Utilitarianism proposes the moral worth of an action is determined only by its contribution to overall good. It is a form of consequentialism, which is the moral worth of an action is determined by its outcome – the ends justify the means.
Though most often associated with John Stuart Mill, and his book Utilitarianism, it was Jeremy Bentham who first put the theory forth.
It is better to be a human being dissatisfied, than a pig satisfied; better to be Socrates dissatisfied than a fool satisfied.
– John Stuart Mill (1806-1873)
Your dog may have wholeheartedly adopted the Greatest Happiness Principle, which is the backbone of Utilitarianism. This creeds holds that actions are right and just as long as they promote happiness. And what could make a dog happier than to not step outside in the rain or snow to poop. He sees his humans happily pooping in the house, albeit in a mysterious porcelain water bowl (why is it so high? Only big dogs can use it!). Why should he not enjoy that same level of happiness?
To achieve his profound level of happiness, the Utilitarian dog must poop in the house.
He who thinks and thinks for himself, will always have a claim to thanks; it is no matter whether it be right or wrong, so as it be explicit. If it is right, it will serve as a guide to direct; if wrong, as a beacon to warn. -Jeremy Bentham (From Kathy: I have no idea what this means, but it sounded so pithy)
The ingredients of happiness are very various, and each of them is desirable in itself, and not merely when considered as swelling an aggregate. The principle of utility does not mean that any given pleasure, as music, for instance, or any given exemption from pain, as for example health, are to be looked upon as means to a collective something termed happiness, and to be desired on that account. They are desired and desirable in and for themselves; besides being means, they are a part of the end. Virtue, according to the utilitarian doctrine, is not naturally and originally part of the end, but it is capable of becoming so; and in those who love it disinterestedly it has become so, and is desired and cherished, not as a means to happiness, but as a part of their happiness. -John Stuart Mill
Your dog must search out the Greatest Happiness for himself, which may very well be that of pooping in the house. It may also be NOT being able to read, so that he is not forced to read mind-boggling passages such as the one above.
My greatest happiness is to know, without doubt that the major philosophical schools as relate to dogs pooping in the house have been thoroughly explored.