we are talking about after, I still think that because there are so many factors unknown to us, we would be obliged to do whatever we can to preserve the life. Maybe the man has a family he would rather live to provide for, even if he is wheelchair bound for life. Maybe this, maybe that - I had it when moral considerations are reduced to these details. A life is a life and if it can be saved, that is better than to let it die or suffer more harm than it would if intervening. Maybe you would say the psychological harm of living with the industries is one additional "harm" added by the saving, but I would say death exceeds even that.

a farmer has a grotesquely injured cow or horse. It is ubiquitously understood to be a merciful act to end the animal's pain if practical reasoning suggests there is no way to recover.

Animal and human moral situations are very different. Animals do not have rational, immortal souls. They won't go to hell if they assent to a suicidal relief from suffering, whereas a man might. It just isn't the same.

It seems merciful that I not intervene.

A very similar situation is a comrade-in-arms lying on the ground, his legs and one arm blown off. Do you pull out your pistol and just shoot him? Or pull his tourniquets and get him to the medic? Different soldiers might will different things; some would prefer to die in the battlefield then live with three prosthetic limbs, other would endure any suffering to see their families again. If the soldier cannot communicate to you (is unconscious), I would say the only justifiable course is to presume the latter, pull the tourniquets, and do the best to save him. I find this to be most analogous to the man caught in the machine.

Another layer of complexity is added if the man in the machine can communicate, or the soldier isn't unconscious, and they are both begging for death. Arguing to keep them alive, I recognize, seems simply cruel at such a point. Then again, there are cases of people in great amounts of pain, who have begged for death, but were nonetheless saved, nursed to health, and are overwhelmingly grateful to have not been killed.

And that's what it amounts to. Killing. Of an innocent life (not put to death through just punishment). In other words, murder - however noble or merciful to intention. For there are strong moral arguments that can be made to suggest that inaction, when action is possible, is little different from direct killing.

There would have to be a clear moral proclamation from God that we must save every life if we are able to.

Could not the Fifth Commandment ("Thou shalt not kill") be construed as such a proclamation?

And if not...we have His Church to rule on such things, since God did not rule on every moral issue, as much as wishes he had, and Divine intervention is not expected of God every time we face a moral quandary. This is one purpose the Church exists, to clarify such things.

So what does the Church say about saving lives?

Catechism of the Catholic Church (CCC):

I. Respect for Human Life

2261 Scripture specifies the prohibition contained in the fifth commandment: "Do not slay the innocent and the righteous."61 The deliberate murder of an innocent person is gravely contrary to the dignity of the human being, to the golden rule, and to the holiness of the Creator. The law forbidding it is universally valid: it obliges each and everyone, always and everywhere.

Euthanasia

2276 Those whose lives are diminished or weakened deserve special respect. Sick or handicapped persons should be helped to lead lives as normal as possible.

2277 Whatever its motives and means, direct euthanasia consists in putting an end to the lives of handicapped, sick, or dying persons. It is morally unacceptable.

Thus an act or omission which, of itself or by intention, causes death in order to eliminate suffering constitutes a murder gravely contrary to the dignity of the human person and to the respect due to the living God, his Creator. The error of judgment into which one can fall in good faith does not change the nature of this murderous act, which must always be forbidden and excluded.

2278 Discontinuing medical procedures that are burdensome, dangerous, extraordinary, or disproportionate to the expected outcome can be legitimate; it is the refusal of "over-zealous" treatment. Here one does not will to cause death; one's inability to impede it is merely accepted. The decisions should be made by the patient if he is competent and able or, if not, by those legally entitled to act for the patient, whose reasonable will and legitimate interests must always be respected.

2279 Even if death is thought imminent, the ordinary care owed to a sick person cannot be legitimately interrupted. The use of painkillers to alleviate the sufferings of the dying, even at the risk of shortening their days, can be morally in conformity with human dignity if death is not willed as either an end or a means, but only foreseen and tolerated as inevitable Palliative care is a special form of disinterested charity. As such it should be encouraged.

I would say our man-in-the-machine example more readily falls under Paragraph 2277, and thus must be condemned.

That doesn't make a lot of sense, does it? Why shouldn't he suffer as much as he would have? Why does someone else, through an immoral action, get to determine that someone else should suffer longer in purgatory? (And if it not they who determine it, but God, then they at least "cause" or influence it.)

See the , which I've cited before. God beseeches us to always be ready, because none of us know the day or the hour. It is not the decision of some third party determines our afterlife; we alone determine that, by virtue of the state of grace (or lack thereof) we allow ourselves to be in at any given moment. And of course, if we sin, and are immediately repentant, but die on our way to confession, God sees that we made a perfect act of contrition, which includes an intention to confess at the earliest opportunity, and so we may enter into His kingdom despite this third party's intervention.